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In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing…
We study a coarsening process of one-dimensional cell complexes. We show that if cell boundaries move with velocities proportional to the difference in size of neighboring cells, then the average cell size grows at a prescribed exponential…
Understanding the biological mechanisms of disease is crucial for medicine, and in particular, for drug discovery. AI-powered analysis of genome-scale biological data holds great potential in this regard. The increasing availability of…
In the self-assembly process which drives the formation of cellular membranes, micelles, and capsids, a collection of separated subunits spontaneously binds together to form functional and more ordered structures. In this work, we study the…
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated…
We investigate the distribution of cells by dimension in cylindrical algebraic decompositions (CADs). We find that they follow a standard distribution which seems largely independent of the underlying problem or CAD algorithm used. Rather,…
We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values…
Most microorganisms regulate their cell size. We review here some of the mathematical formulations of the problem of cell size regulation. We focus on coarse-grained stochastic models and the statistics they generate. We review the…
Asymmetric segregation of key proteins at cell division -- be it a beneficial or deleterious protein -- is ubiquitous in unicellular organisms and often considered as an evolved trait to increase fitness in a stressed environment. Here, we…
Spatial models where growth is limited to the edge of the expansions have been instrumental to understand the population dynamics and the clone size distribution in growing cellular populations, such as microbial colonies and avascular…
Populations are heterogeneous, deviating in numerous ways. Phenotypic diversity refers to the range of traits or characteristics across a population, where for cells this could be the levels of signalling, movement and growth activity, etc.…
Processes of random tessellations of the Euclidean space $\mathbb{R}^d$, $d\geq 1$, are considered which are generated by subsequent division of their cells. Such processes are characterized by the laws of the life times of the cells until…
Understanding biological phenomena requires a systemic approach that incorporates different mechanisms acting on different spatial and temporal scales, since in organisms the workings of all components, such as organelles, cells, and organs…
Background: Duplication of genes is important for evolution of molecular networks. Many authors have therefore considered gene duplication as a driving force in shaping the topology of molecular networks. In particular it has been noted…
How far is neuroepithelial cell proliferation in the developing central nervous system a deterministic process? Or, to put it in a more precise way, how accurately can it be described by a deterministic mathematical model? To provide tracks…
A major goal of modern computational biology is to simulate the collective behaviour of large cell populations starting from the intricate web of molecular interactions occurring at the microscopic level. In this paper we describe a…
The employment of nonlocal PDE models to describe biological aggregation and other phenomena has gained considerable traction in recent years. For cell populations, these methods grant a means of accommodating essential elements such as…
We examine the budding of a nanoscale particle through a lipid bilayer using molecular dynamics simulations, free energy calculations, and an elastic theory, with the aim of determining the extent to which equilibrium elasticity theory can…
The evolution of various competing cell types in tissues, and the resulting persistent tissue population, is studied numerically and analytically in a particle-based model of active tissues. Mutations change the properties of cells in…
Computation biology helps to understand all processes in organisms from interaction of molecules to complex functions of whole organs. Therefore, there is a need for mathematical methods and models that deliver logical explanations in a…