Bistability in the actin cortex

Multi-color fluorescence imaging experiments of wave forming Dictyostelium cells have revealed that actin waves separate two domains of the cell cortex that differ in their actin structure and phosphoinositide composition. We propose a bistable model of actin dynamics to account for these experimental observation. The model is based on the simplifying assumption that the actin cytoskeleton is composed of two distinct network types, a dendritic and a bundled network. The two structurally different states that were observed in experiments correspond to the stable fixed points in the bistable regime of this model. Each fixed point is dominated by one of the two network types. The experimentally observed actin waves can be considered as trigger waves that propagate transitions between the two stable fixed points

Cytoskeletal waves in the absence of molecular motors

Waves are a ubiquitous phenomenon in the cytoskeleton of cells crawling or spreading on a substrate. In theoretical analysis, cytoskeletal waves have been attributed to the action of molecular motors that actively cross-link cytoskeletal filaments. Motivated by recent observations of cytoskeletal waves in human neutrophils, we develop a description of treadmilling filaments in the presence of nucleating proteins that are active when bound to the membrane adjacent to the substrate. If these proteins bind cooperatively to the membrane, we find traveling waves even in the absence of molecular motors. In a confined domain the system can organize into a pair of counter-rotating spirals that emit planar waves

Self-organization in systems of treadmilling filaments

The cytoskeleton is an important substructure of living cells, playing essential roles in cell division, cell locomotion, and the internal organization of subcellular components. Physically, the cytoskeleton is an active polar gel, that is, a system of polar filamentous polymers, which is intrinsically out of thermodynamic equilibrium. Active processes are notably involved in filament growth and can lead to net filament assembly at one end and disassembly at the other, a phenomenon called treadmilling. Here, we develop a framework for describing collective effects in systems of treadmilling filaments in the presence of agents regulating filament assembly. We find that such systems can self-organize into asters and moving filament blobs. We discuss possible implications of our findings for subcellular processes

Filament turnover stabilizes contractile cytoskeletal structures

Vital cellular processes depend on contractile stresses generated by the actin cytoskeleton. Commonly, the turnover of actin filaments in the corresponding structures is large. We introduce a mesoscopic theoretical description of motor-filament systems that accounts for filament nucleation, growth, and disassembly. To analyze the dynamic equations, we introduce an expansion of the filament densities in terms of generalized Laguerre polynomials. We find that filament turnover significantly stabilizes contractile structures against rupture. Finally, we relate the mesoscopic description to a phenomenological theory of cytoskeletal dynamics

A mesoscopic description of contractile cytoskeletal meshworks

Epithelial morphogenesis plays a major role in embryonic development. During this process cells within epithelial sheets undergo complex spatial reorganization to form organs with specific shapes and functions. The dynamics of epithelial cell reorganization is driven by forces generated through the cytoskeleton, an active network of polar filaments and motor proteins. Over the relevant time scales, individual cytoskeletal filaments typically undergo turnover, where existing filaments depolymerize into monomers and new filaments are nucleated. Here we extend a previously developed physical description of the force generation by the cytoskeleton to account for the effects of filament turnover. We find that filament turnover can significantly stabilize contractile structures against rupture and discuss several possible routes to instability resulting in the rupture of the cytoskeletal meshwork. Additionally, we show that our minimal description can account for a range of phenomena that were recently observed in fruit fly epithelial morphogenesis

Stochastic model for Soj relocation dynamics in Bacillus subtilis

The Bacillus subtilis Spo0J/Soj proteins, implicated in chromosome segregation and transcriptional regulation, show striking dynamics: Soj undergoes irregular relocations from pole to pole or nucleoid to nucleoid. Here, we report on a mathematical model of the Soj dynamics. Our model, which is closely based on the available experimental data, readily generates dynamic Soj relocations. We show that the irregularity of the relocations may be due to the stochastic nature of the underlying Spo0J/Soj interactions and diffusion. We propose explanations for the behavior of several Spo0J/Soj mutants, including the “freezing” of the Soj dynamics observed in filamentous cells. Our approach underlines the importance of incorporating stochastic effects when modeling spatiotemporal protein dynamics inside cells