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

We have developed a two dimensional stochastic molecular dynamics model for the description of intra cellular collective motion of bio motors, in particular Kinesins, on a microtubular track. The model is capable or reproducing the hand-over-hand mechanism of the directed motion along the microtubule. The model gives the average directed velocity and the current of Kinesins along the microtubule. It is shown that beyond a certain density of Kinesins, the average velocity and ...

Molecular motors are involved in key transport processes inside actin-based cellular protrusions. The motors carry cargo proteins to the protrusion tip which participate in regulating the actin polymerization, and play a key role in facilitating the growth and formation of such protrusions. It is observed that the motors accumulate at the tips of cellular protrusions, and in addition form aggregates that are found to drift towards the protrusion base at the rate of actin trea...

Intracellular transport processes driven by molecular motors can be described by stochastic lattice models of self-driven particles. Here we focus on bidirectional transport models excluding the exchange of particles on the same track. We explore the possibility to have efficient transport in these systems. One possibility would be to have appropriate interactions between the various motors' species, so as to form lanes. However, we show that the lane formation mechanism base...

Motivated by recent experimental results for the step sizes of dynein motor proteins, we develope a cellular automata model for intra-cellular traffic of dynein motors incorporating special features of the hindrance-dependent step size of the individual motors. We begin by investigating the properties of the aggressive driving model (ADM), a simple cellular automata-based model of vehicular traffic, a unique feature of which is that it allows a natural extension to capture th...

The transport of cargo particles which are pulled by several molecular motors in a cooperative manner is studied theoretically. The transport properties depend primarily on the maximal number, $N$, of motor molecules that may pull simultaneously on the cargo particle. Since each motor must unbind from the filament after a finite number of steps but can also rebind to it again, the actual number of pulling motors is not constant but varies with time between zero and $N$. An in...

The traffic of molecular motors which interact through mutual exclusion is studied theoretically for half-open tube-like compartments. These half-open tubes mimic the shapes of axons. The mutual exclusion leads to traffic jams or density plateaus on the filaments. A phase transition is obtained when the motor velocity changes sign. We identify the relevant length scales and characterize the jamming behavior using both analytical approximations and Monte Carlo simulations of l...

The stationary states of systems with many molecular motors are studied theoretically for uniaxial and centered (aster-like) arrangements of cytoskeletal filaments using Monte Carlo simulations and a two-state model. Mutual exclusion of motors from binding sites of the filaments is taken into account. For small overall motor concentration, the density profiles are exponential and algebraic in uniaxial and centered filament systems, respectively. For uniaxial systems, exclusio...

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 unb...

One common feature of a vehicle, an ant and a kinesin motor is that they all convert chemical energy, derived from fuel or food, into mechanical energy required for their forward movement; such objects have been modelled in recent years as {\it self-driven} ``particles''. Cytoskeletal filaments, e.g., microtubules, form a ``rail'' network for intra-cellular transport of vesicular cargo by molecular motors like, for example, kinesins. Similarly, ants move along trails while ve...

We model analytically the dynamics of a cytoskeletal filament in a motility assay. The filament is described as rigid rod free to slide in two dimensions. The motor proteins consist of polymeric tails tethered to the plane and modeled as linear springs and motor heads that bind to the filament. As in related models of rigid and soft two-state motors, the binding/unbinding dynamics of the motor heads and the dependence of the transition rates on the load exerted by the motor t...