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arXiv physics/0703026physics.bio-phq-bio.CB
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一个离散随机活细胞相互作用模型的连续宏观极限

Continuous macroscopic limit of a discrete stochastic model for interaction of living cells

Mark Alber, Nan Chen, Pavel M. Lushnikov, Stuart A. Newman

摘要:

在多尺度生物模型的发展中,建立离散的微观或介观随机模型与基于细胞密度的宏观连续描述之间的联系至关重要。本文导出了一类具有排斥体积的二维细胞Potts模型(CPM)的连续极限,该模型描述细胞在介质中运动,细胞之间通过直接接触和长程趋化作用相互作用。连续宏观模型作为描述细胞概率密度函数演化的Fokker-Planck方程得到。一般宏观模型的所有系数来自CPM的参数和CPM蒙特卡罗模拟和宏观模型的数值解之间表现出非常好的协议。它还表明,在接触细胞-细胞相互作用的情况下,所获得的模型减少到经典的宏观Keller-Segel模型。一般的多尺度方法是通过模拟松质骨形成松散包装间充质细胞通过intramelaminous路线表明,自组织的物理机制可以解释这个发展过程。

英文摘要:

In the development of multiscale biological models it is crucial to establish a connection between discrete microscopic or mesoscopic stochastic models and macroscopic continuous descriptions based on cellular density. In this paper a continuous limit of a two-dimensional Cellular Potts Model (CPM) with excluded volume is derived, describing cells moving in a medium and reacting to each other through both direct contact and long range chemotaxis. The continuous macroscopic model is obtained as a Fokker-Planck equation describing evolution of the cell probability density function. All coefficients of the general macroscopic model are derived from parameters of the CPM and a very good agreement is demonstrated between CPM Monte Carlo simulations and numerical solution of the macroscopic model. It is also shown that in the absence of contact cell-cell interactions, the obtained model reduces to the classical macroscopic Keller-Segel model. General multiscale approach is demonstrated by simulating spongy bone formation from loosely packed mesenchyme via the intramembranous route suggesting that self-organizing physical mechanisms can account for this developmental process.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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