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Intracellular transport along microtubules or actin filaments, powered by molecular motors such as kinesins, dyneins or myosins, has been recently modeled using one-dimensional driven lattice gases. We discuss some generalizations of these…
We study a generic one-dimensional model for an intracellular cargo driven by N motor proteins against an external applied force. The model includes motor-cargo and motor-motor interactions. The cargo motion is described by an over-damped…
This article reviews the mechanical bidomain model, a mathematical description how the extracellular matrix and intracellular cytoskeleton are coupled by integrin proteins. The fundamental hypothesis is that differences between…
Inside cells, cargos such as vesicles and organelles are transported by molecular motors to their correct locations via active motion on cytoskeletal tracks and passive, Brownian diffusion. During the transportation of cargos, motor-cargo…
We consider in this paper a solvable model for the motion of molecular motors. Based on the averaging principle, we reduce the problem to a diffusion process on a graph. We then calculate the effective speed of transportation of these…
Properties of transport of molecular motors are investigated. A simplified model based on the concept of Brownian ratchets is applied. We analyze a stochastic equation of motion by means of numerical methods. The transport is systematically…
Intracellular transport of organelles is fundamental to cell function and health. The mounting evidence suggests that this transport is in fact anomalous. However, the reasons for the anomaly is still under debate. We examined experimental…
The temperature-dependence of dynamical properties (e.g., the asymptotic diffusion coefficient and the sub-diffusive exponent) are calculated for charges and excitons in one-dimensional systems subject to static and dynamic disorder. These…
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…
We present a simple model for the bidirectional dynamics of actin bundles with alternating polarities in gliding assays with non-processive myosin motors. In the model, the bundle is represented as an elastic chain consisting of monomers…
Biological machines like molecular motors and enzymes operate in dynamic cycles representable as stochastic flows on networks. Current stochastic dynamics describes such flows on fixed networks. Here, we develop a scalable approach to…
Protein machines often exhibit long range interplay between different sites in order to achieve their biological tasks. We investigate and characterize the non--linear energy localization and the basic mechanisms of energy transfer in…
Bidirectional variants of stochastic many particle models for transport by molecular motors show a strong tendency to form macroscopic clusters on static lattices. Inspired by the fact that the microscopic tracks for molecular motors are…
The flow of motor proteins on a filamental track is modelled within the the framework of lattice driven diffusive systems. Motors, considered as hopping particles, perform a highly biased asymmetric exclusion process when bound to the…
Endocytosis underlies many cellular functions including signaling and nutrient uptake. The endocytosed cargo gets redistributed across a dynamic network of endosomes undergoing fusion and fission. Here, a theoretical approach is reviewed…
Various charge migration mechanisms in the DNA are studied within the framework of the Peyrard-Bishop-Holstein model which has been widely used to address charge dynamics in this macromolecule. To analyze these mechanisms we consider…
Cytoskeletal motor proteins are involved in major intracellular transport processes which are vital for maintaining appropriate cellular function. The motor exhibits distinct states of motility: active motion along filaments, and…
A paradigm for isothermal, mechanical rectification of stochastic fluctuations is introduced in this paper. The central idea is to transform energy injected by random perturbations into rigid-body rotational kinetic energy. The prototype…
We propose and analyze a mathematical model of cargo transport by non-processive molecular motors. In our model, the motors change states by random discrete events (corresponding to stepping and binding/unbinding), while the cargo position…
The effect of sequence heterogeneity on polynucleotide translocation across a pore and on simple models of molecular motors such as helicases, DNA polymerase/exonuclease and RNA polymerase is studied in detail. Pore translocation of RNA or…