Dowker complex based machine learning (DCML) models for protein-ligand binding affinity prediction
Fig 2
Persistent combinatorial Laplacian matrixes for Dowker complex from C-C pair of PDBID 2POG.
As in the picture, based on the filtration process of bipartite graphes, a filtration of Dowker complexes can be generated and further divided into two disjoint filtration processes in protein and ligand. Then for each filtration process, two sequence of laplacian matrixes in dimension 0 and 1 are depicted. The cutoff extracting the binding core region is 5Å, filtration values are 3.5Å, 4Å, 4.2Å, 4.5Å and 5Å. For 0-D laplacian matrixes, with the increase of filtration value, the matrix size is always same, off-diagonal entries decrease from 0 to -1 until all become -1 and diagonal entries increase until all up to the number of 0-simplexes minus 1. For 1-D laplacian matrixes, the matrix size increase consistently until up to a constant, and off-diagonal entries have nonzero values 1 and -1 due to their oriention and the number of off-diagonal nonzero entries increase at early stage and then decrease until all go to zero, and diagonal entries increase until all up to the number of 0-simplexes.