Showing papers by "Guo-Wei Wei published in 2020"

A topology-based network tree for the prediction of protein-protein binding affinity changes following mutation.

Abstract: The ability to predict protein-protein interactions is crucial to our understanding of a wide range of biological activities and functions in the human body, and for guiding drug discovery. Despite considerable efforts to develop suitable computational methods, predicting protein-protein interaction binding affinity changes following mutation (ΔΔG) remains a severe challenge. Algebraic topology, a champion in recent worldwide competitions for protein-ligand binding affinity predictions, is a promising approach to simplifying the complexity of biological structures. Here we introduce element- and site-specific persistent homology (a new branch of algebraic topology) to simplify the structural complexity of protein-protein complexes and embed crucial biological information into topological invariants. We also propose a new deep learning algorithm called NetTree to take advantage of convolutional neural networks and gradient-boosting trees. A topology-based network tree is constructed by integrating the topological representation and NetTree for predicting protein-protein interaction ΔΔG. Tests on major benchmark datasets indicate that the proposed topology-based network tree is an important improvement over the current state of the art in predicting ΔΔG.

Decoding SARS-CoV-2 Transmission and Evolution and Ramifications for COVID-19 Diagnosis, Vaccine, and Medicine.

Abstract: 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 15 140 genome samples collected up to June 1, 2020, we report that SARS-CoV-2 has undergone 8309 single mutations which can be clustered into six 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 nonconservative. In particular, we have identified mutations on 40% of nucleotides in the nucleocapsid gene in the population level, signaling potential impacts on the ongoing development of COVID-19 diagnosis, vaccines, and antibody and small-molecular drugs.

A review of mathematical representations of biomolecular data

Abstract: 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 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 energies, toxicity, partition coefficients, protein folding stability changes upon mutation, etc.

Are 2D fingerprints still valuable for drug discovery

Abstract: Recently, molecular fingerprints extracted from three-dimensional (3D) structures using advanced mathematics, such as algebraic topology, differential geometry, and graph theory have been paired with efficient machine learning, especially deep learning algorithms to outperform other methods in drug discovery applications and competitions. This raises the question of whether classical 2D fingerprints are still valuable in computer-aided drug discovery. This work considers 23 datasets associated with four typical problems, namely protein-ligand binding, toxicity, solubility and partition coefficient to assess the performance of eight 2D fingerprints. Advanced machine learning algorithms including random forest, gradient boosted decision tree, single-task deep neural network and multitask deep neural network are employed to construct efficient 2D-fingerprint based models. Additionally, appropriate consensus models are built to further enhance the performance of 2D-fingerprint-based methods. It is demonstrated that 2D-fingerprint-based models perform as well as the state-of-the-art 3D structure-based models for the predictions of toxicity, solubility, partition coefficient and protein-ligand binding affinity based on only ligand information. However, 3D structure-based models outperform 2D fingerprint-based methods in complex-based protein-ligand binding affinity predictions.

Host immune response driving SARS-CoV-2 evolution

Abstract: The transmission and evolution of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) are of paramount importance in controlling and combating the coronavirus disease 2019 (COVID-19) pandemic. Currently, over 15,000 SARS-CoV-2 single mutations have been recorded, which have a great impact on the development of diagnostics, vaccines, antibody therapies, and drugs. However, little is known about SARS-CoV-2’s 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 overreaction 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 COVID-19 infection 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.

Repositioning of 8565 Existing Drugs for COVID-19.

Abstract: The coronavirus disease 2019 (COVID-19) pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has infected over 7.1 million people and led to over 0.4 million deaths. Currently, there is no specific anti-SARS-CoV-2 medication. New drug discovery typically takes more than 10 years. Drug repositioning becomes one of the most feasible approaches for combating COVID-19. This work curates the largest available experimental data set for SARS-CoV-2 or SARS-CoV 3CL (main) protease inhibitors. On the basis of this data set, we develop validated machine learning models with relatively low root-mean-square error to screen 1553 FDA-approved drugs as well as another 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 3CL protease inhibitors is analyzed. This work offers a foundation for further experimental studies of COVID-19 drug repositioning.

Generative Network Complex for the Automated Generation of Drug-like Molecules.

Abstract: Current drug discovery is expensive and time-consuming. It remains a challenging task to create a wide variety of novel compounds that not only have desirable pharmacological properties but also are 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 multiproperty 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 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.

Decoding Asymptomatic COVID-19 Infection and Transmission.

Abstract: One of the major challenges in controlling the coronavirus disease 2019 (COVID-19) outbreak is its asymptomatic transmission. The pathogenicity and virulence of asymptomatic COVID-19 remain mysterious. On the basis of the genotyping of 75775 SARS-CoV-2 genome isolates, we reveal that asymptomatic infection is linked to SARS-CoV-2 11083G>T mutation (i.e., L37F at 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 the SARS-CoV-2 transmission capacity. Artificial intelligence, sequence alignment, and network analysis are applied to show that NSP6 mutation L37F may have compromised the virus's ability to undermine the innate cellular defense against viral infection via autophagy regulation. This assessment is in good agreement with our genotyping of the SARS-CoV-2 evolution and transmission across various countries and regions over the past few months.

MathDL: mathematical deep learning for D3R Grand Challenge 4

Abstract: We present the performances of our mathematical deep learning (MathDL) models for D3R Grand Challenge 4 (GC4). This challenge involves pose prediction, affinity ranking, and free energy estimation for beta secretase 1 (BACE) as well as affinity ranking and free energy estimation for Cathepsin S (CatS). We have developed advanced mathematics, namely differential geometry, algebraic graph, and/or algebraic topology, to accurately and efficiently encode high dimensional physical/chemical interactions into scalable low-dimensional rotational and translational invariant representations. These representations are integrated with deep learning models, such as generative adversarial networks (GAN) and convolutional neural networks (CNN) for pose prediction and energy evaluation, respectively. Overall, our MathDL models achieved the top place in pose prediction for BACE ligands in Stage 1a. Moreover, our submissions obtained the highest Spearman correlation coefficient on the affinity ranking of 460 CatS compounds, and the smallest centered root mean square error on the free energy set of 39 CatS molecules. It is worthy to mention that our method on docking pose predictions has significantly improved from our previous ones.

Boosting Tree-Assisted Multitask Deep Learning for Small Scientific Datasets.

Abstract: Machine learning approaches have had tremendous success in various disciplines. However, such success highly depends on the size and quality of datasets. Scientific datasets are often small and dif...

Unveiling the molecular mechanism of SARS-CoV-2 main protease inhibition from 137 crystal structures using algebraic topology and deep learning

Abstract: Currently, there is neither 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 (Mpro) is one of the most favorable drug targets. However, the current understanding of the molecular mechanism of Mpro inhibition is limited by the lack of reliable binding affinity ranking and prediction of existing structures of Mpro-inhibitor complexes. This work integrates mathematics (i.e., algebraic topology) and deep learning (MathDL) to provide a reliable ranking of the binding affinities of 137 SARS-CoV-2 Mpro inhibitor structures. We reveal that Gly143 residue in Mpro is the most attractive site to form hydrogen bonds, followed by Glu166, Cys145, and His163. We also identify 71 targeted covalent bonding inhibitors. MathDL was validated on the PDBbind v2016 core set benchmark and a carefully curated SARS-CoV-2 inhibitor dataset to ensure 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.

Machine intelligence design of 2019-nCoV drugs

Abstract: Wuhan coronavirus, called 2019-nCoV, is a newly emerged virus that infected more than 9692 people and leads to more than 213 fatalities by January 30, 2020. Currently, there is no effective treatment for this epidemic. However, the viral protease of a coronavirus is well-known to be essential for its replication and thus is an effective drug target. Fortunately, the sequence identity of the 2019-nCoV protease and that of severe-acute respiratory syndrome virus (SARS-CoV) is as high as 96.1%. We show that the protease inhibitor binding sites of 2019-nCoV and SARS-CoV are almost identical, which means all potential anti-SARS-CoV chemotherapies are also potential 2019-nCoV drugs. Here, we report a family of potential 2019-nCoV drugs generated by a machine intelligence-based generative network complex (GNC). The potential effectiveness of treating 2019-nCoV by using some existing HIV drugs is also analyzed.

Prediction and mitigation of mutation threats to COVID-19 vaccines and antibody therapies

Abstract: Antibody therapeutics and vaccines are among our last resort to end the raging COVID-19 pandemic. They, however, are prone to over 5,000 mutations on the spike (S) protein uncovered by a Mutation Tracker based on over 200,000 genome isolates. It is imperative to understand how mutations would impact vaccines and antibodies in the development. In this work, we study the mechanism, frequency, and ratio of mutations on the S protein. Additionally, we use 56 antibody structures and analyze their 2D and 3D characteristics. Moreover, we predict the mutation-induced binding free energy (BFE) changes for the complexes of S protein and antibodies or ACE2. By integrating genetics, biophysics, deep learning, and algebraic topology, we reveal that most of 462 mutations on the receptor-binding domain (RBD) will weaken the binding of S protein and antibodies and disrupt the efficacy and reliability of antibody therapies and vaccines. A list of 31 vaccine escape mutants is identified, while many other disruptive mutations are detailed as well. We also unveil that about 65\% existing RBD mutations, including those variants recently found in the United Kingdom (UK) and South Africa, are binding-strengthen mutations, resulting in more infectious COVID-19 variants. We discover the disparity between the extreme values of RBD mutation-induced BFE strengthening and weakening of the bindings with antibodies and ACE2, suggesting that SARS-CoV-2 is at an advanced stage of evolution for human infection, while the human immune system is able to produce optimized antibodies. This discovery implies the vulnerability of current vaccines and antibody drugs to new mutations. Our predictions were validated by comparison with more than 1,400 deep mutations on the S protein RBD. Our results show the urgent need to develop new mutation-resistant vaccines and antibodies and to prepare for seasonal vaccinations.

Persistent spectral graph.

Abstract: 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 shapes 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, that is, 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 powerful tool for data analysis, modeling, and prediction. In this work, fullerene stability is predicted by using both harmonic spectra and non-harmonic persistent spectra, while the latter spectra are successfully devised to analyze the structure of fullerenes and model protein flexibility, which cannot be straightforwardly extracted from the current persistent homology. The proposed method is found to provide excellent predictions of the protein B-factors for which current popular biophysical models break down.

Characterizing SARS-CoV-2 mutations in the United States

Abstract: 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. 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.

Generative network complex for the automated generation of druglike molecules

Abstract: 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.

Mutations strengthened SARS-CoV-2 infectivity.

Abstract: 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.

Topology-Based Machine Learning Strategy for Cluster Structure Prediction

Abstract: In cluster physics, the determination of the ground-state structure of medium-sized and large-sized clusters is a challenge due to the number of local minimal values on the potential energy surface growing exponentially with cluster size. Although machine learning approaches have had much success in materials sciences, their applications in clusters are often hindered by the geometric complexity clusters. Persistent homology provides a new topological strategy to simplify geometric complexity while retaining important chemical and physical information without having to "downgrade" the original data. We further propose persistent pairwise independence (PPI) to enhance the predictive power of persistent homology. We construct topology-based machine learning models to reveal hidden structure-energy relationships in lithium (Li) clusters. We integrate the topology-based machine learning models, a particle swarm optimization algorithm, and density functional theory calculations to accelerate the search of the globally stable structure of clusters.

Structural cavities are critical to balancing stability and activity of a membrane-integral enzyme

Abstract: Packing interaction is a critical driving force in the folding of helical membrane proteins. Despite the importance, packing defects (i.e., cavities including voids, pockets, and pores) are prevalent in membrane-integral enzymes, channels, transporters, and receptors, playing essential roles in function. Then, a question arises regarding how the two competing requirements, packing for stability vs. cavities for function, are reconciled in membrane protein structures. Here, using the intramembrane protease GlpG of Escherichiacoli as a model and cavity-filling mutation as a probe, we tested the impacts of native cavities on the thermodynamic stability and function of a membrane protein. We find several stabilizing mutations which induce substantial activity reduction without distorting the active site. Notably, these mutations are all mapped onto the regions of conformational flexibility and functional importance, indicating that the cavities facilitate functional movement of GlpG while compromising the stability. Experiment and molecular dynamics simulation suggest that the stabilization is induced by the coupling between enhanced protein packing and weakly unfavorable lipid desolvation, or solely by favorable lipid solvation on the cavities. Our result suggests that, stabilized by the relatively weak interactions with lipids, cavities are accommodated in membrane proteins without severe energetic cost, which, in turn, serve as a platform to fine-tune the balance between stability and flexibility for optimal activity.

Mutations on COVID-19 diagnostic targets

Abstract: 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.

Host immune response driving SARS-CoV-2 evolution

Abstract: 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.

Characterizing SARS-CoV-2 mutations in the United States

Abstract: 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.

Atom-specific persistent homology and its application to protein flexibility analysis.

Abstract: Recently, persistent homology has had tremendous success in biomolecular data analysis. It works by examining the topological relationship or connectivity of a group of atoms in a molecule at a variety of scales, then rendering a family of topological representations of the molecule. However, persistent homology is rarely employed for the analysis of atomic properties, such as biomolecular flexibility analysis or B-factor prediction. This work introduces atom-specific persistent homology to provide a local atomic level representation of a molecule via a global topological tool. This is achieved through the construction of a pair of conjugated sets of atoms and corresponding conjugated simplicial complexes, as well as conjugated topological spaces. The difference between the topological invariants of the pair of conjugated sets is measured by Bottleneck and Wasserstein metrics and leads to an atom-specific topological representation of individual atomic properties in a molecule. Atom-specific topological features are integrated with various machine learning algorithms, including gradient boosting trees and convolutional neural network for protein thermal fluctuation analysis and B-factor prediction. Extensive numerical results indicate the proposed method provides a powerful topological tool for analyzing and predicting localized information in complex macromolecules.

Decoding SARS-CoV-2 transmission, evolution and ramification on COVID-19 diagnosis, vaccine, and medicine

Abstract: 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.

Persistent Cohomology for Data With Multicomponent Heterogeneous Information

Abstract: Persistent homology is a powerful tool for characterizing the topology of a data set at various geometric scales. When applied to the description of molecular structures, persistent homology can capture the multiscale geometric features and reveal certain interaction patterns in terms of topological invariants. However, in addition to the geometric information, there is a wide variety of nongeometric information of molecular structures, such as element types, atomic partial charges, atomic pairwise interactions, and electrostatic potential functions, that is not described by persistent homology. Although element-specific homology and electrostatic persistent homology can encode some nongeometric information into geometry based topological invariants, it is desirable to have a mathematical paradigm to systematically embed both geometric and nongeometric information, i.e., multicomponent heterogeneous information, into unified topological representations. To this end, we propose a persistent cohomology based framework for the enriched representation of data. In our framework, nongeometric information can either be distributed globally or reside locally on the datasets in the geometric sense and can be properly defined on topological spaces, i.e., simplicial complexes. Using the proposed persistent cohomology based framework, enriched barcodes are extracted from datasets to represent heterogeneous information. We consider a variety of datasets to validate the present formulation and illustrate the usefulness of the proposed method based on persistent cohomology. It is found that the proposed framework outperforms or at least matches the state-of-the-art methods in the protein-ligand binding affinity prediction from massive biomolecular datasets without resorting to any deep learning formulation.

Evolutionary homology on coupled dynamical systems with applications to protein flexibility analysis.

Abstract: While the spatial topological persistence is naturally constructed from a radius-based filtration, it has hardly been derived from a temporal filtration. Most topological models are designed for the global topology of a given object as a whole. There is no method reported in the literature for the topology of an individual component in an object to the best of our knowledge. For many problems in science and engineering, the topology of an individual component is important for describing its properties. We propose evolutionary homology (EH) constructed via a time evolution-based filtration and topological persistence. Our approach couples a set of dynamical systems or chaotic oscillators by the interactions of a physical system, such as a macromolecule. The interactions are approximated by weighted graph Laplacians. Simplices, simplicial complexes, algebraic groups and topological persistence are defined on the coupled trajectories of the chaotic oscillators. The resulting EH gives rise to time-dependent topological invariants or evolutionary barcodes for an individual component of the physical system, revealing its topology-function relationship. In conjunction with Wasserstein metrics, the proposed EH is applied to protein flexibility analysis, an important problem in computational biophysics. Numerical results for the B-factor prediction of a benchmark set of 364 proteins indicate that the proposed EH outperforms all the other state-of-the-art methods in the field.