Boolean networks are a notable model of gene regulatory networks and, particularly, prominent theories discuss how they can capture cellular differentiation processes. One frequent motif in gene regulatory networks, especially in those circuits involved in cell differentiation, is autoregulation. In spite of this, the impact of autoregulation on Boolean network attractor landscape has not yet been extensively discussed in literature. In this paper we propose to model autoregulation as self-loops, and analyse how the number of attractors and their robustness may change once they are introduced in a well-known and widely used Boolean networks model, namely random Boolean networks. Results show that self-loops provide an evolutionary advantage in dynamic mechanisms of cells, by increasing both number and maximal robustness of attractors. These results provide evidence to the hypothesis that autoregulation is a straightforward functional component to consolidate cell dynamics, mainly in differentiation processes.

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自环对布尔网络吸引子格局的影响及其对细胞分化建模的影响

布尔网络是基因调控网络的一个著名模型，特别是著名的理论讨论了它们如何捕获细胞分化过程。基因调控网络中的一个常见基序，特别是在那些参与细胞分化的电路中，是自动调节。尽管如此，自动调节对布尔网络吸引子景观的影响尚未在文献中得到广泛讨论。在本文中，我们建议将自动调节建模为自环，并分析一旦将它们引入众所周知且广泛使用的布尔网络模型（即随机布尔网络）中，吸引子的数量及其鲁棒性如何变化。结果表明，通过增加吸引子的数量和最大鲁棒性，自环在细胞的动态机制中提供了进化优势。