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We consider a partial differential equation model for the growth of heterogeneous cell populations subdivided into multiple distinct discrete phenotypes. In this model, cells preferentially move towards regions where they feel less…
The time distribution of relaxation events in an aging system is investigated via molecular dynamics simulations. The focus is on the distribution functions of the first passage time, $p_1(\Delta t)$, and the persistence time, $p(\tau)$. In…
A fissioning organism may purge unrepairable damage by bequeathing it preferentially to one of its daughters. Using the mathematical formalism of superprocesses, we propose a flexible class of analytically tractable models that allow quite…
As cells grow and divide under a given environment, they become crowded and resources are limited, as seen in bacterial biofilms and multicellular aggregates. These cells often show strong interactions through exchanging chemicals, as in…
Models of tissue growth are now well established, in particular in relation to their applications to cancer. They describe the dynamics of cells subject to motion resulting from a pressure gradient generated by the death and birth of cells,…
Cell division, aging, and stress recovery triggers spatial reorganization of cellular components in the cytoplasm, including membrane bound organelles, with molecular changes in their compositions and structures. However, it is not clear…
This paper investigates cells proliferation dynamics in small tumor cell aggregates using an individual based model (IBM). The simulation model is designed to study the morphology of the cell population and of the cell lineages as well as…
Cellular functions are established through biological evolution, but are constrained by the laws of physics. For instance, the physics of protein folding limits the lengths of cellular polypeptide chains. Consequently, many cellular…
Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic, or…
Cell sorting, the segregation of cells with different properties into distinct domains, is a key phenomenon in biological processes such as embryogenesis. We use a phase-field model of a confluent cell layer to study the role of activity in…
We discuss relaxation and aging processes in the one- and two-dimensional $ABC$ models. In these driven diffusive systems of three particle types, biased exchanges in one direction yield a coarsening process characterized in the long time…
Recent work on particle-based models of tissues has suggested that any finite rate of cell division and cell death is sufficient to fluidize an epithelial tissue. At the same time, experimental evidence has indicated the existence of glassy…
Maintenance and regeneration of adult tissues rely on the self-renewal of stem cells. Regeneration without over-proliferation requires precise regulation of the stem cell proliferation and differentiation rates. The nature of such…
The dynamical behavior of two types of non-equilibrium systems is discussed: $(a)$ two-dimensional cellular structures, and $(b)$ living polymers. Simple models governing their evolution are introduced and steady state distributions (cell…
We study a stochastic epidemic model with multiple patches (locations), where individuals in each patch are categorized into three compartments, Susceptible, Infected and Recovered/Removed, and may migrate from one patch to another in any…
Keeping in view applications to numerical simulations of the evolution of a nuclear reactor core around criticality, we use a general mathematical framework for describing the evolutions of multiplicative processes (processes involving…
We consider the mean-field approximation of an individual-based model describing cell motility and proliferation, which incorporates the volume exclusion principle, the go-or-grow hypothesis and an explicit cell cycle delay. To utilise the…
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…
From genomes and ecosystems to bureaucracies and cities, the growth of complex systems occurs by adding new types of functions and expanding existing ones. We present a simple generative model that generalizes the Yule-Simon process by…
Under hard-agar and nutrient-rich conditions, a cell of $Bacillus$ $subtilis$ grows as a single filament owing to the failure of cell separation after each growth and division cycle. The self-elongating filament of cells shows sequential…