Major actin nucleators, formins and Arp2/3 complex, are critical players in cell motility and believed to have non-overlapping functions in inducing actin filament bundles and dendritic networks, respectively. We found an unexpected role of mDia2 formin in the formation of dendritic networks in lamellipodia, beside its function in filopodia. mDia2 was specifically recruited to the lamellipodial leading edge, where it nucleated actin filaments, which might serve as “mother” filaments for Arp2/3-dependent dendritic nucleation. mDia2-nucleated filaments in lamellipodia exhibited high tendency to converge into bundles, thereby promoting the reorganization of lamellipodia into filopodia. Both mDia2- and Arp2/3-nucleated filaments jointly participated in this process. Consistently, filopodia were synergistically inhibited by knockdown of mDia2 and Abi1, a critical regulator of the Arp2/3-activating WAVE complex. mDia2 physically interacted with Abi1 and this interaction was important for mDia2 targeting and filopodia induction. Thus, the activities of two distinct nucleators, mDia2 and Arp2/3, orchestrated by Abi1 are essential for the coordinated formation of lamellipodia and filopodia.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

Actin filament dynamics at the cell membrane are important for cell-matrix and cell-cell adhesions and the protrusion of the leading edge. Since actin filaments must be connected to the cell membrane to exert forces, but must also detach from the membrane to allow it to move and evolve, the balance between actin filament tethering and detachment at adhesion sites and the leading edge is key for cell shape changes and motility. Using an oil-water interface as a substrate to mimic the fluid properties of the cell membrane, we study Arp2/3 complex-dependent actin dynamics, and show evidence that filament attachment to polymerization activators is highly dynamic. These dynamics are enhanced in the presence of the actin cytoskeleton protein VASP, and we observe cycles of catastrophic detachment of the actin network from the surface, resulting in stop-and-go motion. These results point to a role for VASP in the modulation of filament anchoring, with implications for actin dynamics at cell adhesions and at the leading edge of the cell.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

The binding sites for ADF and cofilin on G-actin have been mapped by competitive chemical cross-linking using deoxyribonuclease I (DNase I), gelsolin segment 1 (G1), thymosin ß4, and vitamin D-binding protein. To reduce ADF/cofilin induced actin oligomerisation we used ADP-ribosylated actin. Both vitamin D-binding protein and thymosin ß4 inhibit binding by ADF or cofilin, while cofilin or ADF and DNase I bind simultaneously. Competition was observed between ADF or cofilin and G1, supporting the hypothesis that cofilin preferentially binds in the cleft between subdomains 1 and 3, similar to or overlapping the binding site of G1. Because the affinity of G1 is much higher than that of ADF or cofilin, even at a 20-fold excess of the latter, the complexes contained predominantly G1. Nevertheless, cross-linking studies using actin:G1 complexes and ADF or cofilin showed the presence of low concentrations of ternary complexes containing both ADF or cofilin and G1. Thus even with monomeric actin, it is shown for the first time that binding sites for both G1 and ADF or cofilin can be occupied simultaneously, confirming the existence of two separate binding sites. Employing a peptide array with overlapping sequences of actin overlaid by cofilin, we have identified five sequence stretches of actin able to bind cofilin. These sequences are located within the regions of F-actin predicted to bind cofilin in the model derived from image reconstructions of electron microscopical images of cofilin-decorated filaments. Three of the peptides map to the cleft region between subdomains 1 and 3 of the upper actin along the two-start long-pitch helix, while the other two are in the DNase I loop corresponding to the site of the lower actin in the helix. In the absence of any crystal structures of ADF or cofilin in complex with actin, these studies provide further information about the binding sites on F-actin for these important actin regulatory proteins.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

We have developed a model to explain the initiation of adhesions on the ventral surface of a cell. An analysis of the energetics of membrane bending and the effects of a composite system of freely diffusing repellers and receptors and a fixed network of ligands on the extracellular matrix demonstrates that a small bundle of actin filaments is able to push the membrane down to the extracellular matrix and nucleate a nascent adhesion. This model is consistent with experiments which demonstrate that cell motility requires cycles of actin polymerization and depolymerization at the leading edge of cell protrusions - the leading lamella adheres to the extracellular matrix and stable focal contacts form which can resist strong contractile forces. At the tail of the cell, focal adhesions separate allowing tail retraction toward the leading lamella. These mechanisms rely on choreographed actin transients and the directed motion of the cell is determined by the location of the initial protrusion and the site of adhesion. Several of the mechanisms responsible for protrusive force and focal contact formation have been elucidated and the many of molecular players responsible have been cataloged and some of the structures that they are associated with have been identified. The detailed processes leading to the formation of the earliest adhesions, however, have remained elusive. Based upon the energetics of adhesion formation, our model predicts the shape of the membrane at the nucleated adhesion.
We have developed a novel form of confocal interference microscopy to measure the distance between the ventral surface of a cell and the substratum with several nanometer precision and we plan to measure the topography of nascent adhesions. We have combined phase shifting laser feedback interferometry with a high numerical aperture inverted microscope in order to determine the topography of the ventral surface of a cell. We have obtained a map of both the topography and reflectivity of the ventral surface of fixed metastatic mammary adenocarcinoma cells. We have quantified the ventral surface topography at focal adhesions and we have shown that these changes are correlated with markers for a focal adhesion adaptor protein.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

We present a mathematical model for the Actin-cytoskeleton in the lamellipodium. We base our modelling on cross-links between existing filaments as primary structures and take account of graded length. We avoid taking into account branching of filaments. Our modelling approach differs from previous ones in that we describe the entire lamellipodium and in that we derive the model from an initially discrete description of its principal constituents, filaments and cross-links. We describe the regular turnover of cross-links with a family of "age-structured" models and use a quasi-stationary approach for the determination of the structure of the mesh-work. We assume a short life-time of cross-links and therefore pass to an asymptotic limit where the model take the form of a (rather general) gradient flow model. With a selected set of parameters we simulate the non-moving steady state of the lamellipodium as well as its reaction to an external pushing force. The simulations reproduce tread-milling, lateral flow, an adequate deformation reaction to the outer force as well as the recuperation towards the symmetric shape in the absence of outer forces.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

The dynamics of actin cellular networks are an essential motor of cell movements and shape changes. Bacterial pathogens, such as Listeria monocytogenes, have been shown to hijack the actin polymerization machinery of the infected cells in order to propel themselves forward. This mechanism is often studied replacing the bacteria by beads coated with an actin polymerization activator. Such beads recruit an actin shell that spontaneously breaks and gives rise to an actin comet that propels the bead forward. Various physical models have been proposed to explain how actin polymerization can generate forces. It has been well documented that symmetry breaking preceding comet formation, results from the elastic properties of the actin network. However, the importance of elasticity in bead propulsion is still debated. Using a simple assay composed of purified commercial proteins, we provide direct evidence that the actin gel in the comet undergoes deformations even after symmetry breaking. Depending on the protein composition in the motility medium, deformations arise from either gel elasticity or monomer diffusion through the actin comet. Our findings demonstrate that actin-based movement is governed by the mechanical properties of the actin network, which are fine-tuned by proteins involved in actin dynamics and assembly.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

The mechanical and dynamical properties of actin networks are essential for many cellular processes like cell division and motility. The leading edge of migrating cells is pushed out by the polymerization of actin networks. This process is orchestrated by crosslinkers and other actin binding proteins that have been shown to affect the elastic properties of actin gels in vitro. Here we use beads coated with an activator of actin polymerization to assess the role of mechanical properties of the actin gel in propulsion. When placed in a mixture of purified proteins, the beads accumulate an actin gel which ruptures at a given thickness due to the mechanical stress that builds up due to stretching of the gel layers. After rupture, the beads start moving, propelled by an actin comet tail. By monitoring the evolution of marked parts of the comet, we provide direct experimental evidence that the actin gel continuously undergoes deformations during the growth of the comet, which could indicate relaxation of stresses accumulated in the gel. Moreover, we find that the presence of crosslinkers affects the speed of bead movement in a manner that depends on the density of the gel. To explain our results we propose that there are different motility regimes. When the gel density is high, the movement is limited by diffusion of monomers, whereas at low density, the movement is governed by an elastic propulsion mechanism. We summarize these findings in a state diagram.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

Hair cells are the mechano-sensor of the inner ear that grant us with hearing and balance. Their mechano sensitive organelle, the hair bundle, is made of a few dozens of stiff rods of actin, the stereocilia, that are deflected upon stimulation by e.g. sound or fluid flow. This organelle has a complex and rich motility: it can oscillate spontaneously, or display forms of mechanical excitability with contrasted kinetics in response to force steps. Combining Ca2+ iontophoresis with mechanical stimulation, we found that polarity and kinetics of active hair-bundle movements in the bullfrog’s sacculus depended on the bundle’s operating point within its force-displacement relation. Only three ingredients were necessary to account for the various incarnations of active hair-bundle motility: strong non-linear gating compliance of the hair bundle, myosin-based adaptation and Ca2+ feedback on the motor’s activity. Simulations successfully accounted for a wide range of observations from different laboratories and animal species, thereby suggesting that myosin-based adaptation suffice to describe the main features of both fast and slow active hair-bundle movements.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

Concentrations of polymeric and monomeric actin in lamellipodia Protrusion in cell motility is driven by the polymerization of actin filaments at the cell front in structures termed lamellipodia. Considerable progress has been made in identifying the major players involved in regulating actin turnover, but conclusions drawn about the polymerization and depolymerisation mechanisms are largely based on the properties of actin and actin-associated proteins in vitro. In the test tube, the critical concentration for polymerization at the barbed end of actin filaments is around 0.1µM and at the pointed end, 0.6µM and the treadmilling rate is at least 100 times slower than in a protruding lamellipodium . To understand the regulation in the cell, information about local concentrations of monomeric and polymeric actin are required and here the data is very limited. The aim of the present study was to combine live cell imaging and electron microscopy to obtain concentration values for filamentous and globular actin in lamellipodia.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

Lamellipodia are thin, actin-rich, veil-like structures that are believed to play a central role in cell locomotion and guidance. One or more are usually found at the front edge of the leading lamella in motile cells in culture. Various forms of microscopy reveal a continuous cycle of actin polymerisation, retrograde flow and depolymerisation within them. We examine a simple steady-state model of these actin dynamics incorporating a Monte-Carlo diffusion algorithm for the return of unpolymerised actin to the leading edge. Firstly, we explore the properties of the model when examined by different methods of microscopy including the FLAP (fluorescence localisation after photobleaching) method recently developed in our laboratory. Secondly, we compare these properties with those of several types of real cell examined by equivalent methods. Finally, we consider how the model needs to be modified to account for the range of actin dynamics found in the living cells. We conclude that molecular diffusion cannot always account for the return of unpolymerised actin to the leading edge.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

It is now a classical assay in cell biology to mechanically wound a monolayer of cells and then observe how the freed surface of the underlying substrate is reoccupied with time. That assay is rich in information on the migrating properties of the observed cells. However, it present many drawbacks and especially a very poor control of the initial conditions of migration.
So as to overcome what can be considered as an issue, we have designed in the Curie Institute a microfabrication process (using soft lithography) which finally leads to the production of micro-stencils for cells with holes of chosen shapes. Those stencils allow us to deposit assemblies of living cells on a surface of interest. After cell deposition, stencils are withdrawn and the formed assemblies of cells (of controlled geometries) are then free to colonise the newly offered surface. We could verify that the colonisation process was mainly done by active migration of cells on the surface.
In the case on cohesive assemblies of cells (MDCK) the well defined initial conditions have allowed us to evidence a finger-shaped organised migration of cells in addition to the well described cell-sheet collective motion.
I will also present some surprising average behaviours of such cell assemblies of simple initial geometries.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

We present a model which couples the membrane with the protrusive forces of actin polymerization and contractile forces of molecular motors, such as myosin. The actin polymerization at the membrane is activated by freely diffusing membrane proteins, that may have a distinct spontaneous curvature. Molecular motors are recruited to the polymerizing actin filaments, from a constant reservoir, and produce a contractile force. All the forces and variables are treated in the linear limit, which allows us to derive analytic solutions. Our results show that for concave membrane proteins the myosin activity gives rise to propagating membrane waves similar to those observed on different cells. For convex membrane proteins the myosin activity gives rise to an unstable contraction, which yields a length-"quantization" of the mitosis process.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

We present a model which couples the membrane with the protrusive forces of actin polymer- ization and contractile forces of molecular motors, such as myosin. The actin polymerization at the membrane is activated by freely diffusing membrane proteins, that have a distinct spontaneous curvature. Molecular motors are recruited to the polymerizing actin laments, from a constant reservoir, and produce a contractile force. All the forces and variables are treated in the linear limit, which allows us to derive analytic solutions. Our results show that for convex membrane proteins the myosin activity gives rise to transverse membrane waves, similar to those observed on different cells.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

The actin cytoskeleton is a dynamic meshwork of proteanous filaments that is disposed beneath the plasma membrane. Actin monomers self-assemble into filaments to generate forces and movements during cell morphogenesis and movement. However, the high supra-molecular and organisational complexity of the cell cytoskeleton renders it difficult to study actin-based movement in a cellular environment. Therefore, a-cellular assays are currently used to unravel how controlled actin polymerisation contributes to cell movement. Several biophysical models were proposed for the mechanisms by which actin filament assembly generates force that is translated into the movement [1-3]. Among those, stochastic simulations have considerable potential to assess the dynamic processes in the cell regulatory system. Results obtained with this approach are often in closer approximations to the molecular reality than those yielded by classical analytical models based on a set of differential equations. However, so fare, no comprehensive and systematic comparative study or evaluation of modelling approaches used in cytoskeleton research is available. Our work aimed at developing an advanced computer-simulation approach, based on stochastic and analytical modelling algorithms, for the simulation and analysis of the actin filament formation and its effect on small-bodies (beads, bacteria) motility in terms of forces and velocities. Our approach combined stochastic simulations of the biochemical reactions, mechanical filament-filament interactions and force-filed constrains. The biochemical reactions were simulated using the modified Gillespie's method with the discrete time introduced. The mechanical model, including filament-filament and filament-bead (or bacteria) interactions, viscous friction and Brownian effects were realized to simulate the forces in the considered systems. The simulation models and computation algorithms were developed as the C++ classes and integrated in the stand-alone executable software package. We developed a simulation model of a simplified biochemical network that reproduced an actin-polymerization process in a limited volume of a cell. The model generated 8 first-order chemical reactions, linked with a 3D spatial model of the system, including filaments and other solid bodies (beads or bacteria). The homogeneity of the concentrations in the volume was validated via Monte Carlo simulation of diffusion. The preliminary results of our simulations, in particular some selected biochemical parameters, like the rate of actin-polymerization and the actin-monomer diffusion constant, are in good agreement with those published elsewhere and with the results of FRAP experiments carried out in our lab on some selected actin-polymerization systems.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

Invasive pathogens (such as Listeria monocytogenes) and vesicles can be propelled intracellularly by actin polymerization in a mechanism that remains controversial and poorly understood. Based on thermodynamic, mechanical, and kinetic considerations, we have proposed that the dominant mechanism of propulsion is force-insensitive processive polymerization of surface-tethered actin filament plus-ends, using filament end-tracking proteins attached to the particle surface. As a consequence of this mechanism, the propelled particle is in a tight quasi-static force balance between compressed and tense filaments, a state created by stochastic variation in elongation rates of end-tethered filament and/or the axial monomer concentration gradient arising from monomer conversion into filaments at the particle surface. We support these arguments using mathematical models on various length scales to demonstrate that this mechanism can quantitatively account for numerous experimental observations of particle propulsion by actin based motility, such as stepwise motion, small fluctuations, rotations in Listeria trajectories, as well as the speed and saltatory dynamics of biomimetic hard and soft particles.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

Molecular biology provides today an extremely detailed description of the components of living cells. However, the physical properties of the cell cytoskeleton, such as its mechanical properties, are still poorly understood. The complexity of the microscopic processes involved in cytoskeleton dynamics is such that it is necessary to introduce effective coarse-grained models to study its macroscopic properties. Here we describe the cytoskeleton as an out-of-equilibrium viscoelastic polar gel. We show in particular that the "activity" of the gel, induced by the molecular motors consuming ATP, can give rise to spontaneous flows in the gel, and trigger different kinds of instabilities. We give a generic phase diagram of thin films of active gels, which is in qualitative agreement with available observations.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

Cell migration is initiated by the protrusion of meshworks and bundles of actin filaments at the cell front, called lamellipodia and filopodia, respectively. The generation and maitntenance of these structures requires dynamic actin assembly and disassembly. In recent years, we have witnessed the discovery of key molecular players driving actin polymerisation in lamellipodia, although the precise molecular mechanisms regulating them are still under intense investigation. Key players include the Arp2/3-complex, the expression of which is essential for lamellipodia but not filopodia protrusion, and some of its activators, i.e. Scar/WAVE proteins, which are also now established to assemble into large protein complexes. Work presented here aims at addressing the precise spatial and temporal features of Arp2/3-complex activation within lamellipodia, by employing state-of-the-art imaging approaches such as FRAP and photoactivation. Moreover, the dynamics of “type I”-Arp2/3-complex activators is compared with that of additional prominent actin regulators at these sites, such as ADF/cofilin or the actin filament and Arp2/3-complex interactor cortactin.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

This work is divided into two parts. In the first part we considered various models on lipid bilayers and biomembranes with the help of energy functionals and variational calculus. As a result of this the membrane shape equation is derived. In the second part we consider the lamellipodium of crawling cells and develop a dynamic equation for the movement with the contribution of the membrane. Here we use the fact from the first part, that the membrane resistance is proportional to the curvature. The dynamic equation is then numerically solved and we also ran various simulations.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

Cell motility is a complex phenomenon, emerging from interactions between multiple levels of cell organisation. We model this process by describing the molecular kinetics of small G-proteins and actin filaments, the mutual interactions between the small G-proteins, the effect of the small G-proteins on capping and side-branching of the actin filaments, the force transduction of the cytoskeleton on the cell's membrane, and the resultant membrane deformation. For experimental parameters gleaned from the literature and using the fish keratocyte cell as a paradigm system, the model produces a quantitatively correct description of polarity, cell shape, cell movement and turning behaviour. We show that these global cell behaviours result from information transfer through the different levels of organisation, in which feedback between all levels is essential. This self-regulation guarantees robustness in cell motion, while concomitantly allowing for high sensitivity to external stimuli.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

Spatially-localized control of actin polymerization and network formation is essential for eukaryotic cell motility. Numerous actin binding proteins controlling the dynamic properties of actin networks have been studied and models such as the dendritic nucleation scheme have been proposed for the functional integration of at least a minimal set of such regulatory proteins. However, a complete understanding of actin network dynamics is still lacking. In this talk we will describe recent work on the evolution of the distribution of filament lengths and the dynamics of nucleotide profiles under various scenarios for the action of control proteins, with emphasis on the role of these proteins in fixing the transient and steady state length distribution of the filaments. We will also discuss work aimed at integrating microscopic models of actin dynamics into cell-level descriptions of motility.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)

The molecular-level processes by which actin polymerization exerts forces in cell motility remain incompletely understood despite intensive experimental and theoretical investigation. We will describe calculations of actin polymerization performed via Brownian dynamics, stochastic-growth dynamics, and analytic theory, which explore the consequences of differing assumptions regarding the force-generation process. The Brownian-dynamics calculations treat a single actin filament propelling a finite obstacle. They validate the preexisting Brownian-ratchet theory, and show that a filament strongly attached to an obstacle can generate motile force efficiently. The stochastic-growth simulations treat the growth of an actin network against a hard obstacle, including the key molecular level processes mediated by the most important actin-binding proteins. These simulations show that the density of filament ends pushing the obstacle depends strongly on the opposing force; if new filam! ents are formed exclusively by autocatalytic branching processes, the speed decreases very slowly with opposing force. This effect is combined with the Brownian-dynamics results in a multiscale model of biomimetic bead motility, which describes the measured force-velocity relation well. In addition, we describe calculations quantifying the effects of actin-binding proteins on the extent of actin polymerization. These calculations show that, surprisingly, filament severing often enhances polymerization.

• Thematic program: Multiscale Modeling in Cell Biology (2006)
• Event: Mathematical Modelling of Actin-Based Motility (2006)