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As motivated by studies of cellular motility driven by spatiotemporal chemotactic gradients in microdevices, we develop a framework for constructing approximate analytical solutions for the location, speed and cellular densities for cell…
Cell migration is essential for regulating many biological processes in physiological or pathological conditions, including embryonic development and cancer invasion. In vitro and in silico studies suggest that collective cell migration is…
Collective cell migration plays a crucial role in numerous biological processes, including tumour growth, wound healing, and the immune response. Often, the migrating population consists of cells with various different phenotypes. This…
Non-local and non-convex energies represent fundamental interacting effects regulating the complex behavior of many systems in biophysics and materials science. We study one dimensional, prototypical schemes able to represent the behavior…
The large scale behaviour of a population of cells that grow and interact through the concentration field of the chemicals they secrete is studied using dynamical renormalization group methods. The combination of the effective long-range…
We introduce a model for describing the dynamics of large numbers of interacting cells. The fundamental dynamical variables in the model are sub-cellular elements, which interact with each other through phenomenological intra- and…
A broad range of dynamical systems involve multi-body interactions, or group interactions, which may not be encoded in traditional graphical structures. In this work, we focus on a canonical example from opinion dynamics, the Majority Rule,…
The article proposes generalizations of the macroscopic model of plasma of scalar charged particles to the cases of inter-particle interaction with multiple scalar fields and negative effective masses of these particles. The model is based…
The importance of collective cellular migration during embryogenesis and tissue repair asks for a sound understanding of underlying principles and mechanisms. Here, we address recent in vitro experiments on cell monolayers which show that…
Evaluating accessible conformational space is computationally expensive and thermal motions are partly neglected in computer models of molecular interactions. This produces error into the estimates of binding strength. We introduce a method…
We construct explicit examples of spontaneous energy generation and non-uniqueness for the compressible Euler system, with and without pressure, by taking limits of Hamiltonian dynamics as the number of molecules increases to infinity. The…
Recently, there has been a surge in the interest of non-equilibrium collective quantum models, where particle dispersion and spin are examples of effects taken into account. Here, we derive a kinetic plasma model con- taining fermion…
Although tissues are usually studied in isolation, this situation rarely occurs in biology, as cells, tissues, and organs, coexist and interact across scales to determine both shape and function. Here, we take a quantitative approach…
Tissue dynamics and collective cell motion are crucial biological processes. Their biological machinery is mostly known, and simulation models such as the "active vertex model" (AVM) exist and yield reasonable agreement with experimental…
We present a systematic review of some basic results on the derivation of classical epidemiological models from simple agent-based dynamics. The evolution of large populations is coupled with the dynamics of the contact distribution,…
While it is commonly observed that the shape dynamics of mammalian cells can undergo large random fluctuations, theoretical models aiming at capturing cell mechanics often focus on the deterministic part of the motion. In this paper, we…
This paper studies a chemotaxis system where cells move in response to a chemical signal within a confined habitat. The model includes external source terms that combine local and nonlocal growth with dampening effects. The main focus is on…
Advances in synthetic biology allow us to engineer bacterial collectives with pre-specified characteristics. However, the behavior of these collectives is difficult to understand, as cellular growth and division as well as extra-cellular…
The Vicsek model is a very popular individual based model which describes collective behavior among animal societies. A macroscopic version of the Vicsek model has been derived from a large scale limit of this individual based model…
This paper deals with the kinetic theory modeling of crowd dynamics with the aim of showing how the dynamics at the micro-scale is transferred to the dynamics of collective behaviors. The derivation of a new model is followed by a…