Search for: All records

Abstract Khovanov homology has been the subject of much study in knot theory and low dimensional topology since 2000. This work introduces a Khovanov Laplacian and a Khovanov Dirac to study knot and link diagrams. The harmonic spectrum of the Khovanov Laplacian or the Khovanov Dirac retains the topological invariants of Khovanov homology, while their non-harmonic spectra reveal additional information that is distinct from Khovanov homology. 

ABSTRACT Protein structural fluctuations, measured by Debye‐Waller factors or B‐factors, are known to be closely associated with protein flexibility and function. Theoretical approaches have also been developed to predict B‐factor values, which reflect protein flexibility. Previous models have made significant strides in analyzing B‐factors by fitting experimental data. In this study, we propose a novel approach for B‐factor prediction using differential geometry theory, based on the assumption that the intrinsic properties of proteins reside on a family of low‐dimensional manifolds embedded within the high‐dimensional space of protein structures. By analyzing the mean and Gaussian curvatures of a set of low‐dimensional manifolds defined by kernel functions, we develop effective and robust multiscale differential geometry (mDG) models. Our mDG model demonstrates a 27% increase in accuracy compared to the classical Gaussian network model (GNM) in predicting B‐factors for a dataset of 364 proteins. Additionally, by incorporating both global and local protein features, we construct a highly effective machine‐learning model for the blind prediction of B‐factors. Extensive least‐squares approximations and machine learning‐based blind predictions validate the effectiveness of the mDG modeling approach for B‐factor predictions. 

Abstract The fast evolution of SARS-CoV-2 and other infectious viruses poses a grand challenge to the rapid response in terms of viral tracking, diagnostics, and design and manufacture of monoclonal antibodies (mAbs) and vaccines, which are both time-consuming and costly. This underscores the need for efficient computational approaches. Recent advancements, like topological deep learning (TDL), have introduced powerful tools for forecasting emerging dominant variants, yet they require deep mutational scanning (DMS) of viral surface proteins and associated three-dimensional (3D) protein–protein interaction (PPI) complex structures. We propose an AlphaFold 3 (AF3)-assisted multi-task topological Laplacian (MT-TopLap) strategy to address this need. MT-TopLap combines deep learning with TDA models, such as persistent Laplacians (PL) to extract detailed topological and geometric characteristics of PPIs, thereby enhancing the prediction of DMS and binding free energy (BFE) changes upon virus mutations. Validation with four experimental DMS datasets of SARS-CoV-2 spike receptor-binding domain (RBD) and the human angiotensin-converting enzyme-2 (ACE2) complexes indicates that our AF3-assisted MT-TopLap strategy maintains robust performance, with only an average 1.1% decrease in Pearson correlation coefficients (PCC) and an average 9.3% increase in root mean square errors (RMSE), compared with the use of experimental structures. Additionally, AF3-assisted MT-TopLap achieved a PCC of 0.81 when tested with a SARS-CoV-2 HK.3 variant DMS dataset, confirming its capability to accurately predict BFE changes and adapt to new experimental data, thereby showcasing its potential for rapid and effective response to fast viral evolution. 

Abstract The escalating drug addiction crisis in the United States underscores the urgent need for innovative therapeutic strategies. This study embarked on an innovative and rigorous strategy to unearth potential drug repurposing candidates for opioid and cocaine addiction treatment, bridging the gap between transcriptomic data analysis and drug discovery. We initiated our approach by conducting differential gene expression analysis on addiction-related transcriptomic data to identify key genes. We propose a novel topological differentiation to identify key genes from a protein–protein interaction network derived from DEGs. This method utilizes persistent Laplacians to accurately single out pivotal nodes within the network, conducting this analysis in a multiscale manner to ensure high reliability. Through rigorous literature validation, pathway analysis and data-availability scrutiny, we identified three pivotal molecular targets, mTOR, mGluR5 and NMDAR, for drug repurposing from DrugBank. We crafted machine learning models employing two natural language processing (NLP)-based embeddings and a traditional 2D fingerprint, which demonstrated robust predictive ability in gauging binding affinities of DrugBank compounds to selected targets. Furthermore, we elucidated the interactions of promising drugs with the targets and evaluated their drug-likeness. This study delineates a multi-faceted and comprehensive analytical framework, amalgamating bioinformatics, topological data analysis and machine learning, for drug repurposing in addiction treatment, setting the stage for subsequent experimental validation. The versatility of the methods we developed allows for applications across a range of diseases and transcriptomic datasets. 

Abstract Pain is a significant global health issue, and the current treatment options for pain management have limitations in terms of effectiveness, side effects, and potential for addiction. There is a pressing need for improved pain treatments and the development of new drugs. Voltage-gated sodium channels, particularly Nav1.3, Nav1.7, Nav1.8, and Nav1.9, play a crucial role in neuronal excitability and are predominantly expressed in the peripheral nervous system. Targeting these channels may provide a means to treat pain while minimizing central and cardiac adverse effects. In this study, we construct protein–protein interaction (PPI) networks based on pain-related sodium channels and develop a corresponding drug–target interaction network to identify potential lead compounds for pain management. To ensure reliable machine learning predictions, we carefully select 111 inhibitor data sets from a pool of more than 1000 targets in the PPI network. We employ 3 distinct machine learning algorithms combined with advanced natural language processing (NLP)–based embeddings, specifically pretrained transformer and autoencoder representations. Through a systematic screening process, we evaluate the side effects and repurposing potential of more than 150,000 drug candidates targeting Nav1.7 and Nav1.8 sodium channels. In addition, we assess the ADMET (absorption, distribution, metabolism, excretion, and toxicity) properties of these candidates to identify leads with near-optimal characteristics. Our strategy provides an innovative platform for the pharmacological development of pain treatments, offering the potential for improved efficacy and reduced side effects. 

Abstract Protein engineering is an emerging field in biotechnology that has the potential to revolutionize various areas, such as antibody design, drug discovery, food security, ecology, and more. However, the mutational space involved is too vast to be handled through experimental means alone. Leveraging accumulative protein databases, machine learning (ML) models, particularly those based on natural language processing (NLP), have considerably expedited protein engineering. Moreover, advances in topological data analysis (TDA) and artificial intelligence-based protein structure prediction, such as AlphaFold2, have made more powerful structure-based ML-assisted protein engineering strategies possible. This review aims to offer a comprehensive, systematic, and indispensable set of methodological components, including TDA and NLP, for protein engineering and to facilitate their future development. 

The multiscale topological learning framework, based on persistent topological Laplacians, captures complex interactions and enhances energy prediction accuracy in multi-atom systems. 

AI-driven drug discovery accelerates anti-addiction treatment by enhancing precision and targeting key neurochemical systems.