Related papers: Macroscopic dynamics of biological cells interacti…
A biophysical issue how the nuclear size dynamically scales with the cellular size remains mysterious. We develop a theoretical framework in which the interactions between polydisperse biomolecules and the mechanical elasticity of the cell…
Recent advancements in the ability to construct three-dimensional (3D) tissues and organoids from stem cells and biomaterials have not only opened abundant new research avenues in disease modeling and regenerative medicine but also have…
We study a chemotaxis-consumption mechanism, in which some chemical signal and cells density interact each other. In order to control the concentration of such a population, sources involving gradient nonlinearities, which introduce a…
Cell cultures exhibit rich and complex behaviors driven by dynamic metabolic interactions among cells. In this work, we present a model that captures these interactions through a framework inspired by statistical mechanics. Using Monte…
The calcium transport in biological systems is modelled as a reaction-diffusion process. Nonlinear calcium waves are then simulated using a stochastic cellular automaton whose rules are derived from the corresponding coupled partial…
The filtration of fluid in 2D porous medium is simulated by the molecular dynamics technique. The high concentration of fluid is created at the initial point in time and the number of fluid particles is investigated in all porous. The…
Chemotaxis refers to the directed movement of cells in response to a chemical signal called chemoattractant. A crucial point in the mathematical modeling of chemotactic processes is the correct description of the chemotactic sensitivity and…
We develop and analyse a discrete, one-dimensional model of cell motility which incorporates the effects of volume filling, cell-to-cell adhesion and chemotaxis. The formal continuum limit of the model is a nonlinear generalisation of the…
We study the dynamics of proliferating cell collectives whose microscopic constituents' growth is inhibited by macroscopic growth-induced stress. Discrete particle simulations of a growing collective show the emergence of concentric-ring…
Recently, hybrid models have emerged that combine microscopic and mesoscopic regimes in a single stochastic reaction-diffusion simulation. Microscopic simulations track every individual molecule and are generally more accurate. Mesoscopic…
Many living and physical systems such as cell aggregates, tissues or bacterial colonies behave as unconventional systems of particles that are strongly constrained by volume exclusion and shape interactions. Understanding how these…
A molecule traveling in a realistic propagation environment can experience stochastic interactions with other molecules and the environment boundary. The statistical behavior of some isolated phenomena, such as dilute unbounded molecular…
We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…
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…
A stochastic differential equation for the plasma density dynamics is derived, consistent with the experimentally measured distribution and the theoretical quadratic nonlinearity. The plasma density is driven by a multiplicative Wiener…
Chemotaxis, the directional locomotion of cells towards a source of a chemical gradient, is an integral part of many biological processes - for example, bacteria motion, single-cell or multicellular organisms development, immune response,…
We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two…
We propose a three dimensional mechanical model of embryonic tissue dynamics. Mechanically coupled adherent cells are represented as particles interconnected with elastic beams which can exert non-central forces and torques. Tissue…
Unlike macroscopic engines, the molecular machinery of living cells is strongly affected by fluctuations. Stochastic Thermodynamics uses Markovian jump processes to model the random transitions between the chemical and configurational…
We consider here a discrete system of spheres interacting through a lubrication force. This force is dissipative, and singular near contact: it behaves like the reciprocal of interparticle distance. We propose a macroscopic constitutive…