论文标题
布尔网络轻松可控性的基础
The basis of easy controllability in Boolean networks
论文作者
论文摘要
通常可以通过控制少数不同的不同变量来控制生物系统的有效控制。我们使用布尔动力网络的形式主义来清楚这种结果，分析外部控制在选择所需的最终状态时的有效性，当时该状态是动力学的原始吸引者之一。分析49个现有的生物网络模型，我们发现有力的数值证据表明，必须与原始吸引子数量对数进行对数的平均节点数量。这表明，即使相互作用的组件数量很大，生物网络通常也很容易控制。我们通过将控制节点分为三种类型来提供对缩放的理论解释：那些充当输入的节点，那些在吸引子之间区分吸引子和任何其余节点的类型。我们进一步确定动态的特征，这些动力学可能使这种缩放无效，并推测这与非生物系统更广泛地联系在一起。
Effective control of biological systems can often be achieved through the control of a surprisingly small number of distinct variables. We bring clarity to such results using the formalism of Boolean dynamical networks, analyzing the effectiveness of external control in selecting a desired final state when that state is among the original attractors of the dynamics. Analyzing 49 existing biological network models, we find strong numerical evidence that the average number of nodes that must be forced scales logarithmically with the number of original attractors. This suggests that biological networks may be typically easy to control even when the number of interacting components is large. We provide a theoretical explanation of the scaling by separating controlling nodes into three types: those that act as inputs, those that distinguish among attractors, and any remaining nodes. We further identify characteristics of dynamics that can invalidate this scaling, and speculate about how this relates more broadly to non-biological systems.
