Rämö Pauli, Kesseli Juha, Yli-Harja Olli
Institute of Signal Processing, Tampere University of Technology, P.O.Box 553, 33101 Tampere, Finland.
Chaos. 2005 Sep;15(3):34101. doi: 10.1063/1.1996927.
Boolean networks are used to model large nonlinear systems such as gene regulatory networks. We will present results that can be used to understand how the choice of functions affects the network dynamics. The so called bias-map and its fixed points depict much of the function's dynamical role in the network. We define the concept of stabilizing functions and show that many Post and canalizing functions are also stabilizing functions. Boolean networks constructed using the same type of stabilizing functions are always stable regardless of the average in-degree of network functions. We derive the number of all stabilizing functions and find it to be much larger than the number of Post and canalizing functions. We also discuss the implementation of functions and apply the presented results to biological data that give an approximation of the distribution of regulatory functions in eucaryotic cells. We find that the obtained theoretical results on the number of active genes are biologically plausible. Finally, based on the presented results, we discuss why canalizing and Post regulatory functions seem to be common in cells.
布尔网络用于对大型非线性系统进行建模，如基因调控网络。我们将展示一些结果，这些结果可用于理解函数的选择如何影响网络动态。所谓的偏差图及其不动点描绘了该函数在网络中的大部分动态作用。我们定义了稳定函数的概念，并表明许多波斯特函数和渠道化函数也是稳定函数。无论网络函数的平均入度如何，使用相同类型稳定函数构建的布尔网络总是稳定的。我们推导出所有稳定函数的数量，发现其比波斯特函数和渠道化函数的数量大得多。我们还讨论了函数的实现，并将所展示的结果应用于生物数据，这些数据给出了真核细胞中调控函数分布的近似值。我们发现，关于活跃基因数量的理论结果在生物学上是合理的。最后，基于所展示的结果，我们讨论了为什么渠道化和波斯特调控函数在细胞中似乎很常见。
