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The three-dimensional (3D) chromosomal structure plays an essential role in all DNA-templated processes, including gene transcription, DNA replication and other cellular processes. Although developing chromosome conformation capture (3C) methods, such as Hi-C, which can generate chromosomal contact data characterized genome-wide chromosomal structural properties, understanding 3D genomic nature-based on Hi-C data remains lacking. Here, we propose a persistent spectral simplicial complex (PerSpectSC) model to describe Hi-C data for the first time. Specifically, a filtration process is introduced to generate a series of nested simplicial complexes at different scales. For each of these simplicial complexes, its spectral information can be calculated from the corresponding Hodge Laplacian matrix. PerSpectSC model describes the persistence and variation of the spectral information of the nested simplicial complexes during the filtration process. Different from all previous models, our PerSpectSC-based features provide a quantitative global-scale characterization of chromosome structures and topology. Our descriptors can successfully classify cell types and also cellular differentiation stages for all the 24 types of chromosomes simultaneously. In particular, persistent minimum best characterizes cell types and Dim (1) persistent multiplicity best characterizes cellular differentiation. These results demonstrate the great potential of our PerSpectSC-based models in polymeric data analysis., (© The Author(s) 2022. Published by Oxford University Press.)

Protein-protein interactions (PPIs) play a significant role in nearly all cellular and biological activities. Data-driven machine learning models have demonstrated great power in PPIs. However, the design of efficient molecular featurization poses a great challenge for all learning models for PPIs. Here, we propose persistent spectral (PerSpect) based PPI representation and featurization, and PerSpect-based ensemble learning (PerSpect-EL) models for PPI binding affinity prediction, for the first time. In our model, a sequence of Hodge (or combinatorial) Laplacian (HL) matrices at various different scales are generated from a specially designed filtration process. PerSpect attributes, which are statistical and combinatorial properties of spectrum information from these HL matrices, are used as features for PPI characterization. Each PerSpect attribute is input into a 1D convolutional neural network (CNN), and these CNN networks are stacked together in our PerSpect-based ensemble learning models. We systematically test our model on the two most commonly used datasets, i.e. SKEMPI and AB-Bind. It has been found that our model can achieve state-of-the-art results and outperform all existing models to the best of our knowledge., (© The Author(s) 2022. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

Artificial intelligence (AI) techniques have already been gradually applied to the entire drug design process, from target discovery, lead discovery, lead optimization and preclinical development to the final three phases of clinical trials. Currently, one of the central challenges for AI-based drug design is molecular featurization, which is to identify or design appropriate molecular descriptors or fingerprints. Efficient and transferable molecular descriptors are key to the success of all AI-based drug design models. Here we propose Forman persistent Ricci curvature (FPRC)-based molecular featurization and feature engineering, for the first time. Molecular structures and interactions are modeled as simplicial complexes, which are generalization of graphs to their higher dimensional counterparts. Further, a multiscale representation is achieved through a filtration process, during which a series of nested simplicial complexes at different scales are generated. Forman Ricci curvatures (FRCs) are calculated on the series of simplicial complexes, and the persistence and variation of FRCs during the filtration process is defined as FPRC. Moreover, persistent attributes, which are FPRC-based functions and properties, are employed as molecular descriptors, and combined with machine learning models, in particular, gradient boosting tree (GBT). Our FPRC-GBT models are extensively trained and tested on three most commonly-used datasets, including PDBbind-2007, PDBbind-2013 and PDBbind-2016. It has been found that our results are better than the ones from machine learning models with traditional molecular descriptors., (© The Author(s) 2021. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)