Branching, Capping, and Severing in Dynamic Actin Structures

Branched actin networks at the leading edge of a crawling cell evolve via protein-regulated processes such as polymerization, depolymerization, capping, branching, and severing. A formulation of these processes is presented and analyzed to study steady-state network morphology. In bulk, we identify several scaling regimes in severing and branching protein concentrations and find that the coupling between severing and branching is optimally exploited for conditions {\it in vivo}. Near the leading edge, we find qualitative agreement with the {\it in vivo} morphology.Comment: 4 pages, 2 figure

Symmetry-Breaking Motility

Locomotion of bacteria by actin polymerization, and in vitro motion of spherical beads coated with a protein catalyzing polymerization, are examples of active motility. Starting from a simple model of forces locally normal to the surface of a bead, we construct a phenomenological equation for its motion. The singularities at a continuous transition between moving and stationary beads are shown to be related to the symmetries of its shape. Universal features of the phase behavior are calculated analytically and confirmed by simulations. Fluctuations in velocity are shown to be generically non-Maxwellian and correlated to the shape of the bead.Comment: 4 pages, 2 figures, REVTeX; formatting of references correcte

Soft Listeria: actin-based propulsion of liquid drops

We study the motion of oil drops propelled by actin polymerization in cell extracts. Drops deform and acquire a pear-like shape under the action of the elastic stresses exerted by the actin comet. We solve this free boundary problem and calculate the drop shape taking into account the elasticity of the actin gel and the variation of the polymerization velocity with normal stress. The pressure balance on the liquid drop imposes a zero propulsive force if gradients in surface tension or internal pressure are not taken into account. Quantitative parameters of actin polymerization are obtained by fitting theory to experiment.Comment: 5 pages, 4 figure

Dynamics of an inchworm nano-walker

An inchworm processive mechanism is proposed to explain the motion of dimeric molecular motors such as kinesin. We present here preliminary results for this mechanism focusing on observables like mean velocity, coupling ratio and efficiency versus ATP concentration and the external load F.Comment: 6 pages, 2 figure

Reverse engineering forces responsible for dynamic clustering and spreading of multiple nuclei in developing muscle cells

How cells position organelles is a fundamental biological question. During Drosophila embryonic muscle development, multiple nuclei transition from being clustered together, to splitting into two smaller clusters, to spreading along the myotube's length. Perturbations of microtubules and motor proteins disrupt this sequence of events. These perturbations do not allow intuiting which molecular forces govern the nuclear positioning; we therefore used computational screening to reverse engineer and identify these forces. The screen reveals three models: two suggest that the initial clustering is due to the nuclear repulsion from the cell poles, while the third, most robust, model poses that this clustering is due to a short-ranged internuclear attraction. All three models suggest that the nuclear spreading is due to the long-ranged internuclear repulsion. We test the robust model quantitatively by comparing it to data from perturbed muscle cells. We also test the model by using agent-based simulations with elastic dynamic microtubules and molecular motors. The model predicts that, in longer mammalian myotubes with a great number of nuclei, the spreading stage would be preceded with segregation of the nuclei into a large number of clusters, proportional to the myotube length, with a small average number of nuclei per cluster

The Force-Velocity Relation for Growing Biopolymers

The process of force generation by the growth of biopolymers is simulated via a Langevin-dynamics approach. The interaction forces are taken to have simple forms that favor the growth of straight fibers from solution. The force-velocity relation is obtained from the simulations for two versions of the monomer-monomer force field. It is found that the growth rate drops off more rapidly with applied force than expected from the simplest theories based on thermal motion of the obstacle. The discrepancies amount to a factor of three or more when the applied force exceeds 2.5kT/a, where a is the step size for the polymer growth. These results are explained on the basis of restricted diffusion of monomers near the fiber tip. It is also found that the mobility of the obstacle has little effect on the growth rate, over a broad range.Comment: Latex source, 9 postscript figures, uses psfig.st

Nuclear Scaling Is Coordinated among Individual Nuclei in Multinucleated Muscle Fibers

Optimal cell performance depends on cell size and the appropriate relative size, i.e., scaling, of the nucleus. How nuclear scaling is regulated and contributes to cell function is poorly understood, especially in skeletal muscle fibers, which are among the largest cells, containing hundreds of nuclei. Here, we present a Drosophila in vivo system to analyze nuclear scaling in whole multinucleated muscle fibers, genetically manipulate individual components, and assess muscle function. Despite precise global coordination, we find that individual nuclei within a myofiber establish different local scaling relationships by adjusting their size and synthetic activity in correlation with positional or spatial cues. While myonuclei exhibit compensatory potential, even minor changes in global nuclear size scaling correlate with reduced muscle function. Our study provides the first comprehensive approach to unraveling the intrinsic regulation of size in multinucleated muscle fibers. These insights to muscle cell biology will accelerate the development of interventions for muscle diseases

Anomalous dynamics of cell migration

Cell movement, for example during embryogenesis or tumor metastasis, is a complex dynamical process resulting from an intricate interplay of multiple components of the cellular migration machinery. At first sight, the paths of migrating cells resemble those of thermally driven Brownian particles. However, cell migration is an active biological process putting a characterization in terms of normal Brownian motion into question. By analyzing the trajectories of wildtype and mutated epithelial (MDCK-F) cells we show experimentally that anomalous dynamics characterizes cell migration. A superdiffusive increase of the mean squared displacement, non-Gaussian spatial probability distributions, and power-law decays of the velocity autocorrelations are the basis for this interpretation. Almost all results can be explained with a fractional Klein- Kramers equation allowing the quantitative classification of cell migration by a few parameters. Thereby it discloses the influence and relative importance of individual components of the cellular migration apparatus to the behavior of the cell as a whole.Comment: 20 pages, 3 figures, 1 tabl

Single cell mechanics: stress stiffening and kinematic hardening

Cell mechanical properties are fundamental to the organism but remain poorly understood. We report a comprehensive phenomenological framework for the nonlinear rheology of single fibroblast cells: a superposition of elastic stiffening and viscoplastic kinematic hardening. Our results show, that in spite of cell complexity its mechanical properties can be cast into simple, well-defined rules, which provide mechanical cell strength and robustness via control of crosslink slippage.Comment: 4 pages, 6 figure

Self-organization in systems of self-propelled particles

We investigate a discrete model consisting of self-propelled particles that obey simple interaction rules. We show that this model can self-organize and exhibit coherent localized solutions in one- and in two-dimensions.In one-dimension, the self-organized solution is a localized flock of finite extent in which the density abruptly drops to zero at the edges.In two-dimensions, we focus on the vortex solution in which the particles rotate around a common center and show that this solution can be obtained from random initial conditions, even in the absence of a confining boundary. Furthermore, we develop a continuum version of our discrete model and demonstrate that the agreement between the discrete and the continuum model is excellent.Comment: 4 pages, 5 figure