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Dynamic properties of molecular motors that fuel their motion by actively interacting with underlying molecular tracks are studied theoretically via discrete-state stochastic ``burnt-bridge'' models. The transport of the particles is viewed…
The nonequilibrium stationary state of an exclusive genetic switch is considered. The model comprises two competing species and a single binding site which, when bound to by a protein of one species, causes the other species to be…
Proteins are the "work horses" in biological systems. In almost all functions specific proteins are involved. They control molecular transport processes, stabilize the cell structure, enzymatically catalyze chemical reactions; others act as…
Biological molecular machines are bifunctional enzymes that catalyze two processes: one donating free energy and the other accepting it. Recent studies show that most protein enzymes have rich stochastic dynamics of transitions between the…
Molecular simulations can provide microscopic insight into the physical and chemical driving forces of complex molecular processes. Despite continued advancement of simulation methodology, model errors may lead to inconsistencies between…
Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about…
Molecular search phenomena are observed in a variety of chemical and biological systems. During the search the participating particles frequently move in complex inhomogeneous environments with random transitions between different dynamic…
The interrelation of dynamic processes active on separated time-scales in glasses and viscous liquids is investigated using a model displaying two time-scale bifurcations both between fast and secondary relaxation and between secondary and…
The mathematical formulation of the model for molecular movement of single motor proteins driven by cyclic biochemical reactions in an aqueous environment leads to a drifted Brownian motion characterized by coupled diffusion equations. In…
Mass-action chemical reaction systems are frequently used in Computational Biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly…
The effect of interactions on dynamics of coupled motor proteins is investigated theoretically. A simple stochastic discrete model, that allows to calculate explicitly the dynamic properties of the system, is developed. It is shown that…
The evolution of particulate and multiphase systems can transition from dynamic regimes, governed by classical transport equations with well-defined damping coefficients, to anomalously slow relaxation described by rate equations when the…
There are many processes in biology in which mechanical forces are generated. Force-bearing networks can transduce locally developed mechanical signals very extensively over different parts of the cell or tissues. In this article we conduct…
The authors address the problem of downhill protein folding in the framework of a simple statistical mechanical model, which allows an exact solution for the equilibrium and a semianalytical treatment of the kinetics. Focusing on protein…
Equilibrating proteins and other biomacromolecules is cardinal for molecular dynamics simulation of such biological systems in which they perform free dynamics without any externally-applied mechanical constraint, until thermodynamic…
Phase separation and transitions among different molecular states are ubiquitous in living cells. Such transitions can be governed by local equilibrium thermodynamics or by active processes controlled by biological fuel. It remains largely…
Many dense particulate suspensions show a stress induced transformation from a liquid-like state to a solid-like shear jammed (SJ) state. However, the underlying particle-scale dynamics leading to such striking, reversible transition of the…
Multibody systems usually give rise to complex nonlinear dynamics, and the bicycle is not an exception. Even a simple model as the Two-Mass-Skate presents a long expression of the kinetic energy, making difficult to write explicitly the…
Dynamics of molecular motors that move along linear lattices and interact with them via reversible destruction of specific lattice bonds is investigated theoretically by analyzing exactly solvable discrete-state ``burnt-bridge'' models.…
Studying systems where many individual bodies in motion interact with one another is a complex and interesting area. Simple mechanisms that may be determined for biological, chemical, or physical reasons can lead to astonishingly complex…