生物系统的组分被（非）线性调节的程度决定了它们对治疗和控制的可操作性。为更好地理解这种被称为“调节非线性”的属性，我们使用乔治·布尔自己提出的概率布尔逻辑的推广分析了一系列137个公布的布尔网络模型，其中包含各种复杂的非线性调节相互作用。利用这种公式的连续特征，我们使用泰勒展开来近似不同调节非线性水平的模型。使用合适的随机集合比较生物模型的近似序列，发现生物调控往往比预期的非线性更小，这意味着调节输入之间的高阶相互作用往往较少。对生物模型的进一步分类分析表明，癌症和疾病网络的调节非线性不仅有时可能高于预期，而且相对更加变化。我们展示了这种变化是由于在不同调节非线性等级上信息分配的差异所引起的。研究结果表明，生物系统可能存在微弱但明显的选择压力，使其平均演变至线性调节，但对于某些系统，例如癌症，同时演变成更多的非线性规则。©2023.作者。

The extent to which the components of a biological system are (non)linearly regulated determines how amenable they are to therapy and control. To better understand this property termed "regulatory nonlinearity", we analyzed a suite of 137 published Boolean network models, containing a variety of complex nonlinear regulatory interactions, using a probabilistic generalization of Boolean logic that George Boole himself had proposed. Leveraging the continuous-nature of this formulation, we used Taylor decomposition to approximate the models with various levels of regulatory nonlinearity. A comparison of the resulting series of approximations of the biological models with appropriate random ensembles revealed that biological regulation tends to be less nonlinear than expected, meaning that higher-order interactions among the regulatory inputs tend to be less pronounced. A further categorical analysis of the biological models revealed that the regulatory nonlinearity of cancer and disease networks could not only be sometimes higher than expected but also be relatively more variable. We show that this variation is caused by differences in the apportioning of information among the various orders of regulatory nonlinearity. Our results suggest that there may have been a weak but discernible selection pressure for biological systems to evolve linear regulation on average, but for certain systems such as cancer, on the other hand, to simultaneously evolve more nonlinear rules.© 2023. The Author(s).