Identification of Autism Spectrum Disorder Using Topological Data Analysis.

Autism spectrum disorder (ASD) is a pervasive brain development disease. Recently, the incidence rate of ASD has increased year by year and posed a great threat to the lives and families of individuals with ASD. Therefore, the study of ASD has become very important. A suitable feature representation that preserves the data intrinsic information and also reduces data complexity is very vital to the performance of established models. Topological data analysis (TDA) is an emerging and powerful mathematical tool for characterizing shapes and describing intrinsic information in complex data. In TDA, persistence barcodes or diagrams are usually regarded as visual representations of topological features of data. In this paper, the Regional Homogeneity (ReHo) data of subjects obtained from Autism Brain Imaging Data Exchange (ABIDE) database were used to extract features by using TDA. The average accuracy of cross validation on ABIDE I database was 95.6% that was higher than any other existing methods (the highest accuracy among existing methods was 93.59%). The average accuracy for sampling with the same resolutions with the ABIDE I on the ABIDE II database was 96.5% that was also higher than any other existing methods (the highest accuracy among existing methods was 75.17%).

An application of topological data analysis in predicting sumoylation sites.

Sumoylation is a reversible post-translational modification that regulates certain significant biochemical functions in proteins. The protein alterations caused by sumoylation are associated with the incidence of some human diseases. Therefore, identifying the sites of sumoylation in proteins may provide a direction for mechanistic research and drug development. Here, we propose a new computational approach for identifying sumoylation sites using an encoding method based on topological data analysis. The features of our model captured the key physical and biological properties of proteins at multiple scales. In a 10-fold cross validation, the outcomes of our model showed 96.45% of sensitivity (Sn), 94.65% of accuracy (Acc), 0.8946 of Matthew's correlation coefficient (MCC), and 0.99 of area under curve (AUC). The proposed predictor with only topological features achieves the best MCC and AUC in comparison to the other released methods. Our results suggest that topological information is an additional parameter that can assist in the prediction of sumoylation sites and provide a novel perspective for further research in protein sumoylation.

Persistent homology and application on residues 1 to 28 of amyloid beta peptide.

This article combines the principal component analysis (PCA) with persistent homology for applications in biomolecular data analysis. We extend the technique of persistent homology to localized weighted persistent homology to fit the properties of molecules. We introduce this novel PCA in the study of the folding process of residues 1 to 28 of amyloid beta peptide in solution. We are able to determine seven metastable states of amyloid beta 1 to 28 using homology of dimension 2, corresponding to seven local minimums in the free energy landscape. We also give the transition information between the seven types and the disconnectivity graph. Our result is very robust under change of parameters. Furthermore persistent homology of dimension 1 also give consistent results. This method can be applied to different peptides and molecules.