Influence of fluctuations in actin structure on myosin V step size

We study the influence of disorder in the helical actin structure on the myosin V step size, predicted from the elastic lever arm model. We show that fluctuations of +-5 degrees per actin subunit, as proposed by Egelman et al., significantly alter the distribution of step sizes and improve the agreement with experimental data.Comment: 5 pages, 4 figures, to appear in J. Chem. Inf. Mode

The binding dynamics of tropomyosin on actin

We discuss a theoretical model for the cooperative binding dynamics of tropomyosin to actin filaments. Tropomyosin binds to actin by occupying seven consecutive monomers. The model includes a strong attraction between attached tropomyosin molecules. We start with an empty lattice and show that the binding goes through several stages. The first stage represents fast initial binding and leaves many small vacancies between blocks of bound molecules. In the second stage the vacancies annihilate slowly as tropomyosin molecules detach and re-attach. Finally the system approaches equilibrium. Using a grain-growth model and a diffusion-coagulation model we give analytical approximations for the vacancy density in all regimes.Comment: REVTeX, 10 pages, 9 figures; to appear in Biophysical Journal; minor correction

Efficiency limits of the three-sphere swimmer

We consider a swimmer consisting of a collinear assembly of three spheres connected by two slender rods. This swimmer can propel itself forward by varying the lengths of the rods in a way that is not invariant under time reversal. Although any non-reciprocal strokes of the arms can lead to a net displacement, the energetic efficiency of the swimmer is strongly dependent on the details and sequences of these strokes, and also the sizes of the spheres. We define the efficiency of the swimmer using Lighthill's criterion, i.e., the power that is needed to pull the swimmer by an external force at a certain speed, divided by the power needed for active swimming with the same average speed. Here, we determine numerically the optimal stroke sequences and the optimal size ratio of the spheres, while limiting the maximum extension of the rods. Our calculation takes into account both far-field and near-field hydrodynamic interactions. We show that, surprisingly, the three-sphere swimmer with unequal spheres can be more efficient than the equally-sized case. We also show that the variations of efficiency with size ratio is not monotonic and there exists a specific size ratio at which the swimmer has the highest efficiency. We find that the swimming efficiency initially rises by increasing the maximum allowable extension of the rods, and then converges to a maximum value. We calculate this upper limit analytically and report the highest value of efficiency that the three-sphere swimmer can reach.Comment: 7 pages, 3 figure

Elastically coupled molecular motors

We study the influence of filament elasticity on the motion of collective molecular motors. It is found that for a backbone flexibility exceeding a characteristic value (motor stiffness divided through the mean displacement between attached motors), the ability of motors to produce force reduces as compared to rigidly coupled motors, while the maximum velocity remains unchanged. The force-velocity-relation in two different analytic approximations is calculated and compared with Monte-Carlo simulations. Finally, we extend our model by introducing motors with a strain-dependent detachment rate. A remarkable crossover from the nearly hyperbolic shape of the Hill curve for stiff backbones to a linear force-velocity relation for very elastic backbones is found. With realistic model parameters we show that the backbone flexibility plays no role under physiological conditions in muscles, but it should be observable in certain in vitro assays.Comment: REVTeX, 13 pages, 11 figures; presentation improved; to appear in European Physical Journal B; a Java applet showing the simulation is accessible at http://www.physik.tu-muenchen.de/~avilfan/ecmm

Lorentz Reciprocal Theorem in Fluids with Odd Viscosity

The Lorentz reciprocal theorem -- that is used to study various transport phenomena in hydrodynamics -- is violated in chiral active fluids that feature odd viscosity with broken time-reversal and parity symmetries. Here we show that the theorem can be generalized to fluids with odd viscosity by choosing an auxiliary problem with the opposite sign of the odd viscosity. We demonstrate the application of the theorem to two categories of microswimmers. Swimmers with prescribed surface velocity are not affected by odd viscosity, while those with prescribed active forces are. In particular, a torque-dipole can lead to directed motion.Comment: 10 pages, 3 figure

Nonreciprocal interactions give rise to fast cilium synchronisation in finite systems

Motile cilia beat in an asymmetric fashion in order to propel the surrounding fluid. When many cilia are located on a surface, their beating can synchronise such that their phases form metachronal waves. Here, we computationally study a model where each cilium is represented as a spherical particle, moving along a tilted trajectory with a position-dependent active driving force and a position-dependent internal drag coefficient. The model thus takes into account all the essential broken symmetries of the ciliary beat. We show that taking into account the near-field hydrodynamic interactions, the effective coupling between cilia can become nonreciprocal: the phase of a cilium is more strongly affected by an adjacent cilium on one side than by a cilium at the same distance in the opposite direction. As a result, synchronisation starts from a seed at the edge of a group of cilia and propagates rapidly across the system, leading to a synchronisation time that scales proportionally to the linear dimension of the system. We show that a ciliary carpet is characterised by three different velocities: the velocity of fluid transport, the phase velocity of metachronal waves and the group velocity of order propagation. Unlike in systems with reciprocal coupling, boundary effects are not detrimental for synchronisation, but rather enable the formation of the initial seed.Comment: 14 pages, 7 figures, 2 ancillary video