## Abstract

We propose a hypothesis for a unified understanding of the persistent and biased random walk behavior of leukocytes exhibiting random motility and chemotaxis, respectively. This hypothesis is based on a description of the leukocyte as an integrated system sensing and responding to a "noisy" receptor signal: random fluctuations inherent in receptor-sensing of chemoattractant concentrations underlie the random walk behavior. Noise arises from real fluctuations in the receptor binding process, which translate into perceived fluctuations in receptor-measured concentration. The unbiased random walk characteristic of random motility arises from perceived fluctuating gradients without a mean reference direction and the biased random walk in chemotaxis arises due to the occurrence of perceived concentration fluctuations around the mean gradient. Analysis of a stochastic model based on this hypothesis yields an objective index of directional randomness in random motility, the directional persistence time, in terms of model parameters associated with receptor binding, receptor signal transduction, and the cell turning response. Simulation of the model equations yields cell paths from which the orientation behavior in a chemoattractant gradient is characterized in terms of the same model parameters. Our results provide a theoretical relationship between directional persistence and orientation bias and suggest quantitative answers to the questions: Is there an optimal level of persistence with respect to maximizing orientation bias? Do directional persistence and orientation bias both display the same parametric sensitivity? How does this sensitivity depend on the sensing, transduction, and response components of the cell system?

Original language | English (US) |
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Pages (from-to) | 229-262 |

Number of pages | 34 |

Journal | Journal of Mathematical Biology |

Volume | 25 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1 1987 |

## Keywords

- Cell migration
- Cell orientation
- Chemoreception
- Chemotaxis
- Mathematical model
- Random motility
- Receptor sensing
- Stochastic model