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We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…
The formation of a body-axis is central to animal development and involves both polarity and morphology. While polarity is traditionally associated with biochemical patterning, the morphological aspect of axis formation remains elusive. In…
We typically think of cells as responding to external signals independently by regulating their gene expression levels, yet they often locally exchange information and coordinate. Can such spatial coupling be of benefit for conveying…
The gradual accumulation of damage and dysregulation during the aging of living organisms can be quantified. Even so, the aging process is complex and has multiple interacting physiological scales -- from the molecular to cellular to whole…
The bulk-surface wave pinning model is a reaction-diffusion system for studying cell polarisation. It is constituted by a surface reaction-diffusion equation, coupled to a bulk diffusion equation with a non-linear boundary condition. Cell…
Intracellular protein patterns regulate many vital cellular functions, such as the processing of spatiotemporal information or the control of shape deformations. To do so, pattern-forming systems can be sensitive to the cell geometry by…
Active matter has played a pivotal role in advancing our understanding of non-equilibrium systems, leading to a fundamental shift in the study of biophysical phenomena. The foundation of active matter research is built on assumptions…
Traditional top-down robotic design often lacks the adaptability needed to handle real-world complexities, prompting the need for more flexible approaches. Therefore, this study introduces a novel cellular plasticity model tailored for…
We propose a theoretical and computational approach to investigate temporal behavior of a nonlinear polarization in perturbative regime induced by an intense and ultrashort pulsed electric field. First-principles time-dependent density…
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…
A dynamic model for cell differentiation is studied, where cells with internal chemical reaction dynamics interact with each other and replicate. It leads to spontaneous differentiation of cells and determination, as is discussed in the…
The organization of live cells to tissues is associated with the mechanical interaction between cells, which is mediated through their elastic environment. We model cells as spherical active force dipoles surrounded by an infinite elastic…
Cell spreading is investigated at various scales in order to understand motility of living cells which is essential for a range of physiological activities in higher organisms as well as in microbes. At a microscopic scale, it has been seen…
The organization of live cells into tissues and their subsequent biological function involves inter-cell mechanical interactions, which are mediated by their elastic environment. To model this interaction, we consider cells as spherical…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
We propose a model for cell polarization based on the Becker-D\"oring equations with the first coagulation coefficient equal to zero. We show convergence to equilibrium for power-law coagulation and fragmentation rates and obtain a loss of…
We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…
This paper deals with the derivation of a collective model of cell populations out of an individual-based description of the underlying physical particle system. By looking at the spatial distribution of cells in terms of time-evolving…
Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for…
In bacterial populations, cells are able to cooperate in order to yield complex collective functionalities. Interest in population-level cellular behaviour is increasing, due to both our expanding knowledge of the underlying biological…