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arXiv 2005.03144q-bio.MNcond-mat.dis-nn
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基因调控网络上的渗流

Percolation on the gene regulatory network

Giuseppe Torrisi, Reimer Kühn, Alessia Annibale

摘要:

我们考虑一个简化的基因调控模型,其中基因表达受转录因子(TF)调控,TF是单一蛋白质或蛋白质复合物。蛋白质又由表达的基因合成,形成一个调节的反馈回路。这导致有向二分网络,其中如果基因编码对TF有贡献的蛋白质,则存在从基因到TF的链接,并且如果TF调节基因的表达,则存在从TF到基因的链接。基因和TF都被建模为二元变量,分别表示基因是否表达,TF是否合成。我们考虑的情况下,TF被合成,其所有的贡献基因必须表达。这导致TF的动态的“与”门逻辑。通过将渗流理论应用于有向二分图,根据AND逻辑动力学进行演化,我们能够确定必要条件,在网络参数空间中,在该条件下,二分网络可以支持多种稳定的基因表达模式,在嘈杂的条件下,如稳定细胞类型所需。特别是,分析揭示了一个双稳定区域的可能性,其中广泛的集群是或不是弹性扰动。这与在标准渗流理论中观察到的转变明显不同。最后,我们考虑扰动涉及单节点删除模仿基因敲除实验。结果揭示了基因敲除级联对底层网络动力学中实现的逻辑的强烈依赖,特别强调了雪崩大小不能轻易与基因-基因相互作用网络相关。

英文摘要:

We consider a simplified model for gene regulation, where gene expression is regulated by transcription factors (TFs), which are single proteins or protein complexes. Proteins are in turn synthesised from expressed genes, creating a feedback loop of regulation. This leads to a directed bipartite network in which a link from a gene to a TF exists if the gene codes for a protein contributing to the TF, and a link from a TF to a gene exists if the TF regulates the expression of the gene. Both genes and TFs are modelled as binary variables, which indicate, respectively, whether a gene is expressed or not, and a TF is synthesised or not. We consider the scenario where for a TF to be synthesised, all of its contributing genes must be expressed. This results in an ``AND'' gate logic for the dynamics of TFs. By adapting percolation theory to directed bipartite graphs, evolving according to the AND logic dynamics, we are able to determine the necessary conditions, in the network parameter space, under which bipartite networks can support a multiplicity of stable gene expression patterns, under noisy conditions, as required in stable cell types. In particular, the analysis reveals the possibility of a bi-stability region, where the extensive percolating cluster is or is not resilient to perturbations. This is remarkably different from the transition observed in standard percolation theory. Finally, we consider perturbations involving single node removal that mimic gene knockout experiments. Results reveal the strong dependence of the gene knockout cascade on the logic implemented in the underlying network dynamics, highlighting in particular that avalanche sizes cannot be easily related to gene-gene interaction networks.

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