Multistability and Hysteresis-Based Mechanism of Pattern Formation in Biology
Multistability and Hysteresis-Based Mechanism of Pattern Formation in Biology
复制标题
生物学中模式形成的多稳定性和基于滞后的机制
DOI：
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
A. Marciniak
中科院分区：
文献类型：
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作者：
Alexander Köthe;A. Marciniak
多稳定性在细胞信号传导中起着重要作用。再加上扩散过程，它可能在化学和生物系统中产生空间格局。这些过程导致具有多个稳态的非线性动力学模型，这与通常的反应扩散系统不同。为了研究基于这些概念的模式形成机制，我们提出了一个由反应扩散方程与常微分方程耦合组成的模型。数学建模的试验生物是一种淡水水螅。这里考虑的模型是Marciniak-Czochra （Math Biosci 199:97 - 119,2006）提出的具有多稳定性的基于受体的模型的最小版本。它描述了通过扩散分子耦合到细胞间通信的非线性细胞内信号的动力学，并显示了动力学系统中的双稳定性和滞后性如何导致空间模式。特别指出，没有迟滞效应的多重稳定性不足以产生稳定的模式。在生物学上，这个模型解释了诸如接枝之类的实验结果，这些结果不容易用纯粹的反应-扩散（图灵型）模式来解释。
Multistability plays an important role in cell signalling. Coupled with the diffusion process, it may give rise to spatial patterns in chemical and biological systems. Such processes lead to nonlinear dynamical models with multiple steady states, which differ from the usual reaction–diffusion systems. To investigate mechanism of pattern formation based on these concepts we propose a model consisting of a reaction–diffusion equation coupled with an ordinary differential equation. The test organism for mathematical modelling is a fresh-water polyp Hydra. The model considered here is a minimal version of the receptor-based model with multistability proposed by Marciniak-Czochra (Math Biosci 199:97–119, 2006). It describes the dynamics of nonlinear intracellular signalling coupled to cell-to-cell communication via diffusive molecules and shows how bistability and hysteresis in the kinetic system may result in spatial patterning. In particular, it is shown that multistability without the hysteresis effect is not enough for creation of stable patterns. Biologically, this model explains results of experiments such as grafting which are not easily explicable by the pure reaction–diffusion (Turing type) patterning.
DOI：
10.1387/ijdb.072493rb
发表时间：
2009
期刊：
The International journal of developmental biology
影响因子：
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作者：
Baker RE;Schnell S;Maini PK
通讯作者：
Maini PK
DOI：
10.1073/pnas.0510398103
发表时间：
2006-08
影响因子：
11.1
作者：
David M. Umulis;M. Serpe;M. O’Connor;H. Othmer
通讯作者：
David M. Umulis;M. Serpe;M. O’Connor;H. Othmer
影响因子：
3.3
作者：
Cross, FR;Archambault, V;Klovstad, M
通讯作者：
Klovstad, M