Many-body theory of chemotactic cell-cell interactions

T. J. Newman, R. Grima

    Research output: Contribution to journalArticle

    61 Citations (Scopus)

    Abstract

    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
    Volume70
    Issue number5
    DOIs
    Publication statusPublished - 29 Nov 2004

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    Cell
    cells
    Interaction
    Necklace
    statistical correlation
    interactions
    Mean-field Limit
    Individual-based Model
    Cell Adhesion
    Langevin Dynamics
    Odds
    Stochastic Simulation
    Approximation
    Strong Coupling
    approximation
    Renormalization
    Mean Field
    Diffusion Coefficient
    Perturbation Theory
    closures

    Cite this

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    title = "Many-body theory of chemotactic cell-cell interactions",
    abstract = "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.",
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    Many-body theory of chemotactic cell-cell interactions. / Newman, T. J.; Grima, R.

    In: Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, Vol. 70, No. 5, 051916, 29.11.2004.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Many-body theory of chemotactic cell-cell interactions

    AU - Newman, T. J.

    AU - Grima, R.

    PY - 2004/11/29

    Y1 - 2004/11/29

    N2 - 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.

    AB - 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.

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