Modeling biological tissue growth: Discrete to continuum representations
Modeling biological tissue growth: Discrete to continuum representations
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DOI：
10.1103/physreve.88.032704
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发表时间：
2013-09-04
影响因子：
2.4
通讯作者：
Landman, Kerry A.
中科院分区：
文献类型：
--
作者：
Hywood, Jack D.;Hackett-Jones, Emily J.;Landman, Kerry A.
有很大的兴趣，建立确定性的连续模型从离散的基于代理的模型，由当地的随机规则，代理代表一个生物细胞。在发育生物学中，细胞能够在生长的组织上和组织内移动和进行细胞分裂。一个不断增长的组织本身是由细胞进行细胞分裂，从而提供了一个显着的运输机制，为其他cells within it. We开发了一个离散的代理为基础的模型，域代理代表组织细胞。每种试剂具有经历增殖事件的能力，由此将另外的结构域试剂并入晶格中。如果一个概率分布描述了个体代理在增殖事件之间的等待时间，那么域的总长度是一个随机变量。这些随机增殖剂的平均行为定义的增长晶格确定的福克-普朗克方程，对流和扩散项。扩散项不同于Landman和Binder [J. Theor. 259，541（2009）]，但试剂的选择是随机的。通过确定这个过程的离散时间主方程和相关的不对称非排斥随机游走，以及考虑同步和异步更新方案，这种差异是协调的。所有的理论结果都与数值模拟结果相吻合。这项研究进一步加深了我们对基于代理的规则，它们的实现，以及它们相关的偏微分方程之间的关系的理解。由于组织生长是胚胎生长过程中重要的细胞运输机制，因此在与其他细胞功能结合时，使用正确的偏微分方程描述是很重要的。
There is much interest in building deterministic continuum models from discrete agent-based models governed by local stochastic rules where an agent represents a biological cell. In developmental biology, cells are able to move and undergo cell division on and within growing tissues. A growing tissue is itself made up of cells which undergo cell division, thereby providing a significant transport mechanism for other cells within it. We develop a discrete agent-based model where domain agents represent tissue cells. Each agent has the ability to undergo a proliferation event whereby an additional domain agent is incorporated into the lattice. If a probability distribution describes the waiting times between proliferation events for an individual agent, then the total length of the domain is a random variable. The average behavior of these stochastically proliferating agents defining the growing lattice is determined in terms of a Fokker-Planck equation, with an advection and diffusion term. The diffusion term differs from the one obtained Landman and Binder [J. Theor. Biol. 259, 541 (2009)] when the rate of growth of the domain is specified, but the choice of agents is random. This discrepancy is reconciled by determining a discrete-time master equation for this process and an associated asymmetric nonexclusion random walk, together with consideration of synchronous and asynchronous updating schemes. All theoretical results are confirmed with numerical simulations. This study furthers our understanding of the relationship between agent-based rules, their implementation, and their associated partial differential equations. Since tissue growth is a significant cellular transport mechanism during embryonic growth, it is important to use the correct partial differential equation description when combining with other cellular functions.