We consider a randomly flashing ratchet, where the potential acting can be switched to another at random. Using coupled Fokker-Planck equations, we formulate the expressions of quantities measuring dynamics and thermodynamics. Extended numerical calculations present how the potential landscapes and the transitions affect the motility and energetics. Load-dependent velocity and energetic efficiency of motor proteins, kinesin and dynein, further exemplify the randomly flashing ratchet model. We also discuss the system with two shifted sawtooth potentials.
We study, using Monte Carlo simulations, the steady state properties of a system of particles interacting via hard core exclusion and moving in a discrete flashing disordered ratchet potential. Quenched disorder is introduced by breaking the periodicity of the ratchet potential through changing shape of the potential across randomly chosen but fixed periods. We show that the effects of quenched disorder can be broadly classified as strong or weak with qualitatively different behaviour of the steady state particle flux as a function of overall particle density. We further show that most of the …
We study a system of independent Brownian particles in a flashing ratchet potential that can be turned on or off depending on the position of the particles, with the aim of maximising the speed of the center of mass in the long run. First, an explanation on how to find the optimal protocol using Bellman's principle of optimality for any number of particles is given. Then the problem is numerically solved for a system of 2 particles. Simulations show that the optimal protocol performs better than the maximisation of instantaneous center-of-mass speed, a protocol known to give better results for…
We study subdiffusive ratchet transport in periodically and randomly flashing potentials. Central Brownian particle is elastically coupled to surrounding auxiliary Brownian quasi-particles which account for the influence of viscoelastic environment. Similar to standard dynamical modeling of Brownian motion, the external force influences only the motion of central particle not affecting directly the environmental degrees of freedom (see video). Just a handful of auxiliary Brownian particles suffice to model subdiffusion over many temporal decades. Time-modulation of the potential violates the s…
Additive symmetric Lévy noise can induce directed transport of overdamped particles in a static asymmetric potential. We study, numerically and analytically, the effect of an additional dichotomous random flashing in such Lévy ratchet system. For this purpose we analyze and solve the corresponding fractional Fokker-Planck equations and we check the results with Langevin simulations. We study the behavior of the current as function of the stability index of the Lévy noise, the noise intensity and the flashing parameters. We find that flashing allows both to enhance and diminish in a broad range…
The flashing Brownian ratchet is a stochastic process that alternates between two regimes, a one-dimensional Brownian motion and a Brownian ratchet, the latter being a one-dimensional diffusion process that drifts towards a minimum of a periodic asymmetric sawtooth potential. The result is directed motion. In the presence of a static homogeneous force that acts in the direction opposite that of the directed motion, there is a reduction (or even a reversal) of the directed motion effect. Such a process may be called a tilted flashing Brownian ratchet. We show how one can study this process nume…
Molecular motors convert chemical energy derived from the hydrolysis of ATP into mechanical energy. A well-studied model of a molecular motor is the flashing ratchet model. We show that this model exhibits a fluctuation relation known as the Gallavotti-Cohen symmetry. Our study highlights the fact that the symmetry is present only if the chemical and mechanical degrees of freedom are both included in the description.
Korea Advanced Institute of Science and Technology（韩国科学技术院）
A collective flashing ratchet transports Brownian particles using a spatially periodic, asymmetric, and time-dependent on-off switchable potential. The net current of the particles in this system can be substantially increased by feedback control based on the particle positions. Several feedback policies for maximizing the current have been proposed, but optimal policies have not been found for a moderate number of particles. Here, we use deep reinforcement learning (RL) to find optimal policies, with results showing that policies built with a suitable neural network architecture outperform th…
Molecules with complex internal structure in time-dependent periodic potentials are studied by using short Rubinstein-Duke model polymers as an example. We extend our earlier work on transport in stochastically varying potentials to cover also deterministic potential switching mechanisms, energetic efficiency and non-uniform charge distributions. We also use currents in the non-equilibrium steady state to identify the dominating mechanisms that lead to polymer transportation and analyze the evolution of the macroscopic state (e.g., total and head-to-head lengths) of the polymers. Several numer…
The burnt-bridges ratchet (BBR) mechanism is a model for biased molecular motion whereby the construct destroys track binding sites as it progresses, and therefore acts as a diffusing forager, seeking new substrate sites. Using Monte Carlo simulations that implement the Gillespie algorithm, we investigate the kinetic characteristics of simple polyvalent BBRs as they move on tracks of increasing width. We find that as the track width is increased the BBRs remain nearly ballistic for considerable track widths proportional to the span (leg length) of the polyvalent walker, before transitioning to…
Many forms of cell motility rely on Brownian ratchet mechanisms that involve multiple stochastic processes. We present a computational and theoretical study of the nonequilibrium statistical dynamics of such a many-body ratchet, in the specific form of a growing polymer gel that pushes a diffusing obstacle. We find that oft-neglected correlations among constituent filaments impact steady-state kinetics and significantly deplete the gel's density within molecular distances of its leading edge. These behaviors are captured quantitatively by a self-consistent theory for extreme fluctuations in fi…
