Related papers: Continuous macroscopic limit of a discrete stochas…
A statistical mechanical distance constraint model (DCM) is presented that explicitly accounts for network rigidity among constraints present within a system. Constraints are characterized by local microscopic free energy functions.…
The macroscopic continuous approach of the mechanics of granular media assumes that the whole system of discrete variables (contact locations, contact forces,...) can be replaced by continuous field equations relating stress and strain on…
The migratory dynamics of cells in physiological processes, ranging from wound healing to cancer metastasis, rely on contact-mediated cell-cell interactions. These interactions play a key role in shaping the stochastic trajectories of…
Control of cell proliferation is a fundamental aspect of tissue physiology central to morphogenesis, wound healing and cancer. Although many of the molecular genetic factors are now known, the system level regulation of growth is still…
The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mesoscopic mean-filed limit, up to the corresponding…
The pedestrian flow is one of the most complex systems, involving large populations of interacting agents. Models at microscopic and macroscopic scales offer different advantages for studying related problems. In general, microscopic models…
Experimental results on the immune response to cancer indicate that activation of cytotoxic T lymphocytes (CTLs) through interactions with dendritic cells (DCs) can trigger a change in CTL migration patterns. In particular, while CTLs in…
The motile micro-organisms such as E. coli, sperm, or some seaweed are usually modelled by self-propelled particles that move with the run-and-tumble process. Individual-based stochastic models are usually employed to model the aggregation…
In this work, we investigate the dynamics of a non-local model describing spontaneous cell polarisation. It consists in a drift-diffusion equation set in the half-space, with the coupling involving the trace value on the boundary. We…
A recent burst of dynamic single-cell growth-division data makes it possible to characterize the stochastic dynamics of cell division control in bacteria. Different modeling frameworks were used to infer specific mechanisms from such data,…
Experiments show that when a monolayer of cells cultured on an elastic substrate is subject to a cyclic stretch, cells tend to re-orient either perpendicularly or at an oblique angle with respect to the main direction of the stretch. Due to…
In this paper homogenization of a mathematical model for biomechanics of a plant tissue with randomly distributed cells is considered. Mechanical properties of a plant tissue are modelled by a strongly coupled system 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…
Starting from a microscopic model for a system of neurons evolving in time which individually follow a stochastic integrate-and-fire type model, we study a mean-field limit of the system. Our model is described by a system of SDEs with…
At functional scales, cortical behavior results from the complex interplay of a large number of excitable cells operating in noisy environments. Such systems resist to mathematical analysis, and computational neurosciences have largely…
In this paper we propose a systematic approach to construct mathematical models describing populations of cancer-cells at different stages of disease development. The methodology we propose is based on stochastic Concurrent Constraint…
Computer modeling of multicellular systems has been a valuable tool for interpreting and guiding in vitro experiments relevant to embryonic morphogenesis, tumor growth, angiogenesis and, lately, structure formation following the printing of…
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…
In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the…
The dispersal of cells from an initially constrained location is a crucial aspect of many physiological phenomena ranging from morphogenesis to tumour spreading. In such processes, the way cell-cell interactions impact the motion of single…