arXiv subjects

Przemyslaw Chelminiak

Publications and source records attributed to Przemyslaw Chelminiak.

8 recordsLinked to original sources

arXiv2025

Rigorous results for mean first-passage time of harmonically trapped particle

The Ornstein-Uhlenbeck process of diffusion in the harmonic potential is re-examined in the context of the first-passage time problem. We investigate this problem to the extent that it has not yet been fully resolved and demonstrate exact novel results. They mainly concern the mean first-passage time for a particle diffusing downward and upward in the harmonic potential. We verify the main results of this paper by using a number of analytical techniques.

physics.gen-ph↗

arXiv2023

Information processing in biological molecular machines

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 multitude of conformation substates that make up their native state. This dynamics often manifests itself in fluctuating rates of the catalyzed processes and the presence of short-term memory. For such stochastic dynamics, after dividing the free energy into operational and organizational energy, we proved the generalized fluctuation theorem, which leads to the extension of the second law of thermodynamics to include two competing functions of process: dissipation and information. Computer simulation of the course of catalyzed processes taking place on the model network of substates, expressed in jumps of unit values at random moments of time, indicates the possibility of negative dissipation of the organizational free energy at the expense of information temporarily stored in memory, i.e. the behavior like Maxwell's demon. Because similar courses can be registered in observation of real systems, all theses of the paper are open to experimental verification.

physics.bio-ph↗

arXiv2022

First-passage time statistics for non-linear diffusion

Evaluating the completion time of a random algorithm or a running stochastic process is a valuable tip not only from a purely theoretical, but also pragmatic point of view. In the formal sense, this kind of a task is specified in terms of the first-passage time statistics. Although first-passage properties of diffusive processes, usually modeled by different types of the linear differential equations, are permanently explored with unflagging intensity, there still exists noticeable niche in this subject concerning the study of the non-linear diffusive processes. Therefore, the objective of the present paper is to fill this gap, at least to some extent. Here, we consider the non-linear diffusion equation in which a diffusivity is power-law dependent on the concentration/probability density, and analyse its properties from the viewpoint of the first-passage time statistics. Depending on the value of the power-law exponent, we demonstrate the exact and approximate expressions for the survival probability and the first-passage time distribution along with its asymptotic representation. These results refer to the freely and harmonically trapped diffusing particle. While in the former case the mean first-passage time is divergent, even though the first-passage time distribution is normalized to unity, it is finite in the latter. To support this result, we derive the exact formula for the mean first-passage time to the target prescribed in the minimum of the harmonic potential.

cond-mat.stat-mech↗

arXiv2022

Non-linear diffusion with stochastic resetting

Resetting or restart, when applied to a stochastic process, usually brings its dynamics to a time-independent stationary state. In turn, the optimal resetting rate makes the mean time to reach a target to be the shortest one. These and other intriguing problems have been intensively studied in the case of ordinary diffusive processes over the last decade. In this paper we consider the influence of stochastic resetting on a diffusive motion modeled in terms of the non-linear differential equation. The reason for its non-linearity is the power-law dependence of the diffusion coefficient on the probability density function or, in another context, the concentration of particles. We briefly outline this issue at first to prepare the foundations for our further considerations. Then, we derive an exact formula for the mean squared displacement and demonstrate how it attains the steady-state value under the influence of exponential resetting. This mechanism brings also about that the spatial support of the probability density function, which for the free non-linear diffusion is confined to the set of a finite measure, tends to span the entire domain of real numbers. In addition, we explore the first-passage properties for the non-linear diffusion intermittent by the exponential resetting and find analytical expressions for the mean first-passage time and determine numerically the optimal resetting rate which minimizes the mean time needed for a particle to reach a pre-determined target. Finally, we test and confirm the universal property that the relative fluctuation in the mean first-passage time of optimally restarted non-linear diffusion is equal to unity.

cond-mat.stat-mech↗

arXiv2018

Biological molecular machines can process information to reduce energy losses

Biological molecular machines are enzymes that simultaneously catalyze two processes, one donating free energy and second accepting it. Recent studies show that most native protein enzymes have a rich stochastic dynamics that often manifests in fluctuating rates of the catalyzed processes and the presence of short-term memory resulting from transient non-ergodicity. For such dynamics, we prove the generalized fluctuation theorem predicting a possible reduction of energy dissipation at the expense of creating some information stored in memory. The theoretical relationships are verified in computer simulations of random walk on a model critical complex network. The transient utilization of memory may turn out to be crucial for the movement of protein motors and the reason for most protein machines to operate as dimers or higher organized assemblies. From a broader physical point of view, the division of free energy into the operation and organization energy is worth emphasizing. Information can be assigned a physical meaning of a change in the value of both these functions of state.

physics.bio-ph↗

arXiv2017

Do biological molecular machines act as Maxwell's demons?

The nanoscopic isothermal machines are not only energy but also information transducers. We show that the generalized fluctuation theorem with information creation and entropy reduction can be fulfilled for the enzymatic molecular machines with the stochastic dynamics, which offers a choice of the work performance in a variety of ways. A model of such dynamics, specified by a critical complex network, is investigated. The main conclusion of the study is that the processing of free energy has to be distinguished from the processing of organization, which we identify with an adequately defined thermodynamic variable. Maxwell's demon utilizes entropy reduction for creation of information, which, from the former point of view, may be used for a reduction of energy losses, hence ultimately, for the performance of work. From the latter point of view, however, it can be used for other purposes, for example molecular recognition. This can be the case of biological molecular machines. From the biological perspective, the ascertainment is important, that the information creation and storage take place in the long lasting transient stages before completing the free energy transduction cycles. From a broader physical perspective, a supposition could be of special importance, that information is a change of organization, the thermodynamic function of state of the system.

physics.bio-ph↗

arXiv2015

Steady-state distributions of probability fluxes on complex networks

The methodology based on the random walk processes is adapted and applied to a comprehensive analysis of the statistical properties of the probability fluxes. To this aim we define a simple model of the Markovian stochastic dynamics on a complex network extended by the additional transition, called hereafter the gate. The random skips through the gate, driven by the external constant force, violate the detailed balance in the network. We argue, using a theoretical approach and numerical simulations, that the stationary distributions of the probability fluxes emergent under such conditions converge, regardless of the network topology, to the normal distribution. This result, combined with the stationary fluctuation theorem, permits to show that its standard deviation depends directly on the square root of the average flux. In turn, the central result of our paper relates this quantity to the external constant force and the two parameters that entirely characterize the normal distribution of the probability fluxes both close to as well as far from the equilibrium state. Also, the other effects that modify these parameters, such as the addition of shortcuts to the tree-like network, the extension and configuration of the gate and a change in the network size studied by means of the computer simulations are widely discussed in terms of the rigorous theoretical predictions.

cond-mat.stat-mech↗

arXiv2011

Output-input coupling in thermally fluctuating biomolecular machines

Biological molecular machines are proteins that operate under isothermal conditions hence are referred to as free energy transducers. They can be formally considered as enzymes that simultaneously catalyze two chemical reactions: the free energy-donating reaction and the free energy-accepting one. Most if not all biologically active proteins display a slow stochastic dynamics of transitions between a variety of conformational substates composing their native state. In the steady state, this dynamics is characterized by mean first-passage times between transition substates of the catalyzed reactions. On taking advantage of the assumption that each reaction proceeds through a single pair (the gate) of conformational transition substates of the enzyme-substrates complex, analytical formulas were derived for the flux-force dependence of the both reactions, the respective stalling forces and the degree of coupling between the free energy-accepting (output) reaction flux and the free energy-donating (input) one. The theory is confronted with the results of random walk simulations on the 5-dimensional hypercube. The formal proof is given that in the case of reactions proceeding through single gates, the degree of coupling cannot exceed unity. As some experiments suggest such exceeding, looking for conditions of increasing the degree of coupling over unity challenges theory. Though no analytical formulas for models involving more transition substates are available, study simulations of random walks on several model networks indicate that the case of the degree of coupling value higher than one occurs in a natural way for scale-free tree-like networks. This supports a hypothesis that the protein conformational transition networks, like higher level biological networks: the proteome and the metabolome, have evolved in a process of self-organized criticality.

physics.bio-ph↗