Hypergraph Based Persistent Cohomology(HPC) For Machine Learning In Drug Design

With the increasing development of computer and biological data,bioscience has come to big data era,which leads to the arising of machine learning.And machine learning has demonstrated great potential to significantly change the drug design and drug discovery.The key point of machine learning in drug design is a proper molecu-lar representation.Recently,a series of mathematical models from algebraic topology,differential geometry,has been proposed.Compared with traditional models,actually,significant better results have been achieved by using these mathematical models,for various aspects of drug design,including protein-ligand binding affinity prediction,pro-tein stability changes upon mutation and toxicity prediction.Especially the persistent homology based models,which has shown great power and potential to drug design.Actually,persistent homology has been applied to various fields,including image and signal analysis,chaotic dynamics verification,sensor networks,complex networks,data analysis,shape recognition and computational biology.But,there is a problem here,all the previous work related persistent homology are based on simplicial complex,and the simplicial complex is not the best choice in some cases.Hypergraph is more gen-eral concept which is a generalization of the simplicial complex.Here,we propose the first hypergraph based molecular representation.Inspired by the path complex,the embedded homology of hypergraph and corresponding persistent homology has been constructed recently.Here,to incorporate more information into the representation,we propose the hypergraph based embedded cohomology,hypergraph based persistent cohomology(HPC)and hypergraph based weighted persistent cohomology(HWPC),then we combine the HPC/HWPC with machine learning to build the HPC/HWPC-ML model.We apply our HPC/HWPC-ML model to protein-ligand binding affinity pre-diction,one of the most important steps in drug design.Our models are tested on three commonly-used databases,including the PDBbind-2007,PDBbind-2013 and PDBbind-2016.The state-of-the-art results have been achieved for all the three databases,which demonstrates the great power and potential of our model to drug design.