## 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 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) similar to 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.

Original language | English |
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Article number | 051916 |

Number of pages | 15 |

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

Volume | 70 |

Issue number | 5 |

DOIs | |

Publication status | Published - Nov 2004 |

## Keywords

- DIFFERENTIAL ADHESION
- MODEL
- AGGREGATION
- SIMULATION
- INTERPLAY
- WALKS