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Metabolic heterogeneity is widely recognised as the next challenge in our understanding of non-genetic variation. A growing body of evidence suggests that metabolic heterogeneity may result from the inherent stochasticity of intracellular…
Continuous time random walks and Langevin equations are two classes of stochastic models for describing the dynamics of particles in the natural world. While some of the processes can be conveniently characterized by both of them, more…
One of the most important findings in the study of chemotactic process is self-organized cellular aggregation, and a high volume of results are devoted to the analysis of a concentration of single species. Whereas, the multi-species case is…
A novel trait-structured Keller-Segel model that explores the dynamics of a migrating cell population guided by chemotaxis in response to an external ligand concentration is derived and analysed. Unlike traditional Keller-Segel models, this…
Chemotaxis refers to the directed movement of cells in response to a chemical signal called chemoattractant. A crucial point in the mathematical modeling of chemotactic processes is the correct description of the chemotactic sensitivity and…
We investigate a stochastic version of a simple enzymatic reaction which follows the generic Michaelis-Menten kinetics. At sufficiently high concentrations of reacting species, the molecular fluctuations can be approximated as a realization…
Micro-organisms aggregate through chemotaxis against a concentration gradient of signals secreted by themselves. We have numerically studied a model consisting of elements with intracellular dynamics, random walks with a state-dependent…
Biological tissues have been observed to display emergent fluid-like properties, owing to physical interactions between cells. However, it remains unclear in general how these fluid-like properties affect tissue structure and function.…
The purpose of this work is the study of \textit{chemotaxis} and how to model it through the equations of Keller-Segel. \textit{Chemotaxis} is a natural process which induces the organisms to direct their movement according to certain…
Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin process whose friction coefficient depends on the state of a similar, unobserved process. Integrating out the latter, we derive the long…
Biological systems like ciliated microorganisms are capable to respond to the external chemical gradients, a process known as chemotaxis which has been studied here using the chiral squirmer model. This theoretical model considers the…
Binding and unbinding of ligands to specific sites of a macromolecule are one of the most elementary molecular interactions inside the cell that embody the computational processes of biological regulations. The interaction between…
We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation, instead it is based upon a dynamical…
This note provides an introduction to molecular dynamics, the computational implementation of the theory of statistical physics. The discussion is focused on the properties of Langevin dynamics, a degenerate stochastic differential equation…
In this paper we study the dynamics of stochastic microorganism flocculation models. Given the strong influence of environmental and seasonal fluctuations that are present in these models, we propose a stochastic model that includes…
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…
Many physical systems characterized by nonlinear multiscale interactions can be effectively modeled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative…
Molecular motion through pores plays a crucial role in various natural and industrial processes. One of the most fascinating features of biological channel-facilitated transport is a stochastic gating process, when the channels dynamically…
The propagation of signalling molecules within cellular networks is affected by network topology, but also by the spatial arrangement of cells in the networks. Understanding the collective reaction--diffusion behaviour in space of signals…
Collective migration of eukaryotic cells is often guided by chemotaxis, and is critical in several biological processes, such as cancer metastasis, wound healing, and embryogenesis. Understanding collective chemotaxis has challenged…