Related papers: Master Equation Approach to Molecular Motors
Within systems biology there is an increasing interest in the stochastic behavior of genetic and biochemical reaction networks. An appropriate stochastic description is provided by the chemical master equation, which represents a continuous…
Within the framework of a Boltzmann-Lorentz equation, we analyze the dynamics of a granular rotor immersed in a bath of thermalized particles in the presence of a frictional torque on the axis. In numerical simulations of the equation, we…
We derive the general form of a master equation describing the interaction of an arbitrary multipartite quantum system, consisting of a set of subsystems, with an environment, consisting of a large number of sub-envirobments. Each subsystem…
The chemical diffusion master equation (CDME) describes the probabilistic dynamics of reaction--diffusion systems at the molecular level [del Razo et al., Lett. Math. Phys. 112:49, 2022]; it can be considered the master equation for…
We propose a model for motor proteins based on a hierarchical Hamiltonian that we have previously introduced to describe protein folding. The proposed motor model has high efficiency and is consistent with a linear load-velocity response.…
Techniques for simulating molecules whose conformations satisfy constraints are presented. A method for selecting appropriate moves in Monte Carlo simulations is given. The resulting moves not only obey the constraints but also maintain…
For quantum transport through mesoscopic system, a quantum master equation approach is developed in terms of compact expressions for the transport current and the reduced density matrix of the system. The present work is an extension of…
This contribution presents a derivation of the steady-state distribution of velocities and distances of vehicles in freeway traffic which has been suggested for the evaluation of interaction potentials among vehicles (see preprint…
We discuss the approach to equilibrium of systems governed by the Fokker-Planck equation. In particular, we focus on problems involving barrier penetration and the associated Kramers' time. We also describe the connection between stochastic…
The existence of stationary distributions in a multicomponent Boltzmann equation using a non-additive kinetic energy composition rule for binary collisions is discussed. It is found that detailed balance is not achieved when -- in contrast…
The paper analyses stochastic systems describing reacting molecular systems with a combination of two types of state spaces, a finite-dimensional, and an infinite dimenional part. As a typical situation consider the interaction of larger…
A molecular motor is made of either a single macromolecule or a macromolecular complex. Just like their macroscopic counterparts, molecular motors "transduce" input energy into mechanical work. All the nano-motors considered here operate…
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. We discuss analytical and numerical methods for the solution of master equations, keeping our focus on…
We introduce a systematic approximation for an efficient evaluation of Born--Markov master equations for steady state transport studies in open quantum systems out of equilibrium: the energy resolved master equation approach. The master…
A 1D model of interacting particles moving over a periodic substrate and in a position dependent temperature profile is considered. When the substrate and the temperature profile are spatially asymmetric a center-of-mass velocity develops,…
Chemical affinities are responsible for driving active matter systems out of equilibrium. At the nano-scale, molecular machines interact with the surrounding environment and are subjected to external forces. The mechano-chemical coupling…
We propose a new form for the quantum master equation in the theory of open quantum systems. This new formalism allows one to describe the dynamics of two-level systems moving along different hyperbolic trajectories with distinct proper…
Motor-driven cargo transport is a complex phenomenon where multiple motor proteins attached on to a cargo engage in pulling activity, often leading to tug-of-war, displaying bidirectional motion. However, most mathematical and computational…
Enzymatic molecules that actively support many cellular processes, including transport, cell division and cell motility, are known as motor proteins or molecular motors. Experimental studies indicate that they interact with each other and…
Systems out of equilibrium exhibit a net production of entropy. We study the dynamics of a stochastic system represented by a Master Equation that can be modeled by a Fokker-Planck equation in a coarse-grained, mesoscopic description. We…