Buckling of elastic filaments by discrete magnetic moments

We study the buckling of an idealized, semiflexible filament along whose contour magnetic moments are placed. {We give analytic expressions for the critical stiffness of the filament below which it buckles due to the magnetic compression. For this, we consider various scenarios of the attachment of the magnetic particles to the filament. One possible application for this model are the magnetosome chains of magnetotactic bacteria. An estimate of the critical bending stiffness indicates that buckling may occur within the range of biologically relevant parameters and suggests a role for the bending stiffness of the filament to stabilize the filament against buckling, which would compromise the functional relevance of the bending stiffness of the used filament.Comment: accepted for publication in EPJ

Movements of molecular motors: Ratchets, random walks and traffic phenomena

Processive molecular motors which drive the traffic of organelles in cells move in a directed way along cytoskeletal filaments. On large time scales, they perform motor walks, i.e., peculiar random walks which arise from the repeated unbinding from and rebinding to filaments. Unbound motors perform Brownian motion in the surrounding fluid. In addition, the traffic of molecular motors exhibits many cooperative phenomena. In particular, it faces similar problems as the traffic on streets such as the occurrence of traffic jams and the coordination of (two-way) traffic. These issues are studied here theoretically using lattice models.Comment: latex, uses elsart.cls and phyeauth.cls (included), 10 pages, 6 figures, to appear in the proceedings of FQMT'04, Pragu

Cooperative transport by small teams of molecular motors

Molecular motors power directed transport of cargoes within cells. Even if a single motor is sufficient to transport a cargo, motors often cooperate in small teams. We discuss the cooperative cargo transport by several motors theoretically and explore some of its properties. In particular we emphasize how motor teams can drag cargoes through a viscous environment.Comment: 9 pages, 1 figure, uses ws-brl.cls, presented at Bio-Systems conference, Berlin, June 200

Twitching Motility of Bacteria with Type IV Pili: Fractal Walks, First passage time and their Consequences on Microcolonies

A human pathogen, \textit{Neisseria gonorrhoeae} (NG), moves on surfaces by attaching and retracting polymeric structures called Type IV pili. The \textit{tug-of-war} between the pili results in a two-dimensional stochastic motion called \textit{twitching motility}. In this paper, with the help of real time NG trajectories, we develop coarse-grained models for their description. The \textit{fractal properties} of these trajectories are determined and their influence on \textit{first passage time} and formation of bacterial microcolonies is studied. Our main observations are as follows: (i) NG performs a fast ballistic walk on small time scales and a slow diffusive walk over long time scales with a long crossover region; (ii) There exists a characteristic persistent length $l_p^*$ which yields the fastest growth of bacterial aggregates or biofilms. Our simulations reveal that $l_{p}^{*} \sim L^{0.6}$, where $L\times L$ is the surface on which the bacteria move; (iii) The morphologies have distinct fractal characteristics as a consequence of the ballistic and diffusive motion of the constituting bacteria.Comment: 16 pages, 7 figures, accepted PRE (2017

Tug-of-war as a cooperative mechanism for bidirectional cargo transport by molecular motors

Intracellular transport is based on molecular motors that pull cargos along cytoskeletal filaments. One motor species always moves in one direction, e.g. conventional kinesin moves to the microtubule plus end, while cytoplasmic dynein moves to the microtubule minus end. However, many cellular cargos are observed to move bidirectionally, involving both plus-end and minus-end directed motors. The presumably simplest mechanism for such bidirectional transport is provided by a tug-of-war between the two motor species. This mechanism is studied theoretically using the load-dependent transport properties of individual motors as measured in single-molecule experiments. In contrast to previous expectations, such a tug-of-war is found to be highly cooperative and to exhibit seven different motility regimes depending on the precise values of the single motor parameters. The sensitivity of the transport process to small parameter changes can be used by the cell to regulate its cargo traffic.Comment: 17 pages, latex, 11 figures, 4 tables, includes Supporting Informatio

Force-dependent unbinding rate of molecular motors from stationary optical trap data

Molecular motors walk along filaments until they detach stochastically with a force-dependent unbinding rate. Here, we show that this unbinding rate can be obtained from the analysis of experimental data of molecular motors moving in stationary optical traps. Two complementary methods are presented, based on the analysis of the distribution for the unbinding forces and of the motor's force traces. In the first method, analytically derived force distributions for slip bonds, slip-ideal bonds, and catch bonds are used to fit the cumulative distributions of the unbinding forces. The second method is based on the statistical analysis of the observed force traces. We validate both methods with stochastic simulations and apply them to experimental data for kinesin-1

Stochastic simulations of cargo transport by processive molecular motors

We use stochastic computer simulations to study the transport of a spherical cargo particle along a microtubule-like track on a planar substrate by several kinesin-like processive motors. Our newly developed adhesive motor dynamics algorithm combines the numerical integration of a Langevin equation for the motion of a sphere with kinetic rules for the molecular motors. The Langevin part includes diffusive motion, the action of the pulling motors, and hydrodynamic interactions between sphere and wall. The kinetic rules for the motors include binding to and unbinding from the filament as well as active motor steps. We find that the simulated mean transport length increases exponentially with the number of bound motors, in good agreement with earlier results. The number of motors in binding range to the motor track fluctuates in time with a Poissonian distribution, both for springs and cables being used as models for the linker mechanics. Cooperativity in the sense of equal load sharing only occurs for high values for viscosity and attachment time.Comment: 40 pages, Revtex with 13 figures, to appear in Journal of Chemical Physic

Traffic by multiple species of molecular motors

We study the traffic of two types of molecular motors using the two-species symmetric simple exclusion process (ASEP) with periodic boundary conditions and with attachment and detachment of particles. We determine characteristic properties such as motor densities and currents by simulations and analytical calculations. For motors with different unbinding probabilities, mean field theory gives the correct bound density and total current of the motors, as shown by numerical simulations. For motors differing in their stepping probabilities, the particle-hole symmetry of the current-density relationship is broken and mean field theory fails drastically. The total motor current exhibits exponential finite-size scaling, which we use to extrapolate the total current to the thermodynamic limit. Finally, we also study the motion of a single motor in the background of many non-moving motors.Comment: 23 pages, 6 figures, late

Transport by molecular motors in the presence of static defects

The transport by molecular motors along cytoskeletal filaments is studied theoretically in the presence of static defects. The movements of single motors are described as biased random walks along the filament as well as binding to and unbinding from the filament. Three basic types of defects are distinguished, which differ from normal filament sites only in one of the motors' transition probabilities. Both stepping defects with a reduced probability for forward steps and unbinding defects with an increased probability for motor unbinding strongly reduce the velocities and the run lengths of the motors with increasing defect density. For transport by single motors, binding defects with a reduced probability for motor binding have a relatively small effect on the transport properties. For cargo transport by motors teams, binding defects also change the effective unbinding rate of the cargo particles and are expected to have a stronger effect.Comment: 20 pages, latex, 7 figures, 1 tabl