Related papers: From Brownian Dynamics to Markov Chain: an Ion Cha…
A Markovian dichotomic system driven by a deterministic time-periodic force is analyzed in terms of the statistical properties of the switching events between the states. The consideration of the counting process of the switching events…
Einstein's explanation of Brownian motion provided one of the cornerstones which underlie the modern approaches to stochastic processes. His approach is based on a random walk picture and is valid for Markovian processes lacking long-term…
The behaviour of a system of ion channels formed across the cell membrane is presented. The infinite number of channels with an infinite coupling is introduced first as a reference point for the detailed derivation of the…
Transport of particles through channels is of paramount importance in physics, chemistry and surface science due to its broad real world applications. Much insights can be gained by observing the transition paths of a particle through a…
In these lecture notes, we explore the mathematical preliminaries and foundational concepts that connect stochastic processes with partial differential equations. We begin by investigating Brownian motion, which serves as a model for random…
A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local…
Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those…
We present an approximate analytical expression for the escape rate of time-dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrate-and-fire model for neural spiking. The novel approximation is…
We develop a formally exact technique for obtaining steady-state distributions of non-interacting active Brownian particles in a variety of systems. Our technique draws on results from the theory of two-way diffusion equations to solve the…
Neuronal cells present periodic trains of localized voltage spikes involving a large amount of different ionic channels. A relevant question is whether this is a cooperative effect or it could also be an intrinsic property of individual…
The statistical and dynamical properties of ions in the selectivity filter of the KcsA ion channel are considered on the basis of molecular dynamics (MD) simulations of the KcsA protein embedded in a lipid membrane surrounded by an ionic…
Ion-conducting glasses and polymer systems show several characteristic peculiarities in their composition-dependent diffusion properties and in their dynamic response. First we give a brief review of the current understanding of the ion…
This paper investigates the position (state) distribution of the single step binomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this…
Fluctuations in biochemical networks, e.g., in a living cell, have a complex origin that precludes a description of such systems in terms of bipartite or multipartite processes, as is usually done in the framework of stochastic and/or…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…
In this paper we propose a model for open Markov chains that can be interpreted as a system of non-interacting particles evolving according to the rules of a Markov chain. The number of particles in the system is not constant, because we…
We consider an exactly tractable model of the Kramers type for the voltage-dependent gating dynamics of single ion channels. It is assumed that the gating dynamics is caused by the thermally activated transitions in a bistable potential.…
Ion channels are important proteins for physiological information transfer and functional control. To predict the microscopic origins of their voltage-conductance characteristics, we here applied dissipation-corrected targeted Molecular…
We discuss two-dimensional diffusion of a Brownian particle confined to a periodic asymmetric channel with soft walls modeled by a parabolic potential. In the channel, the particle experiences different noise intensities, or temperatures,…
We study gradient drift-diffusion processes on a probability simplex set with finite state Wasserstein metrics, namely finite state Wasserstein common noises. A fact is that the Kolmogorov transition equation of finite reversible Markov…