Subbaroyan Ajay, Martin Olivier C, Samal Areejit
The Institute of Mathematical Sciences (IMSc), Chennai 600113, India.
Homi Bhabha National Institute (HBNI), Mumbai 400094, India.
PNAS Nexus. 2022 Apr 15;1(1):pgac017. doi: 10.1093/pnasnexus/pgac017. eCollection 2022 Mar.
The properties of random Boolean networks have been investigated extensively as models of regulation in biological systems. However, the Boolean functions (BFs) specifying the associated logical update rules should not be expected to be random. In this contribution, we focus on types of BFs, and perform a systematic study of their preponderance in a compilation of 2,687 functions extracted from published models. A surprising feature is that most of these BFs have odd "bias", that is they produce "on" outputs for a total number of input combinations that is odd. Upon further analysis, we are able to explain this observation, along with the enrichment of read-once functions (RoFs) and its nested canalyzing functions (NCFs) subset, in terms of 2 complexity measures: based on string lengths in formal logic, which is yet unexplored in biological contexts, and the so-called . RoFs minimize Boolean complexity and all such functions have odd bias. Furthermore, NCFs minimize not only the Boolean complexity but also the average sensitivity. These results reveal the importance of minimum complexity in the regulatory logic of biological networks.
作为生物系统调控模型，随机布尔网络的特性已得到广泛研究。然而，指定相关逻辑更新规则的布尔函数（BFs）不应被视为随机的。在本论文中，我们聚焦于布尔函数的类型，并对从已发表模型中提取的2687个函数汇编中它们的优势进行了系统研究。一个令人惊讶的特征是，这些布尔函数大多具有奇数“偏差”，也就是说，对于奇数个输入组合，它们会产生“开”输出。通过进一步分析，我们能够根据两种复杂度度量来解释这一观察结果，以及一次性读取函数（RoFs）及其嵌套的可分析函数（NCFs）子集的富集情况：一种基于形式逻辑中的字符串长度，这在生物学背景中尚未被探索，另一种是所谓的……RoFs将布尔复杂度最小化，并且所有此类函数都具有奇数偏差。此外，NCFs不仅将布尔复杂度最小化，还将平均敏感度最小化。这些结果揭示了最小复杂度在生物网络调控逻辑中的重要性。
