# Graph-based algorithm for common topologies of dynamic lipid clusters

## Description

Dataset includes: 1. Tcl scripts to compute H-bonds between lipids, H-bonds between lipid and water molecules (1-water bridges), interactions between lipids and ions from simulations. 2. Matlab scripts to compute lipid H-bond clusters and detect types of cluster topologies using depth-first search (DFS) algorithm. 3. Tcl script to visualize in VMD lipid H-bonds or ion interactions. Lipids are color-coded based on the topology type. 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 topology_analysis folder. "When using these scripts, please cite: " ########################################################################################################### DFS algorithm: To cluster lipid H-bond clusters and detect types of topologies, we perform Connected Component searches based on the Depth-First Search (DFS) algorithm. The DFS algorithm starts from an initial (source) node and performs exhaustive searches of all the nodes along the current path. When all nodes are visited, it moves backwards on the same path to find unvisited nodes. When all nodes of the current path are visited, the algorithm selects the next unexplored path. The computation is completed when the entire graph is explored. The Degree Centrality (DC) of a node ni gives the number of edges of the node. Algorithm computes three main types of topologies linear, star and circular and combinations thereof. All paths are catalogued according to their path length. For each lipid cluster found in the membrane and for each simulation time, the length of each path is defined as the longest number of edges between a start and an end node excluding short branches from star paths, and keep for the circular paths only the edge that connects the longest path to the end node. References: Cormen, T.H., Leiserson, C.E., Rivest, R.L. and Stein, C., 2009. Introduction to Algorithms (3-rd edition). MIT Press and McGraw-Hill. Freeman LC: Centrality in social networks. Conceptual clarification. Social Networks 1979, 1:215-239. V.K. Balakrishnan, Schaum's outline of theory and problems of graph theory, McGraw-Hill, 1997. J.L. Gross, J. Yellen, Graph theory and its applications, CRC Press, 1998.