A MATHEMATICAL FRAMEWORK FOR DESCRIBING AND ANALYZING GENE REGULATORY NETWORKS
A MATHEMATICAL FRAMEWORK FOR DESCRIBING AND ANALYZING GENE REGULATORY NETWORKS
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DOI：
10.1006/jtbi.1995.0199
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发表时间：
1995-09-21
影响因子：
2
通讯作者：
OMHOLT, SW
中科院分区：
文献类型：
--
作者：
MESTL, T;PLAHTE, E;OMHOLT, SW
本文提出了一个用自治微分方程描述和分析基因调控网络的数学框架。它代表了对现有框架的改进，因为它可以处理更广泛的基因调控机制。基因调控网络通常是阈值主导的，即只有当某些基因产物的浓度处于确定的阈值之间时，基因才被激活。在这里，调节域的概念被引入来描述这些区域在相空间中。每个调节域与指示函数相关联，该指示函数的值在域内为1，在域外为0。因此，指标函数反映了网络的逻辑结构。调节域之间的尖锐边界可以通过用连续S形或所谓的logoid函数替换逻辑阶跃函数来平滑。一个logoid函数与阶跃函数一致的阈值附近的一个狭窄的间隔外，并不断上升，从0到I内。使用logoid，寻找稳定状态的任务是相当简单的。相空间中的区域列表，包括所有的稳态躺在接近阈值的检查某种类型的矩阵称为Logoid-Jacobian。此外，这个矩阵导致的稳定状态的稳定性所需的条件。外部信号可以方便地以布尔变量的形式并入。因此，该框架非常适合研究单细胞和多细胞系统中的基因调控网络。(C)1995年学术出版社
This paper presents a mathematical framework for describing and analysing gene regulatory networks by autonomous differential equations. It represents an improvement on existing frameworks in that it may handle a wider range of gene regulatory mechanisms. Gene regulatory networks are frequently threshold-dominated, i.e. genes are activated only when the concentration of certain gene products lie between definite thresholds. Here, the concept of regulatory domain is introduced to describe these regions in the phase space. To each regulatory domain is associated an indicator function whose value is 1 inside and 0 outside the domain. The indicator functions thus reflect the logical structure of the network. The sharp borders between the regulatory domains may be smoothed by replacing the logical step functions by continuous sigmoids or so-called logoid functions. A logoid function coincides with the step function outside a narrow interval around the threshold, and rises continuously from 0 to I inside it. Using logoids, the task of finding steady states is considerably simplified. A list of regions in phase space comprising all steady states lying close to a threshold is obtained by examining a certain type of matrix called the Logoid-Jacobian. In addition, this matrix leads to the conditions necessary for stability of the steady states. External signals may be conveniently incorporated in the form of Boolean variables. Thus the framework is well suited for studying gene regulatory networks both in single cells and multicellular systems. (C) 1995 Academic Press Limited