Manke Thomas, Demetrius Lloyd, Vingron Martin
Max Planck Institute for Molecular Genetics, Ihnestr. 73, 14195 Berlin, Germany.
J R Soc Interface. 2006 Dec 22;3(11):843-50. doi: 10.1098/rsif.2006.0140.
The structure of molecular networks is believed to determine important aspects of their cellular function, such as the organismal resilience against random perturbations. Ultimately, however, cellular behaviour is determined by the dynamical processes, which are constrained by network topology. The present work is based on a fundamental relation from dynamical systems theory, which states that the macroscopic resilience of a steady state is correlated with the uncertainty in the underlying microscopic processes, a property that can be measured by entropy. Here, we use recent network data from large-scale protein interaction screens to characterize the diversity of possible pathways in terms of network entropy. This measure has its origin in statistical mechanics and amounts to a global characterization of both structural and dynamical resilience in terms of microscopic elements. We demonstrate how this approach can be used to rank network elements according to their contribution to network entropy and also investigate how this suggested ranking reflects on the functional data provided by gene knockouts and RNAi experiments in yeast and Caenorhabditis elegans. Our analysis shows that knockouts of proteins with large contribution to network entropy are preferentially lethal. This observation is robust with respect to several possible errors and biases in the experimental data. It underscores the significance of entropy as a fundamental invariant of the dynamical system, and as a measure of structural and dynamical properties of networks. Our analytical approach goes beyond the phenomenological studies of cellular robustness based on local network observables, such as connectivity. One of its principal achievements is to provide a rationale to study proxies of cellular resilience and rank proteins according to their importance within the global network context.
分子网络的结构被认为决定了其细胞功能的重要方面，例如生物体对随机扰动的恢复力。然而，细胞行为最终是由动态过程决定的，而这些动态过程受网络拓扑结构的限制。目前的工作基于动态系统理论中的一个基本关系，该关系表明稳态的宏观恢复力与潜在微观过程中的不确定性相关，这种性质可以用熵来衡量。在这里，我们使用来自大规模蛋白质相互作用筛选的最新网络数据，根据网络熵来表征可能途径的多样性。这个度量起源于统计力学，相当于从微观元素的角度对结构和动态恢复力进行全局表征。我们展示了如何使用这种方法根据网络元素对网络熵的贡献对其进行排序，还研究了这种建议的排序如何反映酵母和秀丽隐杆线虫中基因敲除和RNA干扰实验提供的功能数据。我们的分析表明，对网络熵贡献大的蛋白质的敲除优先导致致死。这一观察结果对于实验数据中几种可能的误差和偏差具有鲁棒性。它强调了熵作为动态系统的一个基本不变量以及作为网络结构和动态特性度量的重要性。我们的分析方法超越了基于局部网络可观测量（如连通性）对细胞鲁棒性的现象学研究。其主要成就之一是为研究细胞恢复力的代理指标并根据蛋白质在全局网络背景下的重要性对其进行排序提供了理论依据。
