Steven D Schwartz

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• Baldo, A. P., Tardiff, J. C., & Schwartz, S. D. (2021). A Proposed Mechanism for the Initial Myosin Binding Event on the Cardiac Thin Filament: A Metadynamics Study. The journal of physical chemistry letters, 12(14), 3509-3513.
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  The movement of tropomyosin over filamentous actin regulates the cross-bridge cycle of the thick with thin filament of cardiac muscle by blocking and revealing myosin binding sites. Tropomyosin exists in three, distinct equilibrium states with one state blocking myosin-actin interactions (blocked position) and the remaining two allowing for weak (closed position) and strong myosin binding (open position). However, experimental information illuminating how myosin binds to the thin filament and influences tropomyosin's transition across the actin surface is lacking. Using metadynamics, we mimic the effect of a single myosin head binding by determining the work required to pull small segments of tropomyosin toward the open position in several distinct regions of the thin filament. We find differences in required work due to the influence of cardiac troponin T lead to preferential binding sites and determine the mechanism of further myosin head recruitment.
• Brown, M., Zoi, I., Antoniou, D., Namanja-Magliano, H. A., Schwartz, S. D., & Schramm, V. L. (2021). Inverse heavy enzyme isotope effects in methylthioadenosine nucleosidases. Proceedings of the National Academy of Sciences of the United States of America, 118(40).
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  Heavy enzyme isotope effects occur in proteins substituted with H-, C-, and N-enriched amino acids. Mass alterations perturb femtosecond protein motions and have been used to study the linkage between fast motions and transition-state barrier crossing. Heavy enzymes typically show slower rates for their chemical steps. Heavy bacterial methylthioadenosine nucleosidases (MTANs from and ) gave normal isotope effects in steady-state kinetics, with slower rates for the heavy enzymes. However, both enzymes revealed rare inverse isotope effects on their chemical steps, with faster chemical steps in the heavy enzymes. Computational transition-path sampling studies of and MTANs indicated closer enzyme-reactant interactions in the heavy MTANs at times near the transition state, resulting in an improved reaction coordinate geometry. Specific catalytic interactions more favorable for heavy MTANs include improved contacts to the catalytic water nucleophile and to the adenine leaving group. Heavy bacterial MTANs depart from other heavy enzymes as slowed vibrational modes from the heavy isotope substitution caused improved barrier-crossing efficiency. Improved sampling frequency and reactant coordinate distances are highlighted as key factors in MTAN transition-state stabilization.
• Chakraborti, A., Baldo, A. P., Tardiff, J. C., & Schwartz, S. D. (2021). Investigation of the Recovery Stroke and ATP Hydrolysis and Changes Caused Due to the Cardiomyopathic Point Mutations in Human Cardiac β Myosin. The journal of physical chemistry. B, 125(24), 6513-6521.
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  Human cardiac β myosin undergoes the cross-bridge cycle as part of the force-generating mechanism of cardiac muscle. The recovery stroke is considered one of the key steps of the kinetic cycle as it is the conformational rearrangement required to position the active site residues for hydrolysis of ATP and interaction with actin. We explored the free-energy surface of the transition and investigated the effect of the genetic cardiomyopathy causing mutations R453C, I457T, and I467T on this step using metadynamics. This work extends previous studies on myosin II with engineered mutations. Here, like previously, we generated an unbiased thermodynamic ensemble of reactive trajectories for the chemical step using transition path sampling. Our methodologies were able to predict the changes to the dynamics of the recovery stroke as well as predict the pathway of breakdown of ATP to ADP and HPO with the stabilization of the metaphosphate intermediate. We also observed clear differences between the myosin II and human cardiac β myosin for ATP hydrolysis as well as predict the effect of the mutation I467T on the chemical step.
• Mason, A. B., Lynn, M. L., Baldo, A. P., Deranek, A. E., Tardiff, J. C., & Schwartz, S. D. (2021). Computational and biophysical determination of pathogenicity of variants of unknown significance in cardiac thin filament. JCI insight, 6(23).
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  Point mutations within sarcomeric proteins have been associated with altered function and cardiomyopathy development. Difficulties remain, however, in establishing the pathogenic potential of individual mutations, often limiting the use of genotype in management of affected families. To directly address this challenge, we utilized our all-atom computational model of the human full cardiac thin filament (CTF) to predict how sequence substitutions in CTF proteins might affect structure and dynamics on an atomistic level. Utilizing molecular dynamics calculations, we simulated 21 well-defined genetic pathogenic cardiac troponin T and tropomyosin variants to establish a baseline of pathogenic changes induced in computational observables. Computational results were verified via differential scanning calorimetry on a subset of variants to develop an experimental correlation. Calculations were performed on 9 independent variants of unknown significance (VUS), and results were compared with pathogenic variants to identify high-resolution pathogenic signatures. Results for VUS were compared with the baseline set to determine induced structural and dynamic changes, and potential variant reclassifications were proposed. This unbiased, high-resolution computational methodology can provide unique structural and dynamic information that can be incorporated into existing analyses to facilitate classification both for de novo variants and those where established approaches have provided conflicting information.
• Antoniou, D., & Schwartz, S. D. (2020). Role of Protein Motions in Catalysis by Formate Dehydrogenase. The journal of physical chemistry. B, 124(43), 9483-9489.
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  We have analyzed the reaction catalyzed by formate dehydrogenase using transition path sampling. This system has recently received experimental attention using infrared spectroscopy and heavy-enzyme studies. Some of the experimental results point to the possible importance of protein motions that are coupled to the chemical step. We found that the residue Val123 that lies behind the nicotinamide ring occasionally comes into van der Waals contact with the acceptor and that in all reactive trajectories, the barrier-crossing event is preceded by this contact, meaning that the motion of Val123 is part of the reaction coordinate. Experimental results have been interpreted with a two-dimensional formula for the chemical rate, which cannot capture effects such as the one we describe.
• Baldo, A. P., Tardiff, J. C., & Schwartz, S. D. (2020). Mechanochemical Function of Myosin II: Investigation into the Recovery Stroke and ATP Hydrolysis. The journal of physical chemistry. B, 124(45), 10014-10023.
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  Myosin regulates muscle function through a complex cycle of conformational rearrangements coupled with the hydrolysis of adenosine triphosphate (ATP). The recovery stroke reorganizes the myosin active site to hydrolyze ATP and cross bridge with the thin filament to produce muscle contraction. Engineered mutations K84M and R704E in myosin have been designed to specifically inhibit the recovery stroke and have been shown to indirectly affect the ATPase activity of myosin. We investigated these mutagenic perturbations to the recovery stroke and generated thermodynamically correct and unbiased trajectories for native ATP hydrolysis with computationally enhanced sampling methods. Our methodology was able to resolve experimentally observed changes to kinetic and equilibrium dynamics for the recovery stroke with the correct prediction in the severity of these changes. For ATP hydrolysis, the sequential nature along with the stabilization of a metaphosphate intermediate was observed in agreement with previous studies. However, we observed glutamate 459 being utilized as a proton abstractor to prime the attacking water instead of a lytic water, a phenomenon not well categorized in myosin but has in other ATPases. Both rare event methodologies can be extended to human myosin to investigate isoformic differences from and scan cardiomyopathic mutations to see differential perturbations to kinetics of other conformational changes in myosin such as the power stroke.
• Chen, X., & Schwartz, S. D. (2020). Multiple Reaction Pathways in the Morphinone Reductase-Catalyzed Hydride Transfer Reaction. ACS omega, 5(36), 23468-23480.
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  Morphinone reductase (MR) is an important model system for studying the contribution of protein motions to H-transfer reactions. In this research, we used quantum mechanical/molecular mechanics (QM/MM) simulation together with transition path sampling (TPS) simulation to study two important topics of current research on MR: the existence of multiple catalytic reaction pathways and the involvement of fast protein motions in the catalytic process. We have discovered two reaction pathways for the wild type and three reaction pathways for the N189A mutant. With the committor distribution analysis method, we found reaction coordinates for all five reaction pathways. Only one wild-type reaction pathway has a rate-promoting vibration from His186, while all of the other four pathways do not involve any protein motions in their catalytic process through the transition state. The rate-promoting vibration in the wild-type MR, which comes from a direction perpendicular to the donor-acceptor axis, functions to decrease the donor-acceptor distance by causing a subtle "out-of-plane" motion of a donor atom. By comparing reaction pathways between the two enzymes, we concluded that the major effect of the N189A point mutation is to increase the active site volume by altering the active site backbone and eliminating the Asn189 side chain. This effect causes a different NADH geometry at the reactant state, which very well explains the different reaction mechanisms between the two enzymes, as well as the disappearance of the His186 rate-promoting vibrations in the N189A mutant. The unfavorable geometry of the NADH pyridine ring induced by the N189A point mutation is the potential cause of multiple reaction pathways in N189A mutants.
• Luft, C. M., Munusamy, E., Pemberton, J. E., & Schwartz, S. D. (2020). A Classical Molecular Dynamics Simulation Study of Interfacial and Bulk Solution Aggregation Properties of Dirhamnolipids. The journal of physical chemistry. B, 124(5), 814-827.
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  The rhamnolipids are a unique class of biosurfactants produced by the bacteria . These molecules display a high level of surface activity as well as biodegradability. In this study nonionic dirhamnolipid was investigated by utilizing molecular dynamics simulation at the air-water interface as well as in bulk water. Detailed structural analysis is presented for both the interfacial simulations and the simulations in solution. A systematic comparison was made between our previous work on the monorhamnolipid at the air-water interface and in bulk water. The presence of a second rhamnose group in dirhamnolipid did not show any significant change in the aggregation at the air-water interface. An increase in the molecular weight resulted in the larger surface area per monomer for dirhamnolipid compared to monorhamnolipid at the air-water interface. However, aggregation of dirhamnolipid in bulk water was affected by the presence of a second rhamnose group. Dirhamnolipid aggregates into micellar structure around ∼N22 which was lower than the monorhamnolipid aggregation number ∼N40. The hydrophobic component of the dirhamnolipid was enhanced to balance the higher hydrophilic component. An increase in alkyl chain length has shown that the enhanced hydrophobic component supports the formation of micellar aggregates up to ∼N30 and above, which was not observed in dirhamnolipid with a shorter alkyl chain length.
• Powers, J. D., Kooiker, K. B., Mason, A. B., Teitgen, A. E., Flint, G. V., Tardiff, J. C., Schwartz, S. D., McCulloch, A. D., Regnier, M., Davis, J., & Moussavi-Harami, F. (2020). Modulating the tension-time integral of the cardiac twitch prevents dilated cardiomyopathy in murine hearts. JCI insight, 5(20).
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  Dilated cardiomyopathy (DCM) is often associated with sarcomere protein mutations that confer reduced myofilament tension-generating capacity. We demonstrated that cardiac twitch tension-time integrals can be targeted and tuned to prevent DCM remodeling in hearts with contractile dysfunction. We employed a transgenic murine model of DCM caused by the D230N-tropomyosin (Tm) mutation and designed a sarcomere-based intervention specifically targeting the twitch tension-time integral of D230N-Tm hearts using multiscale computational models of intramolecular and intermolecular interactions in the thin filament and cell-level contractile simulations. Our models predicted that increasing the calcium sensitivity of thin filament activation using the cardiac troponin C (cTnC) variant L48Q can sufficiently augment twitch tension-time integrals of D230N-Tm hearts. Indeed, cardiac muscle isolated from double-transgenic hearts expressing D230N-Tm and L48Q cTnC had increased calcium sensitivity of tension development and increased twitch tension-time integrals compared with preparations from hearts with D230N-Tm alone. Longitudinal echocardiographic measurements revealed that DTG hearts retained normal cardiac morphology and function, whereas D230N-Tm hearts developed progressive DCM. We present a computational and experimental framework for targeting molecular mechanisms governing the twitch tension of cardiomyopathic hearts to counteract putative mechanical drivers of adverse remodeling and open possibilities for tension-based treatments of genetic cardiomyopathies.
• Schafer, J. W., & Schwartz, S. D. (2020). Directed Evolution's Influence on Rapid Density Fluctuations Illustrates How Protein Dynamics Can Become Coupled to Chemistry. ACS catalysis, 10(15), 8476-8484.
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  Protein engineering is a growing field with a variety of experimental techniques available for altering protein function. However, creating an enzyme is still in its infancy, so far yielding enzymes of modest catalytic efficiency. In this study, a system of artificial retro-aldolase enzymes found to have chemistry coupled to protein dynamics was examined. The original design was created computationally, and this protein was then subjected to directed evolution to improve the initial low catalytic efficiency. We found that this re-engineering of the enzyme resulted in rapid density fluctuations throughout the enzyme being reshaped via alterations in the hydrogen bonding network. This work also led to the discovery of a second important motion which aids in the release of an intermediate product. These results provide compelling evidence that to engineer efficient protein catalysts, fast protein dynamics need to be considered in the design.
• Schwartz, S. D., Pemberton, J. E., Munusamy, E., & Luft, C. M. (2020). A Classical Molecular Dynamics Simulation Study of Interfacial and Bulk Solution Aggregation Properties of Dirhamnolipids. J. Phys. Chem. B, 124, 814-827. doi:10.1021/acs.jpcb.9b08800
• Abdullah, S., Lynn, M. L., McConnell, M. T., Klass, M. M., Baldo, A. P., Schwartz, S. D., & Tardiff, J. C. (2019). FRET-based analysis of the cardiac troponin T linker region reveals the structural basis of the hypertrophic cardiomyopathy-causing Δ160E mutation. The Journal of biological chemistry, 294(40), 14634-14647.
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  Mutations in the cardiac thin filament (TF) have highly variable effects on the regulatory function of the cardiac sarcomere. Understanding the molecular-level dysfunction elicited by TF mutations is crucial to elucidate cardiac disease mechanisms. The hypertrophic cardiomyopathy-causing cardiac troponin T (cTnT) mutation Δ160Glu (Δ160E) is located in a putative "hinge" adjacent to an unstructured linker connecting domains TNT1 and TNT2. Currently, no high-resolution structure exists for this region, limiting significantly our ability to understand its role in myofilament activation and the molecular mechanism of mutation-induced dysfunction. Previous regulated motility data have indicated mutation-induced impairment of weak actomyosin interactions. We hypothesized that cTnT-Δ160E repositions the flexible linker, altering weak actomyosin electrostatic binding and acting as a biophysical trigger for impaired contractility and the observed remodeling. Using time-resolved FRET and an all-atom TF model, here we first defined the WT structure of the cTnT-linker region and then identified Δ160E mutation-induced positional changes. Our results suggest that the WT linker runs alongside the C terminus of tropomyosin. The Δ160E-induced structural changes moved the linker closer to the tropomyosin C terminus, an effect that was more pronounced in the presence of myosin subfragment (S1) heads, supporting previous findings. Our model fully supported this result, indicating a mutation-induced decrease in linker flexibility. Our findings provide a framework for understanding basic pathogenic mechanisms that drive severe clinical hypertrophic cardiomyopathy phenotypes and for identifying structural targets for intervention that can be tested and .
• Chen, X., & Schwartz, S. D. (2019). Examining the Origin of Catalytic Power of Catechol O-Methyltransferase. ACS catalysis, 9(11), 9870-9879.
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  For decades, there has been debate regarding the origin of the catalytic power of enzymes. In this work, we use the approach of computational chemistry to study the enzyme catechol O-methyltransferase (COMT) and reveal that the two current views on the catalytic mechanism of enzymes, the rate-promoting vibrations and the electric field, may both be viewed as part of the chemical step catalyzed by COMT. However, we show that the rate-promoting vibrations cause the electrostatic effect. This work provides insight into the catalytic mechanism of COMT and resolves a longstanding controversy regarding this enzyme's mechanism.
• Schafer, J. W., Zoi, I., Antoniou, D., & Schwartz, S. D. (2019). Optimization of the Turnover in Artificial Enzymes via Directed Evolution Results in the Coupling of Protein Dynamics to Chemistry. Journal of the American Chemical Society, 141(26), 10431-10439.
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  The design of artificial enzymes is an emerging field of research. Although progress has been made, the catalytic proficiency of many designed enzymes is low compared to natural enzymes. Nevertheless, recently Hilvert et al. ( Nat. Chem. 2017, 9, 50-56) created a series of five artificial retro-aldolase enzymes via directed evolution, with the final variant exhibiting a rate comparable to the naturally occurring enzyme fructose 1,6 bisphosphate aldolase. We present a study of this system in atomistic detail that elucidates the effects of mutational changes on the chemical step. Transition path sampling is used to create ensembles of reactive trajectories, and committor analysis is used to identify the stochastic separatrix of each ensemble. The application of committor distribution analysis to constrained trajectories allows the identification of changes in important protein motions coupled to reaction across the generated series of the artificial retro-aldolases. We observed two different reaction mechanisms and analyzed the role of the residues participating in the reaction coordinate of each enzyme. However, only in the most evolved variant we identified a fast motion that promotes catalysis, suggesting that this rate promoting vibration was introduced during directed evolution. This study provides further evidence that protein dynamics must be taken into account in designing efficient artificial enzymes.
• Szatkowski, L., Lynn, M. L., Holeman, T., Williams, M. R., Baldo, A. P., Tardiff, J. C., & Schwartz, S. D. (2019). Proof of Principle that Molecular Modeling Followed by a Biophysical Experiment Can Develop Small Molecules that Restore Function to the Cardiac Thin Filament in the Presence of Cardiomyopathic Mutations. ACS omega, 4(4), 6492-6501.
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  This article reports a coupled computational experimental approach to design small molecules aimed at targeting genetic cardiomyopathies. We begin with a fully atomistic model of the cardiac thin filament. To this we dock molecules using accepted computational drug binding methodologies. The candidates are screened for their ability to repair alterations in biophysical properties caused by mutation. Hypertrophic and dilated cardiomyopathies caused by mutation are initially biophysical in nature, and the approach we take is to correct the biophysical insult prior to irreversible cardiac damage. Candidate molecules are then tested experimentally for both binding and biophysical properties. This is a proof of concept study-eventually candidate molecules will be tested in transgenic animal models of genetic (sarcomeric) cardiomyopathies.
• Brás, N. F., Fernandes, P. A., Ramos, M. J., & Schwartz, S. D. (2018). Mechanistic Insights on Human Phosphoglucomutase Revealed by Transition Path Sampling and Molecular Dynamics Calculations. Chemistry (Weinheim an der Bergstrasse, Germany), 24(8), 1978-1987.
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  Human α-phosphoglucomutase 1 (α-PGM) catalyzes the isomerization of glucose-1-phosphate into glucose-6-phosphate (G6P) through two sequential phosphoryl transfer steps with a glucose-1,6-bisphosphate (G16P) intermediate. Given that the release of G6P in the gluconeogenesis raises the glucose output levels, α-PGM represents a tempting pharmacological target for type 2 diabetes. Here, we provide the first theoretical study of the catalytic mechanism of human α-PGM. We performed transition-path sampling simulations to unveil the atomic details of the two catalytic chemical steps, which could be key for developing transition state (TS) analogue molecules with inhibitory properties. Our calculations revealed that both steps proceed through a concerted S 2-like mechanism, with a loose metaphosphate-like TS. Even though experimental data suggests that the two steps are identical, we observed noticeable differences: 1) the transition state ensemble has a well-defined TS region and a late TS for the second step, and 2) larger coordinated protein motions are required to reach the TS of the second step. We have identified key residues (Arg23, Ser117, His118, Lys389), and the Mg ion that contribute in different ways to the reaction coordinate. Accelerated molecular dynamics simulations suggest that the G16P intermediate may reorient without leaving the enzymatic binding pocket, through significant conformational rearrangements of the G16P and of specific loop regions of the human α-PGM.
• Chen, X., & Schwartz, S. D. (2018). Directed Evolution as a Probe of Rate Promoting Vibrations Introduced via Mutational Change. Biochemistry, 57(23), 3289-3298.
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  In this article, we study with transition path sampling and reaction coordinate analysis how directed evolution in the Kemp eliminase family of artificial enzymes makes differential use of rapid rate promoting vibrations as a component of their chemical mechanism. Even though this family was initially created by placing the expected active site in a fixed protein matrix, we find a shift from largely static to more dynamic active sites that make use of donor-acceptor compression as the evolutionary process proceeds. We see that this introduction of dynamics significantly shifts the order of processes in the reaction. We also suggest that the lack of "design for dynamics" may help explain the relatively low proficiency of such designed enzymes.
• Harijan, R. K., Zoi, I., Antoniou, D., Schwartz, S. D., & Schramm, V. L. (2018). Inverse enzyme isotope effects in human purine nucleoside phosphorylase with heavy asparagine labels. Proceedings of the National Academy of Sciences of the United States of America, 115(27), E6209-E6216.
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  Transition path-sampling calculations with several enzymes have indicated that local catalytic site femtosecond motions are linked to transition state barrier crossing. Experimentally, femtosecond motions can be perturbed by labeling the protein with amino acids containing C, N, and nonexchangeable H. A slowed chemical step at the catalytic site with variable effects on steady-state kinetics is usually observed for heavy enzymes. Heavy human purine nucleoside phosphorylase (PNP) is slowed significantly (/ = 1.36). An asparagine (Asn243) at the catalytic site is involved in purine leaving-group activation in the PNP catalytic mechanism. In a PNP produced with isotopically heavy asparagines, the chemical step is faster (/ = 0.78). When all amino acids in PNP are heavy except for the asparagines, the chemical step is also faster (/ = 0.71). Substrate-trapping experiments provided independent confirmation of improved catalysis in these constructs. Transition path-sampling analysis of these partially labeled PNPs indicate altered femtosecond catalytic site motions with improved Asn243 interactions to the purine leaving group. Altered transition state barrier recrossing has been proposed as an explanation for heavy-PNP isotope effects but is incompatible with these isotope effects. Rate-limiting product release governs steady-state kinetics in this enzyme, and kinetic constants were unaffected in the labeled PNPs. The study suggests that mass-constrained femtosecond motions at the catalytic site of PNP can improve transition state barrier crossing by more frequent sampling of essential catalytic site contacts.
• Luft, C. M., Munusamy, E., Pemberton, J. E., & Schwartz, S. D. (2018). Molecular Dynamics Simulation of the Oil Sequestration Properties of a Nonionic Rhamnolipid. The journal of physical chemistry. B, 122(14), 3944-3952.
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  A detailed molecular dynamics simulation study is presented on the behavior of aggregates composed of the nonionic monorhamnolipid α-rhamnopyranosyl-β-hydroxydecanoyl-β-hydroxydecanoate (Rha-C10-C10) and decane in bulk water. A graph theoretical approach was utilized to characterize the size and composition of the many aggregates generated in our simulations. Overall, we observe that the formation of oil in Rha-C10-C10 aggregates is a favorable process. Detailed analysis on the surfactant/oil aggregate shows that larger aggregates are stable. The shape and size of the aggregates are widely distributed, with the majority of the aggregates preferring ellipsoidal or cylindrical structures. Irrespective of the decane concentration in the system, we did not observe free decane in any of the simulations. Further insights into the binding energy of decane were carried out using free-energy perturbation calculations. The results showed that the trapped decane molecules provide stability to the Rha-C10-C10 aggregates of size N = 50 which are shown to be unstable in our previous study and allow for the growth of larger aggregates than pure Rha-C10-C10 in water. The density profile plots show that decane molecules encapsulated inside the aggregate preferred to remain closer to the center of mass. This study points to the feasibility of using this biosurfactant as an environmental remediation agent.
• Munusamy, E., Luft, C. M., Pemberton, J. E., & Schwartz, S. D. (2018). Unraveling the Differential Aggregation of Anionic and Nonionic Monorhamnolipids at Air-Water and Oil-Water Interfaces: A Classical Molecular Dynamics Simulation Study. The journal of physical chemistry. B, 122(24), 6403-6416.
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  The molecular structure of a surfactant molecule is known to have a great effect on the interfacial properties. We employ molecular dynamics simulations for a detailed atomistic study of monolayers of the nonionic and anionic form of the most common congener of monorhamnolipids, α-rhamnopyranosyl-β-hydroxydecanoyl-β-hydroxydecanoate (( R, R)-Rha-C10-C10), at the air-water and oil-water interfaces. An atomistic-level understanding of monolayer aggregation is necessary to explain a recent experimental observation indicating that nonionic and anionic Rha-C10-C10 show surprisingly different surface area per molecule at the critical micelle concentration. Surface-pressure analysis, interface formation energy calculations, and mass density profiles of the monolayers at the air-water interface show similar properties between nonionic and anionic Rha-C10-C10 aggregation. It is found that there is a significant difference in the headgroup conformations of Rha-C10-C10 in the nonionic and anionic monolayers. Hydrogen bonding interactions between the Rha-C10-C10 molecules in the monolayers is also significantly different between nonionic and anionic forms. Representative snapshots of the simulated system at different surface concentrations show the segregation of molecular aggregates from the interface into the bulk water in the anionic Rha-C10-C10 monolayer at higher concentrations, whereas in the nonionic Rha-C10-C10 monolayer, the molecules are still located at the interface. The present work provides insight into the different aggregation properties of nonionic and anionic Rha-C10-C10 at the air-water interface. Further analyses were carried out to understand the aggregation behavior of nonionic and anionic Rha-C10-C10 at the oil-water interface. It is observed that the presence of oil molecules does not significantly influence the aggregation properties of Rha-C10-C10 as compared to those of the air-water interface.
• Schramm, V. L., & Schwartz, S. D. (2018). Promoting Vibrations and the Function of Enzymes. Emerging Theoretical and Experimental Convergence. Biochemistry, 57(24), 3299-3308.
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  A complete understanding of enzyme catalysis requires knowledge of both transition state features and the detailed motions of atoms that cause reactant molecules to form and traverse the transition state. The seeming intractability of the problem arises from the femtosecond lifetime of chemical transition states, preventing most experimental access. Computational chemistry is admirably suited to short time scale analysis but can be misled by inappropriate starting points or by biased assumptions. Kinetic isotope effects provide an experimental approach to transition state structure and a method for obtaining transition state analogues but, alone, do not inform how that transition state is reached. Enzyme structures with transition state analogues provide computational starting points near the transition state geometry. These well-conditioned starting points, combined with the unbiased computational method of transition path sampling, provide realistic atomistic motions involved in transition state formation and passage. In many, but not all, enzymatic systems, femtosecond local protein motions near the catalytic site are linked to transition state formation. These motions are not inherently revealed by most approaches of transition state theory, because transition state theory replaces dynamics with the statistics of the transition state. Experimental and theoretical convergence of the link between local catalytic site vibrational modes and catalysis comes from heavy atom ("Born-Oppenheimer") enzymes. Fully labeled and catalytic site local heavy atom labels perturb the probability of finding enzymatic transition states in ways that can be analyzed and predicted by transition path sampling. Recent applications of these experimental and computational approaches reveal how subpicosecond local catalytic site protein modes play important roles in creating the transition state.
• Schwartz, S. D., Luft, C. M., Pemberton, J. E., & Munusamy, E. (2018). Unraveling the Differential Aggregation of Anionic and Nonionic Monorhamnolipids at the Interfaces: A Classical Molecular Dynamics Simulation Study. J. Phys. Chem. B, 122, 6403-6416. doi:10.1021/acs.jpcb.8b03037
• Schwartz, S. D., Pemberton, J. E., Munusamy, E., & Luft, C. M. (2018). Molecular Dynamics Simulation of the Oil Sequestration Properties of a Nonionic Rhamnolipid. J. Phys. Chem. B, 122, 3944-3952. doi:10.1021/acs.jpcb.7b11959
• Williams, M. R., Tardiff, J. C., & Schwartz, S. D. (2018). Mechanism of Cardiac Tropomyosin Transitions on Filamentous Actin As Revealed by All-Atom Steered Molecular Dynamics Simulations. The journal of physical chemistry letters, 9(12), 3301-3306.
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  The three-state model of tropomyosin (Tm) positioning along filamentous actin allows for Tm to act as a gate for myosin head binding with actin. The blocked state of Tm prevents myosin binding, while the open state allows for strong binding. Intermediate to this transition is the closed state. The details of the transition from the blocked to the closed state and then finally to the open state by Tm have not been fully accessible to experiment. Utilizing steered molecular dynamics, we investigate the work required to move the Tm strand through the extant set of proposed transitions. We find that an azimuthal motion around the actin filament by Tm is most probable in spite of increased initial energy barrier from the topographical landscape of actin.
• Eismin, R. J., Munusamy, E., Kegel, L. L., Hogan, D. E., Maier, R. M., Schwartz, S. D., & Pemberton, J. E. (2017). Evolution of Aggregate Structure in Solutions of Anionic Monorhamnolipids: Experimental and Computational Results. Langmuir : the ACS journal of surfaces and colloids, 33(30), 7412-7424.
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  The evolution of solution aggregates of the anionic form of the native monorhamnolipid (mRL) mixture produced by Pseudomonas aeruginosa ATCC 9027 is explored at pH 8.0 using both experimental and computational approaches. Experiments utilizing surface tension measurements, dynamic light scattering, and both steady-state and time-resolved fluorescence spectroscopy reveal solution aggregation properties. All-atom molecular dynamics simulations on self-assemblies of the most abundant monorhamnolipid molecule, l-rhamnosyl-β-hydroxydecanoyl-β-hydroxydecanoate (Rha-C10-C10), in its anionic state explore the formation of aggregates and the role of hydrogen bonding, substantiating the experimental results. At pH 8.0, at concentrations above the critical aggregation concentration of 201 μM but below ∼7.5 mM, small premicelles exist in solution; above ∼7.5 mM, micelles with hydrodynamic radii of ∼2.5 nm dominate, although two discrete populations of larger lamellar aggregates (hydrodynamic radii of ∼10 and 90 nm) are also present in solution in much smaller number densities. The critical aggregation number for the micelles is determined to be ∼26 monomers/micelle using fluorescence quenching measurements, with micelles gradually increasing in size with monorhamnolipid concentration. Molecular dynamics simulations on systems with between 10 and 100 molecules of Rha-C10-C10 indicate the presence of stable premicelles of seven monomers with the most prevalent micelle being ∼25 monomers and relatively spherical. A range of slightly larger micelles of comparable stability can also exist that become increasing elliptical with increasing monomer number. Intermolecular hydrogen bonding is shown to play a significant role in stabilization of these aggregates. In total, the computational results are in excellent agreement with the experimental results.
• Harijan, R. K., Zoi, I., Antoniou, D., Schwartz, S. D., & Schramm, V. L. (2017). Catalytic-site design for inverse heavy-enzyme isotope effects in human purine nucleoside phosphorylase. Proceedings of the National Academy of Sciences of the United States of America, 114(25), 6456-6461.
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  Heavy-enzyme isotope effects (15N-, 13C-, and 2H-labeled protein) explore mass-dependent vibrational modes linked to catalysis. Transition path-sampling (TPS) calculations have predicted femtosecond dynamic coupling at the catalytic site of human purine nucleoside phosphorylase (PNP). Coupling is observed in heavy PNPs, where slowed barrier crossing caused a normal heavy-enzyme isotope effect (kchemlight/kchemheavy > 1.0). We used TPS to design mutant F159Y PNP, predicted to improve barrier crossing for heavy F159Y PNP, an attempt to generate a rare inverse heavy-enzyme isotope effect (kchemlight/kchemheavy < 1.0). Steady-state kinetic comparison of light and heavy native PNPs to light and heavy F159Y PNPs revealed similar kinetic properties. Pre-steady-state chemistry was slowed 32-fold in F159Y PNP. Pre-steady-state chemistry compared heavy and light native and F159Y PNPs and found a normal heavy-enzyme isotope effect of 1.31 for native PNP and an inverse effect of 0.75 for F159Y PNP. Increased isotopic mass in F159Y PNP causes more efficient transition state formation. Independent validation of the inverse isotope effect for heavy F159Y PNP came from commitment to catalysis experiments. Most heavy enzymes demonstrate normal heavy-enzyme isotope effects, and F159Y PNP is a rare example of an inverse effect. Crystal structures and TPS dynamics of native and F159Y PNPs explore the catalytic-site geometry associated with these catalytic changes. Experimental validation of TPS predictions for barrier crossing establishes the connection of rapid protein dynamics and vibrational coupling to enzymatic transition state passage.
• McConnell, M., Tal Grinspan, L., Williams, M. R., Lynn, M. L., Schwartz, B. A., Fass, O. Z., Schwartz, S. D., & Tardiff, J. C. (2017). Clinically Divergent Mutation Effects on the Structure and Function of the Human Cardiac Tropomyosin Overlap. Biochemistry, 56(26), 3403-3413.
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  The progression of genetically inherited cardiomyopathies from an altered protein structure to clinical presentation of disease is not well understood. One of the main roadblocks to mechanistic insight remains a lack of high-resolution structural information about multiprotein complexes within the cardiac sarcomere. One example is the tropomyosin (Tm) overlap region of the thin filament that is crucial for the function of the cardiac sarcomere. To address this central question, we devised coupled experimental and computational modalities to characterize the baseline function and structure of the Tm overlap, as well as the effects of mutations causing divergent patterns of ventricular remodeling on both structure and function. Because the Tm overlap contributes to the cooperativity of myofilament activation, we hypothesized that mutations that enhance the interactions between overlap proteins result in more cooperativity, and conversely, those that weaken interaction between these elements lower cooperativity. Our results suggest that the Tm overlap region is affected differentially by dilated cardiomyopathy-associated Tm D230N and hypertrophic cardiomyopathy-associated human cardiac troponin T (cTnT) R92L. The Tm D230N mutation compacts the Tm overlap region, increasing the cooperativity of the Tm filament, contributing to a dilated cardiomyopathy phenotype. The cTnT R92L mutation causes weakened interactions closer to the N-terminal end of the overlap, resulting in decreased cooperativity. These studies demonstrate that mutations with differential phenotypes exert opposite effects on the Tm-Tn overlap, and that these effects can be directly correlated to a molecular level understanding of the structure and dynamics of the component proteins.
• Munusamy, E., Luft, C. M., Pemberton, J. E., & Schwartz, S. D. (2017). Structural Properties of Nonionic Monorhamnolipid Aggregates in Water Studied by Classical Molecular Dynamics Simulations. The journal of physical chemistry. B, 121(23), 5781-5793.
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  Molecular dynamics simulations were carried out to investigate the structure and stabilizing factors of aggregates of the nonionic form of the most common congener of monorhamnolipids, α-rhamnopyranosyl-β-hydroxydecanoyl-β-hydroxydecanoate (Rha-C10-C10), in water. Aggregates of size ranging from 5 to 810 monomers were observed in the simulation forming spherical and ellipsoidal structures, a torus-like structure, and a unilamellar vesicle. The effects of the hydrophobic chain conformation and alignment in the aggregate, role of monomer···monomer and monomer···water H-bonds, and conformations of monomers in the aggregate were studied in detail. The unilamellar vesicle is highly stable due to the presence of isolated water molecules inside the core adding to the binding energy. Dissociation of a monomer from a larger micellar aggregate is relatively easy compared to that from smaller aggregates as seen from potential of mean force calculations. This analysis also shows that monomers are held more strongly in aggregates of Rha-C10-C10 than the widely used surfactant sodium dodecyl sulfate. Comparisons between the aggregation behavior of nonionic and anionic forms of Rha-C10-C10 are presented.
• Pemberton, J. E., Schwartz, S. D., Maier, R. M., Hogan, D. E., Kegel, L. M., Munusamy, E., & Eisman, R. J. (2017). Evolution of aggregate structure in solutions of anionic monorhamnolipids: experimental and computational results. Langmuir, 33, 7412-7424.
• Schwartz, S. D., Schwartz, S. D., Pemberton, J. E., Pemberton, J. E., Luft, C. M., Luft, C. M., Munusamy, E., & Munusamy, E. (2017). Structural Properties of Nonionic Monorhamnolipid Aggregates in Water Studied by Classical Molecular Dynamics Simulations. Journal of Physical Chemistry B, 121, 5781-5793.
• Varga, M. J., Dzierlenga, M. W., & Schwartz, S. D. (2017). Structurally Linked Dynamics in Lactate Dehydrogenases of Evolutionarily Distinct Species. Biochemistry, 56(19), 2488-2496.
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  We present new findings about how primary and secondary structure affects the role of fast protein motions in the reaction coordinates of enzymatic reactions. Using transition path sampling and committor distribution analysis, we examined the difference in the role of these fast protein motions in the reaction coordinate of lactate dehydrogenases (LDHs) of Apicomplexa organisms Plasmodium falciparum and Cryptosporidium parvum. Having evolved separately from a common malate dehydrogenase ancestor, the two enzymes exhibit several important structural differences, notably a five-amino acid insertion in the active site loop of P. falciparum LDH. We find that these active site differences between the two organisms' LDHs likely cause a decrease in the contribution of the previously determined LDH rate-promoting vibration to the reaction coordinate of P. falciparum LDH compared to that of C. parvum LDH, specifically in the coupling of the rate-promoting vibration and the hydride transfer. This effect, while subtle, directly shows how changes in structure near the active site of LDH alter catalytically important motions. Insights provided by studying these alterations would prove to be useful in identifying LDH inhibitors that specifically target the isozymes of these parasitic organisms.
• Zoi, I., Antoniou, D., & Schwartz, S. D. (2017). Electric Fields and Fast Protein Dynamics in Enzymes. The journal of physical chemistry letters, 8(24), 6165-6170.
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  In recent years, there has been much discussion regarding the origin of enzymatic catalysis and whether including protein dynamics is necessary for understanding catalytic enhancement. An important contribution in this debate was made with the application of the vibrational Stark effect spectroscopy to measure electric fields in the active site. This provided a window on electric fields at the transition state in enzymatic reactions. We performed computational studies on two enzymes where we have shown that fast dynamics is part of the reaction mechanism and calculated the electric field near the bond-breaking event. We found that the fast motions that we had identified lead to an increase of the electric field, thus preparing an enzymatic configuration that is electrostatically favorable for the catalytic chemical step. We also studied the enzyme that has been the subject of Stark spectroscopy, ketosteroid isomerase, and found electric fields of a similar magnitude to the two previous examples.
• Zoi, I., Antoniou, D., & Schwartz, S. D. (2017). Incorporating Fast Protein Dynamics into Enzyme Design: A Proposed Mutant Aromatic Amine Dehydrogenase. The journal of physical chemistry. B, 121(30), 7290-7298.
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  In recent years, there has been encouraging progress in the engineering of enzymes that are designed to catalyze reactions not accelerated by natural enzymes. We tested the possibility of reengineering an existing enzyme by introducing a fast protein motion that couples to the reaction. Aromatic amine dehydrogenase is a system that has been shown to use a fast substrate motion as part of the reaction mechanism. We identified a mutation that preserves this fast motion but also introduces a favorable fast motion near the active site that did not exist in the native enzyme. Transition path sampling was used for the analysis of the atomic details of the mechanism.
• Antoniou, D., & Schwartz, S. D. (2016). Phase Space Bottlenecks in Enzymatic Reactions. The journal of physical chemistry. B, 120(3), 433-9.
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  The definition of a transition state on an individual reactive trajectory is made via a committor analysis. In the past, the bottleneck definition has often been applied in configuration space. This is an approximation, and in order to expand this definition, we are revisiting an enzyme in which we had identified a fast subpicosecond motion that makes the reaction possible. First we used a time-series analysis method to identify the exact time when this motion initiates donor-acceptor compression. Then we modified the standard committor analysis of transition path sampling to identify events in phase space and found that there is a dividing surface in phase space significantly earlier than the configurationally defined transition-state crossing.
• Dzierlenga, M. W., & Schwartz, S. D. (2016). Targeting a Rate-Promoting Vibration with an Allosteric Mediator in Lactate Dehydrogenase. The journal of physical chemistry letters, 7(13), 2591-6.
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  We present a new type of allosteric modulation in which a molecule bound outside the active site modifies the chemistry of an enzymatic reaction through rapid protein dynamics. As a test case for this type of allostery, we chose an enzyme with a well-characterized rate-promoting vibration, lactate dehydrogenase; identified a suitable small molecule for binding; and used transition path sampling to obtain ensembles of reactive trajectories. We found that the small molecule significantly affected the reaction by changing the position of the transition state and, through applying committor distribution analysis, showed that it removed the protein component from the reaction coordinate. The ability of a small-molecule to disrupt enzymatic reactions through alteration of subpicosecond protein motion opens the door for new experimental studies on protein motion coupled to enzymatic reactions and possibly the design of drugs to target these enzymes.
• Dzierlenga, M. W., Varga, M. J., & Schwartz, S. D. (2016). Path Sampling Methods for Enzymatic Quantum Particle Transfer Reactions. Methods in enzymology, 578, 21-43.
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  The mechanisms of enzymatic reactions are studied via a host of computational techniques. While previous methods have been used successfully, many fail to incorporate the full dynamical properties of enzymatic systems. This can lead to misleading results in cases where enzyme motion plays a significant role in the reaction coordinate, which is especially relevant in particle transfer reactions where nuclear tunneling may occur. In this chapter, we outline previous methods, as well as discuss newly developed dynamical methods to interrogate mechanisms of enzymatic particle transfer reactions. These new methods allow for the calculation of free energy barriers and kinetic isotope effects (KIEs) with the incorporation of quantum effects through centroid molecular dynamics (CMD) and the full complement of enzyme dynamics through transition path sampling (TPS). Recent work, summarized in this chapter, applied the method for calculation of free energy barriers to reaction in lactate dehydrogenase (LDH) and yeast alcohol dehydrogenase (YADH). We found that tunneling plays an insignificant role in YADH but plays a more significant role in LDH, though not dominant over classical transfer. Additionally, we summarize the application of a TPS algorithm for the calculation of reaction rates in tandem with CMD to calculate the primary H/D KIE of YADH from first principles. We found that the computationally obtained KIE is within the margin of error of experimentally determined KIEs and corresponds to the KIE of particle transfer in the enzyme. These methods provide new ways to investigate enzyme mechanism with the inclusion of protein and quantum dynamics.
• Pan, X., & Schwartz, S. D. (2016). Conformational Heterogeneity in the Michaelis Complex of Lactate Dehydrogenase: An Analysis of Vibrational Spectroscopy Using Markov and Hidden Markov Models. The journal of physical chemistry. B, 120(27), 6612-20.
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  Lactate dehydrogenase (LDH) catalyzes the interconversion of pyruvate and lactate. Recent isotope-edited IR spectroscopy suggests that conformational heterogeneity exists within the Michaelis complex of LDH, and this heterogeneity affects the propensity toward the on-enzyme chemical step for each Michaelis substate. By combining molecular dynamics simulations with Markov and hidden Markov models, we obtained a detailed kinetic network of the substates of the Michaelis complex of LDH. The ensemble-average electric fields exerted onto the vibrational probe were calculated to provide a direct comparison with the vibrational spectroscopy. Structural features of the Michaelis substates were also analyzed on atomistic scales. Our work not only clearly demonstrates the conformational heterogeneity in the Michaelis complex of LDH and its coupling to the reactivities of the substates, but it also suggests a methodology to simultaneously resolve kinetics and structures on atomistic scales, which can be directly compared with the vibrational spectroscopy.
• Varga, M. J., & Schwartz, S. D. (2016). Enzymatic Kinetic Isotope Effects from First-Principles Path Sampling Calculations. Journal of chemical theory and computation, 12(4), 2047-54.
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  In this study, we develop and test a method to determine the rate of particle transfer and kinetic isotope effects in enzymatic reactions, specifically yeast alcohol dehydrogenase (YADH), from first-principles. Transition path sampling (TPS) and normal mode centroid dynamics (CMD) are used to simulate these enzymatic reactions without knowledge of their reaction coordinates and with the inclusion of quantum effects, such as zero-point energy and tunneling, on the transferring particle. Though previous studies have used TPS to calculate reaction rate constants in various model and real systems, it has not been applied to a system as large as YADH. The calculated primary H/D kinetic isotope effect agrees with previously reported experimental results, within experimental error. The kinetic isotope effects calculated with this method correspond to the kinetic isotope effect of the transfer event itself. The results reported here show that the kinetic isotope effects calculated from first-principles, purely for barrier passage, can be used to predict experimental kinetic isotope effects in enzymatic systems.
• Wang, Z., Antoniou, D., Schwartz, S. D., & Schramm, V. L. (2016). Hydride Transfer in DHFR by Transition Path Sampling, Kinetic Isotope Effects, and Heavy Enzyme Studies. Biochemistry, 55(1), 157-66.
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  Escherichia coli dihydrofolate reductase (ecDHFR) is used to study fundamental principles of enzyme catalysis. It remains controversial whether fast protein motions are coupled to the hydride transfer catalyzed by ecDHFR. Previous studies with heavy ecDHFR proteins labeled with (13)C, (15)N, and nonexchangeable (2)H reported enzyme mass-dependent hydride transfer kinetics for ecDHFR. Here, we report refined experimental and computational studies to establish that hydride transfer is independent of protein mass. Instead, we found the rate constant for substrate dissociation to be faster for heavy DHFR. Previously reported kinetic differences between light and heavy DHFRs likely arise from kinetic steps other than the chemical step. This study confirms that fast (femtosecond to picosecond) protein motions in ecDHFR are not coupled to hydride transfer and provides an integrative computational and experimental approach to resolve fast dynamics coupled to chemical steps in enzyme catalysis.
• Williams, M. R., Lehman, S. J., Tardiff, J. C., & Schwartz, S. D. (2016). Atomic resolution probe for allostery in the regulatory thin filament. Proceedings of the National Academy of Sciences of the United States of America, 113(12), 3257-62.
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  Calcium binding and dissociation within the cardiac thin filament (CTF) is a fundamental regulator of normal contraction and relaxation. Although the disruption of this complex, allosterically mediated process has long been implicated in human disease, the precise atomic-level mechanisms remain opaque, greatly hampering the development of novel targeted therapies. To address this question, we used a fully atomistic CTF model to test both Ca(2+) binding strength and the energy required to remove Ca(2+) from the N-lobe binding site in WT and mutant troponin complexes that have been linked to genetic cardiomyopathies. This computational approach is combined with measurements of in vitro Ca(2+) dissociation rates in fully reconstituted WT and cardiac troponin T R92L and R92W thin filaments. These human disease mutations represent known substitutions at the same residue, reside at a significant distance from the calcium binding site in cardiac troponin C, and do not affect either the binding pocket affinity or EF-hand structure of the binding domain. Both have been shown to have significantly different effects on cardiac function in vivo. We now show that these mutations independently alter the interaction between the Ca(2+) ion and cardiac troponin I subunit. This interaction is a previously unidentified mechanism, in which mutations in one protein of a complex indirectly affect a third via structural and dynamic changes in a second to yield a pathogenic change in thin filament function that results in mutation-specific disease states. We can now provide atom-level insight that is potentially highly actionable in drug design.
• Zoi, I., Suarez, J., Antoniou, D., Cameron, S. A., Schramm, V. L., & Schwartz, S. D. (2016). Modulating Enzyme Catalysis through Mutations Designed to Alter Rapid Protein Dynamics. Journal of the American Chemical Society, 138(10), 3403-9.
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  The relevance of sub-picosecond protein motions to the catalytic event remains a topic of debate. Heavy enzymes (isotopically substituted) provide an experimental tool for bond-vibrational links to enzyme catalysis. A recent transition path sampling study with heavy purine nucleoside phosphorylase (PNP) characterized the experimentally observed mass-dependent slowing of barrier crossing (Antoniou, D.; Ge, X.; Schramm, V. L.; Schwartz, S. D. J. Phys. Chem. Lett. 2012, 3, 3538). Here we computationally identify second-sphere amino acid residues predicted to influence the freedom of the catalytic site vibrational modes linked to heavy enzyme effects in PNP. We mutated heavy and light PNPs to increase the catalytic site vibrational freedom. Enzymatic barrier-crossing rates were converted from mass-dependent to mass-independent as a result of the mutations. The mutagenic uncoupling of femtosecond motions between catalytic site groups and reactants decreased transition state barrier crossing by 2 orders of magnitude, an indication of the femtosecond dynamic contributions to catalysis.
• Dzierlenga, M. W., Antoniou, D., & Schwartz, S. D. (2015). Another Look at the Mechanisms of Hydride Transfer Enzymes with Quantum and Classical Transition Path Sampling. The journal of physical chemistry letters, 6(7), 1177-81.
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  The mechanisms involved in enzymatic hydride transfer have been studied for years, but questions remain due, in part, to the difficulty of probing the effects of protein motion and hydrogen tunneling. In this study, we use transition path sampling (TPS) with normal mode centroid molecular dynamics (CMD) to calculate the barrier to hydride transfer in yeast alcohol dehydrogenase (YADH) and human heart lactate dehydrogenase (LDH). Calculation of the work applied to the hydride allowed for observation of the change in barrier height upon inclusion of quantum dynamics. Similar calculations were performed using deuterium as the transferring particle in order to approximate kinetic isotope effects (KIEs). The change in barrier height in YADH is indicative of a zero-point energy (ZPE) contribution and is evidence that catalysis occurs via a protein compression that mediates a near-barrierless hydride transfer. Calculation of the KIE using the difference in barrier height between the hydride and deuteride agreed well with experimental results.
• Masterson, J. E., & Schwartz, S. D. (2015). Evolution alters the enzymatic reaction coordinate of dihydrofolate reductase. The journal of physical chemistry. B, 119(3), 989-96.
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  How evolution has affected enzyme function is a topic of great interest in the field of biophysical chemistry. Evolutionary changes from Escherichia coli dihydrofolate reductase (ecDHFR) to human dihydrofolate reductase (hsDHFR) have resulted in increased catalytic efficiency and an altered dynamic landscape in the human enzyme. Here, we show that a subpicosecond protein motion is dynamically coupled to hydride transfer catalyzed by hsDHFR but not ecDHFR. This motion propagates through residues that correspond to mutational events along the evolutionary path from ecDHFR to hsDHFR. We observe an increase in the variability of the transition states, reactive conformations, and times of barrier crossing in the human system. In the hsDHFR active site, we detect structural changes that have enabled the coupling of fast protein dynamics to the reaction coordinate. These results indicate a shift in the DHFR family to a form of catalysis that incorporates rapid protein dynamics and a concomitant shift to a more flexible path through reactive phase space.
• Pan, X., & Schwartz, S. D. (2015). Free energy surface of the Michaelis complex of lactate dehydrogenase: a network analysis of microsecond simulations. The journal of physical chemistry. B, 119(17), 5430-6.
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  It has long been recognized that the structure of a protein creates a hierarchy of conformations interconverting on multiple time scales. The conformational heterogeneity of the Michaelis complex is of particular interest in the context of enzymatic catalysis in which the reactant is usually represented by a single conformation of the enzyme/substrate complex. Lactate dehydrogenase (LDH) catalyzes the interconversion of pyruvate and lactate with concomitant interconversion of two forms of the cofactor nicotinamide adenine dinucleotide (NADH and NAD(+)). Recent experimental results suggest that multiple substates exist within the Michaelis complex of LDH, and they show a strong variance in their propensity toward the on-enzyme chemical step. In this study, microsecond-scale all-atom molecular dynamics simulations were performed on LDH to explore the free energy landscape of the Michaelis complex, and network analysis was used to characterize the distribution of the conformations. Our results provide a detailed view of the kinetic network of the Michaelis complex and the structures of the substates at atomistic scales. They also shed light on the complete picture of the catalytic mechanism of LDH.
• Van der Poorten, O., Fehér, K., Buysse, K., Feytens, D., Zoi, I., Schwartz, S. D., Martins, J. C., Tourwé, D., Cai, M., Hruby, V. J., & Ballet, S. (2015). Azepinone-Containing Tetrapeptide Analogues of Melanotropin Lead to Selective hMC4R Agonists and hMC5R Antagonist. ACS medicinal chemistry letters, 6(2), 192-7.
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  To address the need for highly potent, metabolically stable, and selective agonists, antagonists, and inverse agonists at the melanocortin receptor subtypes, conformationally constrained indolo- and benzazepinone residues were inserted into the α-MSH pharmacophore, His(6)-Phe(7)-Arg(8)-Trp(9)-domain. Replacement of His(6) by an aminoindoloazepinone (Aia) or aminobenzazepinone (Aba) moiety led to hMC4R and hMC5R selective agonist and antagonist ligands, respectively (tetrapeptides 1 to 3 and 4, respectively). In peptides 1 to 3 and depending on the para-substituent of the d-Phe residue in position 2, the activity goes from allosteric partial agonism (1, R = H) to allosteric full agonism (2, R = F) and finally allosteric partial agonism (3, R = Br).
• Zoi, I., Motley, M. W., Antoniou, D., Schramm, V. L., & Schwartz, S. D. (2015). Enzyme Homologues Have Distinct Reaction Paths through Their Transition States. The journal of physical chemistry. B, 119(9), 3662-8.
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  Recent studies of the bacterial enzymes EcMTAN and VcMTAN showed that they have different binding affinities for the same transition state analogue. This was surprising given the similarity of their active sites. We performed transition path sampling simulations of both enzymes to reveal the atomic details of the catalytic chemical step, which may be the key for explaining the inhibitor affinity differences. Even though all experimental data would suggest the two enzymes are almost identical, subtle dynamic differences manifest in differences of reaction coordinate, transition state structure, and eventually significant differences in inhibitor binding. Unlike EcMTAN, VcMTAN has multiple distinct transition states, which is an indication that multiple sets of coordinated protein motions can reach a transition state. Reaction coordinate information is only accessible from transition path sampling approaches, since all experimental approaches report averages. Detailed knowledge could have a significant impact on pharmaceutical design.
• Masterson, J., & Schwartz, S. D. (2014). The enzymatic reaction catalyzed by lactate dehydrogenase exhibits one dominant reaction path,. Journal of Physical Chemistry B, 442(17), 132-136.
• Masterson, J. E., & Schwartz, S. D. (2013). Changes in protein architecture and subpicosecond protein dynamics impact the reaction catalyzed by lactate dehydrogenase. Journal of Physical Chemistry A, 117(32), 7107-7113.
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  PMID: 23441954;PMCID: PMC3695017;Abstract: We have previously established the importance of a promoting vibration, a subpicosecond protein motion that propagates through a specific axis of residues, in the reaction coordinate of lactate dehydrogenase (LDH). To test the effect that perturbation of this motion would have on the enzymatic reaction, we employ transition path sampling to obtain transition path ensembles for four independent LDH enzymatic systems: the wild type enzyme, a version of the enzyme expressing heavy isotopic substitution, and two enzymes with mutations in the promoting vibration axis. We show that even slight changes in the promoting vibration of LDH result in dramatic changes in enzymatic chemistry. In the "heavy" version of the enzyme, we find that the dampening of the subpicosecond dynamics from heavy isotopic substitution leads to a drastic increase in the time of barrier crossing. Furthermore, we see that mutation of the promoting vibration axis causes a decrease in the variability of transition paths available to the enzymatic reaction. The combined results reveal the importance of the protein architecture of LDH in enzymatic catalysis by establishing how the promoting vibration is finely tuned to facilitate chemistry. © 2013 American Chemical Society.
• Motley, M. W., Schramm, V. L., & Schwartz, S. D. (2013). Conformational freedom in tight binding enzymatic transition-state analogues. Journal of Physical Chemistry B, 117(33), 9591-9597.
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  PMID: 23895500;PMCID: PMC3786605;Abstract: Transition-state analogues of bacterial 5′-methylthioadenosine/S- adenosylhomocysteine nucleosidases (MTANs) disrupt quorum-sensing pathways in Escherichia coli and Vibrio cholerae, demonstrating the potential to limit pathogenicity without placing bacteria under intense selective pressure that leads to antibiotic resistance. Despite the similarity of the crystal structures of E. coli MTAN (EcMTAN) and V. cholerae MTAN (VcMTAN) bound to DADMe-Immucillin-A transition-state (TS) analogues, EcMTAN demonstrates femtomolar affinity for BuT-DADMe-Immucillin-A (BDIA) whereas VcMTAN possesses only picomolar affinity. Protein dynamic interactions are therefore implicated in this inhibitor affinity difference. We conducted molecular dynamics simulations of both EcMTAN and VcMTAN in complex with BDIA to explore differences in protein dynamic architecture. Simulations revealed that electrostatic and hydrophobic interactions with BDIA are similar for both enzymes and thus unlikely to account for the difference in inhibitor affinity. The EcMTAN-BDIA complex reveals a greater flexibility and conformational freedom of catalytically important atoms. We propose that conserved motions related to the EcMTAN transition state correlate with the increased affinity of BDIA for EcMTAN. Transition-state analogues permitting protein motion related to formation of the transition state are better mimics of the enzymatic transition state and can bind more tightly than those immobilizing catalytic site dynamics. © 2013 American Chemical Society.
• Schwartz, S. D. (2013). Protein dynamics and the enzymatic reaction coordinate. Topics in Current Chemistry, 337, 189-208.
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  PMID: 23508766;Abstract: This chapter discusses progress over the past 15 years in understanding the role of protein dynamics in enzymatically catalyzed chemical reactions. Research has shown that protein motion on all timescales from femtoseconds to milliseconds can contribute to function, and in particular in some enzymes there are sub-picosecond motions, on the same timescale as barrier passage, the couple directly to chemical transformation, and are thus part of the reaction coordinate. Approaches such as transition path sampling and committor analysis have greatly enhanced our understanding of these processes. © Springer-Verlag Berlin Heidelberg 2013.
• Schwartz, S., & Schwartz, S. D. (2013). Protein dynamics and the enzymatic reaction coordinate. Topics in current chemistry, 337.
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  This chapter discusses progress over the past 15 years in understanding the role of protein dynamics in enzymatically catalyzed chemical reactions. Research has shown that protein motion on all timescales from femtoseconds to milliseconds can contribute to function, and in particular in some enzymes there are sub-picosecond motions, on the same timescale as barrier passage, the couple directly to chemical transformation, and are thus part of the reaction coordinate. Approaches such as transition path sampling and committor analysis have greatly enhanced our understanding of these processes.
• Schwartz, S., Masterson, J. E., & Schwartz, S. D. (2013). Changes in protein architecture and subpicosecond protein dynamics impact the reaction catalyzed by lactate dehydrogenase. The journal of physical chemistry. A, 117(32).
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  We have previously established the importance of a promoting vibration, a subpicosecond protein motion that propagates through a specific axis of residues, in the reaction coordinate of lactate dehydrogenase (LDH). To test the effect that perturbation of this motion would have on the enzymatic reaction, we employ transition path sampling to obtain transition path ensembles for four independent LDH enzymatic systems: the wild type enzyme, a version of the enzyme expressing heavy isotopic substitution, and two enzymes with mutations in the promoting vibration axis. We show that even slight changes in the promoting vibration of LDH result in dramatic changes in enzymatic chemistry. In the "heavy" version of the enzyme, we find that the dampening of the subpicosecond dynamics from heavy isotopic substitution leads to a drastic increase in the time of barrier crossing. Furthermore, we see that mutation of the promoting vibration axis causes a decrease in the variability of transition paths available to the enzymatic reaction. The combined results reveal the importance of the protein architecture of LDH in enzymatic catalysis by establishing how the promoting vibration is finely tuned to facilitate chemistry.
• Schwartz, S., Motley, M. W., Schramm, V. L., & Schwartz, S. D. (2013). Conformational freedom in tight binding enzymatic transition-state analogues. The journal of physical chemistry. B, 117(33).
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  Transition-state analogues of bacterial 5'-methylthioadenosine/S-adenosylhomocysteine nucleosidases (MTANs) disrupt quorum-sensing pathways in Escherichia coli and Vibrio cholerae, demonstrating the potential to limit pathogenicity without placing bacteria under intense selective pressure that leads to antibiotic resistance. Despite the similarity of the crystal structures of E. coli MTAN (EcMTAN) and V. cholerae MTAN (VcMTAN) bound to DADMe-Immucillin-A transition-state (TS) analogues, EcMTAN demonstrates femtomolar affinity for BuT-DADMe-Immucillin-A (BDIA) whereas VcMTAN possesses only picomolar affinity. Protein dynamic interactions are therefore implicated in this inhibitor affinity difference. We conducted molecular dynamics simulations of both EcMTAN and VcMTAN in complex with BDIA to explore differences in protein dynamic architecture. Simulations revealed that electrostatic and hydrophobic interactions with BDIA are similar for both enzymes and thus unlikely to account for the difference in inhibitor affinity. The EcMTAN-BDIA complex reveals a greater flexibility and conformational freedom of catalytically important atoms. We propose that conserved motions related to the EcMTAN transition state correlate with the increased affinity of BDIA for EcMTAN. Transition-state analogues permitting protein motion related to formation of the transition state are better mimics of the enzymatic transition state and can bind more tightly than those immobilizing catalytic site dynamics.
• Antoniou, D., Xiaoxia, G. e., Schramm, V. L., & Schwartz, S. D. (2012). Mass modulation of protein dynamics associated with barrier crossing in purine nucleoside phosphorylase. Journal of Physical Chemistry Letters, 3(23), 3538-3544.
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  Abstract: The role of protein dynamics on different time scales in enzyme catalysis remains an area of active debate. The connection between enzyme dynamics on the femtosecond time scale and transition state formation has been demonstrated in human purine nucleoside phosphorylase (PNP) through the study of a mass-altered enzyme. Isotopic substitution in human PNP (heavy PNP) decreased the rate of on-enzyme chemistry but did not alter either the transition state structure or steady-state kinetic parameters. Here we investigate the underlying atomic motions associated with altered barrier crossing probability for heavy PNP. Transition path sampling was employed to illuminate the molecular differences between barrier crossing in light and heavy enzymes. The mass effect is apparent in promoting vibrations that polarize the N-ribosidic bond, and that promote the stability of the purine leaving group. These motions facilitate barrier crossing. © 2012 American Chemical Society.
• Dametto, M., Antoniou, D., & Schwartz, S. D. (2012). Barrier crossing in dihydrofolate reductase does not involve a rate-promoting vibration. Molecular Physics, 110(9-10), 531-536.
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  Abstract: We have studied atomic motions during the chemical reaction catalysed by the enzyme dihydrofolate reductase of Escherichia coli (EcDHFR), an important enzyme for nucleic acid synthesis. In our earlier work on the enzymes human lactate dehydrogenase and purine nucleoside phosphorylase, we had identified fast sub-ps motions that are part of the reaction coordinate. We employed Transition Path Sampling (TPS) and our recently developed reaction coordinate identification methodology to investigate if such fast motions couple to the reaction in DHFR on the barrier-crossing timescale. While we identified some protein motions near the barrier crossing event, these motions do not constitute a compressive promoting vibration, and do not appear as a clearly identifiable protein component in reaction. © 2012 Taylor & Francis.
• Manning, E. P., Tardiff, J. C., & Schwartz, S. D. (2012). Molecular effects of familial hypertrophic cardiomyopathy-related mutations in the TNT1 domain of cTnT. Journal of Molecular Biology, 421(1), 54-66.
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  PMID: 22579624;PMCID: PMC3545441;Abstract: Familial hypertrophic cardiomyopathy (FHC) is one of the most common genetic causes of heart disease. Approximately 15% of FHC-related mutations are found in cTnT [cardiac troponin (cTn) T]. Most of the cTnT FHC-related mutations are in or flanking the N-tail TNT1 domain that directly interacts with overlapping tropomyosin (Tm). We investigate two sets of cTnT mutations at opposite ends of TNT1, mutations in residue 92 in the Tm-Tm overlap region of TNT1 and mutations in residues 160 and 163 in the C-terminal portion of TNT1 adjacent to the cTnT H1-H2 linker. Though all the mutations are located within TNT1, they have widely different phenotypes clinically and biophysically. Using a complete atomistic model of the cTn-Tm complex, we identify mechanisms by which the effects of TNT1 mutations propagate to the cTn core and site II of cTnC, where calcium binding and dissociation occurs. We find that mutations in TNT1 alter the flexibility of TNT1, which is inversely proportional to the cooperativity of calcium activation of the thin filament. Further, we identify a pathway of propagation of structural and dynamic changes from TNT1 to site II of cTnC, including TNT1, cTnT linker, I-T arm, regulatory domain of cTnI, the D-E linker of cTnC, and site II cTnC. Mutationally induced changes at site II of cTnC alter calcium coordination that corresponds to biophysical measurements of calcium sensitivity. Finally, we compare this pathway of mutational propagation with that of the calcium activation of the thin filament and find that they are identical but opposite in direction. © 2012 Elsevier Ltd.
• Antoniou, D., & Schwartz, S. D. (2011). Protein dynamics and enzymatic chemical barrier passage. Journal of Physical Chemistry B, 115(51), 15147-15158.
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  PMID: 22031954;PMCID: PMC3245361;Abstract: After many decades of investigation, the manner in which enzymes increase the rate of chemical reactions, at times by a factor of 1017 compared to the rate of the corresponding solution phase reaction, is still opaque. A topic of significant discussion in the literature of the past 5-10 years has been the importance of protein dynamics in this process. This Feature Article will discuss the authors' work on this still controversial topic with focus on both methodology and application to real systems. The end conclusion of this work has been that for specific enzymes under study protein dynamics on both rapid time scales of barrier crossing (termed promoting vibrations by the authors) and of conformational fluctuations are central to the function of biological catalysts. In another enzyme we will discuss, the results are far less clear. The manner of the coupling of chemistry to protein dynamics has deep implications for protein architecture, both natural and created, and recent results reinforce the complexity of the protein form that has evolved to support these functions. © 2011 American Chemical Society.
• Antoniou, D., & Schwartz, S. D. (2011). Reply to "comment on Toward identification of the reaction coordinate directly from the transition state ensemble using the kernel PCA method". Journal of Physical Chemistry B, 115(43), 12674-12675.
• Antoniou, D., & Schwartz, S. D. (2011). Toward identification of the reaction coordinate directly from the transition state ensemble using the kernel PCA method. Journal of Physical Chemistry B, 115(10), 2465-2469.
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  PMID: 21332236;PMCID: PMC3058940;Abstract: We propose a new method for analyzing an ensemble of transition states to extract components of the reaction coordinate. We use the kernel principal component analysis (kPCA), which is a generalization of the ordinary PCA that does not make a linearization approximation We applied this method to a TPS study of human LDH we had previously published [Quaytman, S.; Schwartz, S. D. Proc. Natl. Acad. Sci. U.S.A.2007, 104, 12253] and extracted a reasonable representation for the reaction coordinate. © 2011 American Chemical Society.
• Davarifar, A., Antoniou, D., & Schwartz, S. D. (2011). The promoting vibration in human heart lactate dehydrogenase is a preferred vibrational channel. Journal of Physical Chemistry B, 115(51), 15439-15444.
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  PMID: 22077414;PMCID: PMC3245336;Abstract: We examine whether the rate-promoting vibration of lactate dehydrogenase is a preferred axis of thermal energy transfer. While it seems plausible that such a mechanistically important motion is also a favored direction of energy transfer, none of the previous studies of rate-promoting vibrations in enzymatic catalysis have addressed this question. It is equally likely that the promoting vibration, though catalytically important, has no different properties than any other axis in the protein. Resolution of this issue is important for two reasons: First, if energy is transferred along this axis in a preferred fashion, it shows that the protein is engineered in a way that transfers thermal energy into a motion that is coupled to the chemical step. Second, the discovery of a preferred direction of thermal transfer provides a potential route to experimental verification of the promoting vibration concept. Our computational experiments are specifically designed to mimic potential laser experiment with the deposition of thermal energy in an active-site chromophore with subsequent measurement of temperature at various points in the protein. Our results indicate that the promoting vibration is indeed a preferred channel of energy transfer. In addition, we study the vibrational structure of the protein via the dynamical structure factor to show preferred vibrational motion along the promoting vibration axis is an inherent property of the protein structure via thermal fluctuations. © 2011 American Chemical Society.
• Gelman, D., & Schwartz, S. D. (2011). Finite temperature application of the corrected propagator method to reactive dynamics in a condensed-phase environment. Journal of Chemical Physics, 134(3).
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  PMID: 21261332;PMCID: PMC3041154;Abstract: The recently proposed mixed quantum-classical method is extended to applications at finite temperatures. The method is designed to treat complex systems consisting of a low-dimensional quantum part (the primary system) coupled to a dissipative bath described classically. The method is based on a formalism showing how to systematically correct the approximate zeroth-order evolution rule. The corrections are defined in terms of the total quantum Hamiltonian and are taken to the classical limit by introducing the frozen Gaussian approximation for the bath degrees of freedom. The evolution of the primary system is governed by the corrected propagator yielding the exact quantum dynamics. The method has been tested on a standard model system describing proton transfer in a condensed-phase environment: a symmetric double-well potential bilinearly coupled to a bath of harmonic oscillators. Flux correlation functions and thermal rate constants have been calculated at two different temperatures for a range of coupling strengths. The results have been compared to the fully quantum simulations of Topaler and Makri [J. Chem. Phys. 101, 7500 (1994)] with the real path integral method. © 2011 American Institute of Physics.
• Manning, E. P., Tardiff, J. C., & Schwartz, S. D. (2011). A model of calcium activation of the cardiac thin filament. Biochemistry, 50(34), 7405-7413.
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  PMID: 21797264;PMCID: PMC3165030;Abstract: The cardiac thin filament regulates actomyosin interactions through calcium-dependent alterations in the dynamics of cardiac troponin and tropomyosin. Over the past several decades, many details of the structure and function of the cardiac thin filament and its components have been elucidated. We propose a dynamic, complete model of the thin filament that encompasses known structures of cardiac troponin, tropomyosin, and actin and show that it is able to capture key experimental findings. By performing molecular dynamics simulations under two conditions, one with calcium bound and the other without calcium bound to site II of cardiac troponin C (cTnC), we found that subtle changes in structure and protein contacts within cardiac troponin resulted in sweeping changes throughout the complex that alter tropomyosin (Tm) dynamics and cardiac troponin-actin interactions. Significant calcium-dependent changes in dynamics occur throughout the cardiac troponin complex, resulting from the combination of the following: structural changes in the N-lobe of cTnC at and adjacent to sites I and II and the link between them; secondary structural changes of the cardiac troponin I (cTnI) switch peptide, of the mobile domain, and in the vicinity of residue 25 of the N-terminus; secondary structural changes in the cardiac troponin T (cTnT) linker and Tm-binding regions; and small changes in cTnC-cTnI and cTnT-Tm contacts. As a result of these changes, we observe large changes in the dynamics of the following regions: the N-lobe of cTnC, the mobile domain of cTnI, the I-T arm, the cTnT linker, and overlapping Tm. Our model demonstrates a comprehensive mechanism for calcium activation of the cardiac thin filament consistent with previous, independent experimental findings. This model provides a valuable tool for research into the normal physiology of cardiac myofilaments and a template for studying cardiac thin filament mutations that cause human cardiomyopathies. © 2011 American Chemical Society.
• Gelman, D., & Schwartz, S. D. (2010). Dissipative dynamics with the corrected propagator method. Numerical comparison between fully quantum and mixed quantum/classical simulations. Chemical Physics, 370(1-3), 62-69.
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  Abstract: The recently developed quantum-classical method has been applied to the study of dissipative dynamics in multidimensional systems. The method is designed to treat many-body systems consisting of a low dimensional quantum part coupled to a classical bath. Assuming the approximate zeroth order evolution rule, the corrections to the quantum propagator are defined in terms of the total Hamiltonian and the zeroth order propagator. Then the corrections are taken to the classical limit by introducing the frozen Gaussian approximation for the bath degrees of freedom. The evolution of the primary part is governed by the corrected propagator yielding the exact quantum dynamics. The method has been tested on two model systems coupled to a harmonic bath: (i) an anharmonic (Morse) oscillator and (ii) a double-well potential. The simulations have been performed at zero temperature. The results have been compared to the exact quantum simulations using the surrogate Hamiltonian approach.
• MacHleder, S. Q., Exequiel, J., & Schwartz, S. D. (2010). On the origin of the chemical barrier and tunneling in enzymes. Journal of Physical Organic Chemistry, 23(7), 690-695.
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  Abstract: This paper presents both a review of some recent results from our group and experimental groups, and some new theoretical results all of which are helping to form a more physically rigorous picture of the process of enzymatic catalysis. A common classical picture of enzymatic catalysis is the transition state tight binding model. Schwartz and Schramm (Nat. Chem. Biol. 2009, 5, 551-558.) have recently argued from both theoretical and experimental results that this picture is incorrect.We now investigate what the nature of barriers might be in enzymatic reactions, and what this viewpoint might imply for tunneling in a hydrogen transfer enzyme. For lactate dehydrogenase we conclude that the enzymes role in catalysis is at least partially to hunt through configuration space for those configurations that minimize chemical free energy barriers. Those configurations do not seem to be stable basins on the free energy surface, and in fact the overall free energy barrier to reaction may well largely be due to this stochastic hunt - both probabilistically and energetically. We suggest further computations to test this hypothesis. Copyright © 2010 John Wiley & Sons, Ltd.
• R., J., Antoniou, D., & Schwartz, S. D. (2010). Slow conformational motions that favor sub-picosecond motions important for catalysis. Journal of Physical Chemistry B, 114(48), 15985-15990.
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  PMID: 21077591;PMCID: PMC3018068;Abstract: It has been accepted for many years that functionally important motions are crucial to binding properties of ligands in such molecules as hemoglobin and myoglobin. In enzymatic reactions, theory and now experiment are beginning to confirm the importance of motions on a fast (ps) time scale in the chemical step of the catalytic process. What is missing is a clear physical picture of how slow conformational fluctuations are related to the fast motions that have been identified as crucial. This paper presents a theoretical analysis of this issue for human heart lactate dehydrogenase. We will examine how slow conformational motions bring the system to conformations that are distinguished as catalytically competent because they favor specific fast motions. © 2010 American Chemical Society.
• Antoniou, D., & Schwartz, S. D. (2009). Approximate inclusion of quantum effects in transition path sampling. Journal of Chemical Physics, 131(22).
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  PMID: 20001028;PMCID: PMC2802259;Abstract: We propose a method for incorporating nuclear quantum effects in transition path sampling studies of systems that consist of a few degrees of freedom that must be treated quantum mechanically, while the rest are classical-like. We used the normal mode centroid method to describe the quantum subsystem, which is a method that is not CPU intensive but still reasonably accurate. We applied this mixed centroid/classical transition path sampling method to a model system that has nontrivial quantum behavior, and showed that it can capture the correct quantum dynamical features. © 2009 American Institute of Physics.
• Antoniou, D., & Schwartz, S. D. (2009). The stochastic separatrix and the reaction coordinate for complex systems. Journal of Chemical Physics, 130(15).
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  PMID: 19388729;PMCID: PMC2719472;Abstract: We present a new approach to the identification of degrees of freedom which comprise a reaction coordinate in a complex system. The method begins with the generation of an ensemble of reactive trajectories. Each trajectory is analyzed for its equicommittor position or transition state; then the transition state ensemble is identified as the stochastic separatrix. Numerical analysis of the points along the separatrix for variability of coordinate location correctly identifies the components of the reaction coordinate in a test system of a double well coupled to a promoting vibration and a bath of linearly coupled oscillators. © 2009 American Institute of Physics.
• Gelman, D., & Schwartz, S. D. (2009). Modeling vibrational resonance in linear hydrocarbon chain with a mixed quantum-classical method. Journal of Chemical Physics, 130(13).
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  PMID: 19355720;Abstract: The quantum dynamics of a vibrational excitation in a linear hydrocarbon model system is studied with a new mixed quantum-classical method. The method is suited to treat many-body systems consisting of a low dimensional quantum primary part coupled to a classical bath. The dynamics of the primary part is governed by the quantum corrected propagator, with the corrections defined in terms of matrix elements of zeroth order propagators. The corrections are taken to the classical limit by introducing the frozen Gaussian approximation for the bath degrees of freedom. The ability of the method to describe dynamics of multidimensional systems has been tested. The results obtained by the method have been compared to previous quantum simulations performed with the quasiadiabatic path integral method. © 2009 American Institute of Physics.
• Quaytman, S. L., & Schwartz, S. D. (2009). Comparison studies of the human heart and bacillus stearothermophilus lactate dehydrogreanse by transition path sampling. Journal of Physical Chemistry A, 113(10), 1892-1897.
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  PMID: 19053545;PMCID: PMC3175424;Abstract: Transition path sampling is a well-known technique that generates reactive paths ensembles. Due to the atomic detail of these reactive paths, information about chemical mechanisms can be obtained. We present here a comparative study of Bacillus stearothermophilus and human heart homologues of lactate dehydrogenase (LDH). A comparison of the transition path ensemble of both enzymes revealed that small differences in the active site reverses the order of the particle transfer of the chemical step. Whereas the hydride transfer preceded the proton transfer in the human heart LDH, the order is reversed in the Bacillus stearothermophilis homologue (in the direction of pyruvate to lactate). In addition, transition state analysis revealed that the dividing region that separates reactants and products, the separatrix, is likely wider for B. stearothermophilis LDH as compared to human heart LDH. This would indicate a more variable transition process in the Bacillus enzyme. © 2009 American Chemical Society.
• Schwartz, S. D., & Schramm, V. L. (2009). Enzymatic transition states and dynamic motion in barrier crossing. Nature Chemical Biology, 5(8), 551-558.
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  PMID: 19620996;PMCID: PMC2859820;Abstract: What are the atomic motions at enzymatic catalytic sites on the timescale of chemical change? Combined experimental and computational chemistry approaches take advantage of transition-state analogs to reveal dynamic motions linked to transition-state formation. QM/MM transition path sampling from reactive complexes provides both temporal and dynamic information for barrier crossing. Fast (femtosecond to picosecond) dynamic motions provide essential links to enzymatic barrier crossing by local or promoting-mode dynamic searches through bond-vibrational space. Transition-state lifetimes are within the femtosecond timescales of bond vibrations and show no manifestations of stabilized, equilibrated complexes. The slow binding and protein conformational changes (microsecond to millisecond) also required for catalysis are temporally decoupled from the fast dynamic motions forming the transition state. According to this view of enzymatic catalysis, transition states are formed by fast, coincident dynamic excursions of catalytic site elements, while the binding of transition-state analogs is the conversion of the dynamic excursions to equilibrated states.
• Gelman, D., & Schwartz, S. D. (2008). Tunneling dynamics with a mixed quantum-classical method: Quantum corrected propagator combined with frozen Gaussian wave packets. Journal of Chemical Physics, 129(2).
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  PMID: 18624535;Abstract: The recently developed mixed quantum-classical propagation method is extended to treat tunneling effects in multidimensional systems. Formulated for systems consisting of a quantum primary part and a classical bath of heavier particles, the method employs a frozen Gaussian description for the bath degrees of freedom, while the dynamics of the quantum subsystem is governed by a corrected propagator. The corrections are defined in terms of matrix elements of zeroth-order propagators. The method is applied to a model system of a double-well potential bilinearly coupled to a harmonic oscillator. The extension of the method, which includes nondiagonal elements of the correction propagator, enables an accurate treatment of tunneling in an antisymmetric double-well potential. © 2008 American Institute of Physics.
• Ghanem, M., Saen-oon, S., Zhadin, N., Wing, C., Cahill, S. M., Schwartz, S. D., Callender, R., & Schramm, V. L. (2008). Tryptophan-free human PNP reveals catalytic site interactions. Biochemistry, 47(10), 3202-3215.
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  PMID: 18269249;Abstract: Human purine nucleoside Phosphorylase (PNP) is a homotrimer, containing three nonconserved tryptophan residues at positions 16, 94, and 178, all remote from the catalytic site. The Tip residues were replaced with Tyr to produce Trp-free PNP (Leuko-PNP). Leuko-PNP showed near-normal kinetic properties. It was used (1) to determine the tautomeric form of guanine that produces strong fluorescence when bound to PNP, (2) for thermodynamic binding analysis of binary and ternary complexes with substrates, (3) in temperature-jump perturbation of complexes for evidence of multiple conformational complexes, and (4) to establish the ionization state of a catalytic site tyrosine involved in phosphate nucleophile activation. The 13C NMR spectrum of guanine bound to Leuko-PNP, its fluorescent properties, and molecular orbital electronic transition analysis establish that its fluorescence originates from the lowest singlet excited state of the N1H, 6-keto, N7H guanine tautomer. Binding of guanine and phosphate to PNP and Leuko-PNP are random, with decreased affinity for formation of ternary complexes. Pre-steady-state kinetics and temperature-jump studies indicate that the ternary complex (enzyme-substrate- phosphate) forms in single binding steps without kinetically significant protein conformational changes as monitored by guanine fluorescence. Spectral changes of Leuko-PNP upon phosphate binding establish that the hydroxyl of Tyr88 is not ionized to the phenolate anion when phosphate is bound. A loop region (residues 243-266) near the purine base becomes highly ordered upon substrate/inhibitor binding. A single Tip residue was introduced into the catalytic loop of Leuko-PNP (Y249W-Leuko-PNP) to determine effects on catalysis and to introduce a fluorescence catalytic site probe. Although Y249W-Leuko-PNP is highly fluorescent and catalytically active, substrate binding did not perturb the fluorescence. Thermodynamic boxes, constructed to characterize the binding of phosphate, guanine, and hypoxanthine to native, Leuko-, and Y249W-Leuko-PNPs, establish that Leuko-PNP provides a versatile protein scaffold for introduction of specific Trp catalytic site probes. © 2008 American Chemical Society.
• Saen-Oon, S., Ghanem, M., Schramm, V. L., & Schwartz, S. D. (2008). Remote mutations and active site dynamics correlate with catalytic properties of purine nucleoside phosphorylase. Biophysical Journal, 94(10), 4078-4088.
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  PMID: 18234834;PMCID: PMC2367194;Abstract: It has been found that with mutation of two surface residues (Lys 22 - Glu and His 104 - Arg) in human purine nucleoside phosphorylase (hPNP), there is an enhancement of catalytic activity in the chemical step. This is true although the mutations are quite remote from the active site, and there are no significant changes in crystallographic structure between the wild-type and mutant active sites. We propose that dynamic coupling from the remote residues to the catalytic site may play a role in catalysis, and it is this alteration in dynamics that causes an increase in the chemical step rate. Computational results indicate that the mutant exhibits stronger coupling between promotion of vibrations and the reaction coordinate than that found in native hPNP. Power spectra comparing native and mutant proteins show a correlation between the vibrations of Immucillin-G (ImmG):O5′⋯ImmG: N4′ and H257:Nδ⋯ImmG:O5′ consistent with a coupling of these motions. These modes are linked to the protein promoting vibrations. Stronger coupling of motions to the reaction coordinate increases the probability of reaching the transition state and thus lowers the activation free energy. This motion has been shown to contribute to catalysis. Coincident with the approach to the transition state, the sum of the distances of ImmG:O4′⋯ImmG:O5′-H257:Nδ became smaller, stabilizing the oxacarbenium ion formed at the transition state. Combined results from crystallography, mutational analysis, chemical kinetics, and computational analysis are consistent with dynamic compression playing a significant role in forming the transition state. Stronger coupling of these pairs is observed in the catalytically enhanced mutant enzyme. That motion and catalysis are enhanced by mutations remote from the catalytic site implicates dynamic coupling through the protein architecture as a component of catalysis in hPNP. © 2008 by the Biophysical Society.
• Saen-oon, S., Quaytman-Machleder, S., Schramm, V. L., & Schwartz, S. D. (2008). Atomic detail of chemical transformation at the transition state of an enzymatic reaction. Proceedings of the National Academy of Sciences of the United States of America, 105(43), 16543-16548.
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  PMID: 18946041;PMCID: PMC2575456;Abstract: Transition path sampling (TPS) has been applied to the chemical step of human purine nucleoside phosphorylase (PNP). The transition path ensemble provides insight into the detailed mechanistic dynamics and atomic motion involved in transition state passage. The reaction mechanism involves early loss of the ribosidic bond to form a transition state with substantial ribooxacarbenium ion character, followed by dynamic motion from the enzyme and a conformational change in the ribosyl group leading to migration of the anomeric carbon toward phosphate, to form the product ribose 1-phosphate. Calculations of the commitment probability along reactive paths demonstrated the presence of a broad energy barrier at the transition state. TPS identified (i) compression of the O4′⋯O5′ vibrational motion, (ii) optimized leaving group interactions, and (iii) activation of the phosphate nucleophile as the reaction proceeds through the transition state region. Dynamic motions on the femtosecond timescale provide the simultaneous optimization of these effects and coincide with transition state formation. © 2008 by The National Academy of Sciences of the USA.
• Saen-oon, S., Schramm, V. L., & Schwartz, S. D. (2008). Transition path sampling study of the reaction catalyzed by purine nucleoside phosphorylase. Zeitschrift fur Physikalische Chemie, 222(8-9), 1359-1374.
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  Abstract: The Transition Path Sampling (TPS) method is a powerful technique for studying rare events in complex systems, that allows description of reactive events in atomic detail without prior knowledge of reaction coordinates and transition states. We have applied TPS in combination with a hybrid Quantum Mechanical/Molecular Mechanical (QM/MM) method to study the enzyme human purine nucleoside Phosphorylase (hPNP). This enzyme catalyzes the reversible phosphorolysis of 6-oxypurine (deoxy)nucleosides to generate the corresponding purine base and (deoxy)ribose 1-phosphate. Hundreds of reactive trajectories were generated. Analysis of this transition path ensembles provides insight into the detailed mechanistic dynamics of reaction in the enzyme. Our studies have indicated a reaction mechanism involving the cleavage of the N-ribosidic bond to form transition states with substantial ribooxacarbenium ion character, that is then followed by conformational changes in the enzyme and the ribosyl group leading to migration of the anomeric carbon of the ribosyl group toward phosphate to form the product ribose 1-phosphate. This latter process is crucial in PNP, because several strong H-bonds form between active site residues in order to capture and align the phosphate nucleophile. Calculations of the commitment probability along reactive paths demonstrated the presence of a broad energy barrier at the transition state. Analysis of these transition state structures showed that bond-breaking and bond-forming distances are not a good choice for the reaction coordinate, but that the pseudorotational phase of the ribose ring is also a significant variable. © by Oldenbourg Wissenschaftsverlag.
• Antoniou, D., Gelman, D., & Schwartz, S. D. (2007). New mixed quantumsemiclassical propagation method. Journal of Chemical Physics, 126(18).
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  PMID: 17508792;Abstract: The authors developed a new method for calculating the quantum evolution of multidimensional systems, for cases in which the system can be assumed to consist of a quantum subsystem and a bath subsystem of heavier atoms. The method combines two ideas: starting from a simple frozen Gaussian description of the bath subsystem, then calculate quantum corrections to the propagation of the quantum subsystem. This follows from recent work by one of them, showing how one can calculate corrections to approximate evolution schemes, even when the Hamiltonian that corresponds to these approximate schemes is unknown. Then, they take the limit in which the width of the frozen Gaussians approaches zero, which makes the corrections to the evolution of the quantum subsystem depend only on classical bath coordinates. The test calculations they present use low-dimensional systems, in which comparison to exact quantum dynamics is feasible. © 2007 American Institute of Physics.
• Guinto, P. J., Manning, E. P., Schwartz, S. D., & Tardiff, J. C. (2007). Computational characterization of mutations in cardiac troponin T known to cause familial hypertrophic cardiomyopathy. Journal of Theoretical and Computational Chemistry, 6(3), 413-419.
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  Abstract: Cardiac Troponin T (cTnT) is a central modulator of thin filament regulation of myofilament activation. The lack of structural data for the TNT1 tail domain, a proposed a-helical region, makes the functional implications of the FHC mutations difficult to determine. Studies have suggested that flexibility of TNT1 is important in normal protein-protein interactions within the thin filament. Our groups have previously shown through molecular dynamics (MD) simulations that some FHC mutations, Arg92Leu (R92L) and Arg92Trp (R92W), result in increased flexibility at a critical hinge region 18 Angstroms distant from the mutation. To explain this distant effect and its implications for FHC mutations, we characterized the dynamics of wild type and mutational segments of cTnT using MD. Our data shows an opening of the helix between residues 105-110 in mutants. Consequently, the dihedral angles of these residues correspond to non-α-helical regions on Ramachandran plots. We hypothesize the removal of a charged residue decreases electrostatic repulsion between the point mutation and the surrounding residues resulting in local helical compaction. Constrained ends of the helix and localized compaction result in expansion within the nearest non-charged helical turn from the mutation site, residues 105-109. © World Scientific Publishing Company.
• Quaytman, S. L., & Schwartz, S. D. (2007). Reaction coordinate of an enzymatic reaction revealed by transition path sampling. Proceedings of the National Academy of Sciences of the United States of America, 104(30), 12253-12258.
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  PMID: 17640885;PMCID: PMC1941458;Abstract: The transition path sampling method previously applied in our group to the reaction catalyzed by lactate dehydrogenase was used to generate a transition path ensemble for this reaction. Based on analysis of the reactive trajectories generated, important residues behind the active site were implicated in a compressional motion that brought the donor-acceptor atoms of the hydride closer together. In addition, residues behind the active site were implicated in a relaxational motion, locking the substrate in product formation. Although this suggested that the compression-relaxation motions of these residues were important to catalysis, it remained unproven. In this work, we used committor distribution analysis to show that these motions are integral components of the reaction coordinate. © 2007 by The National Academy of Sciences of the USA.
• R., J., Callender, R., & Schwartz, S. D. (2007). Ligand binding and protein dynamics in lactate dehydrogenase. Biophysical Journal, 93(5), 1474-1483.
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  PMID: 17483170;PMCID: PMC1948035;Abstract: Recent experimental studies suggest that lactate dehydrogenase (LDH) binds its substrate via the formation of a LDH/NADH·substrate encounter complex through a select-fit mechanism, whereby only a minority population of LDH/NADH is binding-competent. In this study, we perform molecular dynamics calculations to explore the variations in structure accessible to the binary complex with a focus on identifying structures that seem likely to be binding-competent and which are in accord with the known experimental characterization of forming binding-competent species. We find that LDH/NADH samples quite a range of protein conformations within our 2.148 ns calculations, some of which yield quite facile access of solvent to the active site. The results suggest that the mobile loop of LDH is perhaps just partially open in these conformations and that multiple open conformations, yielding multiple binding pathways, are likely. These open conformations do not require large-scale unfolding/melting of the binary complex. Rather, open versus closed conformations are due to subtle protein and water rearrangements. Nevertheless, the large heat capacity change observed between binding-competent and binding-incompetent can be explained by changes in solvation and an internal rearrangement of hydrogen bonds. We speculate that such a strategy for binding may be necessary to get a ligand efficiently to a binding pocket that is located fairly deep within the protein's interior. © 2007 by the Biophysical Society.
• Schwartz, S. D. (2007). The Quantum Kramers Approach to Enzymatic Hydrogen Transfer - Protein Dynamics as it Couples to Catalysis. Hydrogen-Transfer Reactions, 4, 1209-1239.
• Antoniou, D., Basner, J., Núñez, S., & Schwartz, S. D. (2006). Computational and theoretical methods to explore the relation between enzyme dynamics and catalysis. Chemical Reviews, 106(8), 3170-3187.
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  PMID: 16895323;Abstract: With regards to enzyme dynamics, motions of residues near the active site can have an effect on the catalytic mechanism. These motions can influence the standard model of catalysis in different ways: (1) they may be extended motions related to conformational fluctuations; (2) they may be local subpicosecond motions near the active site and (3) they may force a revision of the view of thermodynamic cycles which is often used to describe catalysis. This review covers three kinds of dynamic effects: (1) rate-promoting quasi-harmonic motions, a fast subpicosecond effect usually for reactions that involve proton tunneling; (2) extended correlated motions involving several residues and the theoretical tools needed for studying them and (3) conformational fluctuations. Under the first effect, focus is on quantum theory of proton transfer, rate-promoting vibrations, computational diagnosis of promoting vibrations and experimental ramifications for promoting vibrations. As for conformational fluctuations, focus is on dihydrofolate reductase (DHFR) and conformation space.
• Antoniou, D., Basner, J., Núñez, S., & Schwartz, S. D. (2006). Effect of enzyme dynamics on catalytic activity. Advances in Physical Organic Chemistry, 41, 315-362.
• Núñez, S., Wing, C., Antoniou, D., Schramm, V. L., & Schwartz, S. D. (2006). Insight into catalytically relevant correlated motions in human purine nucleoside phosphorylase. Journal of Physical Chemistry A, 110(2), 463-472.
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  PMID: 16405318;Abstract: The catalytic site of the homotrimeric enzyme human purine nucleoside phosphorylase enzyme (hPNP) features residue F200 and the 241-265 loop directly skirting the purine base and a residue belonging to the adjacent monomer, F159, immediately conterminous to the ribosyl moiety. Crystallographic B-factors of apo human purine nucleoside phosphorylase, and hPNP complexed with substrate/transition state (TS) analogues, show that residue E250 is the centroid of a highly mobile loop region. Furthermore, superimposition of apo hPNP and hPNP complexed with TS analogue Immucillin-H shows a tightening of the active site, caused by the ligand-dependent 241-265 loop rearrangement taking place upon substrate/inhibitor binding, suggesting a putative dynamic role of the loop in binding/catalysis. However, Crystallographic structures reveal only average atomic positions, and more detailed information is needed to discern the dynamic behavior of hPNP. The Essential Dynamics (ED) method is used here to investigate the existence of correlated motions in hPNP and consequently proposes mutagenesis assays to estimate the relative importance of these motions in the phosphorolytic efficiency of the reaction catalyzed by hPNP. We compare the concerted motions obtained from multiple molecular dynamics simulations of apo and Michaelis complex of hPNP both in vacuo and in solution. The results of the principal component analysis for the apo hPNP indicate the existence of strong correlations predominantly in the vicinity of residue F159. However, for the Michaelis complex, concerted motions are seen mostly around both active site residue F200 and loop residue E250. Additionally, for a simulation depicting the relaxation of tight complexed hPNP with a TS analogue, toward its relaxed apo form (after removal of the TS analog), a combination of the apo hPNP and Michaelis complex motions is found, with prominent concerted modes centered around neighboring residues F159, F200, and E250. Finally, we probed the extent to which these concerted motions bear an intrinsic catalytic role by performing experimental site-directed mutagenesis on some residues, followed by kinetic analysis. The F159G and F200G mutants displayed a strong increase in K M and modest decrease in K cat, suggesting that these concerted motions may provide dynamical roles in substrate binding and/or catalysis. However, further structural data for the hPNP mutants are needed to confirm our hypothesis. © 2006 American Chemical Society.
• Pineda, J. R., & Schwartz, S. D. (2006). Protein dynamics and catalysis: The problems of transition state theory and the subtlety of dynamic control. Philosophical Transactions of the Royal Society B: Biological Sciences, 361(1472), 1433-1438.
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  PMID: 16873129;PMCID: PMC1647311;Abstract: This manuscript describes ongoing research on the nature of chemical reactions in enzymes. We will investigate how protein dynamics can couple to chemical reaction in an enzyme. We first investigate in some detail why transition state theory cannot fully describe the dynamics of chemical reactions catalysed by enzymes. We describe quantum theories of chemical reaction in condensed phase including studies of how the symmetry of coupled vibrational modes differentially affects reaction dynamics. We make reference to previous work in our group on a variety of condensed phase chemical reactions (liquid and crystalline) and a variety of enzymatically catalysed reactions including the reactions of lactate dehydrogenase and purine nucleoside phosphorylase. All the protein motions we have studied have been quite rapid. We will propose methods to find motions over a broad range of time-scales in enzymes that couple to chemical catalysis. We report recent findings which show that conformational fluctuations in lactate dehydrogenase can strongly affect its ability to catalyse reactions through protein motion, and that only a tiny minority of conformations appear to be catalytically competent. © 2006 The Royal Society.
• Basner, J. E., & Schwartz, S. D. (2005). How enzyme dynamics helps catalyze a reaction in atomic detail: A transition path sampling study. Journal of the American Chemical Society, 127(40), 13822-13831.
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  PMID: 16201803;Abstract: We have applied the Transition Path Sampling algorithm to the reaction catalyzed by the enzyme Lactate Dehydrogenase. This study demonstrates the ease of scaling Transition Path Sampling for applications on many degree of freedom systems, whose energy surface is a complex terrain of valleys and saddle points. As a Monte Carlo importance sampling method, transition path sampling is capable of surmounting barriers in path phase space and focuses simulation on the rare event of enzyme catalyzed atom transfers. Generation of the transition path ensemble, for this reaction, resolves a paradox in the literature in which some studies exposed the catalytic mechanism of hydride and proton transfer by lactate dehydrogenase to be concerted and others stepwise. Transition path sampling has confirmed both mechanisms as possible paths from reactants to products. With the objective to identify a generalized, reduced reaction coordinate, time series of both donor-acceptor distances and residue distances from the active site have been examined. During the transition from pyruvate to lactate, residues located behind the transferring hydride collectively compress toward the active site causing residues located behind the hydride acceptor to relax away. It is demonstrated that an incomplete compression/relaxation transition across the donor-acceptor axis compromises the reaction. © 2005 American Chemical Society.
• Ertz-Berger, B. R., Huamei, H. e., Dowell, C., Factor, S. M., Haim, T. E., Nunez, S., Schwartz, S. D., Ingwall, J. S., & Tardiff, J. C. (2005). Changes in the chemical and dynamic properties of cardiac troponin T cause discrete cardiomyopathies in transgenic mice. Proceedings of the National Academy of Sciences of the United States of America, 102(50), 18219-18224.
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  PMID: 16326803;PMCID: PMC1298915;Abstract: Cardiac troponin T (cTnT) is a central component of the regulatory thin filament. Mutations in cTnT have been linked to severe forms of familial hypertrophic cardiomyopathy. A mutational "hotspot" that leads to distinct clinical phenotypes has been identified at codon 92. Although the basic functional and structural roles of cTnT in modulating contractility are relatively well understood, the mechanisms that link point mutations in cTnT to the development of this complex cardiomyopathy are unknown. To address this question, we have taken a highly interdisciplinary approach by first determining the effects of the residue 92 mutations on the molecular flexibility and stability of cTnT by means of molecular dynamics simulations. To test whether the predicted alterations in thin filament structure could lead to distinct cardiomyopathies in vivo, we developed transgenic mouse models expressing either the Arg-92-Trp or Arg-92-Leu cTnT proteins in the heart. Characterization of these models at the cellular and whole-heart levels has revealed mutation-specific early alterations in transcriptional activation that result in distinct pathways of ventricular remodeling and contractile performance. Thus, our computational and experimental results show that changes in thin filament structure caused by single amino acid substitutions lead to differences in the biophysical properties of cTnT and alter disease pathogenesis. © 2005 by The National Academy of Sciences of the USA.
• Schwartz, S. D. (2005). A new semiclassical dynamics from the interaction representation. Journal of Theoretical and Computational Chemistry, 4(4), 1093-1100.
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  Abstract: This paper develops a new semiclassical mechanics from an exact quantum prescription. In this formulation, a zeroth order propagation, rather than Hamiltonian, is specified. The exact, full evolution operator is then given from a specific interaction representation of the evolved "perturbation" Hamiltonian. We then investigate a variety of approximate, semiclassical, and mixed Quantum/Classical methods, along with exact methodologies to evaluate this time dependent interaction Hamiltonian. The approximate full evolution operator can be described in a variety of ways including an iterated Lippman-Schwinger like equation, and an expansion of the perturbation propagator generated from the time evolved Hamiltonian. © World Scientific Publishing Company.
• Antoniou, D., Abolfath, M. R., & Schwartz, S. D. (2004). Transition path sampling study of classical rate-promoting vibrations. Journal of Chemical Physics, 121(13), 6442-6447.
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  PMID: 15446943;Abstract: The use of transition path sampling to study the classical rate-promoting vibrations was discussed. A complicated dynamical behavior that cannot be captured by transition state theory was found. It was observed that slow promoting vibrations lead to reactive trajectories that overshoot the saddle point, but on the other hand the short period of fast oscillations allows the reactants to stay only briefly in a low-barrier regime. It was shown that there is a competition between these effects, which results to an intermediate value for the frequency of the rate-promoting vibration that is optimal for enhancing the rate.
• Basner, J. E., & Schwartz, S. D. (2004). Donor-acceptor distance and protein promoting vibration coupling to hydride transfer: A possible mechanism for kinetic control in isozymes of human lactate dehydrogenase. Journal of Physical Chemistry B, 108(1), 444-451.
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  Abstract: Theoretically based computational methods have been developed in our group to identify protein motions, symmetrically coupled to the reaction coordinate, which modulate the width and height of the barrier to reaction. Previous studies have applied the methods to horse liver alcohol dehydrogenase (HLADH), to help explain experimental kinetic isotope effects. In this paper the methods have been applied to the two isoforms of human lactate dehydrogenase (LDH) enzymes which facilitate hydride transfer during the interconversion of pyruvate and lactate. LDH isoforms have evolved to accommodate substrate demand in different parts of the body. The active sites of the isoforms are identical in amino acid content yet the kinetics are distinct. We have performed molecular dynamics simulations for each isoform with either substrate bound. The signature of the protein promoting vibration (PPV) is distinct for each isoform due to differences in the donor-acceptor distance. We hypothesize that kinetic control of hydride transfer may be exerted via a decreased donor-acceptor distance when lactate is bound to the heart isoform and when pyruvate is bound to the skeletal muscle isoform. The identity, frequency, and position of active site amino acid motions correlated to the donor-acceptor motion also vary for each isoform. These results demonstrate that even in almost identical enzymes, subtle differences in protein structure, remote from the active site, can have significant effects on reaction dynamics.
• Mincer, J. S., & Schwartz, S. D. (2004). Rate-promoting vibrations and coupled hydrogen-electron transfer reactions in the condensed phase: A model for enzymatic catalysis. Journal of Chemical Physics, 120(16), 7755-7760.
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  PMID: 15267689;Abstract: A model is proposed for coupled hydrogen-electron transfer reactions in condensed phase in the presence of a promoting vibration. The model is an extension of an earlier model, which modulates the potential the hydrogen atom experiences as it is transferred. Large kinetic isotope effects (KIE) were found when the hydrogen is substituted with deutrium. The results show that a large, temperature-independent KIE is compatible with a tunneling reaction assisted by a promoting vibration.
• Mincer, J. S., Nuñez, S., & Schwartz, S. D. (2004). Coupling protein dynamics to reaction center electron density in enzymes: An electronic protein promoting vibration in human purine nucleoside phosphorylase. Journal of Theoretical and Computational Chemistry, 3(4), 501-509.
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  Abstract: The notable three oxygen stacking that occurs upon binding of ribonucleoside substrate and phosphate nucleophile by human purine nucleoside phosphorylase (hPNP) enables the coupling of protein dynamic modes to compress this stack, squeezing the ribosyl O4′ between ribosyl O5′ and the nuclophilic OP. Created primarily by the motion of active site residue H257, this compression dynamically lowers the barrier height for N9-C1′ ribosidic bond cleavage by as much as 20%. As such, this compression constitutes a protein promoting vibration (PPV) (S. Nuñez et al.). Presently, we demonstrate charge fluctuations in the ribose and purine components of the ribonucleoside substrate, as well as specifically across the N9-C1′ ribosidic bond, that are correlated with the PPV and can explain the decrease in reaction barrier height due to their facilitating cleavage of the ribosidic bond. hPNP apparently employs protein dynamics to push electrons, a finding that suggests that this coupling may be found more generally in enzymes that catalyze substitution and elimination reactions.
• Núñez, S., Antoniou, D., Schramm, V. L., & Schwartz, S. D. (2004). Promoting vibrations in human purine nucleoside phosphorylase. A molecular dynamics and hybrid quantum mechanical/molecular mechanical study. Journal of the American Chemical Society, 126(48), 15720-15729.
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  PMID: 15571394;Abstract: Crystallographic studies of human purine nucleoside phosphorylase (hPNP) with several transition-state (TS) analogues in the immucillin family showed an unusual geometric arrangement of the atoms O-5′, O-4′, and O p, the nucleophilic phosphate oxygen, lying in a close three-oxygen stack. These observations were corroborated by extensive experimental kinetic isotope effect analysis. We propose that protein-facilitated dynamic modes in hPNP cause this stack, centered on the ribosyl O-4′ oxygen, to squeeze together and push electrons toward the purine ring, stabilizing the oxacarbenium character of the TS. As the N-ribosidic bond is cleaved during the reaction, the pKa values of N-7 and O-6 increase by the electron density expelled by the oxygen-stack compression toward the purine ring. Increased electron density in the purine ring improves electrostatic interactions with nearby residues and facilitates the abstraction of a proton from a solvent proton or an unidentified general acid, making the purine a better leaving group, and accelerating catalysis. Classical and mixed quantum/classical molecular dynamics (MD) simulations of the Michaelis complex of hPNP with the substrates guanosine and phosphate were performed to assess the existence of protein-promoting vibrations (PPVs). Analogous simulations were performed for the substrates in aqueous solution. In the catalytic site, the O-5′, O-4′, and Op oxygens vibrate at frequencies of ca. 125 and 465 cm-1, as opposed to 285 cm-1 in the absence of hPNP. The hybrid quantum mechanical/molecular mechanical method was used to assess whether this enzymatic vibration pushing the oxygens together is coupled to the reaction coordinate, and thus has a direct positive impact on catalysis. The potential energy surface for the phosphorolysis reaction for several snapshots taken from the classical MD simulation showed substantial differences in oxygen compression. Our calculations showed the existence of PPVs coupled to the reaction coordinate, which effect electronic alterations in the active site by pushing the three oxygen centers together in proximity, and accelerate substrate turnover in the phosphorolysis reaction catalyzed by hPNP.
• Antoniou, D., & Schwartz, S. D. (2003). Langevin equation in momentum space. Journal of Chemical Physics, 119(21), 11329-11334.
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  Abstract: The Langevin equation in k space was studied. As an example, argon was used for which the pair Lennard-Jones potential does not have a Fourier transform. Despite this fact, a way to study the properties of the friction kernel in momentum space was shown. The contributions of different values of k on the friction kernel were determined.
• Mincer, J. S., & Schwartz, S. D. (2003). A computational method to identify residues important in creating a protein promoting vibration in enzymes. Journal of Physical Chemistry B, 107(1), 366-371.
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  Abstract: In this paper, we present a computational method to screen a large set of protein residues to identify those residues the motions of which help create a protein promoting vibration and are therefore important for catalysis. The method is illustrated for the case of horse liver alcohol dehydrogenase (HLADH). In this system, the protein promoting vibration is the relative motion between hydride donor and acceptor, that is, the benzyl alcohol substrate and the nicotinamide adenine dinucleotide (NAD+) cofactor, respectively. The resulting subset of screened residues compares favorably with existing experimental data and also suggests additional residues as objects for potential study. The method presented in this paper employs correlated motion as the basis for identifying residues important in catalysis. As such, the success of the method in the case of HLADH further supports the importance of protein dynamics in certain enzyme systems.
• Mincer, J. S., & Schwartz, S. D. (2003). Protein promoting vibrations in enzyme catalysis - A conserved evolutionary motif. Journal of Proteome Research, 2(4), 437-439.
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  PMID: 12945535;Abstract: A computational method to identify residues important in creating a protein promoting vibration (PPV) in enzymes was previously developed and applied to horse liver alcohol dehydrogenase (HLADH), resulting in the identification of eight important residues. From these residues, we define a sequence motif, the PPV generating sequence, and find it to be unique and general to a larger group of alcohol dehydrogenases from diverse sources, demonstrating that nature has selected for the PPV generating sequence.
• Antoniou, D., Caratzoulas, S., Kalyanaraman, C., Mincer, J. S., & Schwartz, S. D. (2002). Barrier passage and protein dynamics in enzymatically catalyzed reactions. European Journal of Biochemistry, 269(13), 3103-3112.
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  PMID: 12084050;Abstract: This review describes studies of particular enzymatically catalyzed reactions to investigate the possibility that catalysis is mediated by protein dynamics. That is, evolution has crafted the protein backbone of the enzyme to direct vibrations in such a fashion to speed reaction. The review presents the theoretical approach we have used to investigate this problem, but it is designed for the nonspecialist. The results show that in alcohol dehydrogenase, dynamic protein motion is in fact strongly coupled to chemical reaction in such a way as to promote catalysis. This result is in concert with both experimental data and interpretations for this and other enzyme systems studied in the laboratories of the two other investigators who have published reviews in this issue.
• Caratzoulas, S., Mincer, J. S., & Schwartz, S. D. (2002). Identification of a protein-promoting vibration in the reaction catalyzed by horse liver alcohol dehydrogenase. Journal of the American Chemical Society, 124(13), 3270-3276.
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  PMID: 11916410;Abstract: In this article we present computational studies of horse liver alcohol dehydrogenase (HLADH). The computations identify a rate-promoting vibration that is symmetrically coupled to the reaction coordinate. In HLADH a bulky amino acid (Val203) is positioned at the face of the nicotinamide adenine dinucleotide (NAD+) cofactor distal to alcohol substrate to restrict the separation of reactants and control the stereochemistry. Molecular dynamics simulations were performed on the dimeric HLADH, including the NAD cofactor, the substrate, and the crystallographic waters, for three different configurations, reactants, products, and transition state. From the spectral density for the substrate-NAD relative motion, and that for the NAD-Val203 relative motion, we find that the two motions are in resonance. By computing the associated spectrum, we find that the reaction coordinate is coupled with the substrate-NAD motion, and from the fact that the coupling vanishes at or near the transition state (demonstrated by the disappearance of strong features in the spectral density), we conclude that the substrate-NAD motion plays the role of a promoting vibration symmetrically coupled to the reaction coordinate.
• Kalyanaraman, C., & Schwartz, S. D. (2002). Effect of active site mutation Phe 93 → Trp in the horse liver alcohol dehydrogenase enzyme on catalysis: A molecular dynamics study. Journal of Physical Chemistry B, 106(51), 13111-13113.
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  Abstract: We have studied the effect of the site-directed mutation, Phe 93 → Trp, in the horse liver alcohol dehydrogenase enzyme as it relates to a specific protein motion that plays a crucial role in catalysis. Results obtained from the study suggest that the protein dynamics as it couples to reaction catalysis is not affected and in fact the coupling between the protein oscillation and the reaction coordinate is similar to that seen in the wild-type. This supports the view that this mutation distal from the NAD- cofactor does not change the way protein dynamics influences chemistry.
• Antoniou, D., & Schwartz, S. D. (2001). Harmonic collective modes in atomic liquids. Journal of Chemical Physics, 115(10), 4670-4675.
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  Abstract: A previous study presented an approach where the collective modes arise from the standard procedure of diagonalizing a Hamiltonian that has a potential with nondiagonal quadratic terms. The present work further elucidates the physical picture implied by this formalism. For demonstration purposes, the application of this formalism to a standard test system, liquid argon, is highlighted.
• Antoniou, D., & Schwartz, S. D. (2001). Internal enzyme motions as a source of catalytic activity: Rate-promoting vibrations and hydrogen tunneling. Journal of Physical Chemistry B, 105(23), 5553-5558.
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  Abstract: The standard view of the origin of the catalytic properties of enzymes focuses on the binding energy differences between the ground state and the transition state arising from the arrangement of residues in the active site (i.e., statics). There is an alternative view that suggests that protein motions (i.e., dynamics) might play a role in catalysis. Klinman and co-workers recently published (Kohen, A.; Cannio, R.; Bartolucci, S.; Klinman, J. Nature 1999, 399, 496-499) findings on rate measurements in thermophilic alcohol dehydrogonase (ADH). At lower temperatures (below 30°C), this enzyme undergoes a transition to a more rigid structure, and it was found that the corresponding apparent activation energy increases and the primary kinetic isotope effect (KIE) increases and becomes temperature-dependent. Explaining these results presents a challenge to theory. We show that a model of the reaction coordinate for the rate-determining step, coupled to an enzymatic environment and a specific strongly coupled active complex mode, can simultaneously explain a tunneling-dominated mechanism and the experimental trends reported by Klinman and co-workers. We propose a specific protein internal motion for the rate-promoting vibration and discuss other systems in which such motions might be dominant.
• Caratzoulas, S., & Schwartz, S. D. (2001). Computational method to discover the existence of promoting vibrations for chemical reactions in condensed phases. Journal of Chemical Physics, 114(7), 2910-2918.
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  Abstract: A computational method was used to discover the existence of vibrations, in the context of chemical reactions in condensed phases. It was found that coupled motion of liquid left a unique signature on the spectral density, using the Zwanzig Hamiltonian as a theoretical model and molecular dynamics simulations of a model. Effective frequency of promoting vibration resulted in peak of spectral density.
• Karmacharya, R., Antoniou, D., & Schwartz, S. D. (2001). Nonequilibrium solvation and the quantum kramers problem: Proton transfer in aqueous glycine. Journal of Physical Chemistry A, 105(12), 2563-2567.
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  Abstract: We study the intramolecular proton transfer in the amino acid glycine in aqueous solution. We show that this system is an example of nonequilibrium solvation, where the proton-transfer step is fast and the solvent relaxes afterward. We show how the physical picture of equilibrium vs nonequilibrium solvation arises naturally within the framework of the quantized Zwanzig Hamiltonian. κ 2001 American Chemical Society.
• Braunheim, B. B., & Schwartz, S. D. (2000). Neural network methods for identification and optimization of quantum mechanical features needed for bioactivity. Journal of Theoretical Biology, 206(1), 27-45.
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  PMID: 10968935;Abstract: This paper presents a new approach to the discovery and design of bioactive compounds. The focus of this application will be on the analysis of enzymatic inhibitors. At present the discovery of enzymatic inhibitors for therapeutic use is often accomplished through random searches. The first phase of discovery is a random search through a large pre-fabricated chemical library. Many molecules are tested with refined enzyme for signs of inhibition. Once a group of lead compounds have been discovered the chemical intuition of biochemists is used to find structurally related compounds that are more effective. This step requires new molecules to be conceived and synthesized, and it is the most time-consuming and expensive step. The development of computational and theoretical methods for prediction of the molecular structure that would bind most tightly prior to synthesis and testing, would facilitate the design of novel inhibitors. In the past, our work has focused on solving the problem of predicting the bioactivity of a molecule prior to synthesis. We used a neural network trained with the bioactivity of known compounds to predict the bioactivity of unknown compounds. In our current work, we use a separate neural network in conjunction with a trained neural network in an attempt to gain insight as to how to modify existing compounds and increase their bioactivity. (C) 2000 Academic Press.
• Schwartz, S. D. (2000). Quantum dynamics in condensed phases via extended modes and exact interaction propagator relations. Journal of Chemical Physics, 113(17), 7437-7445.
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  Abstract: A new approach to the computation of exact dynamics in condensed phase systems was presented. An exact model was described which allowed the description of the liquid as a collector of coupled harmonic modes. Transformation of Hamilton function into a quantum Hamiltonian operator was also described.
• Antoniou, D., & Schwartz, S. D. (1999). A molecular dynamics quantum Kramers study of proton transfer in solution. Journal of Chemical Physics, 110(1), 465-472.
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  Abstract: We present a quantum study of a proton transfer reaction AH-B⇌A--H+B in liquid methyl chloride, where the AH-B complex corresponds to phenol-amine. We use the same intramolecular potentials that were used in two earlier studies of this system [H. Azzouzz and D. Borgis, J. Chem. Phys. 98, 7361 (1993); S. Hammes-Schiffer and J. C. Tully, J. Chem. Phys. 101, 4657 (1994).] The former study employed a Landau-Zener approach and a molecular dynamics centroid method, while the latter a surface-hopping method. These studies obtained results that differ by an order of magnitude. In the present work, we first performed a molecular dynamics simulation to obtain the spectral density, which was then used as an input to the method we have developed for the study of the quantum Kramers problem [S. D. Schwartz, J. Chem. Phys. 105, 6871 (1996)]. Thus, in this work both the reaction coordinate and the bath are treated quantum mechanically. © 1999 American Institute of Physics.
• Antoniou, D., & Schwartz, S. D. (1999). Quantum proton transfer with spatially dependent friction: Phenol-amine in methyl chloride. Journal of Chemical Physics, 110(15), 7359-7364.
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  Abstract: In a recent paper [D. Antoniou and S. D. Schwartz, J. Chem. Phys. 110, 465 (1999)] we calculated the reaction rate for a proton transfer reaction in liquid methyl chloride. In that work, we used a spectral density obtained from a molecular dynamics simulation as input to a quantum Zwanzig Hamiltonian which we solved using our exponential resummation method. In the present paper we perform a similar calculation, allowing for a position dependent friction using the method of G. Haynes, G. Voth, and E. Pollak [J. Chem. Phys. 101, 7811 (1994)]. Compared with the results of our previous work, we found that including spatial dependence to the friction led to enhancement of the reaction rate and to reduction of the H/D kinetic isotone effect. © 1999 American Institute of Physics.
• Braunheim, B. B., Miles, R. W., Schramm, V. L., & Schwartz, S. D. (1999). Prediction of inhibitor binding free energies by quantum neural networks. Nucleoside analogues binding to trypanosomal nucleoside hydrolase. Biochemistry, 38(49), 16076-16083.
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  PMID: 10587430;Abstract: A computational method has been developed to predict inhibitor binding energy for untested inhibitor molecules. A neural network is trained from the electrostatic potential surfaces of known inhibitors and their binding energies. The algorithm is then able to predict, with high accuracy, the binding energy of unknown inhibitors. IU-nucleoside hydrolase from Crithidia fasciculata and the inhibitor molecules described previously [Miles, R. W. Tyler, P. C. Evans, G. Fumeaux R. H., ParK(i)n, D. W., and Schramm, V. L. (1999) Biochemistry 38, xxxx-xxxx] are used as the test system. Discrete points on the molecular electrostatic potential surface of inhibitor molecules are input to neural networks to identify the quantum mechanical features that contribute to binding. Feed-forward neural networks with back- propagation of error are trained to recognize the quantum mechanical electrostatic potential and geometry at the entire van der Waals surface of a group of training molecules and to predict the strength of interactions between the enzyme and novel inhibitors. The binding energies of unknown inhibitors were predicted, followed by experimental determination of K(i) values. Predictions of K(i) values using this theory are compared to other methods and are more robust in estimating inhibitory strength. The average deviation in estimating K(i) values for 18 unknown inhibitor molecules, with 21 training molecules, is a factor of 5 x K(i) over a range of 660 000 in K(i) values for all molecules. The a posteriori accuracy of the predictions suggests the method will be effective as a guide for experimental inhibitor design.
• Karmacharya, R., & Schwartz, S. D. (1999). Quantum proton transfer coupled to a quantum anharmonic mode. Journal of Chemical Physics, 110(15), 7376-7381.
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  Abstract: Many model studies of proton tunneling in condensed phase employ a reaction coordinate that is coupled to a bath of harmonic oscillator modes. The nature of the coupled modes and the effect of the coupling parameters on reaction rate is an active area of investigation. Recent experimental results from the Fleming group showed that the spectral density for solvation can be temperature dependent [A. Passino, Y. Nagasawa, and G. R. Fleming, J. Chem. Phys. 107, 6094 (1997)]. Translated from the Langevin picture, this result implies that bath modes are anharmonic, or that a different set of harmonic modes are needed at each temperature. In addition, calculations of proton transfer rates have shown that quantum dynamics can be significantly affected by the variation of spectral densities in the low frequency regime [D. Antoniou and S. D. Schwartz, J. Chem. Phys. 109, 5487 (1998)]. We report a study of proton transfer in which the reaction coordinate is coupled to a Morse oscillator with nonlinear coupling. Comparison with the case of coupling to a harmonic oscillator shows that coupling a Morse oscillator to the reaction coordinate leads to enhanced tunneling. We compare our results with those reported in an earlier study [Y. Dakhnovskii, B. Bursulaya, and H. J. Kim, J. Chem. Phys. 102, 7838 (1995)], where the rate of proton tunneling coupled to a one-dimensional classical anharmonic mode was studied. © 1999 American Institute of Physics.
• Karmacharya, R., Gross, P., & Schwartz, S. D. (1999). The effect of coupled nonreactive modes on laser control of quantum wave packet dynamics. Journal of Chemical Physics, 111(15), 6864-6868.
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  Abstract: The laser control of reactions in solution has recently been a topic of growing interest. The theoretical possibility for such control has now been established. This paper investigates two closely related issues regarding potential practical implementation of condensed phase control schemes. A previous study from our group was able to demonstrate control assuming that a laser field coupled only to a reaction coordinate. The assumption that the laser will not couple to the condensed phase environment is a drastic simplification, and we investigate in this paper how relaxing this simplification may affect the possibility of control. To investigate this phenomenon, we study two cases: that of a laser coupled only to a reaction coordinate which is in turn coupled to a "bath" mode, as compared to the case in which the laser is coupled both to the reaction coordinate and the environmental mode. In another closely related investigation, we study the effect of uncertainty introduced into the controlling pulse. The exact potential of a chemical reaction in solution cannot be known to perfect accuracy. Our results give insights into the challenges which will face attempts at condensed phase chemical reaction control, and point strongly to the need for adaptive algorithms for laser control pulse generation. © 1999 American Institute of Physics.
• Antoniou, D., & Schwartz, S. D. (1998). Activated chemistry in the presence of a strongly symmetrically coupled vibration. Journal of Chemical Physics, 108(9), 3620-3625.
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  Abstract: In the gas phase, tunneling reaction rates can be significantly enhanced if the reaction coordinate is symmetrically coupled to a harmonic oscillation, as has been emphasized by Benderskii and co-workers [Adv. Chem. Phys. 88, 1 (1994)]. This is due to the fact that the symmetric coupling leads to modulation of the barrier height. Similar effects have been observed in reactions in model condensed phase studies, as in the Hamiltonians that have been studied by Borgis and Hynes [J. Chem. Phys. 94, 3619 (1991)] and Suarez and Silbey [J. Chem. Phys. 94, 4809 (1991)]. All of these works assume that tunneling proceeds from the ground state. In this paper, we use the exponential resummation technique that we used in our recent work on the quantum Kramers problem, to study the case when there can be excitations to higher states and activated transmission over a barrier. We present a general methodology to exactly include direct coupling between the reaction coordinate and the symmetrically coupled promoting vibration and find that the rate of reactions in condensed phases is enhanced as in the case of tunneling from the ground state. This effect, however, is strongly modulated by loss of coherence induced by the condensed phase environment. © 1998 American Institute of Physics.
• Antoniou, D., & Schwartz, S. D. (1998). Proton transfer in benzoic acid crystals: Another look using quantum operator theory. Journal of Chemical Physics, 109(6), 2287-2293.
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  Abstract: We present a calculation of the rate of synchronous double proton transfer in benzoic acid crystals. Experiments on these systems have been performed over a wide range of temperatures (roughly 10-400°K). Even though the energetic barrier for proton transfer is rather high, the observed activation energy is low, while kinetic isotope experiments seem to indicate classical transfer. The system exhibits significant quantum character even at high temperatures and we show that the observed low activation energies can be reproduced assuming that the reaction is "assisted" by a low-frequency intramolecular mode, as has been suggested in different contexts by Benderskii [V. A. Benderskii, S. Yu. Grebenshchikov, and G. V. Mil'nikov, Chem. Phys. 194, 1 (1995)], Hynes [D. Borgis and J. Hynes, J. Chem. Phys. 94, 3619 (1991)] and Silbey [A. Suarez and R. Silbey, J. Chem. Phys. 94, 4809 (1991)]. We use our previous work on the quantum Kramers problem to perform a fully quantum calculation that incorporates symmetric coupling to the intramolecular mode and coupling to the condensed environment to all orders. We calculate the activation energies for hydrogen and deuterium transfer and we show that our results are in quantitative agreement with the experiment. © 1998 American Institute of Physics.
• Antoniou, D., & Schwartz, S. D. (1998). Temperature dependent spectral densities and quantum activated rate theory. Journal of Chemical Physics, 109(13), 5487-5492.
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  Abstract: The variability with temperature of spectral densities and rates calculated with quantum activated rate theory is investigated. Classical spectral densities at two temperatures are computed via molecular dynamics for a model of proton transfer in methyl chloride. In addition, quantum dynamics is computed for spectral densities which artificially boost variability at low frequency. We find significant variation in computed spectral densities at moderate frequency. These variations, however, have little effect on overall computed quantum dynamics. In contradistinction, artificial variation in spectral densities at the lowest frequencies can generate fairly significant effects on quantum dynamics. Detailed flux correlation function calculations are presented which illustrate this phenomenon. © 1998 American Institute of Physics.
• Gross, P., & Schwartz, S. D. (1998). External field control of condensed phase reactions. Journal of Chemical Physics, 109(12), 4843-4851.
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  Abstract: Control of tunneling in a symmetric double well coupled to a bath via an external field is demonstrated. Optimal control theory is employed to design a laser field which couples to the reaction coordinate and drives a localized wave packet on the reactant side to the product side at a specified target time τ. Both a very quantumlike system (high barrier) and a low barrier double well are examined; excellent results are obtained for a range of reduced bath viscosities. Analysis of the control fields and corresponding localization dynamics shows that the frequency components of the control field are more or less in resonance with eigenstates of the double well and that the laser field enhances the natural dynamics of the individual wells. Future extension to more complicated models where the field couples to the bath is discussed. © 1998 American Institute of Physics.
• Antoniou, D., & Schwartz, S. D. (1997). Large kinetic isotope effects in enzymatic proton transfer and the role of substrate oscillations. Proceedings of the National Academy of Sciences of the United States of America, 94(23), 12360-12365.
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  PMID: 9356454;PMCID: PMC24944;Abstract: We propose an interpretation of the experimental findings of Klinman and coworkers [Cha, Y., Murray, C. J. and Klinman, J.P. (1989) Science 243, 1325- 1330; Grant, K. L. and Klinman, J.P. (1989) Biochemistry 28, 6597-6605; and Bahnson, B. J. and Klinman, J.P. (1995) Methods Enzymol. 249, 373.-397], who showed that proton transfer reactions that are catalyzed by bovine serum amine oxidase proceed through tunneling. We show that two different tunneling models are consistent with the experiments. In the first model, the proton tunnels from the ground state. The temperature dependence of the kinetic isotope effect is caused by a thermally excited substrate mode that modulates the barrier, as has been suggested by Borgis and Hynes [Borgis, D. and Hynes, J. T. (1991) J. Chem. Phys. 94, 3619-3628]. In the second model, there is both over-the-barrier transfer and tunneling from excited states. Finally, we propose two experiments that can distinguish between the possible mechanisms.
• Schwartz, S. D. (1997). Quantum reaction in a condensed phase: Turnover behavior from new adiabatic factorizations and corrections. Journal of Chemical Physics, 107(7), 2424-2429.
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  Abstract: This paper further investigates quantum activated rate theory from the viewpoint of quantum evolution operators. It is shown that a new adiabatic separation of the quantum system-bath Hamiltonian can, in a single time step, account for quantum turnover behavior at moderate temperatures, and it is also shown how this turnover exponentially vanishes at low temperatures. It is further shown that incorporation of nonadiabatic (interaction representation form) corrections produces quantitatively accurate results at low temperatures, thus extending the applicability of the interaction representation form of nonadiabatic corrections to adiabatic evolution operators. © 1997 American Institute of Physics.
• Antoniou, D., & Schwartz, S. D. (1996). Nonadiabatic effects in a method that combines classical and quantum mechanics. Journal of Chemical Physics, 104(10), 3526-3530.
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  Abstract: We have included nonadiabatic effects in the calculation of the dynamical evolution of a system where a quantum particle in a double well is coupled to a classical oscillator. By performing an exponential resummation of the evolution operator we have included "polarization" effects (similar to the self-energy corrections for an electron that moves in a polarizable medium) which lead to a renormalizatiori of the energy of the quantum particle. © 1996 American Institute of Physics.
• Bagdassarian, C. K., Braunheim, B. B., Schramm, V. L., & Schwartz, S. D. (1996). Quantitative measures of molecular similarity: Methods to analyze transition-state analogs for enzymatic reactions. International Journal of Quantum Chemistry, 60(8), 1797-1804.
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  Abstract: A formalism is presented for quantifying the similarity between any two molecules. The chemical descriptor used for comparison is the molecular electrostatic potential at the van der Waals surface. Thus, both the spatial properties of a molecule and its chemical features are captured in this approach. For molecules that are geometrically alike, the most useful similarity measure stems from orienting the two species so that their physical surfaces are aligned as well as possible, without regard to chemical patterns. After this alignment is achieved, a single measure sensitive to the spatial distribution of the electrostatic potential is used to rank the electronic similarity. Molecular similarity measures are applied to the enzyme systems AMP deaminase and AMP nucleosidase in order to understand quantitatively why their respective transition-state inhibitors bind more tightly than do their substrates. © 1996 John Wiley & Sons, Inc.
• Bagdassarian, C. K., Schramm, V. L., & Schwartz, S. D. (1996). Molecular electrostatic potential analysis for enzymatic substrates, competitive inhibitors, and transition-state inhibitors. Journal of the American Chemical Society, 118(37), 8825-8836.
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  Abstract: Recent advances in the application of kinetic isotope effects to enzyme-catalyzed reactions have provided reliable information for enzymatic transition state structures. A method is presented for quantifying the similarity of substrates and inhibitors with their enzyme-stabilized transition states. On the basis of transition-state stabilization theory for enzymatic reactions, molecules most similar to the transition state structure bind with greatest affinity. Molecular similarity measures are applied to compare substrates, competitive inhibitors, and transition state inhibitors with the transition state structures stabilized by the enzymes AMP deaminase, adenosine deaminase, and AMP nucleosidase. (R)- and (S)-Coformycin 5'-phosphate are inhibitors for AMP deaminase, with the R-species superior to its enantiomer. Formycin 5'-phosphate 4-aminopyrazolo[3,4-d]pyrimidine-1-ribonucleotide, and tubercidin 5'-phosphate inhibit AMP nucleosidase. The transition state for adenosine deaminase is analogous to that for AMP deaminase, allowing analysis of the tight-binding hydrate of purine ribonucleoside and of a weaker inhibitor, 1,6-dihydropurine ribonucleoside. The basis for ranking molecules for similarity to the transition state is the distribution of electrostatic potential at the molecular van der Waals surface. Spatial properties of a molecule are described through the topography of the surface, while the electrostatics capture ionic, hydrogen-bonding, and hydrophobic features. A test molecule is compared with the transition state by orienting the two species so that their van der Waals surfaces are maximally coincident. At this orientation, a single measure sensitive both to the electrostatic potential and its spatial distribution is used to rank the electronic similarity. For AMP deaminase, adenosine deaminase, and AMP nucleosidase, the transition state inhibitors are quantitatively more similar to the transition states than are the substrates. A strong correlation between the binding free energies and the similarity measures is found for most of the transition-state inhibitors in all three enzyme systems. This method is useful in the logical design of transition state inhibitors and may be applied to similarity searches of chemical libraries.
• Mitra, S., & Schwartz, S. D. (1996). A mixed momentum-position space representation to study quantum vibrational energy transfer. Journal of Chemical Physics, 104(19), 7539-7544.
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  Abstract: In this paper we describe a new technique that enables us to study vibrational energy transfer in linear hydrocarbon chains significantly more efficiently than by earlier approaches. The principal feature of our method is that the conjugate momentum operators that appear in the coupling terms in the Hamiltonian for the system are projected in the complete set of momentum states of the bonds. This allows us to express the expectation values of the time evolution operator in various energy eigenstates as one-dimensional momentum integrals which can be performed very rapidly and stored. All survival probabilities can then be expressed in terms of these stored integrals. We have evaluated the survival probability for HC2 and HC6 for up to eight time steps. Finally, we indicate how our approach may be extended to more general coupling terms. © 1996 American Institute of Physics.
• Schramm, V. L., Horenstein, B. A., Bagdassarian, C. K., Schwartz, S. D., Berti, P. J., Rising, K. A., Scheuring, J., Kline, P. C., Parkin, D. W., & Merkler, D. J. (1996). Enzymatic transition states and inhibitor design from principles of classical and quantum chemistry. International Journal of Quantum Chemistry, 60(8), 1805-1813.
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  Abstract: A procedure is described which leads to experimentally based models for the transitionstate structures of enzyme-catalyzed reactions. Substrates for an enzymic reaction are synthesized with isotopically enriched atoms at every position in which bonding changes are anticipated at the enzyme-enforced transition state. Kinetic isotope effects are measured for each atomic substitution and corrected for diminution of the isotope effects from nonchemical steps of the enzymic mechanism. A truncated geometric model of the transition-state structure is fitted to the kinetic isotope effects using bond-energy bondorder vibrational analysis. Full molecularity is restored to the transition state while maintaining the geometry of the bonds which define the transition state. Electronic wave functions are calculated for the substrate and the transition-state molecules. The molecular electrostatic potential energies are defined for the van der Waal surfaces of substrate and transition state and displayed in numerical and color-coded constructs. The electronic differences between substrate and transition state reveal characteristics of the transition state which permits the extraordinary binding affinity of enzyme-transition state interactions. The information has been used to characterize several enzymatic transition states and to design powerfully inhibitory transition-state analogues. Enzymatic examples are provided for the reactions catalyzed by AMP deaminase, nucleoside hydrolase, purine nucleoside phosphorylase, and for several bacterial toxins. The results demonstrate that the combination of experimental, classical, and quantum chemistry approaches is capable of providing reliable transition-state structures and sufficient information to permit the design of transition-state inhibitors. © 1996 John Wiley & Sons, Inc.
• Schwartz, S. D. (1996). Quantum activated rates - An evolution operator approach. Journal of Chemical Physics, 105(16), 6871-6879.
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  Abstract: This article presents a derivation of the rate of reaction in the quantum activated rate problem. In this problem, one studies the rate of a chemical reaction when the reaction is placed in a dissipative bath. Our derivation defines the rate in terms of the flux autocorrelation function and proceeds via the recently developed interaction representation for nonadiabatic corrections to adiabatic evolution operators. This methodology is an infinite order resummation of nonadiabatic corrections to evolution operators. The approach produces an analytic expression which yields accurate results over a ranse of temperatures, viscosities and system parameters through the Kramers turnover region. © 1996 American Institute of Physics.
• Schwartz, S. D. (1996). The interaction representation and nonadiabatic corrections to adiabatic evolution operators. Journal of Chemical Physics, 104(4), 1394-1398.
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  Abstract: This paper presents a new approach to operator resummation corrections to adiabatic evolution operators. It is shown that an infinite order correction produces an operator that is equivalent to a propagator in the interaction representation. For a problem in which the adiabatic approximation assumes that certain degrees of freedom are held fixed, the interaction representation correction is just the interaction propagator of the coupling for these degrees of freedom. This formulation allows simple physical interpretation and simple mathematical evaluation of the full correction. No power series or cumulant methods are needed. Application to double well splitting when coupled to a bath oscillator shows the approach to be highly accurate. © 1996 American Institute of Physics.
• Schwartz, S. D. (1996). The interaction representation and nonadiabatic corrections to adiabatic evolution operators. II. Nonlinear quantum systems. Journal of Chemical Physics, 104(20), 7985-7987.
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  Abstract: This paper reports further applications of the recently developed interaction representation form of infinite order operator corrections to adiabatic evolution operators. Previous work derived the form of the correction, and applied the methodology to a bilinearly coupled system bath model. In this paper we present results on coupled quantum systems in which the coupling is highly nonlinear. The method is both easy to implement and numerically accurate. © 1996 American Institute of Physics.
• Antoniou, D., & Schwartz, S. D. (1995). Vibrational energy transfer in linear hydrocarbon chains: New quantum results. The Journal of Chemical Physics, 103(17), 7277-7286.
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  Abstract: In this paper we report quantum calculations of the survival probability in linear hydrocarbon chains. We have performed both adiabatic gauge transform calculations and calculations that include corrections beyond the adiabatic approximation. We have managed to perform intermediate steps of the calculations analytically. We require the initial basis set expansion and final summations to be performed numerically. The corrections beyond the adiabatic approximation are shown to be small for this system for multiple time step calculations and large for single time step calculations. We have proved an identity that allows the extension of the calculations for HC2 to longer chains at little computational cost. In particular, we have proved that the quantum solution for any linear hydrocarbon chain can be obtained from the solution of a problem with 3 degrees of freedom. We have performed multi-step adiabatic calculations for HC2 and HC6 that converge at up to 35-40 fs. We have devised a simple diagrammatic scheme that summarizes our method in a very compact form. Finally, we propose an alternative strategy of calculation that might lead to very fast solutions of the quantum dynamics of this system. © 1995 American Institute of Physics.
• Schwartz, S. D. (1994). Accurate quantum mechanics from high order resummed operator expansions. The Journal of Chemical Physics, 100(12), 8795-8801.
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  Abstract: In this paper we report new developments in the expansion and partial resummation of the evolution operator. Higher order resummations allow derivation of an effective one-dimensional potential which accurately represents quantum dynamics for even strongly coupled low-frequency modes. This allows a system bath approximation which can accurately reproduce multidimensional quantum mechanics. In addition the formulation presented in this paper should prove significantly easier to extend to many-body problems than previous formulations we have derived. The accuracy of the method for even highly nonadiabatic applications, and the ease of implementation suggests that this approach will be useful in the calculation of the quantum dynamics of many dimensional systems. © 1994 American Institute of Physics.
• Schwartz, S. D. (1994). Vibrational energy transfer from resummed evolution operators. The Journal of Chemical Physics, 101(12), 10436-10441.
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  Abstract: This paper describes the application of our recently derived infinite order evolution operator expansion and resummation technique to the problem of vibrational energy redistribution in molecules. For a standard mass tensor coupled model of a linear hydrocarbon we show how the resummation technique allows the derivation of an approximate evolution operator that in a single time step accurately reproduces vibrational dynamics for over 25 fs in hydrocarbons. This single time evolution operator can be calculated efficiently enough so that long time dynamics with multiple time steps seem to now be within reach. In addition, the structure of the theory is such that longer chain hydrocarbons can be efficiently "built up" from shorter chain molecules. The theory starts with an adiabatic approximation which describes coupled vibrational degrees of freedom by uncoupled but guage shifted evolution operators. A modified version of this adiabatic approximation shows promise for application to molecules of a size too large to be handled exactly. © 1994 American Institute of Physics.
• Schwartz, S. D. (1992). Effective Feynman propagators and Schrödinger equations for processes coupled to many degrees of freedom. The Journal of Chemical Physics, 96(8), 5952-5957.
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  Abstract: AT&T Bell Laboratories. This paper presents a new approach to quantum evolution in the presence of a quantum bath. We develop an equation of motion for an observed system evolving under the influence of an unobserved quantum bath. The methodology we follow uses operator expansions of the Feynman propagator. Corrections to the zeroth order approximation are corrections to an adiabatic approximation. In this paper we explicitly develop an approximation which is infinite order in bath and system coupling, but first order in system degree of freedom. This infinite order approximation is found through a resummation of an infinite class of terms in the operator expansion. We first present a simplified single time (Markovian) version of the theory. We then present a derivation for including the effects of memory. The approach developed in this paper also has the potential for systematic improvement. In other words, while the bath and system coupling in this calculation is treated to infinite order, the system itself is only treated to first order. We will briefly discuss how these higher order corrections can be found. Finally, we present a test calculation of the our approach with comparison to exact results. For a two-dimensional test problem with potential much like that for collinear H + H2 the effective one-dimensional approximation we apply produces essentially exact results. © 1992 American Institute of Physics.
• Schwartz, S. D. (1992). Operator expansions for multidimensional problems: New developments and applications. The Journal of Chemical Physics, 97(10), 7377-7382.
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  Abstract: In this paper we report a new method for resummation of operator expansions of the evolution operator. These resummation techniques are applied to the Feynman propagator and then to the derivation of an effective Schrödinger equation for general system-bath problems. This paper presents a significant advance over work previously reported by us [J. Chem. Phys. 96, 5952 (1992)], and it provides a highly accurate way to calculate quantum mechanical data for many dimensional systems. We then apply this new analytic resummation technique to the calculation of flux-flux correlation functions for two, three, and four dimensional problems in order to study the range of applicability of the approach. For moderate frequencies and coupling strengths, not only is the resummed operator calculational method essentially exact, it also requires a fraction of the computer time that the exact calculation consumes. For truly many dimensional problems this approach should provide the first accurate quantum mechanics of rate processes. © 1992 American Institute of Physics.
• Schwartz, S. D. (1991). A density matrix formulation for potential scattering in an oscillating/controlled potential: a model for some biophysical systems. Chemical Physics Letters, 185(1-2), 16-22.
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  Abstract: A mathematical model of control of reactivity in biomolecules is described. It is motivated by the extraordinary level of detail new experiments have brought to the understanding of the functioning of the hemoglobin molecule as it interacts with ligands. Experimental evidence has shown that these systems control their activity to ligands by modifying potentials seen by these ligands in response to environmental conditions. We have developed a simple microscopic model of this control mechanism. We employ a density operator formulation which allows computation of such quantities as rebound percentages, rebinding flux, and position distribution moments for rebinding wavepackets. For a specific model of the rebinding barrier we calculate explicit formulae for rebinding probability as a function of time. © 1991.
• Ash, G. R., & Schwartz, S. D. (1990). Traffic control architectures for integrated broadband networks. International journal of digital and analog communication systems, 3(2), 167-176.
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  Abstract: This paper examines alternative traffic network architectures for integrated broadband networks, and provides integrated network routeing methods, bandwidth allocation strategies and traffic/routeing control plans for these networks. These architectures extend dynamic routeing control concepts to integrated broadband networks, and suggest perhaps radically different traffic architectures to which broadband networks might evolve. Strategies are examined for dynamic traffic routeing and dynamic trunk capacity routeing, which can adapt to load variations in customer requirements or to network resource failure conditions. Bandwidth allocation procedures are investigated which manage network bandwidth according to a virtual trunk concept, in which dynamic reservation controls are placed on the number of connections for each service category. We analyse the alternative traffic network architectures, for example broadband networks. The examples show that the architectures provide, to varying degrees, the advantages of increased network efficiency, improved customer service and increased network flexibility. Fully shared ring networks which integrate dynamic traffic and trunk capacity routeing yield many of these advantages and also provide greatly simplified network operation along with maximum flexibility to apportion network resources, especially when implemented with asynchronous transfer mode (ATM) technology.
• Schwartz, S. D. (1989). Propagator expansions for softly coupled potentials: A model for complex reaction dynamics. The Journal of Chemical Physics, 91(12), 7621-7629.
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  Abstract: In this paper we investigate a new approach to reduced dimensionality descriptions of quantum mechanical systems resident in a bath. We study physical situations in which the coupling between the system and the bath is slowly varying. Our method involves an operator expansion of the Feynman propagator following the Zassenhaus theorem. From this general expansion we are able to derive an especially simple special case in which the coupling is a slowly varying function of the position operators of the system and the bath. From the approximate propagator after tracing over bath degrees, we are able to derive a short time propagator which yields both a form for efficient numerical calculation and an effective Schrödinger equation for the evolution of the system under the average influence of the bath. This theory is then applied to tunneling rearrangement in mixed crystals of benzoic acid. We find that independent of potential energy perturbations, dynamic system bath couplings increase the rate of tunneling. A central goal of this type of approach is to model the increasingly complex experimental data for large (often biological) systems. © 1989 American Institute of Physics.
• Miller, W. H., Schwartz, S. D., & Tromp, J. W. (1983). Quantum mechanical rate constants for bimolecular reactions. The Journal of Chemical Physics, 79(10), 4889-4898.
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  Abstract: Several formally exact expressions for quantum mechanical rate constants (i.e., bimolecular reactive cross sections suitably averaged and summed over initial and final states) are derived and their relation to one another analyzed. It is suggested that they may provide a useful means for calculating quantum mechanical rate constants accurately without having to solve the complete state-to-state quantum mechanical reactive scattering problem. Several ways are discussed for evaluating the quantum mechanical traces involved in these expressions, including a path integral evaluation of the Boltzmann operator/time propagator and a discrete basis set approximation. Both these methods are applied to a one-dimensional test problem (the Eckart barrier). © 1983 American Institute of Physics.
• Schwartz, S. D., & Miller, W. H. (1983). System-bath decomposition of the reaction path Hamiltonian. II. Rotationally inelastic reactive scattering of H+H₂ in three dimensions. The Journal of Chemical Physics, 79(8), 3759-3764.
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  Abstract: Earlier work of the authors [J. Chem. Phys. 77, 2378 (1982)] has shown how the reaction path Hamiltonian of Miller, Handy, and Adams [J. Chem. Phys. 72, 99 (1980)] can be divided into a "system" of the reaction coordinate and modes strongly coupled to it, plus a "bath" of more weakly coupled modes. Quantum mechanical perturbation theory was used to show how one can combine an exact description of the system dynamics with an approximate (perturbative) treatment of the effect of the bath. The present paper applies this approach to the 3d H+H2 reaction, where the two collinear degrees of freedom constitute the system, and the two bending modes the bath. Comparison with the accurate scattering calculations of Schatz and Kupermann [J. Chem. Phys. 65, 4668 (1976)] shows it to provide a good description of the coupling between bending (i.e., rotational) and collinear modes. © 1983 American Institute of Physics.
• Miller, W. H., & Schwartz, S. (1982). System-bath decomposition of the reaction path Hamiltonian for polyatomic scattering: Quantum perturbative treatment. The Journal of Chemical Physics, 77(5), 2378-2382.
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  Abstract: An approach to quantum mechanical reactive scattering in polyatomic molecular systems is described. The formulation is based on the reaction path Hamiltonian of Miller, Handy, and Adams [J. Chem. Phys. 72, 99 (1980)]. The essential physical idea is that the reaction coordinate in even polyatomic systems may be coupled strongly to only a few (one or two) of the vibrational modes orthogonal to it, and rather weakly coupled to the (perhaps many) remaining modes. This leads naturally to a "system-bath" decomposition of the reaction process, and this paper shows how this is carried through for the reaction path Hamiltonian. If only one transverse mode is included with the reaction coordinate to form the "system," for example, then the overall model is that of a collinearlike reaction, whose dynamics are treated accurately, taking place in a (harmonic) "bath" to which it is weakly coupled. © 1982 American Institute of Physics.

Presentations

• Schwartz, S. D. (2019, April). Promoting vibrations and enzymatic catalysis. ACS national meeting, invited speaker.
• Schwartz, S. D. (2019, July). New views of catalysis. Isotopes 2019. Munich, Germans.
• Schwartz, S. D. (2019, July). Session organizer. Enzymes and co-enzymes Gordon Conference. New Hampshire.
• Schwartz, S. D. (2019, June). New theories of enzymatic function. Invited seminar. Peking University Dept of Chemistry.
• Schwartz, S. D. (2019, June). Protein dynamics and enzyme function. Invited seminar Southern University of Science and Technology. Shenzhen China.
• Schwartz, S. D. (2019, November). Invited talk. Conference on Theoretical Chemistry in honor of Bill Jorgenson. Peking University Shenzhen Graduate center.
• Schwartz, S. D. (2019, October). Plenary lecture. American Physical Society 4 corners section.
• Schwartz, S. D. (2018, April). University of Illinois, Chicago. Dept of Bioengineering Invited speaker.
• Schwartz, S. D. (2018, December). UT Southwestern Dept of Biophysics Seminar. Dept seminar. Green Center UT Southwestern.
• Schwartz, S. D. (2018, February). Panelist on Cardiac Biophysics. UC Davis Symposium on Cardiac Biophysics.
• Schwartz, S. D. (2018, March). Trinity University Dept of Chemistry Invited Speaker. Dept Seminar.
• Schwartz, S. D. (2018, May). Invited Plenary Speaker. Memorial Symposium for Ahmed Zewail. National Technical University, Singapore.
• Schwartz, S. D. (2018, September). Department of Chemistry Seminar. Michigan State University.
• Schwartz, S. D. (2017, April). Invited talk. ACS national meeting San Francisco. San Francisco: ACS.
• Schwartz, S. D. (2017, July). Invited talk. Gordon research conference on Enzymes, Coenzymes and Metabolic Pathways. New Hampshire: GRC.
• Schwartz, S. D. (2017, June). Invited talk. Internation union of pure and applied physics - biophysics division. Rio DeJaneiro Brazil: IUPAP.
• Schwartz, S. D. (2017, March). Department of Physics Seminar. State University of NY at Buffalo. SUNY Buffalo: SUNY Buffalo.
• Schwartz, S. D. (2017, March). Invited seminar. Center for Nonlinear studies. Los Alamos National Laboratory: Los Alamos National Laboratory.
• Schwartz, S. D. (2017, October). Invited speaker. Scott Symposium. College Station Texas: Texas A&M University.
• Eismin, R. J., Palos Pacheco, R., Munusamy, E., Hogan, D. E., Maier, R. M., Polt, R. L., Schwartz, S. D., & Pemberton, J. E. (2016, Summer). Microenvironment of Monorhamnolipid Aggregates and their Synthetically Produced Diastereomers as a Function of Solution Conditions. 252nd American Chemical Society National Meeting & Exposition. Philadelphia, PA: American Chemical Society.
• Pemberton, J. E., Polt, R. L., Schwartz, S. D., Maier, R. M., & Klimecki, W. (2016, Summer). Biosynthetic and Bio-inspired Glycolipid Surfactants: Properties, Biodegradability, and Toxicity. 20th Annual Green Chemistry & Engineering Conference. Portland, OR: American Chemical Society Green Chemistry Institute.
• Schwartz, S. D. (2016, August). ACS National meeting in Philadelphia invited speaker. ACS National Meeting.
• Schwartz, S. D. (2016, February). Departmental Seminar. Uppsala University.
• Schwartz, S. D. (2016, January). Departmental Seminar. UC Davis department of Chemistry.
• Schwartz, S. D. (2016, July). Departmental Seminar. Shanghai Xiaotong University Chemistry Dept.
• Schwartz, S. D. (2016, July). Invited Talk. Shanghai workshop on frontiers of molecular biophysics.
• Schwartz, S. D. (2016, March). ACS National meeting in San Diego invited speaker. ACS National meeting.
• Schwartz, S. D. (2015, August). Computational Studies of Enzymatically Catalyzed Chemistry. Conference on Computational Chemical Biology. Cairns, Australia.
• Schwartz, S. D. (2015, December). Protein Dynamics and Protein Design for Enzymatic Catalysis. Pacifichem. Honolulu, Hawaii: ACS.
• Schwartz, S. D. (2015, February). How Enzymes Work. Chemistry Dept Seminar, University of Manitoba,. Winnipeg, CA: Dept of Chemistry.
• Schwartz, S. D. (2015, June). Isotope Effects and Protein Dynamics. Isotopes 2015. Jerusalem, Israel.
• Schwartz, S. D. (2015, March). Program Chair. American Physical Society Meeting. San Antonio, Texas: American Physical Society.
• Schwartz, S. D. (2014, June). Protein dynamics and Enzymes. EMBO conference - enzyme mechanisms. Manchester England.
• Schwartz, S. D. (2014, June). Protein dynamics and Enzymes. International Conference on spectroscopy and computation. Shanghai.
• Schwartz, S. D. (2014, March). Protein dynamics and Enzymes. American Physical Society March Meeting.
• Schwartz, S. D. (2014, fall). Protein dynamics and Enzymes. Isotope GRC.
• Schwartz, S. D. (2014, june). Protein dynamics and Enzymes. IUPAP international conference on biological physics. Beijing.
• Schwartz, S. D. (2014, march). Protein dynamics and Enzymes. American Chemical Society spring meeting.
• Schwartz, S. D. (2014, sprint). Cardiac Thin filament modeling. Biophysical Society.