Related papers: Collective motion driven by nutrient consumption
A packed community of exponentially proliferating microbes will spread in size exponentially. However, due to nutrient depletion, mechanical constraints, or other limitations, exponential proliferation is not indefinite, and the spreading…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Swarming or collective motion of living entities is one of the most common and spectacular manifestations of living systems having been extensively studied in recent years. A number of general principles have been established. The…
Behavior of the mixture of particles and dimers moving with different jump rates at reconstructed surfaces is described. Collective diffusion coefficient is calculated by the variational approach. Anisotropy of the collective particle…
Cells move differently on substrates with different elasticities. In particular, the persistence time of their motion is higher on stiffer substrates. We show that this behavior will result in a net transport of cells directed up a…
The mechanisms driving the collective movement of cells remain poorly understood. To contribute toward resolving this mystery, a model was formulated to theoretically explore the possible functions of polarized cell-cell adhesion in…
To explore the coupling between a growing population of microorganisms such as E. coli and a nonuniform nutrient distribution, we formulate a minimalistic model. It consists of active Brownian particles that divide and grow at a…
Spontaneous directed motion, a hallmark of cell biology, is unusual in classical statistical physics. Here we study, using both numerical and analytical methods, organized motion in models of the cytoskeleton in which constituents are…
We explore the emergence of nonequilibrium collective motion in disordered non-thermal active matter when persistent motion and crowding effects compete, using simulations of a two-dimensional model of size polydisperse self-propelled…
The main purpose of this work is the mathematical modelling of large populations of cells under different deterministic interactions among themselves, in balance with naturally random diffusion. We focus on cell-cell adhesion mechanisms for…
We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior. Our aim is to provide a balanced discussion of the…
Collective cell migration is a key driver of embryonic development, wound healing, and some types of cancer invasion. Here we provide a physical perspective of the mechanisms underlying collective cell migration. We begin with a catalogue…
The spread of a particular trait in a cell population often is modelled by an appropriate system of ordinary differential equations describing how the sizes of subpopulations of the cells with the same genome change in time. On the other…
In this paper we develop mathematical models for collective cell motility. Initially we develop a model using a linear diffusion-advection type equation and fit the parameters to data from cell motility assays. This approach is helpful in…
Diffusion of a two component fluid is studied in the framework of differential equations, but where these equations are systematically derived from a well-defined microscopic model. The model has a finite carrying capacity imposed upon it…
Tracking experiments in dense biological tissues reveal a diversity of sources f or local energy injection at the cell scale. The effect of cell motility has been largely studied, but much less is known abo ut the effect of the observed…
The dynamical equation satisfied by the density matrix, when a quantum system is subjected to one or more constraints arising from conserved quantities, is derived. The resulting nonlinear motion of the density matrix has the property that…
An ordinary differential equation perturbed by a null-recurrent diffusion will be considered in the case where the averaging type perturbation is strong only when a fast motion is close to the origin. The normal deviations of these…
We revisit the classical population genetics model of a population evolving under multiplicative selection, mutation and drift. The number of beneficial alleles in a multi-locus system can be considered a trait under exponential selection.…
Many natural and industrial processes rely on constrained transport, such as proteins moving through cells, particles confined in nanocomposite materials or gels, individuals in highly dense collec- tives and vehicular traffic conditions.…