Centrality measures and H-bond clustering in proteins

Dataset includes :

1. MATLAB workflow to compute and plot centrality measures in protein structures,
2. Tcl script to visualize centrality measures in protein structures in VMD,
3. Matlab workflow to compute H-bond clusters in protein structures,
4. Tcl script to visualize clusters in protein structures in VMD,
5. Folder sample_folder contains output results after running the scripts in folders centrality_measures & hbond_clusters
for SARS-CoV-2 spike glycoprotein in closed conformation (PDB ID: 6VXX).

Workflow is generated and tested in MATLAB R2017b and VMD 1.9.3.
Guidelines for running the scripts are in README text file in the analysis_code folder.

"When using these scripts, please cite:

Karathanou, K., Lazaratos, M., Bertalan, É., Siemers, M., Buzar, K., Schertler, G.F., Del Val, C. and Bondar, A.N., 2020. A graph-based approach identifies dynamic H-bond communication networks in spike protein S of SARS-CoV-2. Journal of structural biology, p.107617."

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Betweenness & Degree centrality measures:

The Betweenness Centrality (BC) of a node ni gives the number of shortest-distance paths between any two other nodes
nj and nk that pass via node ni divided by the total number of shortest paths that connect nj and nk irrespective of
whether they pass via node ni.
The normalized BC value of node ni is computed by dividing its BC by the number of pairs of nodes not including ni.

The Degree Centrality (DC) of a node ni gives the number of edges of the node.
The normalized DC value of node ni is computed by dividing its DC by the maximum possible edges to ni
(which is N-1, where N is the number of nodes in the graph).

References:

Freeman LC: A set of measures of centrality based on betweenness. Sociometry 1977, 40:35-41.
Freeman LC: Centrality in social networks. Conceptual clarification. Social Networks 1979, 1:215-239.
Brandes U: A faster algorithm for betweenness centrality. Journal of Mathematical Sociology 2001, 25:163-177.

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The Connected Component search gives a sub-graph of H bonds, in which at least two nodes are connected
to each other by H-bond pathways and no other nodes are connected in the sub-graph. We denote those
sub-graphs as H-bond clusters.

The cluster size is given by the total number of nodes (H-bonding amino-acid residues) of each cluster.

References:
Cormen TH, Leiserson CE, Rivest RL, Sten C (2009). Introduction to algorithms, 3rd edn. Massachusetts Institute of Technology

本数据集包含以下内容：
1. 用于计算并绘制蛋白质结构中心性指标的MATLAB工作流
2. 用于在VMD中可视化蛋白质结构中心性指标的Tcl脚本
3. 用于计算蛋白质结构氢键簇的MATLAB工作流
4. 用于在VMD中可视化蛋白质结构氢键簇的Tcl脚本
5. sample_folder文件夹包含了针对闭合构象的SARS-CoV-2刺突糖蛋白（PDB ID: 6VXX）运行上述脚本后得到的输出结果，结果分别存放于centrality_measures与hbond_clusters子文件夹中。

本工作流在MATLAB R2017b及VMD 1.9.3中开发并完成测试。脚本运行指南位于analysis_code文件夹下的README文本文件中。

使用本脚本时，请引用如下文献：
Karathanou, K., Lazaratos, M., Bertalan, É., Siemers, M., Buzar, K., Schertler, G.F., Del Val, C. 和 Bondar, A.N., 2020. 基于图论的方法识别SARS-CoV-2刺突蛋白S的动态氢键通信网络. 结构生物学杂志, 第107617页。

介数中心性（Betweenness Centrality, BC）与度中心性（Degree Centrality, DC）指标：
节点$n_i$的介数中心性（BC）为：任意其他节点$n_j$与$n_k$之间经过$n_i$的最短路径数量，除以$n_j$与$n_k$之间的总最短路径数量（无论是否经过$n_i$）。
节点$n_i$的标准化BC值为其BC值除以不包含$n_i$的节点对总数。

节点$n_i$的度中心性（DC）为该节点的边数。节点$n_i$的标准化DC值为其DC值除以该节点可连接的最大可能边数（即$N-1$，其中$N$为图中节点总数）。

参考文献：
Freeman LC: 基于介数的一系列中心性测度. 社会测量学, 1977, 40:35-41.
Freeman LC: 社会网络中的中心性：概念澄清. 社会网络, 1979, 1:215-239.
Brandes U: 一种更快的介数中心性算法. 数学社会学杂志, 2001, 25:163-177.

连通分量搜索可得到氢键子图，其中至少有两个节点通过氢键通路相互连接，且无其他节点接入该子图。我们将此类子图称为氢键簇。
簇的大小由每个簇所包含的节点（即形成氢键的氨基酸残基）总数决定。

参考文献：
Cormen TH, Leiserson CE, Rivest RL, Sten C (2009). 《算法导论》（第3版）. 麻省理工学院出版社。