Charles William Wolgemuth
- Professor, Physics
- Associate Professor, Molecular and Cellular Biology
- Associate Professor, Applied Mathematics - GIDP
- Ph.D. Physics
- University of Arizona, Tucson, Arizona, USA
- Thin Life at Low Reynolds Number
- M.S. Physics
- University of Arizona, Tucson, Arizona, USA
- B.S. Physics
- University of Arizona, Tucson, Arizona, USA
- Honors Professor
- Fall 2015
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Directed ResearchPHYS 492 (Spring 2018)
DissertationMCB 920 (Spring 2018)
DissertationPHYS 920 (Spring 2018)
Independent StudyPHYS 399 (Spring 2018)
Independent StudyPHYS 599 (Spring 2018)
Lab Presentations & DiscussionMCB 696A (Spring 2018)
ResearchMCB 900 (Spring 2018)
Science of Good CookingPHYS 200 (Spring 2018)
Special Topics in ScienceHNRS 195I (Spring 2018)
DissertationMCB 920 (Fall 2017)
Honors Independent StudyPHYS 199H (Fall 2017)
Honors Independent StudyPHYS 399H (Fall 2017)
Independent StudyPHYS 299 (Fall 2017)
Independent StudyPHYS 499 (Fall 2017)
Independent StudyPHYS 599 (Fall 2017)
Introductory MechanicsPHYS 140 (Fall 2017)
Introductory MechanicsPHYS 141 (Fall 2017)
Lab Presentations & DiscussionMCB 696A (Fall 2017)
ResearchMCB 900 (Fall 2017)
Directed ResearchPHYS 492 (Spring 2017)
Independent StudyPHYS 299 (Spring 2017)
Independent StudyPHYS 499 (Spring 2017)
Independent StudyPHYS 599 (Spring 2017)
Lab Presentations & DiscussionMCB 696A (Spring 2017)
Molecular BiophysicsPHYS 431 (Spring 2017)
Molecular BiophysicsPHYS 531 (Spring 2017)
ResearchMCB 900 (Spring 2017)
Directed ResearchPHYS 392 (Fall 2016)
Directed ResearchPHYS 492 (Fall 2016)
Honors Independent StudyPHYS 199H (Fall 2016)
Independent StudyPHYS 299 (Fall 2016)
Independent StudyPHYS 599 (Fall 2016)
Introduction to ResearchMCB 795A (Fall 2016)
Introductory MechanicsPHYS 141 (Fall 2016)
Lab Presentations & DiscussionMCB 696A (Fall 2016)
ResearchMCB 900 (Fall 2016)
Special Topics in ScienceHNRS 195I (Fall 2016)
- Argudo, D., Bethel, N. P., Marcoline, F. V., Wolgemuth, C. W., & Grabe, M. (2017). New Continuum Approaches for Determining Protein-Induced Membrane Deformations. BIOPHYSICAL JOURNAL, 112(10), 2159-2172.
- Li, Y., He, L., Gonzalez, N., Graham, J., Wolgemuth, C., Wirtz, D., & Sun, S. X. (2017). Going with the Flow: Water Flux and Cell Shape during Cytokinesis. BIOPHYSICAL JOURNAL, 113(11), 2487-2495.
- Marchenko, O. O., Das, S., Yu, J. i., Novak, I. L., Rodionov, V. I., Efimova, N., Svitkina, T., Wolgemuth, C. W., & Loew, L. M. (2017). A minimal actomyosin-based model predicts the dynamics of filopodia on neuronal dendrites. MOLECULAR BIOLOGY OF THE CELL, 28(8), 1021-1033.
- Vig, D. K., Hamby, A. E., & Wolgemuth, C. W. (2017). Cellular Contraction Can Drive Rapid Epithelial Flows. BIOPHYSICAL JOURNAL, 113(7), 1613-1622.
- Wolgemuth, C. W. (2016). On the Quantification of Cellular Velocity Fields. Biophysical Journal, 110, 1469-1475.
- Wolgemuth, C. W. (2016). Physical Mechanisms of Cancer in the Transition to Metastasis. Biophysical Journal, 111, 256-266.
- Wolgemuth, C. W. (2015). Flagellar motility of the pathogenic spirochetes. Seminars in Cell & Developmental Biology, 46, 104-112.
- Wolgemuth, C. W., & Lee, P. (2016). An immersed boundary method for two-phase fluids and gels and the swimming of Caenorhabditis elegans through viscoelastic fluids. Phys. Fluids, 28, 011901.
- Fuhs, T., Goegler, M., Brunner, C. A., Wolgemuth, C. W., & Kaes, J. A. (2014). Causes of retrograde flow in fish keratocytes. Cytoskeleton, 71(1), 24-35.More infoAbstract: Confronting motile cells with obstacles doubling as force sensors we tested the limits of the driving actin and myosin machinery. We could directly measure the force necessary to stop actin polymerization as well as the force present in the retrograde actin flow. Combined with detailed measurements of the retrograde flow velocity and specific manipulation of actin and myosin we found that actin polymerization and myosin contractility are not enough to explain the cells behavior. We show that ever-present depolymerization forces, a direct entropic consequence of actin filament recycling, are sufficient to fill this gap, even under heavy loads. © 2013 Wiley Periodicals, Inc.
- Vig, D. K., & Wolgemuth, C. W. (2014). Spatiotemporal evolution of erythema migrans, the hallmark rash of lyme disease. Biophysical Journal, 106(3), 763-768.More infoAbstract: To elucidate pathogen-host interactions during early Lyme disease, we developed a mathematical model that explains the spatiotemporal dynamics of the characteristic first sign of the disease, a large (≥5-cm diameter) rash, known as an erythema migrans. The model predicts that the bacterial replication and dissemination rates are the primary factors controlling the speed that the rash spreads, whereas the rate that active macrophages are cleared from the dermis is the principle determinant of rash morphology. In addition, the model supports the clinical observations that antibiotic treatment quickly clears spirochetes from the dermis and that the rash appearance is not indicative of the efficacy of the treatment. The quantitative agreement between our results and clinical data suggest that this model could be used to develop more efficient drug treatments and may form a basis for modeling pathogen-host interactions in other emerging infectious diseases. © 2014 Biophysical Society.
- Wolgemuth, C. W. (2014). Junctional angle of a bihanded helix. Physical Review E, 90, 042722.
- Belgrave, A. M., & Wolgemuth, C. W. (2013). Elasticity and biochemistry of growth relate replication rate to cell length and cross-link density in rod-shaped bacteria. Biophysical Journal, 104(12), 2607-2611.More infoPMID: 23790368;PMCID: PMC3686348;Abstract: In rod-shaped bacteria, cell morphology is correlated with the replication rate. For a given species, cells that replicate faster are longer and have less cross-linked cell walls. Here, we propose a simple mechanochemical model that explains the dependence of cell length and cross-linking on the replication rate. Our model shows good agreement with existing experimental data and provides further evidence that cell wall synthesis is mediated by multienzyme complexes; however, our results suggest that these synthesis complexes only mediate glycan insertion and cross-link severing, whereas recross-linking is performed independently. © 2013 Biophysical Society.
- Harman, M., Vig, D. K., Radolf, J. D., & Wolgemuth, C. W. (2013). Viscous dynamics of lyme disease and syphilis spirochetes reveal flagellar torque and drag. Biophysical Journal, 105(10), 2273-2280.More infoPMID: 24268139;PMCID: PMC3838743;Abstract: The spirochetes that cause Lyme disease (Borrelia burgdorferi) and syphilis (Treponema pallidum) swim through viscous fluids, such as blood and interstitial fluid, by undulating their bodies as traveling, planar waves. These undulations are driven by rotation of the flagella within the periplasmic space, the narrow (∼20-40 nm in width) compartment between the inner and outer membranes. We show here that the swimming speeds of B. burgdorferi and T. pallidum decrease with increases in viscosity of the external aqueous milieu, even though the flagella are entirely intracellular. We then use mathematical modeling to show that the measured changes in speed are consistent with the exertion of constant torque by the spirochetal flagellar motors. Comparison of simulations, experiments, and a simple model for power dissipation allows us to estimate the torque and resistive drag that act on the flagella of these major spirochetal pathogens. © 2013 Biophysical Society.
- Yang, J., Wolgemuth, C. W., & Huber, G. (2013). Force and torque on a cylinder rotating in a narrow gap at low Reynolds number: Scaling and lubrication analyses. Physics of Fluids, 25(5).More infoAbstract: The hydrodynamic forces and torques on a rotating cylinder in a narrow channel are investigated in this paper using lubrication analysis and scaling analysis. To explore the effect of the shape of the gap, three different geometries are considered. The force and torque expressions from lubrication analysis agree well with numerical solutions when the gap between cylinder and wall is small. The solutions from scaling analysis can be applied over a broader range, but only if the scaling coefficients are properly deduced from numerical solution or lubrication analysis. Self-similarity in the solutions is discussed as well. © 2013 AIP Publishing LLC.
- Charon, N. W., Cockburn, A., Chunhao, L. i., Liu, J., Miller, K. A., Miller, M. R., Motaleb, M. A., & Wolgemuth, C. W. (2012). The unique paradigm of spirochete motility and chemotaxis. Annual Review of Microbiology, 66, 349-370.More infoPMID: 22994496;PMCID: PMC3771095;Abstract: Spirochete motility is enigmatic: It differs from the motility of most other bacteria in that the entire bacterium is involved in translocation in the absence of external appendages. Using the Lyme disease spirochete Borrelia burgdorferi (Bb) as a model system, we explore the current research on spirochete motility and chemotaxis. Bb has periplasmic flagella (PFs) subterminally attached to each end of the protoplasmic cell cylinder, and surrounding the cell is an outer membrane. These internal helix-shaped PFs allow the spirochete to swim by generating backward-moving waves by rotation. Exciting advances using cryoelectron tomography are presented with respect to in situ analysis of cell, PF, and motor structure. In addition, advances in the dynamics of motility, chemotaxis, gene regulation, and the role of motility and chemotaxis in the life cycle of Bb are summarized. The results indicate that the motility paradigms of flagellated bacteria do not apply to these unique bacteria. © 2012 by Annual Reviews. All rights reserved.
- Harman, M. W., Dunham-Ems, S. M., Caimano, M. J., Belperron, A. A., Bockenstedt, L. K., Fu, H. C., Radolf, J. D., & Wolgemuth, C. W. (2012). The heterogeneous motility of the Lyme disease spirochete in gelatin mimics dissemination through tissue. Proceedings of the National Academy of Sciences of the United States of America, 109(8), 3059-3064.More infoPMID: 22315410;PMCID: PMC3286914;Abstract: The Lyme disease spirochete Borrelia burgdorferi exists in nature in an enzootic cycle that involves the arthropod vector Ixodes scapularis and mammalian reservoirs. To disseminate within and between these hosts, spirochetes must migrate through complex, polymeric environments such as the basement membrane of the tick midgut and the dermis of the mammal. To date, most research on the motility of B. burgdorferi has been done in media that do not resemble the tissue milieus that B. burgdorferi encounter in vivo. Here we show that the motility of Borrelia in gelatin matrices in vitro resembles the pathogen's movements in the chronically infected mouse dermis imaged by intravital microscopy. More specifically, B. burgdorferi motility in mouse dermis and gelatin is heterogeneous, with the bacteria transitioning between at least three different motility states that depend on transient adhesions to the matrix. We also show that B. burgdorferi is able to penetrate matrices with pore sizes much smaller than the diameter of the bacterium. We find a complex relationship between the swimming behavior of B. burgdorferi and the rheological properties of the gelatin, which cannot be accounted for by recent theoretical predictions for microorganism swimming in gels. Our results also emphasize the importance of considering borrelial adhesion as a dynamic rather than a static process.
- Strawbridge, E. M., & Wolgemuth, C. W. (2012). Surface traction and the dynamics of elastic rods at low Reynolds number. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 86(3).More infoAbstract: Molecular and cell biological processes often use proteins and structures that are significantly longer in one dimension than they are in the other two, for example, DNA, actin, and bacterial flagella. The dynamics of these structures are the consequence of the balance between the elastic forces from the structure itself and viscous forces from the surrounding fluid. Typically, the motion of these filamentary objects is described using variations of the Kirchhoff rod equations with resistive forces from the fluid treated as body forces acting on the centerline. In reality, though, these forces are applied to the surface of the filament; however, the standard derivation of the Kirchhoff equations ignores surface traction stresses. Here, we rederive the Kirchhoff rod equations in the presence of resistive traction stresses and determine the conditions under which treating the drag forces as body forces is reasonable. We show that in most biologically relevant cases the standard implementation of resistive forces into the Kirchhoff rod equations is applicable; however, we note one particular biological system where the Kirchhoff rod formalism may not apply. © 2012 American Physical Society.
- Vig, D. K., & Wolgemuth, C. W. (2012). Swimming dynamics of the lyme disease spirochete. Physical Review Letters, 109(21).More infoAbstract: The Lyme disease spirochete, Borrelia burgdorferi, swims by undulating its cell body in the form of a traveling flat wave, a process driven by rotating internal flagella. We study B. burgdorferi's swimming by treating the cell body and flagella as linearly elastic filaments. The dynamics of the cell are then determined from the balance between elastic and resistive forces and moments. We find that planar, traveling waves only exist when the flagella are effectively anchored at both ends of the bacterium and that these traveling flat waves rotate as they undulate. The model predicts how the undulation frequency is related to the torque from the flagellar motors and how the stiffness of the cell body and flagella affect the undulations and morphology. © 2012 American Physical Society.
- Wolgemuth, C. W. (2012). Biomechanics of cell motility. Comprehensive Biophysics, 7, 168-193.More infoAbstract: In order to move, cells exert force on the environment and, for cellular-sized objects, resistive drag forces are comparable to the forces that a cell can produce. Therefore, inertia is negligible: A cell that stops producing force is almost immediately brought to a halt by the environment. The effective absence of inertia means that the net force on a motile cell is zero. Here there is a subtlety. If a cell exerts force on the environment, then the environment must push back with an equal but opposite force. This is the thrust force that propels the cell. But the environment also resists the motion of the cell and exerts a force on the cell that opposes the motion. It is the environment that allows motion and yet impedes it. © 2012 Elsevier B.V. All rights reserved.
- Cogan, N. G., & Wolgemuth, C. W. (2011). Two-dimensional patterns in bacterial veils arise from self-generated, three-dimensional fluid flows. Bulletin of Mathematical Biology, 73(1), 212-229.More infoPMID: 20376573;Abstract: The behavior of collections of oceanic bacteria is controlled by metabolic (chemotaxis) and physical (fluid motion) processes. Some sulfur-oxidizing bacteria, such as Thiovulum majus, unite these two processes via a material interface produced by the bacteria and upon which the bacteria are transiently attached. This interface, termed a bacterial veil, is formed by exo-polymeric substances (EPS) produced by the bacteria. By adhering to the veil while continuing to rotate their flagella, the bacteria are able to exert force on the fluid surroundings. This behavior induces a fluid flow that, in turn, causes the bacteria to aggregate leading to the formation of a physical pattern in the veil. These striking patterns are very similar in flavor to the classic convection instability observed when a shallow fluid is heated from below. However, the physics are very different since the flow around the veil is mediated by the bacteria and affects the bacterial densities. In this study, we extend a model of a one-dimensional veil in a two-dimensional fluid to the more realistic two-dimensional veil in a three-dimensional fluid. The linear stability analysis indicates that the Peclet number serves as a bifurcation parameter, which is consistent with experimental observations. We also solve the nonlinear problem numerically and are able to obtain patterns that are similar to those observed in the experiments. © 2010 Society for Mathematical Biology.
- Krzyszczyk, P., & Wolgemuth, C. W. (2011). Mechanosensing can result from adhesion molecule dynamics. Biophysical Journal, 101(10), L53-L55.More infoPMID: 22098759;PMCID: PMC3218332;Abstract: When plated onto a substrate, cells spread. Many cell types, including smooth muscle cells and fibroblasts, spread more effectively on stiffer substrates, and a simple empirical relationship has been determined that relates a cell's spread area to the substrate stiffness. In addition, some crawling cells when plated onto a stiff substrate will not migrate onto soft substrate, a process called "durotaxis". Here we show that the resistive force predicted previously for dynamic adhesion molecules can account for both of these mechanosensory effects. © 2011 Biophysical Society.
- Lee, P., & Wolgemuth, C. (2011). Advent of complex flows in epithelial tissues. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 83(6).More infoPMID: 21797416;Abstract: The collective migration of cells in tissue pervades many important biological processes, such as wound healing, organism development, and cancer metastasis. Recent experiments on wound healing show that the collective migratory behavior of cells can be quite complex, including transient vortices and long-range correlations. Here, we explore cellular flows in epithelial tissues using a model that considers the force distribution and polarity of a single cell along with cell-cell adhesion. We show that the dipole nature of a crawling cell's force distribution destabilizes steady cellular motion. We determine the values of the physical parameters that are necessary to produce these complex motions and use numerical simulation to verify the linear analysis and to demonstrate the complex flows. We find that the tendency for cells to align is the dominant physical parameter that determines the stability of steady flows in the epithelium. © 2011 American Physical Society.
- Lee, P., & Wolgemuth, C. W. (2011). Crawling cells can close wounds without purse strings or signaling. PLoS Computational Biology, 7(3).More infoPMID: 21423710;PMCID: PMC3053312;Abstract: When a gash or gouge is made in a confluent layer of epithelial cells, the cells move to fill in the "wound." In some cases, such as in wounded embryonic chick wing buds, the movement of the cells is driven by cortical actin contraction (i.e., a purse string mechanism). In adult tissue, though, cells apparently crawl to close wounds. At the single cell level, this crawling is driven by the dynamics of the cell's actin cytoskeleton, which is regulated by a complex biochemical network, and cell signaling has been proposed to play a significant role in directing cells to move into the denuded area. However, wounds made in monolayers of Madin-Darby canine kidney (MDCK) cells still close even when a row of cells is deactivated at the periphery of the wound, and recent experiments show complex, highly-correlated cellular motions that extend tens of cell lengths away from the boundary. These experiments suggest a dominant role for mechanics in wound healing. Here we present a biophysical description of the collective migration of epithelial cells during wound healing based on the basic motility of single cells and cell-cell interactions. This model quantitatively captures the dynamics of wound closure and reproduces the complex cellular flows that are observed. These results suggest that wound healing is predominantly a mechanical process that is modified, but not produced, by cell-cell signaling. © 2011 Lee, Wolgemuth.
- Wolgemuth, C. W., Stajic, J., & Mogilner, A. (2011). Redundant mechanisms for stable cell locomotion revealed by minimal models. Biophysical Journal, 101(3), 545-553.More infoPMID: 21806922;PMCID: PMC3145291;Abstract: Crawling of eukaryotic cells on flat surfaces is underlain by the protrusion of the actin network, the contractile activity of myosin II motors, and graded adhesion to the substrate regulated by complex biochemical networks. Some crawling cells, such as fish keratocytes, maintain a roughly constant shape and velocity. Here we use moving-boundary simulations to explore four different minimal mechanisms for cell locomotion: 1), a biophysical model for myosin contraction-driven motility; 2), a G-actin transport-limited motility model; 3), a simple model for Rac/Rho-regulated motility; and 4), a model that assumes that microtubule-based transport of vesicles to the leading edge limits the rate of protrusion. We show that all of these models, alone or in combination, are sufficient to produce half-moon steady shapes and movements that are characteristic of keratocytes, suggesting that these mechanisms may serve redundant and complementary roles in driving cell motility. Moving-boundary simulations demonstrate local and global stability of the motile cell shapes and make testable predictions regarding the dependence of shape and speed on mechanical and biochemical parameters. The models shed light on the roles of membrane-mediated area conservation and the coupling of mechanical and biochemical mechanisms in stabilizing motile cells. © 2011 Biophysical Society.
- Yang, J., Huber, G., & Wolgemuth, C. W. (2011). Forces and torques on rotating spirochete flagella. Physical Review Letters, 107(26).More infoPMID: 22243185;PMCID: PMC3484371;Abstract: Spirochetes are a unique group of motile bacteria that are distinguished by their helical or flat-wave shapes and the location of their flagella, which reside within the tiny space between the bacterial cell wall and the outer membrane (the periplasm). In Borrelia burgdorferi, rotation of the flagella produces cellular undulations that drive swimming. How these shape changes arise due to the forces and torques that act between the flagella and the cell body is unknown. It is possible that resistive forces come from friction or from fluid drag, depending on whether or not the flagella are in contact with the cell wall. Here, we consider both of these cases. By analyzing the motion of an elastic flagellum rotating in the periplasmic space, we show that the flagella are most likely separated from the bacterial cell wall by a lubricating layer of fluid. This analysis then provides drag coefficients for rotation and sliding of a flagellum within the periplasm. © 2011 American Physical Society.
- Fu, H. C., Shenoy, V., Powers, T., & Wolgemuth, C. W. (2010). Swimming microorganisms in complex media. Proceedings of the ASME 1st Global Congress on NanoEngineering for Medicine and Biology 2010, NEMB2010, 285-286.
- Sliusarenko, O., Cabeen, M. T., Wolgemuth, C. W., Jacobs-Wagner, C., & Emonet, T. (2010). Processivity of peptidoglycan synthesis provides a built-in mechanism for the robustness of straight-rod cell morphology. Proceedings of the National Academy of Sciences of the United States of America, 107(22), 10086-10091.More infoPMID: 20479277;PMCID: PMC2890421;Abstract: The propagation of cell shape across generations is remarkably robust in most bacteria. Even when deformations are acquired, growing cells progressively recover their original shape once the deforming factors are eliminated. For instance, straight-rod-shaped bacteria grow curved when confined to circular microchambers, but straighten in a growth-dependent fashion when released. Bacterial cell shape is maintained by the peptidoglycan (PG) cell wall, a giant macromolecule of glycan strands that are synthesized by processive enzymes and cross-linked by peptide chains. Changes in cell geometry require modifying the PG and therefore depend directly on the molecular-scale properties of PG structure and synthesis. Using a mathematical model we quantify the straightening of curved Caulobacter crescentus cells after disruption of the cell-curving crescentin structure. We observe that cells straighten at a rate that is about half (57%) the cell growth rate. Next we show that in the absence of other effects there exists a mathematical relationship between the rate of cell straightening and the processivity of PG synthesis - the number of subunits incorporated before termination of synthesis. From the measured rate of cell straightening this relationship predicts processivity values that are in good agreement with our estimates from published data. Finally, we consider the possible role of three other mechanisms in cell straightening. We conclude that regardless of the involvement of other factors, intrinsic properties of PG processivity provide a robust mechanism for cell straightening that is hardwired to the cell wall synthesis machinery.
- Sun, S. X., Walcott, S., & Wolgemuth, C. W. (2010). Cytoskeletal cross-linking and bundling in motor-independent contraction. Current Biology, 20(15), R649-R654.More infoPMID: 20692617;PMCID: PMC3633214;Abstract: Eukaryotic and prokaryotic cells use cytoskeletal proteins to regulate and modify cell shape. During cytokinesis or eukaryotic cell crawling, contractile forces are generated inside the cell to constrict the division site or to haul the rear of the cell forward, respectively. In many cases, these forces have been attributed to the activity of molecular motors, such as myosin II, which, by pulling on actin filaments, can produce contraction of the actin cytoskeleton. However, prokaryotic division is driven by the tubulin-like protein FtsZ and does not seem to require additional molecular motors to constrict the division site. Likewise, Dictyostelium discoideum and Saccharomyces cerevisiae can perform cytokinesis under motor-free conditions. In addition, many crawling cells can translocate when myosin is inhibited or absent. In this review, we point out another force-generation mechanism that can play a significant role in driving these processes in eukaryotes and prokaryotes. This mechanism is mediated by cross-linking and bundling proteins that form effective interactions between cytoskeletal filaments. Some recent studies in this area are reviewed and the physical underpinnings of this force-generation mechanism are explained. © 2010 Elsevier Ltd All rights reserved.
- Wolgemuth, C. W., & Zajac, M. (2010). The moving boundary node method: A level set-based, finite volume algorithm with applications to cell motility. Journal of Computational Physics, 229(19), 7287-7308.More infoAbstract: Eukaryotic cell crawling is a highly complex biophysical and biochemical process, where deformation and motion of a cell are driven by internal, biochemical regulation of a poroelastic cytoskeleton. One challenge to built quantitative models that describe crawling cells is solving the reaction-diffusion-advection dynamics for the biochemical and cytoskeletal components of the cell inside its moving and deforming geometry. Here we develop an algorithm that uses the level set method to move the cell boundary and uses information stored in the distance map to construct a finite volume representation of the cell. Our method preserves Cartesian connectivity of nodes in the finite volume representation while resolving the distorted cell geometry. Derivatives approximated using a Taylor series expansion at finite volume interfaces lead to second order accuracy even on highly distorted quadrilateral elements. A modified, Laplacian-based interpolation scheme is developed that conserves mass while interpolating values onto nodes that join the cell interior as the boundary moves. An implicit time stepping algorithm is used to maintain stability. We use the algorithm to simulate two simple models for cellular crawling. The first model uses depolymerization of the cytoskeleton to drive cell motility and suggests that the shape of a steady crawling cell is strongly dependent on the adhesion between the cell and the substrate. In the second model, we use a model for chemical signalling during chemotaxis to determine the shape of a crawling cell in a constant gradient and to show cellular response upon gradient reversal. © 2010 Elsevier Inc.
- Yogurtcu, O. N., Wolgemuth, C. W., & Sun, S. X. (2010). Mechanical response and conformational amplification in α-Helical coiled coils. Biophysical Journal, 99(12), 3895-3904.More infoPMID: 21156131;PMCID: PMC3000483;Abstract: α-Helical coiled coils (CCs) are ubiquitous tertiary structural domains that are often found in mechanoproteins. CCs have mechanical rigidity and are often involved in force transmission between protein domains. Although crystal structures of CCs are available, information about their conformational flexibility is limited. The role of hydrophobic interactions in determining the CC conformation is not clear. In this work we examined the mechanical responses of typical CCs and constructed a coarse-grained mechanical model to describe the conformation of the protein. The model treats α-helices as elastic rods. Hydrophobic bonds arranged in a repeated pattern determine the CC structure. The model is compared with moleculardynamics simulations of CCs under force. We also estimate the effective bending and twisting persistence length of the CC. The model allows us to examine unconventional responses of the CC, including significant conformational amplification upon binding of a small molecule. We find that the CC does not behave as a simple elastic rod and shows complex nonlinear responses. These results are significant for understanding the role of CC structures in chemoreceptors, motor proteins, and mechanotransduction in general. © 2010 by the Biophysical Society.
- Charon, N. W., Goldstein, S. F., Marko, M., Hsieh, C., Gebhardt, L. L., Motaleb, M. A., Wolgemuth, C. W., Limberger, R. J., & Rowe, N. (2009). The flat-ribbon configuration of the periplasmic flagella of Borrelia burgdorferi and its relationship to motility and morphology. Journal of Bacteriology, 191(2), 600-607.More infoPMID: 19011030;PMCID: PMC2620816;Abstract: Electron cryotomography was used to analyze the structure of the Lyme disease spirochete, Borrelia burgdorferi. This methodology offers a new means for studying the native architecture of bacteria by eliminating the chemical fixing, dehydration, and staining steps of conventional electron microscopy. Using electron cryotomography, we noted that membrane blebs formed at the ends of the cells. These blebs may be precursors to vesicles that are released from cells grown in vivo and in vitro. We found that the periplasmic space of B. burgdorferi was quite narrow (16.0 nm) compared to those of Escherichia coli and Pseudomonas aeruginosa. However, in the vicinity of the periplasmic flagella, this space was considerably wider (42.3 nm). In contrast to previous results, the periplasmic flagella did not form a bundle but rather formed a tight-fitting ribbon that wraps around the protoplasmic cell cylinder in a right-handed sense. We show how the ribbon configuration of the assembled periplasmic flagella is more advantageous than a bundle for both swimming and forming the flat-wave morphology. Previous results indicate that B. burgdorferi motility is dependent on the rotation of the periplasmic flagella in generating backward-moving waves along the length of the cell. This swimming requires that the rotation of the flagella exerts force on the cell cylinder. Accordingly, a ribbon is more beneficial than a bundle, as this configuration allows each periplasmic flagellum to have direct contact with the cell cylinder in order to exert that force, and it minimizes interference between the rotating filaments. Copyright © 2009, American Society for Microbiology. All Rights Reserved.
- Dombrowski, C., Kan, W., Motaleb, M. A., Charon, N. W., Goldstein, R. E., & Wolgemuth, C. W. (2009). The elastic basis for the shape of Borrelia burgdorferi. Biophysical Journal, 96(11), 4409-4417.More infoPMID: 19486665;PMCID: PMC3325120;Abstract: The mechanisms that determine bacterial shape are in many ways poorly understood. A prime example is the Lyme disease spirochete, Borrelia burgdorferi (B. burgdorferi), which mechanically couples its motility organelles, helical flagella, to its rod-shaped cell body, producing a striking flat-wave morphology. A mathematical model is developed here that accounts for the elastic coupling of the flagella to the cell cylinder and shows that the flat-wave morphology is in fact a natural consequence of the geometrical and material properties of the components. Observations of purified periplasmic flagella show two flagellar conformations. The mathematical model suggests that the larger waveform flagellum is the more relevant for determining the shape of B. burgdorferi. Optical trapping experiments were used to measure directly the mechanical properties of these spirochetes. These results imply relative stiffnesses of the two components, which confirm the predictions of the model and show that the morphology of B. burgdorferi is completely determined by the elastic properties of the flagella and cell body. This approach is applicable to a variety of other structures in which the shape of the composite system is markedly different from that of the individual components, such as coiled-coil domains in proteins and the eukaryotic axoneme. © 2009 by the Biophysical Society.
- Dunham-Ems, S. M., Caimano, M. J., Pal, U., Wolgemuth, C. W., Eggers, C. H., Balic, A., & Radolf, J. D. (2009). Live imaging reveals a biphasic mode of dissemination of Borrelia burgdorferi within ticks. Journal of Clinical Investigation, 119(12), 3652-3665.More infoPMID: 19920352;PMCID: PMC2786795;Abstract: Lyme disease is caused by transmission of the spirochete Borrelia burgdorferi from ticks to humans. Although much is known about B. burgdorferi replication, the routes and mechanisms by which it disseminates within the tick remain unclear. To better understand this process, we imaged live, infectious B. burgdorferi expressing a stably integrated, constitutively expressed GFP reporter. Using isolated tick midguts and salivary glands, we observed B. burgdorferi progress through the feeding tick via what we believe to be a novel, biphasic mode of dissemination. In the first phase, replicating spirochetes, positioned at varying depths throughout the midgut at the onset of feeding, formed networks of nonmotile organisms that advanced toward the basolateral surface of the epithelium while adhering to differentiating, hypertrophying, and detaching epithelial cells. In the second phase of dissemination, the nonmotile spirochetes transitioned into motile organisms that penetrated the basement membrane and entered the hemocoel, then migrated to and entered the salivary glands. We designated the first phase of dissemination "adherence-mediated migration" and provided evidence that it involves the inhibition of spirochete motility by one or more diffusible factors elaborated by the feeding tick midgut. Our studies, which we believe are the first to relate the transmission dynamics of spirochetes to the complex morphological and developmental changes that the midgut and salivary glands undergo during engorgement, challenge the conventional viewpoint that dissemination of Lyme disease-causing spirochetes within ticks is exclusively motility driven.
- Fu, H. C., Wolgemuth, C. W., & Powers, T. R. (2009). Swimming speeds of filaments in nonlinearly viscoelastic fluids. Physics of Fluids, 21(3).More infoAbstract: Many micro-organisms swim through gels and non-Newtonian fluids in their natural environments. In this paper, we focus on micro-organisms which use flagella for propulsion. We address how swimming velocities are affected in nonlinearly viscoelastic fluids by examining the problem of an infinitely long cylinder with arbitrary beating motion in the Oldroyd-B fluid. We solve for the swimming velocity in the limit in which deflections of the cylinder from its straight configuration are small relative to the radius of the cylinder and the wavelength of the deflections; furthermore, the radius of the cylinder is small compared to the wavelength of deflections. We find that swimming velocities are diminished by nonlinear viscoelastic effects. We apply these results to examine what types of swimming motions can produce net translation in a nonlinear fluid, comparing to the Newtonian case, for which Purcell's "scallop" theorem describes how time-reversibility constrains which swimming motions are effective. We find that a leading order violation of the scallop theorem occurs for reciprocal motions in which the backward and forward strokes occur at different rates. © 2009 American Institute of Physics.
- Stajic, J., & Wolgemuth, C. W. (2009). Biochemical mechanisms for regulating protrusion by nematode major sperm protein. Biophysical Journal, 97(3), 748-757.More infoPMID: 19651033;PMCID: PMC2718177;Abstract: Crawling motion is ubiquitous in eukaryotic cells and contributes to important processes such as immune response and tumor growth. To crawl, a cell must adhere to the substrate, while protruding at the front and retracting at the rear. In most crawling cells protrusion is driven by highly regulated polymerization of the actin cytoskeleton, and much of the biochemical network for this process is known. Nematode sperm utilize a cytoskeleton composed of Major Sperm Protein (MSP), which is considered to form a simpler, yet similar, crawling motility apparatus. Key components involved in the polymerization of MSP have been identified; however, little is known about the chemical kinetics for this system. Here we develop a model for MSP polymerization that takes into account the effects of several of the experimentally identified cytosolic and membrane-bound proteins. To account for some of the data, the model requires force-dependent polymerization, as is predicted by Brownian ratchet mechanisms. Using the tethered polymerization ratchet model with our biochemical kinetic model for MSP polymerization, we find good agreement with experimental data on MSP-driven protrusion. In addition, our model predicts the force-velocity relation that is expected for in vitro protrusion assays. © 2009 by the Biophysical Society.
- Wolgemuth, C. W. (2009). Plant Biomechanics: Using Shape to Steal Motion. Current Biology, 19(10), R409-R410.More infoPMID: 19467208;Abstract: For grass species to spread efficiently through their environment requires seeds that can disperse over large distances and burrow into the ground. Recent work using awns from Hordeum murinum in conjunction with mathematical modelling shows that awn shape leverages environmental oscillations in order to produce these directional translations. © 2009 Elsevier Ltd. All rights reserved.
- Wolgemuth, C., Dombrowski, C., Kan, W., Motaleb, M. A., Charon, N. W., Goldstein, R. E., & Wolgemuth, C. W. (2009). The elastic basis for the shape of Borrelia burgdorferi. Biophysical journal, 96(11).More infoThe mechanisms that determine bacterial shape are in many ways poorly understood. A prime example is the Lyme disease spirochete, Borrelia burgdorferi (B. burgdorferi), which mechanically couples its motility organelles, helical flagella, to its rod-shaped cell body, producing a striking flat-wave morphology. A mathematical model is developed here that accounts for the elastic coupling of the flagella to the cell cylinder and shows that the flat-wave morphology is in fact a natural consequence of the geometrical and material properties of the components. Observations of purified periplasmic flagella show two flagellar conformations. The mathematical model suggests that the larger waveform flagellum is the more relevant for determining the shape of B. burgdorferi. Optical trapping experiments were used to measure directly the mechanical properties of these spirochetes. These results imply relative stiffnesses of the two components, which confirm the predictions of the model and show that the morphology of B. burgdorferi is completely determined by the elastic properties of the flagella and cell body. This approach is applicable to a variety of other structures in which the shape of the composite system is markedly different from that of the individual components, such as coiled-coil domains in proteins and the eukaryotic axoneme.
- Yang, J., Wolgemuth, C. W., & Huber, G. (2009). Kinematics of the swimming of spiroplasma. Physical Review Letters, 102(21).More infoPMID: 19519138;Abstract: Spiroplasma swimming is studied with a simple model based on resistive-force theory. Specifically, we consider a bacterium shaped in the form of a helix that propagates traveling-wave distortions which flip the handedness of the helical cell body. We treat cell length, pitch angle, kink velocity, and distance between kinks as parameters and calculate the swimming velocity that arises due to the distortions. We find that, for a fixed pitch angle, scaling collapses the swimming velocity (and the swimming efficiency) to a universal curve that depends only on the ratio of the distance between kinks to the cell length. Simultaneously optimizing the swimming efficiency with respect to interkink length and pitch angle, we find that the optimal pitch angle is 35.5° and the optimal interkink length ratio is 0.338, values in good agreement with experimental observations. © 2009 The American Physical Society.
- Chunhao, L. i., Wolgemuth, C. W., Marko, M., Morgan, D. G., & Charon, N. W. (2008). Genetic analysis of spirochete flagellin proteins and their involvement in motility, filament assembly, and flagellar morphology. Journal of Bacteriology, 190(16), 5607-5615.More infoPMID: 18556797;PMCID: PMC2519375;Abstract: The filaments of spirochete periplasmic flagella (PFs) have a unique structure and protein composition. In most spirochetes, the PFs consist of a core of at least three related proteins (FlaB1, FlaB2, and FlaB3) and a sheath of FlaA protein. The functions of these filament proteins remain unknown. In this study, we used a multidisciplinary approach to examine the role of these proteins in determining the composition, shape, and stiffness of the PFs and how these proteins impact motility by using the spirochete Brachyspira (formerly Treponema, Serpulina) hyodysenteriae as a genetic model. A series of double mutants lacking combinations of these PF proteins was constructed and analyzed. The results show the following. First, the diameters of PFs are primarily determined by the sheath protein FlaA, and that FlaA can form a sheath in the absence of an intact PF core. Although the sheath is important to the PF structure and motility, it is not essential. Second, the three core proteins play unequal roles in determining PF structure and swimming speed. The functions of the core proteins FlaB1 and FlaB2 overlap such that either one of these proteins is essential for the spirochete to maintain the intact PF structure and for cell motility. Finally, linear elasticity theory indicates that flagellar stiffness directly affects the spirochete's swimming speed. Copyright © 2008, American Society for Microbiology. All Rights Reserved.
- Fu, H. C., Wolgemuth, C. W., & Powers, T. R. (2008). Beating patterns of filaments in viscoelastic fluids. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 78(4).More infoPMID: 18999461;Abstract: Many swimming microorganisms, such as bacteria and sperm, use flexible flagella to move through viscoelastic media in their natural environments. In this paper we address the effects a viscoelastic fluid has on the motion and beating patterns of elastic filaments. We treat both a passive filament which is actuated at one end and an active filament with bending forces arising from internal motors distributed along its length. We describe how viscoelasticity modifies the hydrodynamic forces exerted on the filaments, and how these modified forces affect the beating patterns. We show how high viscosity of purely viscous or viscoelastic solutions can lead to the experimentally observed beating patterns of sperm flagella, in which motion is concentrated at the distal end of the flagella. © 2008 The American Physical Society.
- Wolgemuth, C. W. (2008). Collective swimming and the dynamics of bacterial turbulence. Biophysical Journal, 95(4), 1564-1574.More infoPMID: 18469071;PMCID: PMC2483759;Abstract: To swim, a bacterium pushes against the fluid within which it is immersed, generating fluid flow that dies off on a length scale comparable to the size of the bacterium. However, in dense colonies of bacteria, the bacteria are close enough that flow generated by swimming is substantial. For these cases, complex flows can arise due to the interaction and feedback between the bacteria and the fluid. Recent experiments on dense populations of swimming Bacillus subtilis have revealed a volume fraction-dependent transition from random swimming to transient jet and vortex patterns in the bacteria/fluid mixture. The fluid motions that are observed are reminiscent of flows that are observed around translating objects at moderate to high Reynolds numbers. In this work, I present a two-phase model for the bacterial/fluid mixture. The model explains turbulent flows in terms of the dipole stress that the bacteria exert on the fluid, entropic elasticity due to the rod shape of each bacterium, and the torque on the bacteria due to fluid gradients. Solving the equations in two dimensions using realistic parameters, the model reproduces empirically observed velocity fields. Dimensional analysis provides scaling relations for the dependence of the characteristic scales on the model parameters. © 2008 by the Biophysical Society.
- Wolgemuth, C. W., & Sun, S. X. (2008). Erratum: Elasticity of α-Helical coiled coils (Physical Review Letters (2006) 97 (248101)). Physical Review Letters, 100(16).
- Wolgemuth, C., Goldstein, S. F., & Charon, N. W. (2008). Electron cryotomography reveals novel structures of a recently cultured termite gut spirochete. Molecular Microbiology, 67(6), 1181-1183.More infoPMID: 18221263;Abstract: Electron cryotromography, a relatively new methodology in the field of microbiology, has been exploited by Murphy et al. (in this issue of Molecular Microbiology) in their analysis of the recently isolated termite gut spirochete Treponema primitia. Unique structures (bowls, arcades of hooks, cones at the cell ends, two layers of wall material) were evident from the analysis of its surface and internal constituents. These results, coupled to video microscopy analysis of swimming cells, allowed the authors to propose a model of cell motility. This highly significant paper highlights the importance of electron cryotomography to the field of microbiology. It also illustrates that newly cultured recalcitrant bacteria from complex environments are likely to possess novel structures not previously seen in other species. © 2008 The Authors.
- Zajac, M., Dacanay, B., Mohler, W. A., & Wolgemuth, C. W. (2008). Depolymerization-driven flow in nematode spermatozoa relates crawling speed to size and shape. Biophysical Journal, 94(10), 3810-3823.More infoPMID: 18227129;PMCID: PMC2367178;Abstract: Cell crawling is an inherently physical process that includes protrusion of the leading edge, adhesion to the substrate, and advance of the trailing cell body. Research into advance of the cell body has focused on actomyosin contraction, with cytoskeletal disassembly regarded as incidental, rather than causative; however, extracts from nematode spermatozoa, which use Major Sperm Protein rather than actin, provide at least one example where cytoskeletal disassembly apparently generates force in the absence of molecular motors. To test whether depolymerization can explain force production during nematode sperm crawling, we constructed a mathematical model that simultaneously describes the dynamics of both the cytoskeleton and the cytosol. We also performed corresponding experiments using motile Caenorhabditis elegans spermatozoa. Our experiments reveal that crawling speed is an increasing function of both cell size and anterior-posterior elongation. The quantitative,depolymerization-driven model robustly predicts that cell speed should increase with cell size and yields a cytoskeletal disassembly rate that is consistent with previous measurements. Notably, the model requires anisotropic elasticity, with the cell being stiffer along the direction of motion, to accurately reproduce the dependence of speed on elongation. Our simulations also predict that speed should increase with cytoskeletal anisotropy and disassembly rate. © 2008 by the Biophysical Society.
- Fu, H. C., Powers, T. R., & Wolgemuth, C. W. (2007). Theory of swimming filaments in viscoelastic media. Physical Review Letters, 99(25).More infoPMID: 18233558;Abstract: Motivated by our desire to understand the biophysical mechanisms underlying the swimming of sperm in the non-Newtonian fluids of the female mammalian reproductive tract, we examine the swimming of filaments in the nonlinear viscoelastic upper convected Maxwell model. We obtain the swimming velocity and hydrodynamic force exerted on an infinitely long cylinder with prescribed beating pattern. We use these results to examine the swimming of a simplified sliding-filament model for a sperm flagellum. Viscoelasticity tends to decrease swimming speed, and changes in the beating patterns due to viscoelasticity can reverse swimming direction. © 2007 The American Physical Society.
- Kan, W., & Wolgemuth, C. W. (2007). The shape and dynamics of the Leptospiraceae. Biophysical Journal, 93(1), 54-61.More infoPMID: 17434949;PMCID: PMC1914434;Abstract: Most swimming bacteria produce thrust by rotating helical filaments called flagella. Typically, the flagella stick out into the external fluid environment; however, in the spirochetes, a unique group that includes some highly pathogenic species of bacteria, the flagella are internalized, being incased in the periplasmic space; i.e., between the outer membrane and the cell wall. This coupling between the periplasmic flagella and the cell wall allows the flagella to serve a skeletal, as well as a motile, function. In this article, we propose a mathematical model for spirochete morphology based on the elastic interaction between the cell body and the periplasmic flagella. This model describes the mechanics of the composite structure of the cell cylinder and periplasmic flagella and accounts for the morphology of Leptospiraceae. This model predicts that the cell cylinder should be roughly seven times stiffer than the flagellum. In addition, we explore how rotation of the periplasmic flagellum deforms the cell cylinder during motility. We show that the transition between hook-shaped and spiral-shaped ends is purely a consequence of the change in direction of the flagellar motor and does not require flagellar polymorphism. © 2007 by the Biophysical Society.
- Lan, G., Wolgemuth, C. W., & Sun, S. X. (2007). Z-ring force and cell shape during division in rod-like bacteria. Proceedings of the National Academy of Sciences of the United States of America, 104(41), 16110-16115.More infoPMID: 17913889;PMCID: PMC2042170;Abstract: The life cycle of bacterial cells consists of repeated elongation, septum formation, and division. Before septum formation, a division ring called the Z-ring, which is made of a filamentous tubulin analog, FtsZ, is seen at the mid cell. Together with several other proteins, FtsZ is essential for cell division. Visualization of strains with GFP-labeled FtsZ shows that the Z-ring contracts before septum formation and pinches the cell into two equal halves. Thus, the Z-ring has been postulated to act as a force generator, although the magnitude of the contraction force is unknown. In this article, we develop a mathematical model to describe the process of growth and Z-ring contraction in rod-like bacteria. The elasticity and growth of the cell wall is incorporated in the model to predict the contraction speed, the cell shape, and the contraction force. With reasonable parameters, the model shows that a small force from the Z-ring (8 pN in Escherichia coli) is sufficient to accomplish division. © 2007 by The National Academy of Sciences of the USA.
- Dacanay, B., & Wolgemuth, C. (2006). pH and the crawling of nematode sperm. Bioengineering, Proceedings of the Northeast Conference, 2006, 71-72.More infoAbstract: Tissue formation, wound healing, immune surveillance and most importantly, inhibition of cancer and tumor metastasis is of prime interest. In order to study translocation within these intriguing cells, we focus on cellular crawling motility in sperm from the nematode Caenorhabditis elegans, which is similar to the crawling motility of many other eukaryotic cells. C. elegans spermatozoa utilize a cytoskeleton composed of Major Sperm Protein (MSP) to produce the force necessary for cellular movement. A complete understanding of the mechanics of this process and how it is regulated is still lacking. In the sperm from Ascaris suum, another nematode, internal pH has been suggested as a regulator of motility. The focus of this study is to determine the role of pH in regulating motility in C. elegans sperm and to determine how the cell maintains its internal pH. Using ratiometric imaging we show that C. elegans sperm maintain a substantial pH gradient between the front and back of the cell. A mathematical model suggests how the cell maintains this gradient. © 2006 IEEE.
- Wolgemuth, C. W. (2006). Erratum: Lamellipodial contractions during crawling and spreading (Biophysical Journal (2005) 89, (1643-1649)). Biophysical Journal, 90(2), 708-.
- Wolgemuth, C. W., & Sun, S. X. (2006). Elasticity of α-helical coiled coils. Physical Review Letters, 97(24).More infoPMID: 17280328;Abstract: Predicting large scale conformations of protein structures is computationally demanding. Here we compute the conformation and elasticity of double-stranded coiled coils using a simple coarse-grained elastic model. By maximizing the contact between hydrophobic residues and minimizing the elastic energy, we show that the minimum energy structure of a coiled coil is a supercoiled double helix of α helices. For realistic binding energies, the elastic energy of the α helices requires binding every 7th residue, which leads to a pitch and helix angle for the structure that is consistent with experimental measurements. Analysis of the model equations shows how the pitch varies with the helical repeat of the hydrophobic residues and with the ratio of the twisting modulus to the bending modulus and provides an estimate of the persistence length of around 150 nm, in agreement with previous experimental estimates. © 2006 The American Physical Society.
- Wolgemuth, C. W., Charon, N. W., Goldstein, S. F., & Goldstein, R. E. (2006). The flagellar cytoskeleton of the spirochetes. Journal of Molecular Microbiology and Biotechnology, 11(3-5), 221-227.More infoPMID: 16983197;Abstract: The recent discoveries of prokaryotic homologs of all three major eukaryotic cytoskeletal proteins (actin, tubulin, intermediate filaments) have spurred a resurgence of activity in the field of bacterial morphology. In spirochetes, however, it has long been known that the flagellar filaments act as a cytoskeletal protein structure, contributing to their shape and conferring motility on this unique phylum of bacteria. Therefore, revisiting the spirochete cytoskeleton may lead to new paradigms for exploring general features of prokaryotic morphology. This review discusses the role that the periplasmic flagella in spirochetes play in maintaining shape and producing motility. We focus on four species of spirochetes: Borrelia burgdorferi, Treponema denticola, Treponema phagedenis and Leptonema (formerly Leptospira) illini. In spirochetes, the flagella reside in the periplasmic space. Rotation of the flagella in the above species by a flagellar motor induces changes in the cell morphology that drives motility. Mutants that do not produce flagella have a markedly different shape than wild-type cells. Copyright © 2006 S. Karger AG.
- Cogan, N. G., & Wolgemuth, C. W. (2005). Pattern formation by bacteria-driven flow. Biophysical Journal, 88(4), 2525-2529.More infoPMID: 15681651;PMCID: PMC1305349;Abstract: Some marine bacterial species form mucosal layers, called veils, on sulfidic marine sediment. The bacteria attached to this veil actively swim and exert force on the surrounding fluid. The bacteria can break free of the veil and swim, chemotacting back to the veil. Over time the veil forms holes arranged in a hexagonal pattern. Motivated by this system, we present a simplified model to describe pattern formation induced by force-generating bodies embedded in a layer surrounded by fluid. When the bacteria break free of the layer, they are advected by the flow and diffuse. Competition between the fluid flow generated by the embedded bacteria and diffusion of the swimmers leads to a novel instability that drives bacterial aggregation. Analytic and numeric analysis of this system correctly defines the length scale and developmental timescale for the biological system. Similar flow dynamics may also play a role in other biological systems such as encrusting bryozoan colonies. © 2005 by the Biophysical Society.
- Tuval, I., Cisneros, L., Dombrowski, C., Wolgemuth, C. W., Kessler, J. O., & Goldstein, R. E. (2005). Bacterial swimming and oxygen transport near contact lines. Proceedings of the National Academy of Sciences of the United States of America, 102(7), 2277-2282.More infoPMID: 15699341;PMCID: PMC548973;Abstract: Aerobic bacteria often live in thin fluid layers near solid-air-water contact lines, in which the biology of chemotaxis, metabolism, and cell-cell signaling is intimately connected to the physics of buoyancy, diffusion, and mixing. Using the geometry of a sessile drop, we demonstrate in suspensions of Bacillus subtilis the self-organized generation of a persistent hydrodynamic vortex that traps cells near the contact line. Arising from upward oxygentaxis and downward gravitational forcing, these dynamics are related to the Boycott effect in sedimentation and are explained quantitatively by a mathematical model consisting of oxygen diffusion and consumption, chemotaxis, and viscous fluid dynamics. The vortex is shown to advectively enhance uptake of oxygen into the suspension, and the wedge geometry leads to a singularity in the chemotactic dynamics near the contact line.
- Wolgemuth, C. W. (2005). Force and flexibility of flailing myxobacteria. Biophysical Journal, 89(2), 945-950.More infoPMID: 15908584;PMCID: PMC1366643;Abstract: Myxococcus xanthus is a common Gram-negative bacterium that moves by a process called gliding motility. In myxobacteria, two distinct mechanisms for gliding have been discovered. S-type motility requires the extension, attachment, and retraction of type IV pili. The other mechanism, designated as A-type motility, may be driven by the secretion and swelling of slime; however, experiments to confirm or refute this model are still lacking and the force exerted by this mechanism has not been measured. A previously published experiment found that when an M. xanthus cell became stuck at one end, the cell underwent flailing motions. Based on this experiment, I propose an elastic model that can estimate the force produced by the A-motility engine and the bending modulus of a single myxobacterial cell. The model estimates a bending modulus of 3 × 10-14 erg cm and a force between 50-150 pN. This force is comparable to that predicted by slime extrusion, and the bending modulus is 30-fold smaller than that measured in Bacillus subtilis. This model suggests experiments that can further quantify this process. © 2005 by the Biophysical Society.
- Wolgemuth, C. W. (2005). Lamellipodial contractions during crawling and spreading. Biophysical Journal, 89(3), 1643-1649.More infoPMID: 16006627;PMCID: PMC1366668;Abstract: Most eukaryotic cells can crawl over surfaces. In general, this motility requires three distinct actions: polymerization at the leading edge, adhesion to the substrate, and retraction at the rear. Recent experiments with mouse embryonic fibroblasts showed that during spreading and crawling the lamellipodium undergoes periodic contractions that are substrate-dependent. Here I show that a simple model incorporating stick-slip adhesion and a simplified mechanism for the generation of contractile forces is sufficient to explain periodic lamellipodial contractions. This model also explains why treatment of cells with latrunculin modifies the period of these contractions. In addition, by coupling a diffusing chemical species that can bind actin, such as myosin light-chain kinase, with the contractile model leads to periodic rows and waves in the chemical species, similar to what is observed in experiments. This model provides a novel and simple explanation for the generation of contractile waves during cell spreading and crawling that is only dependent on stick-slip adhesion and the generation of contractile force and suggests new experiments to test this mechanism. © 2005 by the Biophysical Society.
- Wolgemuth, C. W. (2005). MSP dynamics and retraction in nematode sperm. AIP Conference Proceedings, 755, 145-152.More infoAbstract: Most eukaryotic cells can crawl over surfaces. In general, this motility requires three distinct actions: polymerization at the leading edge, adhesion to the substrate, and retraction at the rear. Recent in vitro experiments with extracts from spermatozoa from the nematode Ascaris suum suggest that retraction forces are generated by depolymerization of the Major Sperm Protein (MSP) cytoskeleton. Combining polymer entropy with a simple kinetic model for disassembly I propose a model for disassembly-induced retraction that fit the in vitro experimental data. This model explains the mechanism by which deconstruction of the cytoskeleton produces the force necessary to pull the cell body forward and suggest further experiments that can test the validity of the model. © 2005 American Institute of Physics .
- Wolgemuth, C. W., & Charon, N. W. (2005). The kinky propulsion of Spiroplasma. Cell, 122(6), 827-828.More infoPMID: 16179250;Abstract: Bacteria have evolved many different means of generating movement. In this issue of Cell, Shaevitz et al. (2005) describe the swimming movement of a helical bacterium called Spiroplasma. They discover that Spiroplasma propels itself by generating two temporally distinct kinks that travel the length of the bacterium. These results point to the existence of a contractile apparatus that drives cell movement.
- Wolgemuth, C. W., Inclan, Y. F., Quan, J., Mukherjee, S., Oster, G., & Koehl, M. A. (2005). How to make a spiral bacterium. Physical Biology, 2(3), 189-199.More infoPMID: 16224124;Abstract: The motility of some kinds of bacteria depends on their spiral form, as does the virulence of certain pathogenic species. We propose a novel mechanism for the development of spiral shape in bacteria and the supercoiling of chains ('filaments') of many cells. Recently discovered actin-like proteins lying just under the cell wall form fibers that play a role in maintaining cell shape. Some species have a single actin-like fiber helically wrapped around the cell, while others have two fibers wrapped in the same direction. Here, we show that if these fibers elongate more slowly than growth lengthens the cell, the cell both twists and bends, taking on a spiral shape. We tested this mechanism using a mathematical model of expanding fiber-wound structures and via experiments that measure the shape changes of elongating physical models. Comparison of the model with in vivo experiments on stationary phase Caulobacter crescentus filaments provide the first evidence that mechanical stretching of cytoskeletal fibers influences cell morphology. Any hydraulic cylinder can spiral by this mechanism if it is reinforced by stretch-resistant fibers wrapped helically in the same direction, or shortened by contractile elements. This might be useful in the design of man-made actuators. © 2005 IOP Publishing Ltd.
- Wolgemuth, C. W., Miao, L., Vanderlinde, O., Roberts, T., & Oster, G. (2005). MSP dynamics drives nematode sperm locomotion. Biophysical Journal, 88(4), 2462-2471.More infoPMID: 15665134;PMCID: PMC1305345;Abstract: Most eukaryotic cells can crawl over surfaces. In general, this motility requires three sequential actions: polymerization at the leading edge, adhesion to the substrate, and retraction at the rear. Recent in vitro experiments with extracts from spermatozoa from the nematode Ascaris suum suggest that retraction forces are generated by depolymerization of the major sperm protein cytoskeleton. Combining polymer entropy with a simple kinetic model for disassembly we propose a model for disassembly-induced retraction that fits the in vitro experimental data. This model explains the mechanism by which disassembly of the cytoskeleton generates the force necessary to pull the cell body forward and suggests further experiments that can test the validity of the models. © 2005 by the Biophysical Society.
- Basu, S., Wolgemuth, C. W., & Campagnola, P. J. (2004). Measurement of normal and anomalous diffusion of dyes within protein structures fabricated via multiphoton excited cross-linking. Biomacromolecules, 5(6), 2347-2357.More infoPMID: 15530051;Abstract: We demonstrate microscale spatial and chemical control of diffusion within protein matrixes created through the use of nonlinear multiphoton excited photochemistry. The mobility of fluorescent dyes of different mass and composition within controlled cross-linked environments has been measured using two-photon excited fluorescence recovery after photobleaching (FRAP). The diffusion times for several rhodamine and sulforhodamine dyes within these fabricated structures were found to be approximately 3-4 orders of magnitude slower than in free solution. The precise diffusion times can be tuned by varying the laser exposure during the fabrication of the matrix, and the diffusion can be correlated with the mesh size determined by TEM and Flory-Rehner analysis. We find that the hydrophobic Texas Red dyes (sulforhodamines) exhibit diffusion that is highly anomalous, indicative of a strong interaction with the hydrophobic cross-linked protein matrix. These results suggests the use of these cross-linked protein matrixes as ideal model systems in which to systematically study anomalous diffusion. Finally, the diffusion can be tuned within a multilayered protein matrix, and this in conjunction with slow diffusion also suggests the use of these structures in controlled release applications. © 2004 American Chemical Society.
- Wolgemuth, C. W., & Oster, G. (2004). The junctional pore complex and the propulsion of bacterial cells. Journal of Molecular Microbiology and Biotechnology, 7(1-2), 72-77.More infoPMID: 15170405;Abstract: Gliding motility is defined as translocation in the direction of the long axis of the bacterium while in contact with a surface. This definition leaves unspecified any mechanism and, indeed, it appears that there is more than one physiological system underlying the same type of motion. Currently, two distinct mechanisms have been discovered in myxobacteria. One requires the extension, attachment, and retraction of type IV pili to pull the cell forwards. Recent experimental evidence suggests that a second mechanism for gliding motility involves the extrusion of slime from an organelle called the 'junctional pore complex'. This review discusses the role of slime extrusion and the junctional pore complex in the gliding motility of both cyanobacteria and myxobacteria. Copyright © 2004 S. Karger AG, Basel.
- Wolgemuth, C. W., Goldstein, R. E., & Powers, T. R. (2004). Dynamic supercoiling bifurcations of growing elastic filaments. Physica D: Nonlinear Phenomena, 190(3-4), 266-289.More infoAbstract: Certain bacteria form filamentous colonies when the cells fail to separate after dividing. In Bacillus subtilis, Bacillus thermus, and Cyanobacteria, the filaments can wrap into complex supercoiled structures as the cells grow. The structures may be solenoids or plectonemes, with or without branches in the latter case. Any microscopic theory of these morphological instabilities must address the nature of pattern selection in the presence of growth, for growth renders the problem nonautonomous and the bifurcations dynamic. To gain insight into these phenomena, we formulate a general theory for growing elastic filaments with bending and twisting resistance in a viscous medium, and study an illustrative model problem: a growing filament with preferred twist, closed into a loop. Growth depletes the twist, inducing a twist strain. The closure of the loop prevents the filament from unwinding back to the preferred twist; instead, twist relaxation is accomplished by the formation of supercoils. Growth also produces viscous stresses on the filament which even in the absence of twist produce buckling instabilities. Our linear stability analysis and numerical studies reveal two dynamic regimes. For small intrinsic twist the instability is akin to Euler buckling, leading to solenoidal structures, while for large twist it is like the classic writhing of a twisted filament, producing plectonemic windings. This model may apply to situations in which supercoils form only, or more readily, when axial rotation of filaments is blocked. Applications to specific biological systems are proposed. © 2003 Elsevier B.V. All rights reserved.
- Wolgemuth, C. W., Mogilner, A., & Oster, G. (2004). The hydration dynamics of polyelectrolyte gels with applications to cell motility and drug delivery. European Biophysics Journal, 33(2), 146-158.More infoPMID: 14574521;Abstract: We combine the physics of gels with the hydrodynamics of two-phase fluids to construct a set of equations that describe the hydration dynamics of polyelectrolyte gels. We use the model to address three problems. First, we express the effective diffusion constants for neutral and charged spherically distributed gels in terms of microscopic parameters. Second, we use the model to describe the locomotion of nematode sperm cells. Finally, we describe the swelling dynamics of polyelectrolyte gels used for drug release.
- Wolgemuth, C. W., Igoshin, O., & Oster, G. (2003). The motility of mollicutes. Biophysical Journal, 85(2), 828-842.More infoPMID: 12885631;PMCID: PMC1303205;Abstract: Recent experiments show that the conformation of filament proteins play a role in the motility and morphology of many different types of bacteria. Conformational changes in the protein subunits may produce forces to drive propulsion and cell division. Here we present a molecular mechanism by which these forces can drive cell motion. Coupling of a biochemical cycle, such as ATP hydrolysis, to the dynamics of elastic filaments enable elastic filaments to propagate deformations that generate propulsive forces. We demonstrate this possibility for two classes of wall-less bacteria called mollicutes: the swimming of helical-shaped Spiroplasma, and the gliding motility of Mycoplasma.
- Wolgemuth, C., Hoiczyk, E., Kaiser, D., & Oster, G. (2002). How myxobacteria glide. Current Biology, 12(5), 369-377.More infoPMID: 11882287;Abstract: Background: Many microorganisms, including myxobacteria, cyanobacteria, and flexibacteria, move by gliding. Although gliding always describes a slow surface-associated translocation in the direction of the cell's long axis, it can result from two very different propulsion mechanisms: social (S) motility and adventurous (A) motility. The force for S motility is generated by retraction of type 4 pili. A motility may be associated with the extrusion of slime, but evidence has been lacking, and how force might be generated has remained an enigma. Recently, nozzle-like structures were discovered in cyanobacteria from which slime emanated at the same rate at which the bacteria moved. This strongly implicates slime extrusion as a propulsion mechanism for gliding. Results: Here we show that similar but smaller nozzle-like structures are found in Myxococcus xanthus and that they are clustered at both cell poles, where one might expect propulsive organelles. Furthermore, light and electron microscopical observations show that slime is secreted in ribbons from the ends of cells. To test whether the slime propulsion hypothesis is physically reasonable, we construct a mathematical model of the slime nozzle to see if it can generate a force sufficient to propel M. xanthus at the observed velocities. The model assumes that the hydration of slime, a cationic polyelectrolyte, is the force-generating mechanism. Conclusions: The discovery of nozzle-like organelles in various gliding bacteria suggests their role in prokaryotic gliding. Our calculations and our observations of slime trails demonstrate that slime extrusion from such nozzles can account for most of the observed properties of A motile gliding.
- Goldstein, R. E., Goriely, A., Huber, G., & Wolgemuth, C. W. (2000). Bistable Helices. Physical Review Letters, 84(7), 1631-1634.More infoPMID: 11017585;Abstract: We extend elasticity theory of filaments to encompass systems, such as bacterial flagella, that display competition between two helical structures of opposite chirality. A general, fully intrinsic formulation of the dynamics of bend and twist degrees of freedom is developed using the natural frame of space curves, spanning from the inviscid limit to the viscously overdamped regime applicable to cellular biology. Aspects of front propagation found in flagella are discussed.
- Mendelson, N. H., Sarlls, J. E., Wolgemuth, C. W., & Goldstein, R. E. (2000). Chiral Self-Propulsion of Growing Bacterial Macrofibers on a Solid Surface. Physical Review Letters, 84(7), 1627-1630.More infoPMID: 11017584;Abstract: Supercoiling motions that accompany the growth of bacterial macrofibers (multicellular filamentous structures formed in B. subtilis by cell division without separation) are responsible for rolling, pivoting, and walking of fibers on a surface. Fibers possess a fulcrum about which they pivot and step in a chiral manner; forces and torques associated with cell growth, when blocked by friction, result in self-propulsion. The elastic engine that drives macrofiber motions generates torques estimated as μdyncm and femtowatts of power; optical trapping studies yield a first direct measurement of the Young's modulus of the bacterial cell wall, the engine's "working fluid," of ca. 0.05 GPa.
- Wolgemuth, C. W., Powers, T. R., & Goldstein, R. E. (2000). Twirling and Whirling: Viscous Dynamics of Rotating Elastic Filaments. Physical Review Letters, 84(7), 1623-1626.More infoPMID: 11017583;Abstract: Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist and bend elasticity. Competition between twist injection, twist diffusion, and writhing instabilities is described by coupled PDEs for twist and bend evolution. Analytical and numerical methods elucidate the twist/bend coupling and reveal two regimes separated by a Hopf bifurcation: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling. The consequences of these phenomena for self-propulsion are investigated, and experimental tests proposed.
- Wolgemuth, C. W. (2014, August). The motility of Borrelia burgdorferi. SIAM Conference on the Life Sciences 2014. Charlotte, NC.
- Wolgemuth, C. W. (2014, August). The physics of collective cell migration in wound healing and cancer metastasis. SIAM Conference on the Life Sciences 2014. Charlotte, NC.
- Wolgemuth, C. W. (2014, March). What bacterial biomechanics can tell us about early Lyme disease. Ninth Annual Frontiers in Immunobiology and Immunpathogenesis Symposium. Tucson, AZ.
- Wolgemuth, C. W. (2014, September). Is Physics relevant for your health?. Tucson Area Physics Teachers Meeting. Tucson, AZ.