### Abstract

Original language | English |
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Article number | 051916 |

Journal | Physical Review E: Statistical, Nonlinear, and Soft Matter Physics |

Volume | 70 |

Issue number | 5 |

DOIs | |

Publication status | Published - 29 Nov 2004 |

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### Cite this

*Physical Review E: Statistical, Nonlinear, and Soft Matter Physics*,

*70*(5), [051916]. https://doi.org/10.1103/PhysRevE.70.051916

}

*Physical Review E: Statistical, Nonlinear, and Soft Matter Physics*, vol. 70, no. 5, 051916. https://doi.org/10.1103/PhysRevE.70.051916

**Many-body theory of chemotactic cell-cell interactions.** / Newman, T. J.; Grima, R.

Research output: Contribution to journal › Article

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.

UR - http://www.scopus.com/inward/record.url?scp=37649030281&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.70.051916

DO - 10.1103/PhysRevE.70.051916

M3 - Article

VL - 70

JO - Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 5

M1 - 051916

ER -