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We consider an age-size structured cell population model based on the cell cycle length. The model is described by a first order partial differential equation with initial-boundary conditions. Using the theory of semigroups of positive…
Many imaging techniques for biological systems -- like fixation of cells coupled with fluorescence microscopy -- provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics…
Growth patterns generated by filamentous organisms (e.g. actinomycetes and fungi) involve spatial and temporal dynamics at different length scales. Several mathematical models have been proposed in the last thirty years to address these…
Directed growth, anisotropic cell shapes, and confinement drive self-organization in multicellular systems. We investigate the influence of particle shape on the distribution and dynamics of nematic microdomains in a minimal in-silico model…
The processes of gene expression are inherently stochastic, even for essential genes required for growth. How does the cell maximize fitness in light of noise? To answer this question, we build a mathematical model to explore the trade-off…
There is increasing interest in the analysis of biological tissue, its organization and its dynamics with the help of mathematical models. In the ideal case emergent properties on the tissue scale can be derived from the cellular scale.…
Dynamics maintaining diversity of cell types in a multi-cellular system are studied in relationship with the plasticity of cellular states. First, we introduce a new theoretical framework, reaction-diffusion system on `chemical species…
Based on symmetry consideration of migration and shape deformations, we formulate phenomenologically the dynamics of cell crawling in two dimensions. Forces are introduced to change the cell shape. The shape deformations induce migration of…
Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
We study discretisation effects in cellular automata models for pedestrian dynamics by reducing the cell size. Then a particle occupies more than one cell which leads to subtle effects in the dynamics, e.g. non-local conflict situations.…
Dynamics maintaining diversity of cell types in a multi-cellular system are studied in relationship with the plasticity of cellular states. By adopting a simple theoretical framework for intra-cellular chemical reaction dynamics with…
Expression of many genes varies as a cell transitions through different cell-cycle stages. How coupling between stochastic expression and cell cycle impacts cell-to-cell variability (noise) in the level of protein is not well understood. We…
We study the dynamics of gene activities in relatively small size biological networks (up to a few tens of nodes), e.g. the activities of cell-cycle proteins during the mitotic cell-cycle progression. Using the framework of deterministic…
The dynamics of cellular aggregates is driven by the interplay of mechanochemical processes and cellular activity. Although deterministic models may capture mechanical features, local chemical fluctuations trigger random cell responses,…
To maintain renewing epithelial tissues in a healthy, homeostatic state, (stem) cell divisions and differentiation need to be tightly regulated. Mechanisms of homeostatic control often rely on crowding control: cells are able to sense the…
We present feature finding and tracking algorithms in 3D in living cells, and demonstrate their utility to measure metrics important in cell biological processes. We developed a computational imaging hybrid approach that combines automated…
We propose a numerical technique for parameter inference in Markov models of biological processes. Based on time-series data of a process we estimate the kinetic rate constants by maximizing the likelihood of the data. The computation of…
Species or population that proliferate faster than others become dominant in numbers. Catalysis allows catalytic sets within a molecular reaction network to dominate the non catalytic parts of the network by processing most of the available…
Statistical and mathematical modeling are crucial to describe, interpret, compare and predict the behavior of complex biological systems including the organization of hematopoietic stem and progenitor cells in the bone marrow environment.…