Bidirectional cooperative motion of myosin-II motors on actin tracks with randomly alternating polarities

The cooperative action of many molecular motors is essential for dynamic processes such as cell motility and mitosis. This action can be studied by using motility assays in which the motion of cytoskeletal filaments over a surface coated with motor proteins is tracked. In previous studies of actin-myosin II systems, fast directional motion was observed, reflecting the tendency of myosin II motors to propagate unidirectionally along actin filaments. Here, we present a motility assay with actin bundles consisting of short filamentous segments with randomly alternating polarities. These actin tracks exhibit bidirectional motion with macroscopically large time intervals (of the order of several seconds) between direction reversals. Analysis of this bidirectional motion reveals that the characteristic reversal time, $\tau_{rev}$, does not depend on the size of the moving bundle or on the number of motors, $N$. This observation contradicts previous theoretical calculations based on a two-state ratchet model [Badoual et al., Proc. Natl. Acad. Sci. USA, vol. 99, p. 6696 (2002)], predicting an exponential increase of $\tau_{rev}$ with $N$. We present a modified version of this model that takes into account the elastic energy due to the stretching of the actin track by the myosin II motors. The new model yields a very good quantitative agreement with the experimental results.Comment: A slightly revised version. Figures 2 and 7 were modified. Accepted for publication in "Soft Matter

Cooperative molecular motors moving back and forth

We use a two-state ratchet model to study the cooperative bidirectional motion of molecular motors on cytoskeletal tracks with randomly alternating polarities. Our model is based on a previously proposed model [Badoual et al., {\em Proc. Natl. Acad. Sci. USA} {\bf 99}, 6696 (2002)] for collective motor dynamics and, in addition, takes into account the cooperativity effect arising from the elastic tension that develops in the cytoskeletal track due to the joint action of the walking motors. We show, both computationally and analytically, that this additional cooperativity effect leads to a dramatic reduction in the characteristic reversal time of the bidirectional motion, especially in systems with a large number of motors. We also find that bidirectional motion takes place only on (almost) a-polar tracks, while on even slightly polar tracks the motion is unidirectional. We argue that the origin of these observations is the sensitive dependence of the cooperative dynamics on the difference between the number of motors typically working in and against the instantaneous direction of motion.Comment: Accepted for publication in Phys. Rev.

Fluorescence Correlation Spectroscopy analysis of segmental dynamics in Actin filaments

We adapt Fluorescence Correlation spectroscopy (FCS) formalism to the studies of the dynamics of semi-flexible polymers and derive expressions relating FCS correlation function to the longitudinal and transverse mean square displacements of polymer segments. We use the derived expressions to measure the dynamics of actin filaments in two experimental situations: filaments labeled at distinct positions and homogeneously labeled filaments. Both approaches give consistent results and allow to measure the temporal dependence of the segmental mean-square displacement (MSD) over almost five decades in time, from ~0.04ms to 2s. These noninvasive measurements allow for a detailed quantitative comparison of the experimental data to the current theories of semi-flexible polymer dynamics. Good quantitative agreement is found between the experimental results and theories explicitly accounting for the hydrodynamic interactions between polymer segments

Interplay between activity, elasticity, and liquid transport in self-contractile biopolymer gels

Active gels play an important role in biology and in inspiring biomimetic active materials, due to their ability to change shape, size, and create their own morphology. We study a particular class of active gels, generated by polymerizing actin in the presence of cross-linkers and clusters of myosin as molecular motors, which exhibit large contractions. The relevant mechanics for these highly swollen gels is the result of the interplay between activity and liquid flow: gel activity yields a structural reorganization of the gel network and produces a flow of liquid that eventually exits from the gel boundary. This dynamics inherits lengthscales that are typical of the liquid flow processes. The analyses we present provide insights into the contraction dynamics, and they focus on the effects of the geometry on both gel velocity and fluid flow

Arp2/3 Branched Actin Network Mediates Filopodia-Like Bundles Formation In Vitro

During cellular migration, regulated actin assembly takes place at the cell leading edge, with continuous disassembly deeper in the cell interior. Actin polymerization at the plasma membrane results in the extension of cellular protrusions in the form of lamellipodia and filopodia. To understand how cells regulate the transformation of lamellipodia into filopodia, and to determine the major factors that control their transition, we studied actin self-assembly in the presence of Arp2/3 complex, WASp-VCA and fascin, the major proteins participating in the assembly of lamellipodia and filopodia. We show that in the early stages of actin polymerization fascin is passive while Arp2/3 mediates the formation of dense and highly branched aster-like networks of actin. Once filaments in the periphery of an aster get long enough, fascin becomes active, linking the filaments into bundles which emanate radially from the aster's surface, resulting in the formation of star-like structures. We show that the number of bundles nucleated per star, as well as their thickness and length, is controlled by the initial concentration of Arp2/3 complex ([Arp2/3]). Specifically, we tested several values of [Arp2/3] and found that for given initial concentrations of actin and fascin, the number of bundles per star, as well as their length and thickness are larger when [Arp2/3] is lower. Our experimental findings can be interpreted and explained using a theoretical scheme which combines Kinetic Monte Carlo simulations for aster growth, with a simple mechanistic model for bundles' formation and growth. According to this model, bundles emerge from the aster's (sparsely branched) surface layer. Bundles begin to form when the bending energy associated with bringing two filaments into contact is compensated by the energetic gain resulting from their fascin linking energy. As time evolves the initially thin and short bundles elongate, thus reducing their bending energy and allowing them to further associate and create thicker bundles, until all actin monomers are consumed. This process is essentially irreversible on the time scale of actin polymerization. Two structural parameters, L, which is proportional to the length of filament tips at the aster periphery and b, the spacing between their origins, dictate the onset of bundling; both depending on [Arp2/3]. Cells may use a similar mechanism to regulate filopodia formation along the cell leading edge. Such a mechanism may allow cells to have control over the localization of filopodia by recruiting specific proteins that regulate filaments length (e.g., Dia2) to specific sites along lamellipodia