Many-body theory of chemotactic cell-cell interactions

T. J. Newman, R. Grima

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    79 Citations (Scopus)


    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 ?, statistical correlations are non-negligible at large times and lead to a renormalization of the cell diffusion coefficient DR—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 DR is renormalized to zero at a critical value of ?, 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 DR~?-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.
    Original languageEnglish
    Article number051916
    JournalPhysical Review E: Statistical, nonlinear, and soft matter physics
    Issue number5
    Publication statusPublished - 29 Nov 2004


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