Elasticity and Biochemistry of Growth Relate Replication Rate to Cell Length and Cross-link Density in Rod-Shaped Bacteria

AbstractIn 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

Kinematics of the swimming of Spiroplasma

\emph{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 inter-kink length and pitch angle, we find that the optimal pitch angle is 35.5$^\circ$ and the optimal inter-kink length ratio is 0.338, values in good agreement with experimental observations.Comment: 4 pages, 5 figure

Beating patterns of filaments in viscoelastic fluids

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

Twirling and Whirling: Viscous Dynamics of Rotating Elastica

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 a novel pair of coupled PDEs for twist and bend evolution. Analytical and numerical methods elucidate the twist/bend coupling and reveal two dynamical 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.Comment: To be published in Physical Review Letter

MSP dynamics and retraction in nematode sperm

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 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

A general computational framework for the dynamics of single- and multi-phase vesicles and membranes

The dynamics of thin, membrane-like structures are ubiquitous in nature. They play especially important roles in cell biology. Cell membranes separate the inside of a cell from the outside, and vesicles compartmentalize proteins into functional microregions, such as the lysosome. Proteins and/or lipid molecules also aggregate and deform membranes to carry out cellular functions. For example, some viral particles can induce the membrane to invaginate and form an endocytic vesicle that pulls the virus into the cell. While the physics of membranes has been extensively studied since the pioneering work of Helfrich in the 1970's, simulating the dynamics of large scale deformations remains challenging, especially for cases where the membrane composition is spatially heterogeneous. Here, we develop a general computational framework to simulate the overdamped dynamics of membranes and vesicles. We start by considering a membrane with an energy that is a generalized functional of the shape invariants and also includes line discontinuities that arise due to phase boundaries. Using this energy, we derive the internal restoring forces and construct a level set-based algorithm that can stably simulate the large-scale dynamics of these generalized membranes, including scenarios that lead to membrane fission. This method is applied to solve for shapes of single-phase vesicles using a range of reduced volumes, reduced area differences, and preferred curvatures. Our results match well the experimentally measured shapes of corresponding vesicles. The method is then applied to explore the dynamics of multiphase vesicles, predicting equilibrium shapes and conditions that lead to fission near phase boundaries.24 month embargo; available online: 8 November 2021This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Crawling Cells Can Close Wounds without Purse Strings or Signaling

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\u27s 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

A finite volume algorithm for the dynamics of filaments, rods, and beams

Filaments, rods, and beams are ubiquitous in biology and in many man-made products and structures. While a substantial amount of research has been done to understand the statics and dynamics of these long, thin objects, there remain many unanswered and unstudied problems related to the dynamics of bending and twisting filamentary objects. Simulating the general dynamics of these structures in 3D remains challenging. For example, the net force and torque on a free filament immersed in fluid at low Reynolds number must be zero. However, standard finite difference approaches will often fail to preserve the zero force and torque conditions. These numerical artifacts cause spurious rotations and translations that prohibit, or at least limit, their accuracy in simulating the dynamics of filaments, rods, and beams in these contexts (such as the free-swimming motion of a filamentary microorganism). Here we develop a finite volume discretization based on the Kirchoff equations that naturally guarantees the correct total integral of the forces and torques on filaments, rods, or beams. We then couple this discretization to resistive force theory to develop a stable, accurate dynamic algorithm of filament motion at low Reynolds number. We use a range of sample problems to highlight the utility, stability, and accuracy of this method. While our sample problems focus on low Reynolds number dynamics in the context of resistive force theory (RFT), our discretized finite volume algorithm is general and can be applied to inertial dynamics, immersed boundary methods, and boundary integral methods, as well.National Institutes of Health24 month embargo; available online: 10 June 2022This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]