In this work we use a discrete Markov chain approach combined with network centrality measures to identify and predict the location of active sites in globular proteins. To accomplish this, we use a three-dimensional network of protein C _α atoms as nodes connected through weighted edges which represent the varying interaction degree between protein’s atoms. We compute the mean first passage time matrix H = {H _ji } for this Markov chain and evaluate the averaged number of steps ⟨H _j ⟩ to reach single node n _j in order to identify such residues that, on the average, are at the least distant from every other node. We also carry out a graph theory analysis to evaluate closeness centrality C _c, betweenness centrality C _b and eigenvector centrality C _e measures which provide relevant information about the connectivity structure and topology of the C _α protein networks. Finally we also performed an analysis of equivalent random and regular networks of the same size N in terms of the average path length and the average clustering coefficient comparing these with the corresponding values for C _α protein networks. Our results show that the mean-first passage time matrix H and its related quantity ⟨H _j ⟩ together with C _c, C _b and C _e can not only predict with relative high accuracy the location of active sites in globular proteins but also exhibit a high feasibility to use them to predict the existence of new regions in protein’s structure to identify new potential binding or catalytic activity or, in some cases, the presence of new allosteric pathways.

在这项工作中，我们使用离散马尔可夫链方法结合网络中心性度量来识别和预测球状蛋白质中活性位点的位置。为此，我们使用蛋白质C _α原子的三维网络作为通过加权边连接的节点，这些边代表蛋白质原子之间不同的相互作用程度。我们计算该马尔可夫链的平均首次通过时间矩阵H = { H _ji } 并评估到达单个节点n _j的平均步数 ⟨ H _j ⟩ 为了识别这样的残基，这些残基平均而言与每个其他节点的距离最小。我们还进行了图论分析来评估接近中心性C _c、介数中心性C _b和特征向量中心性C _e度量，这些度量提供了有关C _α蛋白质网络的连接结构和拓扑的相关信息。最后，我们还在平均路径长度和平均聚类系数方面对相同大小N的等效随机和规则网络进行了分析，将这些与C _α的相应值进行比较 蛋白质网络。我们的结果表明，平均首次通过时间矩阵H及其相关量 ⟨ H _j ⟩ 连同C _c、C _b和C _e不仅可以相对高精度地预测球状蛋白质中活性位点的位置，而且还表现出使用它们来预测蛋白质结构中新区域的存在以识别新的潜在结合或催化活性，或者在某些情况下，新变构途径的存在具有很高的可行性。