Effect of capping protein on a growing filopodium

Following the footprints of variability during filopodial growth

Filopodia are actin-built finger-like dynamic structures that protrude from the cell cortex. These structures can sense the environment and play key roles in migration and cell-cell interactions. The growth-retraction cycle of filopodia is a complex process exquisitely regulated by intra- and extra-cellular cues, whose nature remains elusive. Filopodia present wide variation in length, lifetime and growth rate. Here, we investigate the features of filopodia patterns in fixed prostate tumor cells by confocal microscopy. Analysis of almost a thousand filopodia suggests the presence of two different populations: one characterized by a narrow distribution of lengths and the other with a much more variable pattern with very long filopodia. We explore a stochastic model of filopodial growth which takes into account diffusion and reactions involving actin and the regulatory proteins formin and capping, and retrograde flow. Interestingly, we found an inverse dependence between the filopodial length and the retrograde velocity. This result led us to propose that variations in the retrograde velocity could explain the experimental lengths observed for these tumor cells. In this sense, one population involves a wider range of retrograde velocities than the other population, and also includes low values of this velocity. It has been hypothesized that cells would be able to regulate retrograde flow as a mechanism to control filopodial length. Thus, we propound that the experimental filopodia pattern is the result of differential retrograde velocities originated from heterogeneous signaling due to cell-substrate interactions or prior cell-cell contacts.

Shape control of lipid bilayer membranes by confined actin bundles

In living cells, lipid membranes and biopolymers determine each other's conformation in a delicate force balance. Cellular polymers such as actin filaments are strongly confined by the plasma membrane in cell protrusions such as lamellipodia and filopodia. Conversely, protrusion formation is facilitated by actin-driven membrane deformation and these protrusions are maintained by dense actin networks or bundles of actin filaments. Here we investigate the mechanical interplay between actin bundles and lipid bilayer membranes by reconstituting a minimal model system based on cell-sized liposomes with encapsulated actin filaments bundled by fascin. To address the competition between the deformability of the membrane and the enclosed actin bundles, we tune the bundle stiffness (through the fascin-to-actin molar ratio) and the membrane rigidity (through protein decoration). Using confocal microscopy and quantitative image analysis, we show that actin bundles deform the liposomes into a rich set of morphologies. For liposomes having a small membrane bending rigidity, the actin bundles tend to generate finger-like membrane protrusions that resemble cellular filopodia. Stiffer bundles formed at high crosslink density stay straight in the liposome body, whereas softer bundles formed at low crosslink density are bent and kinked. When the membrane has a large bending rigidity, membrane protrusions are suppressed. In this case, membrane enclosure forces the actin bundles to organize into cortical rings, to minimize the energy cost associated with filament bending. Our results highlight the importance of taking into account mechanical interactions between the actin cytoskeleton and the membrane to understand cell shape control.

Formin and capping protein together embrace the actin filament in a ménage à trois

Proteins targeting actin filament barbed ends play a pivotal role in motile processes. While formins enhance filament assembly, capping protein (CP) blocks polymerization. On their own, they both bind barbed ends with high affinity and very slow dissociation. Their barbed-end binding is thought to be mutually exclusive. CP has recently been shown to be present in filopodia and controls their morphology and dynamics. Here we explore how CP and formins may functionally coregulate filament barbed-end assembly. We show, using kinetic analysis of individual filaments by microfluidics-assisted fluorescence microscopy, that CP and mDia1 formin are able to simultaneously bind barbed ends. This is further confirmed using single-molecule imaging. Their mutually weakened binding enables rapid displacement of one by the other. We show that formin FMNL2 behaves similarly, thus suggesting that this is a general property of formins. Implications in filopodia regulation and barbed-end structural regulation are discussed.

Modelling the effect of myosin X motors on filopodia growth

We present a numerical simulation study of the dynamics of filopodial growth in the presence of active transport by myosin X motors. We employ both a microscopic agent-based model, which captures the stochasticity of the growth process, and a continuum mean-field theory which neglects fluctuations. We show that in the absence of motors, filopodia growth is overestimated by the continuum mean-field theory. Thus fluctuations slow down the growth, especially when the protrusions are driven by a small number (10 or less) of F-actin fibres, and when the force opposing growth (coming from membrane elasticity) is large enough. We also show that, with typical parameter values for eukaryotic cells, motors are unlikely to provide an actin transport mechanism which enhances filopodial size significantly, unless the G-actin concentration within the filopodium greatly exceeds that of the cytosol bulk. We explain these observations in terms of order-of-magnitude estimates of diffusion-induced and advection-induced growth of a bundle of Brownian ratchets.

Islands of conformational stability for filopodia

Filopodia are long, thin protrusions formed when bundles of fibers grow outwardly from a cell surface while remaining closed in a membrane tube. We study the subtle issue of the mechanical stability of such filopodia and how this depends on the deformation of the membrane that arises when the fiber bundle adopts a helical configuration. We calculate the ground state conformation of such filopodia, taking into account the steric interaction between the membrane and the enclosed semiflexible fiber bundle. For typical filopodia we find that a minimum number of fibers is required for filopodium stability. Our calculation elucidates how experimentally observed filopodia can obviate the classical Euler buckling condition and remain stable up to several tens of . We briefly discuss how experimental observation of the results obtained in this work for the helical-like deformations of enclosing membrane tubes in filopodia could possibly be observed in the acrosomal reactions of the sea cucumber Thyone, and the horseshoe crab Limulus. Any realistic future theories for filopodium stability are likely to rely on an accurate treatment of such steric effects, as analysed in this work.

Protein fluxes along the filopodium as a framework for understanding the growth-retraction dynamics: the interplay between diffusion and active transport

We present a picture of filopodial growth and retraction from physics perspective, where we emphasize the significance of the role played by protein fluxes due to spatially extended nature of the filopodium. We review a series of works, which used stochastic simulations and mean field analytical modeling to find the concentration profile of G-actin inside a filopodium, which, in turn, determines the stationary filopodial length. In addition to extensively reviewing the prior works, we also report some new results on the role of active transport in regulating the length of filopodia. We model a filopodium where delivery of actin monomers towards the tip can occur both through passive diffusion and active transport by myosin motors. We found that the concentration profile of G-actin along the filopodium is rather non-trivial, containing a narrow minimum near the base followed by a broad maximum. For efficient enough actin transport, this non-monotonous shape is expected to occur under a broad set of conditions. We also raise the issue of slow approach to the stationary length and the possibility of multiple steady state solutions.

Actin cross-linkers and the shape of stereocilia

Stereocilia are actin-based cellular protrusions essential for hearing. We propose that they are shaped by the detachment dynamics of actin cross-linkers, in particular espin. We account for experimentally observed stereocilium shapes, treadmilling velocity to length relationship, espin 1 localization profile, and microvillus length to espin level relationship. If the cross-linkers are allowed to reattach, our model yields a dynamical phase transition toward unbounded growth. Considering the simplified case of a noninteracting, one-filament system, we calculate the length probability distribution in the growing phase and its stationary form in a continuum approximation of the finite-length phase. Numerical simulations of interacting filaments suggest an anomalous power-law divergence of the protrusion length at the growth transition, which could be a universal feature of cross-linked depolymerizing systems.