Thermodynamically consistent treatment of the growth of a biopolymer in the presence of a smooth obstacle interaction potential.

We investigate the effect of filament-obstacle interactions on the force-velocity relation of growing biopolymers, via calculations explicitly treating obstacle diffusion and stochastic addition and subtraction of subunits. We first show that the instantaneous subunit on- and off-rates satisfy a rigorous thermodynamic relationship determined by the filament-obstacle interaction potential, which has been violated by several calculations in the literature. The instantaneous rates depend not only on the average force on the obstacle but also on the shape of the potential on the nanometer length scale.

Pulling-force generation by ensembles of polymerizing actin filaments.

The process by which actin polymerization generates pulling forces in cellular processes such as endocytosis is less well understood than pushing-force generation. To clarify the basic mechanisms of pulling-force generation, we perform stochastic polymerization simulations for a square array of polymerizing semiflexible actin filaments, having different interactions with the membrane. The filaments near the array center have a strong attractive component.

A master equation approach to actin polymerization applied to endocytosis in yeast.

We present a Master Equation approach to calculating polymerization dynamics and force generation by branched actin networks at membranes. The method treats the time evolution of the F-actin distribution in three dimensions, with branching included as a directional spreading term. It is validated by comparison with stochastic simulations of force generation by actin polymerization at obstacles coated with actin "nucleation promoting factors" (NPFs).

Membrane bending by actin polymerization.

Actin polymerization provides driving force to aid several types of processes that involve pulling the plasma membrane into the cell, including phagocytosis, cellular entry of large viruses, and endocytosis. In endocytosis, actin polymerization is especially important under conditions of high membrane tension or high turgor pressure. Recent modeling efforts have shown how actin polymerization can give rise to a distribution of forces around the endocytic site, and explored how these forces affect the shape dynamics; experiments have revealed the structure of the endocytic machinery in increasing detail, and demonstrated key feedback interactions between actin assembly and membrane curvature.

Actin growth profile in clathrin-mediated endocytosis.

Clathrin-mediated endocytosis in yeast is driven by a protein patch containing close to 100 different types of proteins. Among the proteins are 5000-10000 copies of polymerized actin, and successful endocytosis requires growth of the actin network. Since it is not known exactly how actin network growth drives endocytosis, we calculate the spatial distribution of actin growth required to generate the force that drives the process.

Local Turgor Pressure Reduction via Channel Clustering.

The primary drivers of yeast endocytosis are actin polymerization and curvature-generating proteins, such as clathrin and BAR domain proteins. Previous work has indicated that these factors may not be capable of generating the forces necessary to overcome turgor pressure. Thus local reduction of the turgor pressure, via localized accumulation or activation of solute channels, might facilitate endocytosis.

Actin-Regulator Feedback Interactions during Endocytosis.

Endocytosis mediated by clathrin, a cellular process by which cells internalize membrane receptors and their extracellular ligands, is an important component of cell signaling regulation. Actin polymerization is involved in endocytosis in varying degrees depending on the cellular context. In yeast, clathrin-mediated endocytosis requires a pulse of polymerized actin and its regulators, which recruit and activate the Arp2/3 complex.

How capping protein enhances actin filament growth and nucleation on biomimetic beads.

Capping protein (CP), which caps the growing ends of actin filaments, accelerates actin-based motility. Recent experiments on biomimetic beads have shown that CP also enhances the rate of actin filament nucleation. Proposed explanations for these phenomena include (i) the actin funneling hypothesis (AFH), in which the presence of CP increases the free-actin concentration, and (ii) the monomer gating model, in which CP binding to actin filament barbed ends makes more monomers available for filament nucleation.

Load sharing in the growth of bundled biopolymers.

To elucidate the nature of load sharing in the growth of multiple biopolymers, we perform stochastic simulations of the growth of biopolymer bundles against obstacles under a broad range of conditions and varying assumptions. The obstacle motion due to thermal fluctuations is treated explicitly. We assume the "Perfect Brownian Ratchet" (PBR) model, in which the polymerization rate equals the free-filament rate as soon as the filament-obstacle distance exceeds the monomer size.

Feedback mechanisms in a mechanical model of cell polarization.

Directed cell migration requires a spatially polarized distribution of polymerized actin. We develop and treat a mechanical model of cell polarization based on polymerization and depolymerization of actin filaments at the two ends of a cell, modulated by forces at either end that are coupled by the cell membrane. We solve this model using both a simulation approach that treats filament nucleation, polymerization, and depolymerization stochastically, and a rate-equation approach based on key properties such as the number of filaments N and the number of polymerized subunits F at either end of the cell.

Modeling large-scale dynamic processes in the cell: polarization, waves, and division.

The past decade has witnessed significant developments in molecular biology techniques, fluorescent labeling, and super-resolution microscopy, and together these advances have vastly increased our quantitative understanding of the cell. This detailed knowledge has concomitantly opened the door for biophysical modeling on a cellular scale. There have been comprehensive models produced describing many processes such as motility, transport, gene regulation, and chemotaxis.

Force generation by endocytic actin patches in budding yeast.

Membrane deformation during endocytosis in yeast is driven by local, templated assembly of a sequence of proteins including polymerized actin and curvature-generating coat proteins such as clathrin. Actin polymerization is required for successful endocytosis, but it is not known by what mechanisms actin polymerization generates the required pulling forces. To address this issue, we develop a simulation method in which the actin network at the protein patch is modeled as an active gel.

Stress generation by myosin minifilaments in actin bundles.

Forces and stresses generated by the action of myosin minifilaments are analyzed in idealized computer-generated actin bundles, and compared to results for isotropic actin networks. The bundles are generated as random collections of actin filaments in two dimensions with constrained orientations, crosslinked and attached to two fixed walls. Myosin minifilaments are placed on actin filament pairs and allowed to move and deform the network so that it exerts forces on the walls.

Quantitative analysis of approaches to measure cooperative phosphate release in polymerized actin.

We use stochastic simulations that treat several experimental probes of actin dynamics to explore the extent to which phosphate dissociation in filamentous actin may be cooperative. Phosphate time-courses from polymerization and copolymerization experiments of ATP- and ADP-actin are studied, including the effects of variations in filament-number concentration as well as single-filament depolymerization time-courses. We find that highly cooperative models are consistent with the treated experimental data.

Molecular analysis of Arp2/3 complex activation in cells.

Many forms of cellular motility are driven by the growth of branched networks of actin filaments, which push against a membrane. In the dendritic nucleation model, Arp2/3 complex is critical, binding to the side of an existing mother filament, nucleating a new daughter filament, and thus creating a branch. Spatial and temporal regulation of Arp2/3 activity is critical for efficient generation of force and movement.

Regimes of wave type patterning driven by refractory actin feedback: transition from static polarization to dynamic wave behaviour.

Patterns of waves, patches, and peaks of actin are observed experimentally in many living cells. Models of this phenomenon have been based on the interplay between filamentous actin (F-actin) and its nucleation promoting factors (NPFs) that activate the Arp2/3 complex. Here we present an alternative biologically-motivated model for F-actin-NPF interaction based on properties of GTPases acting as NPFs.

Self-feedback in actin polymerization.

Polymerization of actin, which is crucial for functions such as cell migration, membrane ruffling, cytokinesis, and endocytosis, must be tightly regulated in order to preserve an adequate supply of free actin monomers to respond to changing external conditions. The paper will describe mechanisms by which F-actin feeds back on its own assembly, thus regulating itself. I will present the experimental evidence for such feedback terms, discuss their use in current models of actin dynamics in cells, and present preliminary calculations for the role of feedback in transient endocytic actin patches.

Damped and persistent oscillations in a simple model of cell crawling.

A very simple, one-dimensional, discrete, autonomous model of cell crawling is proposed; the model involves only three or four coupled first-order differential equations. This form is sufficient to describe many general features of cell migration, including both steady forward motion and oscillatory progress. Closed-form expressions for crawling speeds and internal forces are obtained in terms of dimensionless parameters that characterize active intracellular processes and the passive mechanical properties of the cell.

General mechanism of actomyosin contractility.

Stress generation by myosin minifilaments is analyzed via simulation of their motion in a random actin network. The stresses are overwhelmingly contractile because minifilament equilibrium positions having contractile stress have lower energy than those for expansive stress. Force chains lead to unexpectedly large stresses.

Mechanisms of Cell Propulsion by Active Stresses.

The mechanisms by which cytoskeletal flows and cell-substrate interactions interact to generate cell motion are explored using a simplified model of the cytoskeleton as a viscous gel containing active stresses. This model yields explicit general results relating cell speed and traction forces to the distributions of active stress and cell-substrate friction. It is found that 1) the cell velocity is given by a function that quantifies the asymmetry of the active-stress distribution, 2) gradients in cell-substrate friction can induce motion even when the active stresses are symmetrically distributed, 3) the traction-force dipole is enhanced by protrusive stresses near the cell edges or contractile stresses near the center of the cell, and 4) the cell velocity depends biphasically on the cell-substrate adhesion strength if active stress is enhanced by adhesion.

A model actin comet tail disassembling by severing.

We use a numerical simulation to model an actin comet tail as it grows from the surface of a small object (a bead) and disassembles by severing. We explore the dependence of macroscopic properties such as the local tail radius and tail length on several controllable properties, namely the bead diameter, the bead velocity, the severing rate per unit length, and the actin gel mesh size. The model predicts an F-actin density with an initial exponential decay followed by an abrupt decay at the edge of the tail, and predicts that the comet tail diameter is constant along the length of the tail.

Dendritic actin filament nucleation causes traveling waves and patches.

The polymerization of actin via branching at a cell membrane containing nucleation-promoting factors is simulated using a stochastic-growth methodology. The polymerized-actin distribution displays three types of behavior: (a) traveling waves, (b) moving patches, and (c) random fluctuations. Increasing actin concentration causes a transition from patches to waves.

The effects of filament aging and annealing on a model lamellipodium undergoing disassembly by severing.

We use numerical simulations to study the properties of a model lamellipodium as it disassembles by filament severing. The growing lamellipodium is modeled as a 2D or 3D periodic lattice of crosslinked actin filaments. At each time step a new layer of actin filaments is added at the membrane, existing filaments are severed stochastically and disconnected sections of the network are removed.

Actin dynamics: from nanoscale to microscale.

The dynamic nature of actin in cells manifests itself constantly. Polymerization near the cell edge is balanced by depolymerization in the interior, externally induced actin polymerization is followed by depolymerization, and spontaneous oscillations of actin at the cell periphery are frequently seen. I discuss how mathematical modeling relates quantitative measures of actin dynamics to the rates of underlying molecular level processes.