Numerical modeling of F-.Actin bundles interacting with cell membranes

Actin is one of the most aboundant proteins in eukaryotic cells, where it forms a dendridic network (cytoskeleton) beneath the cell membrane providing mechanical stability and performing fundamental tasks in several functions, including cellular motility. The first step in cell locomotion is the protrusion of a leading edge, for which a significant deformation of the membrane is required: this step relies essentially on the forces generated by actin polymerization pushing the plasma membrane outward. Different types of structures can emerge from the plasma membrane, like lamellipodia (quasi-2d actin mesh) and filopodia (parallel actin bundles). The main topic of the research project is the dynamics of bundles of parallel actin filaments growing against barriers, either rigid (a wall) or flexible (a membrane). In the first part of the thesis, the dynamic behavior of bundles of actin filaments growing against a loaded wall is investigated through a generalized version of the standard multi filaments Brownian Ratchet model in which the (de)polymerizing filaments are treated not as rigid rods but as semi-flexible discrete wormlike chains with a realistic value of the persistence length. A Statistical Mechanics framework is built for bundles of actin filaments growing in optical trap apparatus (harmonic external load) and several equilibrium properties are derived from it, like the maximum force that the filaments can exert (stalling force) or the number of filaments in contact with the wall. Besides, Stochastic Dynamic simulations are employed to study the non-equilibrium relaxation of the bundle of filaments growing in the same optical trap apparatus, interpreting the system evolution by a suitable Markovian approach. Thanks to the observed time scale separation between the wall motion and the filament size relaxation, the optical trap set-up allows to extract the full velocity-load curve V(F) -- the velocity at which the obstacle moves when subject to the combined action of the polymerizing filaments and the external load F -- from a single experiment. The main finding is the observation of a systematic evolution of steady non-equilibrium states over three regimes of bundle lengths L. A first threshold length Λ marks the transition between the rigid dynamic regime (L < Λ), characterized by the usual rigid filament load-velocity relationship V(F), and the flexible dynamic regime (L > Λ), where the velocity V(F,L) is an increasing function of the bundle length L at fixed load F, the enhancement being the result of an improved level of work sharing among the filaments induced by flexibility. A second critical length corresponds to the beginning of an unstable regime characterized by a high probability to develop escaping filaments which start growing laterally and thus do not participate anymore to the generation of the polymerization force. This phenomenon prevents the bundle from reaching at this critical length the limit behavior corresponding to Perfect Load Sharing. In the second part of the thesis, filaments growing against a flexible, deformable membrane are studied by means of Langevin dynamics simulations; the membrane is discretized into a dynamically triangulated network of tethered beads, while the filaments are described as chains of bonded monomers. Both the monomers in the filaments and the membrane beads, which interact with each other via a purely repulsive potential, are followed in space and time integrating its equations of motion with a second order accurate scheme. The elastic properties of the membrane are studied in detail via several methods, showing an unprecedentent level of agreement among them. The onset of filopodial protrusions is observed for N>1 filaments growing from beneath the membrane and pushing it upwards, with a velocity which is systematically larger for flexible filaments than for rigid ones. Since filaments are wrapped by the membrane in the protrusion, escaping filaments are not predicted nor observed in this case.