Cell motility: a viscous fingering analysis of active gels

The symmetry breaking of the actin network from radial to longitudinal symmetry has been identified as the major mechanism for keratocytes (fish cells) motility on solid substrate. For strong friction coefficient, the two dimensional actin flow which includes the polymerisation at the edge and depolymerisation in the bulk can be modelled as a Darcy flow, the cell shape and dynamics being then modelled by standard complex analysis methods. We use the theory of active gels to describe the orientational order of the filaments which varies from the border to the bulk. We show analytically that the reorganisation of the cortex is enough to explain the motility of the cell and find the velocity as a function of the orientation order parameter in the bulk.Comment: 15 pages, 4 figures, accepted for publication in EPJ - Plu

The Human Fungal Pathogen Cryptococcus neoformans Escapes Macrophages by a Phagosome Emptying Mechanism That Is Inhibited by Arp2/3 Complex-Mediated Actin Polymerisation

The lysis of infected cells by disease-causing microorganisms is an efficient but risky strategy for disseminated infection, as it exposes the pathogen to the full repertoire of the host's immune system. Cryptococcus neoformans is a widespread fungal pathogen that causes a fatal meningitis in HIV and other immunocompromised patients. Following intracellular growth, cryptococci are able to escape their host cells by a non-lytic expulsive mechanism that may contribute to the invasion of the central nervous system. Non-lytic escape is also exhibited by some bacterial pathogens and is likely to facilitate long-term avoidance of the host immune system during latency. Here we show that phagosomes containing intracellular cryptococci undergo repeated cycles of actin polymerisation. These actin ‘flashes’ occur in both murine and human macrophages and are dependent on classical WASP-Arp2/3 complex mediated actin filament nucleation. Three dimensional confocal imaging time lapse revealed that such flashes are highly dynamic actin cages that form around the phagosome. Using fluorescent dextran as a phagosome membrane integrity probe, we find that the non-lytic expulsion of Cryptococcus occurs through fusion of the phagosome and plasma membranes and that, prior to expulsion, 95% of phagosomes become permeabilised, an event that is immediately followed by an actin flash. By using pharmacological agents to modulate both actin dynamics and upstream signalling events, we show that flash occurrence is inversely related to cryptococcal expulsion, suggesting that flashes may act to temporarily inhibit expulsion from infected phagocytes. In conclusion, our data reveal the existence of a novel actin-dependent process on phagosomes containing cryptococci that acts as a potential block to expulsion of Cryptococcus and may have significant implications for the dissemination of, and CNS invasion by, this organism.\ud \u

Mathematical modelling and numerical simulations of actin dynamics in the eukaryotic cell

The aim of this article is to study cell deformation and cell movement by considering both the mechanical and biochemical properties of the cortical network of actin filaments and its concentration. Actin is a polymer that can exist either in fil- amentous form (F-actin) or in monometric form (G-actin) (Chen et al. 2000) and the filamentous form is arranged in a paired helix of two protofilaments (Ananthakrish- nan et al. 2006). By assuming that cell deformations are a result of the cortical actin dynamics in the cell cytoskeleton, we consider a continuum mathematical model that couples the mechanics of the network of actin filaments with its bio-chemical dy- namics. Numerical treatment of the model is carried out using the moving grid finite element method (Madzvamuse et al. 2003). Furthermore, by assuming slow deforma- tions of the cell, we use linear stability theory to validate the numerical simulation results close to bifurcation points. Far from bifurcation points, we show that the math- ematical model is able to describe the complex cell deformations typically observed in experimental results. Our numerical results illustrate cell expansion, cell contrac- tion, cell translation and cell relocation as well as cell protrusions. In all these results, the contractile tonicity formed by the association of actin filaments to the myosin II motor proteins is identified as a key bifurcation parameter

A Stochastic model for dynamics of FtsZ filaments and the formation of Z-ring

Understanding the mechanisms responsible for the formation and growth of FtsZ polymers and their subsequent formation of the $Z$-ring is important for gaining insight into the cell division in prokaryotic cells. In this work, we present a minimal stochastic model that qualitatively reproduces {\it in vitro} observations of polymerization, formation of dynamic contractile ring that is stable for a long time and depolymerization shown by FtsZ polymer filaments. In this stochastic model, we explore different mechanisms for ring breaking and hydrolysis. In addition to hydrolysis, which is known to regulate the dynamics of other tubulin polymers like microtubules, we find that the presence of the ring allows for an additional mechanism for regulating the dynamics of FtsZ polymers. Ring breaking dynamics in the presence of hydrolysis naturally induce rescue and catastrophe events in this model irrespective of the mechanism of hydrolysis.Comment: Replaced with published versio

Porous-based rheological model for tissue fluidisation

It has been experimentally observed that cells exhibit a fluidisation process when subjected to a transient stretch, with an eventual recovery of the mechanical properties upon removal of the applied deformation. This fluidisation process is characterised by a decrease of the storage modulus and an increase of the phase angle. We propose a rheological model which is able to reproduce this combined mechanical response. The model is described in the context of continua and adapted to a cell-centred particle system that simulates cell–cell interactions. Mechanical equilibrium is coupled with two evolution laws: (i) one for the reference configuration, and (ii) another for the porosity or polymer density. The first law depends on the actual strain of the tissue, while the second assumes different remodelling rates during porosity increase and decrease. The theory is implemented on a particle based model and tested on a stretching experiment. The numerical results agree with the experimental measurements for different stretching magnitudes.Peer ReviewedPostprint (author's final draft

On the Kinetics of Body versus End Evaporation and Addition of Supramolecular Polymers

Although pathway-specific kinetic theories are fundamentally important to describe and understand reversible polymerisation kinetics, they come in principle at a cost of having a large number of system-specific parameters. Here, we construct a dynamical Landau theory to describe the kinetics of activated linear supramolecular self-assembly, which drastically reduces the number of parameters and still describes most of the interesting and generic behavior of the system in hand. This phenomenological approach hinges on the fact that if nucleated, the polymerisation transition resembles a phase transition. We are able to describe hysteresis, overshooting, undershooting and the existence of a lag time before polymerisation takes off, and pinpoint the conditions required for observing these types of phenomenon in the assembly and disassembly kinetics. We argue that the phenomenological kinetic parameter in our theory is a pathway controller, i.e., it controls the relative weights of the molecular pathways through which self-assembly takes place

Dynamic cofilin phosphorylation in the control of lamellipodial actin homeostasis

During animal cell chemotaxis, signalling at the plasma membrane induces actin polymerisation to drive forward cell movement. Since the cellular pool of actin is limited, efficient protrusion formation also requires the coordinated disassembly of pre-existing actin filaments. To search for proteins that can monitor filamentous and globular actin levels to maintain the balance of polymerisation and disassembly, we followed changes in the proteome induced by RNA interference (RNAi)mediated alterations in actin signalling. This unbiased approach revealed an increase in the levels of an inactive, phosphorylated form of the actin-severing protein cofilin in cells unable to generate actin-based lamellipodia. Conversely, an increase in F-actin levels induced the dephosphorylation and activation of cofilin via activation of the Ssh phosphatase. Similarly, in the context of acute phosphoinositide 3-kinase (PI3K) signalling, dynamic changes in cofilin phosphorylation were found to depend on the Ssh phosphatase and on changes in lamellipodial Factin. These results indicate that changes in the extent of cofilin phosphorylation are regulated by Ssh in response to changes in the levels and/or organisation of F-actin. Together with the recent finding that Ssh phosphatase activity is augmented by F-actin binding, these results identify Ssh-dependent regulation of phosphorylated cofilin levels as an important feedback control mechanism that maintains actin filament homeostasis during actin signalling

Modelling protein localisation and positional information in subcellular systems

Cells and their component structures are highly organised. The correct function of many biological systems relies upon not only temporal control of protein levels but also spatial control of protein localisation within cells. Mathematical modelling allows us to quantitatively test potential mechanisms for protein localisation and spatial organisation. Here we present models of three examples of spatial organisation within individual cells. In the bacterium E. coli, the site of cell division is partly determined by the Min proteins. The Min proteins oscillate between the cell poles and suppress formation of the division ring here, thereby restricting division to midcell. We present a stochastic model of the Min protein dynamics, and use this model to investigate partitioning of the Min proteins between the daughter cells during cell division. The Min proteins determine the correct position for cell division by forming a timeaveraged concentration gradient which is minimal at midcell. Concentration gradients are involved in a range of subcellular processes, and are particularly important for obtaining positional information. By analysing the low copy number spatiotemporal uctuations in protein concentrations for a single polar gradient and two oppositelydirected gradients, we estimate the positional precision that can be achieved in vivo. We nd that time-averaging is vital for high precision. The embryo of the nematode C. elegans has become a model system for the study of cell polarity. At the one-cell stage, the PAR proteins form anterior and posterior domains in a dynamic process driven by contraction of cortical actomyosin. We present a continuum model for this system, including a highly simpli ed model of the actomyosin dynamics. Our model suggests that the known PAR protein interactions 5 are insu cient to explain the experimentally observed cytoplasmic polarity. We discuss a number of modi cations to the model which reproduce the correct cytoplasmic distributions