arXiv subjects
Publications and source records attributed to Guo-Wei Wei.
We establish a new theory which gives a unified topological approach to data science, by being applicable both to point cloud data and to graph data, including networks beyond pairwise interactions. We generalize simplicial complexes and hypergraphs to super-hypergraphs and establish super-hypergraph homology as an extension of simplicial homology. Driven by applications, we also introduce super-persistent homology.
Recently, the SARS-CoV-2 variants from the United Kingdom (UK), South Africa, and Brazil have received much attention for their increased infectivity, potentially high virulence, and possible threats to existing vaccines and antibody therapies. The question remains if there are other more infectious variants transmitted around the world. We carry out a large-scale study of 252,874 SARS-CoV-2 genome isolates from patients to identify many other rapidly growing mutations on the spike (S) protein receptor-binding domain (RDB). We reveal that 88 out of 95 significant mutations that were observed more than 10 times strengthen the binding between the RBD and the host angiotensin-converting enzyme 2 (ACE2), indicating the virus evolves toward more infectious variants. In particular, we discover new fast-growing RBD mutations N439K, L452R, S477N, S477R, and N501T that also enhance the RBD and ACE2 binding. We further unveil that mutation N501Y involved in United Kingdom (UK), South Africa, and Brazil variants may moderately weaken the binding between the RBD and many known antibodies, while mutations E484K and K417N found in South Africa and Brazilian variants can potentially disrupt the binding between the RDB and many known antibodies. Among three newly identified fast-growing RBD mutations, L452R, which is now known as part of the California variant B.1.427, and N501T are able to effectively weaken the binding of many known antibodies with the RBD. Finally, we hypothesize that RBD mutations that can simultaneously make SARS-CoV-2 more infectious and disrupt the existing antibodies, called vaccine escape mutations, will pose an imminent threat to the current crop of vaccines. A list of most likely vaccine escape mutations is given, including N501Y, L452R, E484K, N501T, S494P, and K417N.
The deadly coronavirus disease 2019 (COVID-19) pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has gone out of control globally. Despite much effort by scientists, medical experts, and society in general, the slow progress on drug discovery and antibody therapeutic development, the unknown possible side effects of the existing vaccines, and the high transmission rate of the SARS-CoV-2, remind us of the sad reality that our current understanding of the transmission, infectivity, and evolution of SARS-CoV-2 is unfortunately very limited. The major limitation is the lack of mechanistic understanding of viral-host cell interactions, the viral regulation, protein-protein interactions, including antibody-antigen binding, protein-drug binding, host immune response, etc. This limitation will likely haunt the scientific community for a long time and have a devastating consequence in combating COVID-19 and other pathogens. Notably, compared to the long-cycle, highly cost, and safety-demanding molecular-level experiments, the theoretical and computational studies are economical, speedy, and easy to perform. There exists a tsunami of the literature on molecular modeling, simulation, and prediction of SARS-CoV-2 that has become impossible to fully be covered in a review. To provide the reader a quick update about the status of molecular modeling, simulation, and prediction of SARS-CoV-2, we present a comprehensive and systematic methodology-centered narrative in the nick of time. Aspects such as molecular modeling, Monte Carlo (MC) methods, structural bioinformatics, machine learning, deep learning, and mathematical approaches are included in this review. This review will be beneficial to researchers who are looking for ways to contribute to SARS-CoV-2 studies and those who are assessing the current status in the field.
Coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has a worldwide devastating effect. The understanding of evolution and transmission of SARS-CoV-2 is of paramount importance for the COVID-19 control, combating, and prevention. Due to the rapid growth of both the number of SARS-CoV-2 genome sequences and the number of unique mutations, the phylogenetic analysis of SARS-CoV-2 genome isolates faces an emergent large-data challenge. We introduce a dimension-reduced $k$-means clustering strategy to tackle this challenge. We examine the performance and effectiveness of three dimension-reduction algorithms: principal component analysis (PCA), t-distributed stochastic neighbor embedding (t-SNE), and uniform manifold approximation and projection (UMAP). By using four benchmark datasets, we found that UMAP is the best-suited technique due to its stable, reliable, and efficient performance, its ability to improve clustering accuracy, especially for large Jaccard distanced-based datasets, and its superior clustering visualization. The UMAP-assisted $k$-means clustering enables us to shed light on increasingly large datasets from SARS-CoV-2 genome isolates.
Persistent homology (PH) is one of the most popular tools in topological data analysis (TDA), while graph theory has had a significant impact on data science. Our earlier work introduced the persistent spectral graph (PSG) theory as a unified multiscale paradigm to encompass TDA and geometric analysis. In PSG theory, families of persistent Laplacians (PLs) corresponding to various topological dimensions are constructed via a filtration to sample a given dataset at multiple scales. The harmonic spectra from the null spaces of PLs offer the same topological invariants, namely persistent Betti numbers, at various dimensions as those provided by PH, while the non-harmonic spectra of PLs give rise to additional geometric analysis of the shape of the data. In this work, we develop an open-source software package, called highly efficient robust multidimensional evolutionary spectra (HERMES), to enable broad applications of PSGs in science, engineering, and technology. To ensure the reliability and robustness of HERMES, we have validated the software with simple geometric shapes and complex datasets from three-dimensional (3D) protein structures. We found that the smallest non-zero eigenvalues are very sensitive to data abnormality.
The transmission and evolution of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) are of paramount importance to the controlling and combating of coronavirus disease 2019 (COVID-19) pandemic. Currently, near 15,000 SARS-CoV-2 single mutations have been recorded, having a great ramification to the development of diagnostics, vaccines, antibody therapies, and drugs. However, little is known about SARS-CoV-2 evolutionary characteristics and general trend. In this work, we present a comprehensive genotyping analysis of existing SARS-CoV-2 mutations. We reveal that host immune response via APOBEC and ADAR gene editing gives rise to near 65\% of recorded mutations. Additionally, we show that children under age five and the elderly may be at high risk from COVID-19 because of their overreacting to the viral infection. Moreover, we uncover that populations of Oceania and Africa react significantly more intensively to SARS-CoV-2 infection than those of Europe and Asia, which may explain why African Americans were shown to be at increased risk of dying from COVID-19, in addition to their high risk of getting sick from COVID-19 caused by systemic health and social inequities. Finally, our study indicates that for two viral genome sequences of the same origin, their evolution order may be determined from the ratio of mutation type C$>$T over T$>$C.
The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been mutating since it was first sequenced in early January 2020. The genetic variants have developed into a few distinct clusters with different properties. Since the United States (US) has the highest number of viral infected patients globally, it is essential to understand the US SARS-CoV-2. Using genotyping, sequence-alignment, time-evolution, $k$-means clustering, protein-folding stability, algebraic topology, and network theory, we reveal that the US SARS-CoV-2 has four substrains and five top US SARS-CoV-2 mutations were first detected in China (2 cases), Singapore (2 cases), and the United Kingdom (1 case). The next three top US SARS-CoV-2 mutations were first detected in the US. These eight top mutations belong to two disconnected groups. The first group consisting of 5 concurrent mutations is prevailing, while the other group with three concurrent mutations gradually fades out. Our analysis suggests that female immune systems are more active than those of males in responding to SARS-CoV-2 infections. We identify that one of the top mutations, 27964C$>$T-(S24L) on ORF8, has an unusually strong gender dependence. Based on the analysis of all mutations on the spike protein, we further uncover that three of four US SASR-CoV-2 substrains become more infectious. Our study calls for effective viral control and containing strategies in the US.
Coronavirus disease 2019 (COVID-19) is a continuously devastating public health and the world economy. One of the major challenges in controlling the COVID-19 outbreak is its asymptomatic infection and transmission, which are elusive and defenseless in most situations. The pathogenicity and virulence of asymptomatic COVID-19 remain mysterious. Based on the genotyping of 20656 Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) genome isolates, we reveal that asymptomatic infection is linked to SARS-CoV-2 11083G>T mutation, i.e., leucine (L) to phenylalanine (F) substitution at the residue 37 (L37F) of nonstructure protein 6 (NSP6). By analyzing the distribution of 11083G>T in various countries, we unveil that 11083G>T may correlate with the hypotoxicity of SARS-CoV-2. Moreover, we show a global decaying tendency of the 11083G>T mutation ratio indicating that 11083G>T hinders SARS-CoV-2 transmission capacity. Sequence alignment found both NSP6 and residue 37 neighborhoods are relatively conservative over a few coronaviral species, indicating their importance in regulating host cell autophagy to undermine innate cellular defense against viral infection. Using machine learning and topological data analysis, we demonstrate that mutation L37F has made NSP6 energetically less stable. The rigidity and flexibility index and several network models suggest that mutation L37F may have compromised the NSP6 function, leading to a relatively weak SARS-CoV subtype. This assessment is a good agreement with our genotyping of SARS-CoV-2 evolution and transmission across various countries and regions over the past few months.
Under the global health emergency caused by coronavirus disease 2019 (COVID-19), efficient and specific therapies are urgently needed. Compared with traditional small-molecular drugs, antibody therapies are relatively easy to develop and as specific as vaccines in targeting severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), and thus attract much attention in the past few months. This work reviews seven existing antibodies for SARS-CoV-2 spike (S) protein with three-dimensional (3D) structures deposited in the Protein Data Bank. Five antibody structures associated with SARS-CoV are evaluated for their potential in neutralizing SARS-CoV-2. The interactions of these antibodies with the S protein receptor-binding domain (RBD) are compared with those of angiotensin-converting enzyme 2 (ACE2) and RBD complexes. Due to the orders of magnitude in the discrepancies of experimental binding affinities, we introduce topological data analysis (TDA), a variety of network models, and deep learning to analyze the binding strength and therapeutic potential of the aforementioned fourteen antibody-antigen complexes. The current COVID-19 antibody clinical trials, which are not limited to the S protein target, are also reviewed.
Current drug discovery is expensive and time-consuming. It remains a challenging task to create a wide variety of novel compounds with desirable pharmacological properties and cheaply available to low-income people. In this work, we develop a generative network complex (GNC) to generate new drug-like molecules based on the multi-property optimization via the gradient descent in the latent space of an autoencoder. In our GNC, both multiple chemical properties and similarity scores are optimized to generate and predict drug-like molecules with desired chemical properties. To further validate the reliability of the predictions, these molecules are reevaluated and screened by independent 2D fingerprint-based predictors to come up with a few hundreds of new drug candidates. As a demonstration, we apply our GNC to generate a large number of new BACE1 inhibitors, as well as thousands of novel alternative drug candidates for eight existing market drugs, including Ceritinib, Ribociclib, Acalabrutinib, Idelalisib, Dabrafenib, Macimorelin, Enzalutamide, and Panobinostat.
Currently, there is no effective antiviral drugs nor vaccine for coronavirus disease 2019 (COVID-19) caused by acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Due to its high conservativeness and low similarity with human genes, SARS-CoV-2 main protease (M$^{\text{pro}}$) is one of the most favorable drug targets. However, the current understanding of the molecular mechanism of M$^{\text{pro}}$ inhibition is limited by the lack of reliable binding affinity ranking and prediction of existing structures of M$^{\text{pro}}$-inhibitor complexes. This work integrates mathematics and deep learning (MathDL) to provide a reliable ranking of the binding affinities of 92 SARS-CoV-2 M$^{\text{pro}}$ inhibitor structures. We reveal that Gly143 residue in M$^{\text{pro}}$ is the most attractive site to form hydrogen bonds, followed by Cys145, Glu166, and His163. We also identify 45 targeted covalent bonding inhibitors. Validation on the PDBbind v2016 core set benchmark shows the MathDL has achieved the top performance with Pearson's correlation coefficient ($R_p$) being 0.858. Most importantly, MathDL is validated on a carefully curated SARS-CoV-2 inhibitor dataset with the averaged $R_p$ as high as 0.751, which endows the reliability of the present binding affinity prediction. The present binding affinity ranking, interaction analysis, and fragment decomposition offer a foundation for future drug discovery efforts.
Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infectivity is a major concern in coronavirus disease 2019 (COVID-19) prevention and economic reopening. However, rigorous determination of SARS-COV-2 infectivity is essentially impossible owing to its continuous evolution with over 13752 single nucleotide polymorphisms (SNP) variants in six different subtypes. We develop an advanced machine learning algorithm based on the algebraic topology to quantitatively evaluate the binding affinity changes of SARS-CoV-2 spike glycoprotein (S protein) and host angiotensin-converting enzyme 2 (ACE2) receptor following the mutations. Based on mutation-induced binding affinity changes, we reveal that five out of six SARS-CoV-2 subtypes have become either moderately or slightly more infectious, while one subtype has weakened its infectivity. We find that SARS-CoV-2 is slightly more infectious than SARS-CoV according to computed S protein-ACE2 binding affinity changes. Based on a systematic evaluation of all possible 3686 future mutations on the S protein receptor-binding domain (RBD), we show that most likely future mutations will make SARS-CoV-2 more infectious. Combining sequence alignment, probability analysis, and binding affinity calculation, we predict that a few residues on the receptor-binding motif (RBM), i.e., 452, 489, 500, 501, and 505, have very high chances to mutate into significantly more infectious COVID-19 strains.
The coronavirus disease 2019 (COVID-19) pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has infected near 5 million people and led to over 0.3 million deaths. Currently, there is no specific anti-SARS-CoV-2 medication. New drug discovery typically takes more than ten years. Drug repositioning becomes one of the most feasible approaches for combating COVID-19. This work curates the largest available experimental dataset for SARS-CoV-2 or SARS-CoV main protease inhibitors. Based on this dataset, we develop validated machine learning models with relatively low root mean square error to screen 1553 FDA-approved drugs as well as other 7012 investigational or off-market drugs in DrugBank. We found that many existing drugs might be potentially potent to SARS-CoV-2. The druggability of many potent SARS-CoV-2 main protease inhibitors is analyzed. This work offers a foundation for further experimental studies of COVID-19 drug repositioning.
Effective, sensitive, and reliable diagnostic reagents are of paramount importance for combating the ongoing coronavirus disease 2019 (COVID-19) pandemic at a time there is no preventive vaccine nor specific drug available for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). It would be an absolute tragedy if currently used diagnostic reagents are undermined in any manner. Based on the genotyping of 7818 SARS-CoV-2 genome samples collected up to May 1, 2020, we reveal that essentially all of the current COVID-19 diagnostic targets have had mutations. We further show that SARS-CoV-2 has the most devastating mutations on the targets of various nucleocapsid (N) gene primers and probes, which have been unfortunately used by countries around the world to diagnose COVID-19. Our findings explain what has seriously gone wrong with a specific diagnostic reagent made in China. To understand whether SARS-CoV-2 genes have mutated unevenly, we have computed the mutation ratio and mutation $h$-index of all SARS-CoV genes, indicating that the N gene is the most non-conservative gene in the SARS-CoV-2 genome. Our findings enable researchers to target the most conservative SARS-CoV-2 genes and proteins for the design and development of COVID-19 diagnostic reagents, preventive vaccines, and therapeutic medicines.
Tremendous effort has been given to the development of diagnostic tests, preventive vaccines, and therapeutic medicines for coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Much of this development has been based on the reference genome collected on January 5, 2020. Based on the genotyping of 6156 genome samples collected up to April 24, 2020, we report that SARS-CoV-2 has had 4459 alarmingly mutations which can be clustered into five subtypes. We introduce mutation ratio and mutation $h$-index to characterize the protein conservativeness and unveil that SARS-CoV-2 envelope protein, main protease, and endoribonuclease protein are relatively conservative, while SARS-CoV-2 nucleocapsid protein, spike protein, and papain-like protease are relatively non-conservative. In particular, the nucleocapsid protein has more than half its genes changed in the past few months, signaling devastating impacts on the ongoing development of COVID-19 diagnosis, vaccines, and drugs.
The de Rham-Hodge theory is a landmark of the 20$^\text{th}$ Century's mathematics and has had a great impact on mathematics, physics, computer science, and engineering. This work introduces an evolutionary de Rham-Hodge method to provide a unified paradigm for the multiscale geometric and topological analysis of evolving manifolds constructed from a filtration, which induces a family of evolutionary de Rham complexes. While the present method can be easily applied to close manifolds, the emphasis is given to more challenging compact manifolds with 2-manifold boundaries, which require appropriate analysis and treatment of boundary conditions on differential forms to maintain proper topological properties. Three sets of unique evolutionary Hodge Laplacian operators are proposed to generate three sets of topology-preserving singular spectra, for which the multiplicities of zero eigenvalues correspond to exactly the persistent Betti numbers of dimensions 0, 1, and 2. Additionally, three sets of non-zero eigenvalues further reveal both topological persistence and geometric progression during the manifold evolution. Extensive numerical experiments are carried out via the discrete exterior calculus to demonstrate the utility and usefulness of the proposed method for data representation and shape analysis.
Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for revealing topological persistence and extracting geometric shape from high-dimensional datasets. For a point-cloud dataset, a filtration procedure is used to generate a sequence of chain complexes and associated families of simplicial complexes and chains, from which we construct persistent combinatorial Laplacian matrices. We show that a full set of topological persistence can be completely recovered from the harmonic persistent spectra, i.e., the spectra that have zero eigenvalues, of the persistent combinatorial Laplacian matrices. However, non-harmonic spectra of the Laplacian matrices induced by the filtration offer another power tool for data analysis, modeling, and prediction. In this work, non-harmonic persistent spectra are successfully devised to analyze the structure and stability of fullerenes and predict the B-factors of a protein, which cannot be straightforwardly extracted from the current persistent homology. Extensive numerical experiments indicate the tremendous potential of the proposed persistent spectral analysis in data science.
Recently, machine learning (ML) has established itself in various worldwide benchmarking competitions in computational biology, including Critical Assessment of Structure Prediction (CASP) and Drug Design Data Resource (D3R) Grand Challenges. However, the intricate structural complexity and high ML dimensionality of biomolecular datasets obstruct the efficient application of ML algorithms in the field. In addition to data and algorithm, an efficient ML machinery for biomolecular predictions must include structural representation as an indispensable component. Mathematical representations that simplify the biomolecular structural complexity and reduce ML dimensionality have emerged as a prime winner in D3R Grand Challenges. This review is devoted to the recent advances in developing low-dimensional and scalable mathematical representations of biomolecules in our laboratory. We discuss three classes of mathematical approaches, including algebraic topology, differential geometry, and graph theory. We elucidate how the physical and biological challenges have guided the evolution and development of these mathematical apparatuses for massive and diverse biomolecular data. We focus the performance analysis on the protein-ligand binding predictions in this review although these methods have had tremendous success in many other applications, such as protein classification, virtual screening, and the predictions of solubility, solvation free energy, toxicity, partition coefficient, protein folding stability changes upon mutation, etc.