Ribeiro Andre S, Kauffman Stuart A
Institute for Biocomplexity and Informatics, University of Calgary, Canada.
J Theor Biol. 2007 Aug 21;247(4):743-55. doi: 10.1016/j.jtbi.2007.04.020. Epub 2007 Apr 27.
We investigate the hypothesis that cell types are attractors. This hypothesis was criticized with the fact that real gene networks are noisy systems and, thus, do not have attractors [Kadanoff, L., Coppersmith, S., Aldana, M., 2002. Boolean Dynamics with Random Couplings. http://www.citebase.org/abstract?id=oai:arXiv.org:nlin/0204062]. Given the concept of "ergodic set" as a set of states from which the system, once entering, does not leave when subject to internal noise, first, using the Boolean network model, we show that if all nodes of states on attractors are subject to internal state change with a probability p due to noise, multiple ergodic sets are very unlikely. Thereafter, we show that if a fraction of those nodes are "locked" (not subject to state fluctuations caused by internal noise), multiple ergodic sets emerge. Finally, we present an example of a gene network, modelled with a realistic model of transcription and translation and gene-gene interaction, driven by a stochastic simulation algorithm with multiple time-delayed reactions, which has internal noise and that we also subject to external perturbations. We show that, in this case, two distinct ergodic sets exist and are stable within a wide range of parameters variations and, to some extent, to external perturbations.
我们研究了细胞类型是吸引子这一假设。该假设受到了批评，原因是实际的基因网络是有噪声的系统，因此没有吸引子[卡达诺夫，L.，科普史密斯，S.，阿尔达纳，M.，2002年。具有随机耦合的布尔动力学。http://www.citebase.org/abstract?id=oai:arXiv.org:nlin/0204062]。鉴于“遍历集”的概念，即系统一旦进入该状态集，在受到内部噪声影响时就不会离开，首先，我们使用布尔网络模型表明，如果吸引子上所有状态的节点由于噪声而以概率p发生内部状态变化，那么多个遍历集出现的可能性极小。此后，我们表明，如果这些节点中有一部分被“锁定”（不受内部噪声引起的状态波动影响），就会出现多个遍历集。最后，我们给出一个基因网络的例子，该网络用转录、翻译和基因 - 基因相互作用的现实模型进行建模，由具有多个时间延迟反应的随机模拟算法驱动，存在内部噪声且我们还对其施加外部扰动。我们表明，在这种情况下，存在两个不同的遍历集，并且在广泛的参数变化范围内以及在一定程度上对外部扰动都是稳定的。
