Many-body theory of chemotactic cell-cell interactions.
We consider an individual-based stochastic model of cell movement mediated by chemical signaling fields. This model is formulated using Langevin dynamics, which allows an analytic study using methods from statistical and many-body physics. In particular we construct a diagrammatic framework within which to study cell-cell interactions. In the mean-field limit, where statistical correlations between cells are neglected, we recover the deterministic Keller-Segel equations. Within exact perturbation theory in the chemotactic coupling epsilon , statistical correlations are non-negligible at large times and lead to a renormalization of the cell diffusion coefficient D(R)--an effect that is absent at mean-field level. An alternative closure scheme, based on the necklace approximation, probes the strong coupling behavior of the system and predicts that D(R) is renormalized to zero at a critical value of epsilon, indicating self-localization of the cell. Stochastic simulations of the model give very satisfactory agreement with the perturbative result. At higher values of the coupling simulations indicate that D(R) approximately epsilon(-2) , a result at odds with the necklace approximation. We briefly discuss an extension of our model, which incorporates the effects of short-range interactions such as cell-cell adhesion.
Newman
T J
TJ
Department of Physics and Astronomy, Arizona State University, Tempe, AZ 85284, USA.
Grima
R
R
D000465:Algorithms; D002449:Cell Aggregation / Q000502:physiology*; D002450:Cell Communication / Q000502:physiology*; D002465:Cell Movement / Q000502:physiology; D002633:Chemotaxis / Q000502:physiology*; D003198:Computer Simulation; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted