Serra R, Villani M, Graudenzi A, Kauffman S A
Dipartimento di scienze sociali, cognitive e quantitative, Università di Modena e Reggio Emilia, Via Allegri 9, 42100 Reggio Emilia, Italy.
J Theor Biol. 2007 Jun 7;246(3):449-60. doi: 10.1016/j.jtbi.2007.01.012. Epub 2007 Jan 24.
In a previous study it was shown that a simple random Boolean network model, with two input connections per node, can describe with a good approximation (with the exception of the smallest avalanches) the distribution of perturbations in gene expression levels induced by the knock-out of single genes in Saccharomyces cerevisiae. Here we address the reason why such a simple model actually works: we present a theoretical study of the distribution of avalanches and show that, in the case of a Poissonian distribution of outgoing links, their distribution is determined by the value of the Derrida exponent. This explains why the simulations based on the simple model have been effective, in spite of the unrealistic hypothesis about the number of input connections per node. Moreover, we consider here the problem of the choice of an optimal threshold for binarizing continuous data, and we show that tuning its value provides an even better agreement between model and data, valuable also in the important case of the smallest avalanches. Finally, we also discuss the choice of an optimal value of the Derrida parameter in order to match the experimental distributions: our results indicate a value slightly below the critical value 1.
在之前的一项研究中表明，一种简单的随机布尔网络模型，每个节点有两个输入连接，可以很好地近似描述（除了最小的雪崩）酿酒酵母中单个基因敲除所诱导的基因表达水平扰动的分布。在这里，我们探讨这样一个简单模型实际起作用的原因：我们对雪崩分布进行了理论研究，并表明，在输出链接呈泊松分布的情况下，它们的分布由德里达指数的值决定。这解释了为什么基于简单模型的模拟是有效的，尽管关于每个节点输入连接数量的假设不现实。此外，我们在这里考虑对连续数据进行二值化时最优阈值的选择问题，并且我们表明调整其值能使模型与数据之间的一致性更好，这在最小雪崩的重要情况下也很有价值。最后，我们还讨论了为匹配实验分布而选择德里达参数的最优值：我们的结果表明该值略低于临界值1。
