Critical motor number for fractional steps of cytoskeletal filaments in gliding assays

A nonequilibrium power balance relation for analyzing dissipative filament dynamics

Biofilaments like F-actin or microtubules, as well as cilia, flagella, or filament bundles, are often deformed by distributed and time-dependent external forces. It is highly desirable to characterize these filaments' mechanics in an efficient way, either using a single experiment or a high throughput method. We here propose a dynamic power balance approach to study nonequilibrium filament dynamics and exemplify it both experimentally and theoretically by applying it to microtubule gliding assay dynamics. Its usefulness is highlighted by the experimental determination of the lateral friction coefficient for microtubules on kinesins. In contrast to what is usually assumed, friction is anisotropic, in a similar fashion as hydrodynamic friction. We also exemplify, by considering a microtubule buckling event, that if at least one parameter is known in advance, all other parameters can be determined by analyzing a single time-dependent experiment.

The kinetics of mechanically coupled myosins exhibit group size-dependent regimes

Naturally occurring groups of muscle myosin behave differently from individual myosins or small groups commonly assayed in vitro. Here, we investigate the emergence of myosin group behavior with increasing myosin group size. Assuming the number of myosin binding sites (N) is proportional to actin length (L) (N = L/35.5 nm), we resolve in vitro motility of actin propelled by skeletal muscle myosin for L = 0.2-3 μm. Three distinct regimes were found: L < 0.3 μm, sliding arrest; 0.3 μm ≤ L ≤ 1 μm, alternation between arrest and continuous sliding; L > 1 μm, continuous sliding. We theoretically investigated the myosin group kinetics with mechanical coupling via actin. We find rapid actin sliding steps driven by power-stroke cascades supported by postpower-stroke myosins, and phases without actin sliding caused by prepower-stroke myosin buildup. The three regimes are explained: N = 8, rare cascades; N = 15, cascade bursts; N = 35, continuous cascading. Two saddle-node bifurcations occur for increasing N (mono → bi → mono-stability), with steady states corresponding to arrest and continuous cascading. The experimentally measured dependence of actin sliding statistics on L and myosin concentration is correctly predicted.

Bifurcation of velocity distributions in cooperative transport of filaments by fast and slow motors

Several intracellular processes are governed by two different species of molecular motors, fast and slow ones, that both move in the same direction along the filaments but with different velocities. The transport of filaments arising from the cooperative action of these motors has been recently studied by three in vitro experiments, in which the filament velocity was measured for varying fraction of the fast motors adsorbed onto substrate surfaces in a gliding assay. As the fast motor fraction was increased, two experiments found a smooth change whereas the third one observed an abrupt increase of the filament velocity. Here, we show that all of these experimental results reflect the competition between fast and slow motors and can be understood in terms of an underlying saddle-node bifurcation. The comparison between theory and experiment leads to predictions for the detachment forces of the two motor species. Our theoretical study shows the existence of three different motility regimes: 1), fast transport with a single velocity; 2), slow transport with a single velocity; and 3), bistable transport, where the filament velocity stochastically switches between fast and slow transport. We determine the parameter regions for these regimes in terms of motility diagrams as a function of the surface fraction of fast motors and microscopic single-motor parameters. An abrupt increase of the filament velocity for an increasing fraction of fast motors is associated with the occurrence of bistable transport.