Proteins are the most important biomolecules for living organisms. The understanding of protein structure, function, dynamics and transport is one challenging tasks in biological science. In present work, persistent homology is, first time, introduced extracting molecular topological fingerprints (MTFs) based on persistence invariants. MTFs utilized characterization, identification classification. method slicing proposed to track geometric origin Both all-atom coarse-grained representations...

PerSpect-based machine learning models can significantly improve prediction accuracy for protein-ligand binding affinity.

This work presents a few variational multiscale models for charge transport in complex physical, chemical, and biological systems engineering devices, such as fuel cells, solar battery nanofluidics, transistors, ion channels. An essential ingredient of the present models, introduced an earlier paper [Bull. Math. Biol., 72 (2010), pp. 1562--1622], is use differential geometry theory surfaces natural means to geometrically separate macroscopic domain from microscopic domain, while dynamically...

Persistent homology is a relatively new tool often used for qualitative analysis of intrinsic topological features in images and data originated from scientific engineering applications. In this article, we report novel quantitative predictions the energy stability fullerene molecules, very first attempt using persistent context. The ground-state structures series small molecules are investigated with standard Vietoris–Rips complex. We decipher all barcodes, including both short-lived local...

Abstract Accelerated materials development with machine learning (ML) assisted screening and high throughput experimentation for new photovoltaic holds the key to addressing our grand energy challenges. Data-driven ML is envisaged as a decisive enabler perovskite discovery. However, its full potential can be severely curtailed by poorly represented molecular descriptors (or fingerprints). Optimal are essential establishing effective mathematical representations of quantitative...

The emerging complexity of large macromolecules has led to challenges in their full scale theoretical description and computer simulation. Multiscale multiphysics multidomain models have been introduced reduce the number degrees freedom while maintaining modeling accuracy achieving computational efficiency. A total energy functional is constructed put energies for polar nonpolar solvation, chemical potential, fluid flow, molecular mechanics, elastic dynamics on an equal footing. variational...

Abstract Protein function and dynamics are closely related to its sequence structure.However, prediction of protein from structure is still a fundamental challenge in molecular biology. classification, which typically done through measuring the similarity between proteins based on or physical information, serves as crucial step toward understanding dynamics. Persistent homology new branch algebraic topology that has found success topological data analysis variety disciplines, including The...

Persistent homology has emerged as a popular technique for the topological simplification of big data, including biomolecular data. Multidimensional persistence bears considerable promise to bridge gap between geometry and topology. However, its practical robust construction been challenge. We introduce two families multidimensional persistence, namely pseudomultidimensional multiscale persistence. The former is generated via repeated applications persistent filtration high‐dimensional such...

A suitable feature representation that can both preserve the data intrinsic information and reduce complexity dimensionality is key to performance of machine learning models. Deeply rooted in algebraic topology, persistent homology (PH) provides a delicate balance between simplification structure characterization, has been applied various areas successfully. However, combination PH hindered greatly by three challenges, namely topological data, PH-based distance measurements or metrics,...

Protein structural fluctuation, typically measured by Debye-Waller factors, or B-factors, is a manifestation of protein flexibility, which strongly correlates to function. The flexibility-rigidity index (FRI) newly proposed method for the construction atomic rigidity functions required in theory continuum elasticity with rigidity, new multiscale formalism describing excessively large biomolecular systems. FRI analyzes and flexibility capable predicting B-factors without resorting matrix...

Abstract In this paper, we systematically review weighted persistent homology (WPH) models and their applications in biomolecular data analysis. Essentially, the weight value, which reflects physical, chemical biological properties, can be assigned to vertices (atom centers), edges (bonds), or higher order simplexes (cluster of atoms), depending on structure, function, dynamics properties. Further, propose first localized (LWPH). Inspired by great success element specific (ESPH), do not...

Efficient molecular featurization is one of the major issues for machine learning models in drug design. Here, we propose a persistent Ricci curvature (PRC), particular, Ollivier PRC (OPRC), and feature engineering, first time. The filtration process proposed homology employed to generate series nested graphs. Persistence variation curvatures on these graphs are defined as OPRC. Moreover, attributes, which statistical combinatorial properties OPRCs during process, used descriptors further...

Abstract Artificial intelligence (AI) techniques have already been gradually applied to the entire drug design process, from target discovery, lead optimization and preclinical development final three phases of clinical trials. Currently, one central challenges for AI-based is molecular featurization, which identify or appropriate descriptors fingerprints. Efficient transferable are key success all models. Here we propose Forman persistent Ricci curvature (FPRC)-based featurization feature...

Molecular descriptors are essential to not only quantitative structure activity/property relationship (QSAR/QSPR) models, but also machine learning based chemical and biological data analysis. In this paper, we propose persistent spectral hypergraph (PSH) molecular or fingerprints for the first time. Our PSH-based used in characterization of structures interactions, further combined with particular gradient boosting tree (GBT), protein-ligand binding affinity prediction. Different from...

Abstract Graph neural networks (GNNs) are the most promising deep learning models that can revolutionize non-Euclidean data analysis. However, their full potential is severely curtailed by poorly represented molecular graphs and features. Here, we propose a multiphysical graph network (MP-GNN) model based on developed representation featurization. All kinds of interactions, between different atom types at scales, systematically series scale-specific element-specific with distance-related...

Protein-protein interactions (PPIs) play a significant role in nearly all cellular and biological activities. Data-driven machine learning models have demonstrated great power PPIs. However, the design of efficient molecular featurization poses challenge for Here, we propose persistent spectral (PerSpect) based PPI representation featurization, PerSpect-based ensemble (PerSpect-EL) binding affinity prediction, first time. In our model, sequence Hodge (or combinatorial) Laplacian (HL)...

Molecular representations are of fundamental importance for the modeling and analysing molecular systems. The successes in drug design materials discovery have been greatly contributed by representation models. In this paper, we present a computational framework that is mathematically rigorous based on persistent Dirac operator. properties discrete weighted unweighted matrix systematically discussed, biological meanings both homological non-homological eigenvectors studied. We also evaluate...

Artificial Intelligence (AI) techniques are of great potential to fundamentally change antibiotic discovery industries. Efficient and effective molecular featurization is key all highly accurate learning models for discovery. In this paper, we propose a fingerprint-enhanced graph attention network (FinGAT) model by the combination sequence-based 2D fingerprints structure-based representation. our feature process, sequence information transformed into fingerprint vector, structural encoded...

Geometric deep learning has demonstrated a great potential in non-Euclidean data analysis. The incorporation of geometric insights into architecture is vital to its success. Here we propose curvature-enhanced graph convolutional network (CGCN) for biomolecular interaction prediction. Our CGCN employs Ollivier-Ricci curvature (ORC) characterize local properties and enhance the capability GCNs. More specifically, ORCs are evaluated based on topology from node neighborhoods, further...

With the great advancements in experimental data, computational power and learning algorithms, artificial intelligence (AI) based drug design has begun to gain momentum recently. AI-based promise revolutionize pharmaceutical industries by significantly reducing time cost discovery processes. However, a major issue remains for all model that is efficient molecular representations. Here we propose Dowker complex (DC) interaction representations Riemann Zeta function featurization, first time....

Summary In this work, we introduce persistent homology for the analysis of cryo‐electron microscopy (cryo‐EM) density maps. We identify topological fingerprint or signature noise, which is widespread in cryo‐EM data. For low signal‐to‐noise ratio (SNR) volumetric data, intrinsic features biomolecular structures are indistinguishable from noise. To remove employ geometric flows that found to preserve fingerprints and diminish particular, enables us visualize gradual separation those noise...