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Protein–protein interactions (PPIs) play crucial roles in almost all biological processes from cell-signaling and membrane transport to metabolism and immune systems. Efficient characterization of PPIs at the molecular level is key to the fundamental understanding of PPI mechanisms. Even with the gigantic amount of PPI models from graphs, networks, geometry and topology, it remains as a great challenge to design functional models that efficiently characterize the complicated multiphysical information within PPIs. Here we propose persistent Tor-algebra (PTA) model for a unified algebraic representation of the multiphysical interactions. Mathematically, our PTA is inherently algebraic data analysis. In our PTA model, protein structures and interactions are described as a series of face rings and Tor modules, from which PTA model is developed. The multiphysical information within/between biomolecules are implicitly characterized by PTA and further represented as PTA barcodes. To test our PTA models, we consider PTA-based ensemble learning for PPI binding affinity prediction. The two most commonly used datasets, i.e. SKEMPI and AB-Bind, are employed. It has been found that our model outperforms all the existing models as far as we know. Mathematically, our PTA model provides a highly efficient way for the characterization of molecular structures and interactions.

Background: The open and accessible regions of the chromosome are more likely to be bound by transcription factors which are important for nuclear processes and biological functions. Studying the change of chromosome flexibility can help to discover and analyze disease markers and improve the efficiency of clinical diagnosis. Current methods for predicting chromosome flexibility based on Hi-C data include the Flexibility-Rigidity Index (FRI) and the Gaussian Network Model (GNM), which have been proposed to characterize chromosome flexibility. However, these methods require the chromosome structure data based on 3D biological experiments, which is time-consuming and expensive. Objective: Generally, the folding and curling of the double helix sequence of DNA have a great impact on chromosome flexibility and function. Motivated by the success of genomic sequence analysis in biomolecular function analysis, we hope to propose a method to predict chromosome flexibility only based on genomic sequence data. Methods: We propose a new method (named "DeepCFP") using deep learning models to predict chromosome flexibility based on only genomic sequence features. The model has been tested in the GM12878 cell line. Results: The maximum accuracy of our model has reached 91%. The performance of DeepCFP is close to FRI and GNM. Conclusion: The DeepCFP can achieve high performance only based on genomic sequence.

We establish a new theory which unifies various aspects of topological approaches for 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.

It has long been observed that trimethylamine N-oxide (TMAO) and urea demonstrate dramatically different properties in a protein folding process. Even with the enormous theoretical and experimental research work on these two osmolytes, various aspects of their underlying mechanisms still remain largely elusive. In this paper, we propose to use the weighted persistent homology to systematically study the osmolytes molecular aggregation and their hydrogen-bonding network from a local topological perspective. We consider two weighted models, i.e., localized persistent homology (LPH) and interactive persistent homology (IPH). Boltzmann persistent entropy (BPE) is proposed to quantitatively characterize the topological features from LPH and IPH, together with persistent Betti number (PBN). More specifically, from the localized persistent homology models, we have found that TMAO and urea have very different local topology. TMAO is found to exhibit a local network structure. With the concentration increase, the circle elements in these networks show a clear increase in their total numbers and a decrease in their relative sizes. In contrast, urea shows two types of local topological patterns, i.e., local clusters around 6 Å and a few global circle elements at around 12 Å. From the interactive persistent homology models, it has been found that our persistent radial distribution function (PRDF) from the global-scale IPH has same physical properties as the traditional radial distribution function. Moreover, PRDFs from the local-scale IPH can also be generated and used to characterize the local interaction information. Other than the clear difference of the first peak value of PRDFs at filtration size 4 Å, TMAO and urea also shows very different behaviors at the second peak region from filtration size 5 Å to 10 Å. These differences are also reflected in the PBNs and BPEs of the local-scale IPH. These localized topological information has never been revealed before. Since graphs can be transferred into simplicial complexes by the clique complex, our weighted persistent homology models can be used in the analysis of various networks and graphs from any molecular structures and aggregation systems. Ministry of Education (MOE) Nanyang Technological University Published version This work was supported in part by Nanyang Technological University Startup Grant M4081842 and Singapore Ministry of Education Academic Research fund Tier 1 RG31/18, Tier 2 MOE2018-T2–1–033.

In this paper, we develop and study the theory of weighted fundamental groups of weighted simplicial complexes. When all weights are 1, the weighted fundamental group reduces to the usual fundamental group as a special case. We also study weighted versions of classical theorems like van Kampen's theorem. In addition, we also investigate the abelianization, lower central series and applications of weighted fundamental groups., Comment: 20 pages

Disease X is a hypothetical unknown disease that has the potential to cause an epidemic or pandemic outbreak in the future. Nanosensors are attractive portable devices that can swiftly screen disease biomarkers on site, reducing the reliance on laboratory-based analyses. However, conventional data analytics limit the progress of nanosensor research. In this Perspective, we highlight the integral role of machine learning (ML) algorithms in advancing nanosensing strategies toward Disease X detection. We first summarize recent progress in utilizing ML algorithms for the smart design and fabrication of custom nanosensor platforms as well as realizing rapid on-site prediction of infection statuses. Subsequently, we discuss promising prospects in further harnessing the potential of ML algorithms in other aspects of nanosensor development and biomarker detection. Nanyang Technological University Submitted/Accepted version S.X.L. and N.B.T.L. acknowledge Nanyang President’s Graduate Scholarship support from Nanyang Technological University, Singapore.

Protein-protein interactions (PPIs) are involved in almost all biological processes in the cell. Understanding protein-protein interactions holds the key for the understanding of biological functions, diseases and the development of therapeutics. Recently, artificial intelligence (AI) models have demonstrated great power in PPIs. However, a key issue for all AI-based PPI models is efficient molecular representations and featurization. Here, we propose Hom-complex-based PPI representation, and Hom-complex-based machine learning models for the prediction of PPI binding affinity changes upon mutation, for the first time. In our model, various Hom complexes Hom(G1, G) can be generated for the graph representation G of protein-protein complex by using different graphs G1, which reveal G1-related inner connections within the graph representation G of protein-protein complex. Further, for a specific graph G1, a series of nested Hom complexes are generated to give a multiscale characterization of the PPIs. Its persistent homology and persistent Euler characteristic are used as molecular descriptors and further combined with the machine learning model, in particular, gradient boosting tree (GBT). We systematically test our model on the two most-commonly used data sets, that is, SKEMPI and AB-Bind. It has been found that our model outperforms all the existing models as far as we know, which demonstrates the great potential of our model for the analysis of PPIs. Our model can be used for the analysis and design of efficient antibodies for SARS-CoV-2. Ministry of Education (MOE) Nanyang Technological University This work was supported in part by Nanyang Technological University Startup Grant M4081842 and Singapore Ministry of Education Academic Research fund Tier 1 RG109/19, MOET2EP20120-0013, and MOE-T2EP20220-0010. The first author was supported by Nankai Zhide foundation. The second author was supported by Natural Science Foundation of China (NSFC Grant No. 11221091, 11271062, 11571184). The third author was supported by Natural Science Foundation of China (NSFC Grant No. 11971144), High-level Scientific Research Foundation of Hebei Province and the start-up research fund from BIMSA.

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. Ministry of Education (MOE) Nanyang Technological University Nanyang Technological University Startup Grant (grant no. M4081842.110); Singapore Ministry of Education Academic Research fund (grant nos. Tier 1 RG109/19, Tier 2 MOE2018-T2-1-033, Tier 2 MOE-T2EP20120-0013); National Natural Science Foundation of China (grant no. 31971180); China Scholarship Council (grant no. 201906540026).

Artificial intelligence (AI)-based drug design has great promise to fundamentally change the landscape of the pharmaceutical industry. Even though there are great progress from handcrafted feature-based machine learning models, 3D convolutional neural networks (CNNs) and graph neural networks, effective and efficient representations that characterize the structural, physical, chemical and biological properties of molecular structures and interactions remain to be a great challenge. Here, we propose an equal-sized molecular 2D image representation, known as the molecular persistent spectral image (Mol-PSI), and combine it with CNN model for AI-based drug design. Mol-PSI provides a unique one-to-one image representation for molecular structures and interactions. In general, deep models are empowered to achieve better performance with systematically organized representations in image format. A well-designed parallel CNN architecture for adapting Mol-PSIs is developed for protein–ligand binding affinity prediction. Our results, for the three most commonly used databases, including PDBbind-v2007, PDBbind-v2013 and PDBbind-v2016, are better than all traditional machine learning models, as far as we know. Our Mol-PSI model provides a powerful molecular representation that can be widely used in AI-based drug design and molecular data analysis.

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. Ministry of Education (MOE) Nanyang Technological University This work was supported in part by Nanyang Technological University Startup Grant M4081842.110, Singapore Ministry of Education Academic Research fund Tier 1 RG109/19, Tier 2 MOE-T2EP20120-0013 and MOE-T2EP20220-0010.

In econophysics, the achievements of information filtering methods over the past 20 years, such as the minimal spanning tree (MST) by Mantegna and the planar maximally filtered graph (PMFG) by Tumminello et al., should be celebrated. Here, we show how one can systematically improve upon this paradigm along two separate directions. First, we used topological data analysis (TDA) to extend the notions of nodes and links in networks to faces, tetrahedrons, or k-simplices in simplicial complexes. Second, we used the Ollivier-Ricci curvature (ORC) to acquire geometric information that cannot be provided by simple information filtering. In this sense, MSTs and PMFGs are but first steps to revealing the topological backbones of financial networks. This is something that TDA can elucidate more fully, following which the ORC can help us flesh out the geometry of financial networks. We applied these two approaches to a recent stock market crash in Taiwan and found that, beyond fusions and fissions, other non-fusion/fission processes such as cavitation, annihilation, rupture, healing, and puncture might also be important. We also successfully identified neck regions that emerged during the crash, based on their negative ORCs, and performed a case study on one such neck region. Published version

The development of ultracoarse-grained models for large biomolecules needs to derive the optimal number of coarse-grained (CG) sites to represent the targets. In this work, we propose to use the statistical internal cluster validation indexes to determine the optimal number of CG sites that are optimized based on the essential dynamics coarse-graining method. The calculated curves of Calinski-Harabasz and Silhouette Coefficient indexes exhibit the extrema corresponding to the similar CG numbers. The calculated ratios of the optimal CG numbers to the residue numbers of fine-grained models are in the range from 4 to 2. The comparison of the stability of index results indicates that Calinski-Harabasz index is the better choice to determine the optimal CG representation in coarse-graining. © 2019 Wiley Periodicals, Inc.

Chemically modified peptide nucleic acids (PNAs) show great promise in the recognition of RNA duplexes by major-groove PNA·RNA–RNA triplex formation. Triplex formation is favored for RNA duplexes with a purine tract within one of the RNA duplex strands, and is severely destabilized if the purine tract is interrupted by pyrimidine residues. Here, we report the synthesis of a PNA monomer incorporated with an artificial nucleobase S, followed by the binding studies of a series of S-modified PNAs. Our data suggest that an S residue incorporated into short 8-mer dsRNA-binding PNAs (dbPNAs) can recognize internal Watson–Crick C-G and U-A, and wobble U-G base pairs (but not G-C, A-U, and G-U pairs) in RNA duplexes. The short S-modified PNAs show no appreciable binding to DNA duplexes or single-stranded RNAs. Interestingly, replacement of the C residue in an S·C-G triple with a 5-methyl C results in the disruption of the triplex, probably due to a steric clash between S and 5-methyl C. Previously reported PNA E base shows recognition of U-A and A-U pairs, but not a U-G pair. Thus, S-modified dbPNAs may be uniquely useful for the general recognition of RNA U-G, U-A, and C-G pairs. Shortening the succinyl linker of our PNA S monomer by one carbon atom to have a malonyl linker causes a severe destabilization of triplex formation. Our experimental and modeling data indicate that part of the succinyl moiety in a PNA S monomer may serve to expand the S base forming stacking interactions with adjacent PNA bases. Ministry of Education (MOE) Nanyang Technological University We thank Prof. Tom Brown for providing us a detailed protocol for the synthesis of the S base. This work was supported by NTU start-up grant, Singapore Ministry of Education (MOE) Tier 1 grants (RGT3/13, RG42/15, and RG152/17), and MOE Tier 2 grants (MOE2013-T2-2-024 and MOE2015-T2-1-028) to G.C. The work was also supported by MOE Tier 1 (RG126/16 and RG31/18) and MOE Tier 2 (MOE2018-T2-1-033) to K.X.

Two types of osmolytes, i.e., trimethylamin N-oxide (TMAO) and urea, demonstrate dramatically different properties in a protein folding process. Even with the great progresses in revealing the potential underlying mechanism of these two osmolyte systems, many problems still remain unsolved. In this paper, we propose to use the persistent homology, a newly-invented topological method, to systematically study the osmolytes molecular aggregation and their hydrogen-bonding network from a global topological perspective. It has been found that, for the first time, TMAO and urea show two extremely different topological behaviors, i.e., extensive network and local cluster. In general, TMAO forms highly consistent large loop or circle structures in high concentrations. In contrast, urea is more tightly aggregated locally. Moreover, the resulting hydrogen-bonding networks also demonstrate distinguishable features. With the concentration increase, TMAO hydrogen-bonding networks vary greatly in their total number of loop structures and large-sized loop structures consistently increase. In contrast, urea hydrogen-bonding networks remain relatively stable with slight reduce of the total loop number. Moreover, the persistent entropy (PE) is, for the first time, used in characterization of the topological information of the aggregation and hydrogen-bonding networks. The average PE systematically increases with the concentration for both TMAO and urea, and decreases in their hydrogen-bonding networks. But their PE variances have totally different behaviors. Finally, topological features of the hydrogen-bonding networks are found to be highly consistent with those from the ion aggregation systems, indicating that our topological invariants can characterize intrinsic features of the "structure making" and "structure breaking" systems., Comment: 19 pages; 9 figures; 1 table

Understanding the molecular flexibility and dynamics is central to the analysis of biomolecular functions. In this work, complex multiscale virtual particle model based elastic network models (CMVP-ENMs) have been proposed for the normal mode analysis of biomolecular complexes or biomolecular assemblies. The term complex used in our CMVP-ENMs refers to the multi-material or multi-constituent. Different "materials" or constituents contribute differently to the general flexibility and dynamics of complex biomolecular structures. In our CMVP-ENMs, the key idea is to incorporate relative density or weight information of different components into the spring parameter of elastic network models. Two different models, including the CMVP based Gaussian network model (CMVP-GNM) and the CMVP based anisotropic network model (CMVP-ANM), have been proposed. With the consideration of complex component information, our CMVP-GNM, compared with the traditional GNM, can deliver a better accuracy in the B-factor prediction of protein-nucleic acid complexes. Moreover, our CMVP-ANM can be used to remove the "tip effect" by systematically suppressing the extremely-large vectors, in the highly flexible regions, of the normal modes generated by the ANM. In this way, our CMVP-ANM can be used to handle biomolecular structures with large hanging loops or extruding ends, which usually cause an irrationally-large-vector problem in ANM predictions. Finally, we explore the potential applications of our method by the cryo-EM data analysis. We find that by tuning the relative density ratio, we can systematically enhance or suppress the modes in different components, so that it can reveal the dynamics of the special regions that we are interested in. Ministry of Education (MOE) Nanyang Technological University This work was supported in part by the Nanyang Technological University Startup Grant M4081842 and the Singapore Ministry of Education Academic Research Fund Tier 1 RG126/16 and RG31/18, Tier 2 MOE2018-T2-1-033.

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. Ministry of Education (MOE) Nanyang Technological University Startup (supported in part through Grant M4081842.110); Singapore Ministry of Education Academic Research fund (Tier 1 RG109/19 and Tier 2 MOE2018-T2-1-033).

Efficient molecular featurization is one of the major issues for machine learning models in drug design. Here, we propose a persistent Ricci curvature (PRC), in particular, Ollivier PRC (OPRC), for the molecular featurization and feature engineering, for the first time. The filtration process proposed in the persistent homology is employed to generate a series of nested molecular graphs. Persistence and variation of Ollivier Ricci curvatures on these nested graphs are defined as OPRC. Moreover, persistent attributes, which are statistical and combinatorial properties of OPRCs during the filtration process, are used as molecular descriptors and further combined with machine learning models, in particular, gradient boosting tree (GBT). Our OPRC-GBT model is used in the prediction of the protein-ligand binding affinity, which is one of the key steps in drug design. Based on three of the most commonly used data sets from the well-established protein-ligand binding databank, that is, PDBbind, we intensively test our model and compare with existing models. It has been found that our model can achieve the state-of-the-art results and has advantages over traditional molecular descriptors. Ministry of Education (MOE) Nanyang Technological University This work was supported in part by Nanyang Technological University Startup Grant M4081842.110, Singapore Ministry of Education Academic Research fund Tier 1 RG109/19 and Tier 2 MOE2018-T2-1-033.

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) based molecular descriptors or fingerprints for the first time. Our PSH-based molecular descriptors are used in the characterization of molecular structures and interactions, and further combined with machine learning models, in particular gradient boosting tree (GBT), for protein-ligand binding affinity prediction. Different from traditional molecular descriptors, which are usually based on molecular graph models, a hypergraph-based topological representation is proposed for protein-ligand interaction characterization. Moreover, a filtration process is introduced to generate a series of nested hypergraphs in different scales. For each of these hypergraphs, its eigen spectrum information can be obtained from the corresponding (Hodge) Laplacain matrix. PSH studies the persistence and variation of the eigen spectrum of the nested hypergraphs during the filtration process. Molecular descriptors or fingerprints can be generated from persistent attributes, which are statistical or combinatorial functions of PSH, and combined with machine learning models, in particular, GBT. We test our PSH-GBT model on three most commonly used datasets, including PDBbind-2007, PDBbind-2013 and PDBbind-2016. Our results, for all these databases, are better than all existing machine learning models with traditional molecular descriptors, as far as we know. Ministry of Education (MOE) Nanyang Technological University This work was supported in part by Nanyang Technological University Startup Grant M4081842 and Singapore Ministry of Education Academic Research fund Tier 1 RG109/19, Tier 2 MOE2018-T2-1-033. The third author was supported by Natural Science Foundation of China (NSFC grant no. 11971144) and High-level Scientific Research Foundation of Hebei Province.

PerSpect-based machine learning models can significantly improve prediction accuracy for protein-ligand binding affinity., Molecular descriptors are essential to not only quantitative structure-activity relationship (QSAR) models but also machine learning–based material, chemical, and biological data analysis. Here, we propose persistent spectral–based machine learning (PerSpect ML) models for drug design. Different from all previous spectral models, a filtration process is introduced to generate a sequence of spectral models at various different scales. PerSpect attributes are defined as the function of spectral variables over the filtration value. Molecular descriptors obtained from PerSpect attributes are combined with machine learning models for protein-ligand binding affinity prediction. Our results, for the three most commonly used databases including PDBbind-2007, PDBbind-2013, and PDBbind-2016, are better than all existing models, as far as we know. The proposed PerSpect theory provides a powerful feature engineering framework. PerSpect ML models demonstrate great potential to significantly improve the performance of learning models in molecular data analysis.

Graphical abstract, Traditionally, human microbiology has been strongly built on the laboratory focused culture of microbes isolated from human specimens in patients with acute or chronic infection. These approaches primarily view human disease through the lens of a single species and its relevant clinical setting however such approaches fail to account for the surrounding environment and wide microbial diversity that exists in vivo. Given the emergence of next generation sequencing technologies and advancing bioinformatic pipelines, researchers now have unprecedented capabilities to characterise the human microbiome in terms of its taxonomy, function, antibiotic resistance and even bacteriophages. Despite this, an analysis of microbial communities has largely been restricted to ordination, ecological measures, and discriminant taxa analysis. This is predominantly due to a lack of suitable computational tools to facilitate microbiome analytics. In this review, we first evaluate the key concerns related to the inherent structure of microbiome datasets which include its compositionality and batch effects. We describe the available and emerging analytical techniques including integrative analysis, machine learning, microbial association networks, topological data analysis (TDA) and mathematical modelling. We also present how these methods may translate to clinical settings including tools for implementation. Mathematical based analytics for microbiome analysis represents a promising avenue for clinical translation across a range of acute and chronic disease states.

Microtubules are one of the most important components in the cytoskeleton and play a vital role in maintaining the shape and function of cells. Because single microtubules are some micrometers long, it is difficult to simulate such a large system using an all-atom model. In this work, we use the newly developed convolutional and K-means coarse-graining (CK-CG) method to establish an ultra-coarse-grained (UCG) model of a single microtubule, on the basis of the low electron microscopy density data of microtubules. We discuss the rationale of the micro-coarse-grained microtubule models of different resolutions and explore microtubule models up to 12-micron length. We use the devised microtubule model to quantify mechanical properties of microtubules of different lengths. Our model allows mesoscopic simulations of micrometer-level biomaterials and can be further used to study important biological processes related to microtubule function. Ministry of Education (MOE) Nanyang Technological University Published version This work was supported by the National Natural Science Foundation of China (Grant Nos. 21773065 and 22073029), Nanyang Technological University Startup Grant M4081842, Singapore Ministry of Education Academic Research fund Tier 1 RG31/18 and RG109/19, Tier 2 MOE2018-T2-1-033. FG acknowledges support by the Klaus Tschira Foundation and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy–2082/1–390761711.

Artificial intelligence (AI) based drug design has demonstrated great potential to fundamentally change the pharmaceutical industries. Currently, a key issue in AI-based drug design is efficient transferable molecular descriptors or fingerprints. Here, we present hypergraph-based molecular topological representation, hypergraph-based (weighted) persistent cohomology (HPC/HWPC) and HPC/HWPC-based molecular fingerprints for machine learning models in drug design. Molecular structures and their atomic interactions are highly complicated and pose great challenges for efficient mathematical representations. We develop the first hypergraph-based topological framework to characterize detailed molecular structures and interactions at atomic level. Inspired by the elegant path complex model, hypergraph-based embedded homology and persistent homology have been proposed recently. Based on them, we construct HPC/HWPC, and use them to generate molecular descriptors for learning models in protein-ligand binding affinity prediction, one of the key step in drug design. Our models are tested on three most commonly-used databases, including PDBbind-v2007, PDBbind-v2013 and PDBbind-v2016, and outperform all existing machine learning models with traditional molecular descriptors. Our HPC/HWPC models have demonstrated great potential in AI-based drug design. Ministry of Education (MOE) Nanyang Technological University This work was supported in part by Nanyang Technological University Startup Grant M4081842 and Singapore Ministry of Education Academic Research fund Tier 1 RG31/18 and RG109/19, Tier 2 MOE2018-T2-1-033. The second author was supported by Natural Science Foundation of China (NSFC grant no. 11871284). The third author was supported by Natural Science Foundation of China (NSFC grant no. 11971144) and High-level Scientific Research Foundation of Hebei Province.

With the great significance of biomolecular flexibility in biomolecular dynamics and functional analysis, various experimental and theoretical models are developed. Experimentally, Debye-Waller factor, also known as B-factor, measures atomic mean-square displacement and is usually considered as an important measurement for flexibility. Theoretically, elastic network models, Gaussian network model, flexibility-rigidity model, and other computational models have been proposed for flexibility analysis by shedding light on the biomolecular inner topological structures. Recently, a topology-based machine learning model has been proposed. By using the features from persistent homology, this model achieves a remarkable high Pearson correlation coefficient (PCC) in protein B-factor prediction. Motivated by its success, we propose weighted-persistent-homology (WPH)-based machine learning (WPHML) models for RNA flexibility analysis. Our WPH is a newly-proposed model, which incorporate physical, chemical and biological information into topological measurements using a weight function. In particular, we use local persistent homology (LPH) to focus on the topological information of local regions. Our WPHML model is validated on a well-established RNA dataset, and numerical experiments show that our model can achieve a PCC of up to 0.5822. The comparison with the previous sequence-information-based learning models shows that a consistent improvement in performance by at least 10% is achieved in our current model. Ministry of Education (MOE) Nanyang Technological University Published version This research is supported by Nanyang Technological University Startup Grants M4081840 and M4081842 to CSP, Data Science and Artificial Intelligence Research Centre@NTU M4082115 to CSP, and Singapore Ministry of Education Academic Research Fund Tier 1 RG31/18, RG109/ 19, and Tier 2 MOE2018-T2-1-033 to KX. There was no additional external funding received for this study.

Geometric and electrostatic modeling is an essential component in computational biophysics and molecular biology. Commonly used geometric representations admit geometric singularities such as cusps, tips and self-intersecting facets that lead to computational instabilities in the molecular modeling. The present work explores the use of flexibility and rigidity index (FRI), which has a proved superiority in protein B-factor prediction, for biomolecular geometric representation and associated electrostatic analysis. FRI rigidity surfaces are free of geometric singularities. We proposed a rigidity based Poisson–Boltzmann equation for biomolecular electrostatic analysis. Our approaches to surface and electrostatic modeling are validated by a set of 21 proteins. Our results are compared with those of established methods. Finally, being smooth and analytically differentiable, FRI rigidity functions offer excellent curvature analysis, which characterizes concave and convex regions on protein surfaces. Polarized curvatures constructed by using the product of minimum curvature and electrostatic potential is shown to predict potential protein–ligand binding sites.

We introduce an alignment-free method, the Magnus Representation, to analyze genome sequences. The Magnus Representation captures higher-order information in genome sequences. We combine our approach with the idea ofk-mers to define an effectively computable Mean Magnus Vector. We perform phylogenetic analysis on three datasets: mosquito-borne viruses, filoviruses, and bacterial genomes. Our results on ebolaviruses are consistent with previous phylogenetic analyses, and confirm the modern viewpoint that the 2014 West African Ebola outbreak likely originated from Central Africa. Our analysis also confirms the close relationship betweenBundibugyo ebolavirusandTaï Forest ebolavirus. For bacterial genomes, our method is able to classify relatively well at the family and genus level, as well as at higher levels such as phylum level. The bacterial genomes are also separated well into Gram-positive and Gram-negative subgroups.

RNAs are emerging as important biomarkers and therapeutic targets. The strategy of directly targeting double-stranded RNA (dsRNA) by triplex-formation is relatively underexplored mainly due to the weak binding at physiological conditions for the traditional triplex-forming oligonucleotides (TFOs). Compared to DNA and RNA, peptide nucleic acids (PNAs) are chemically stable and have a neutral peptide-like backbone, and thus, they show significantly enhanced binding to natural nucleic acids. We have successfully developed nucleobase-modified dsRNA-binding PNAs (dbPNAs) to facilitate structure-specific and selective recognition of dsRNA over single-stranded RNA (ssRNA) and dsDNA regions at near-physiological conditions. The triplex formation strategy facilitates the targeting of not only the sequence but also the secondary structure of RNA. Here, we report the development of novel dbPNA-based fluorescent light-up probes through the incorporation of A-U pair-recognizing 5-benzothiophene uracil (btU). The incorporation of btU into dbPNAs does not affect the binding affinity toward dsRNAs significantly, in most cases, as evidenced by our nondenaturing gel shift assay data. The blue fluorescence emission intensity of btU-modified dbPNAs is sequence- and structure-specifically enhanced by dsRNAs, including the influenza viral RNA panhandle duplex and HIV-1–1 ribosomal frameshift-inducing RNA hairpin, but not ssRNAs or DNAs, at 200 mM NaCl, pH 7.5. Thus, dbPNAs incorporating btU-modified and other further modified fluorescent nucleobases will be useful biochemical tools for probing and detecting RNA structures, interactions, and functions. Agency for Science, Technology and Research (A*STAR) Ministry of Education (MOE) Nanyang Technological University This work was supported by NTU-A*STAR Seed Funding Research Award (2018), Singapore Ministry of Education (MOE) Tier 1 grants (RGT3/13, RG42/15, and RG152/17), and MOE Tier 2 grants (MOE2013-T2-2-024 and MOE2015-T2-1-028) to G.C. G.C. thanks Prof. Dongping Zhong for the helpful discussions on TICT.

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 and biological properties, can be assigned to vertices (atom centers), edges (bonds), or higher order simplexes (cluster of atoms), depending on the biomolecular structure, function, and dynamics properties. Further, we propose the first localized weighted persistent homology (LWPH). Inspired by the great success of element specific persistent homology (ESPH), we do not treat biomolecules as an inseparable system like all previous weighted models, instead we decompose them into a series of local domains, which may be overlapped with each other. The general persistent homology or weighted persistent homology analysis is then applied on each of these local domains. In this way, functional properties, that are embedded in local structures, can be revealed. Our model has been applied to systematically studying DNA structures. It has been found that our LWPH based features can be used to successfully discriminate the A-, B-, and Z-types of DNA. More importantly, our LWPH based PCA model can identify two configurational states of DNA structure in ion liquid environment, which can be revealed only by the complicated helical coordinate system. The great consistence with the helical-coordinate model demonstrates that our model captures local structure variations so well that it is comparable with geometric models. Moreover, geometric measurements are usually defined in very local regions. For instance, the helical-coordinate system is limited to one or two basepairs. However, our LWPH can quantitatively characterize structure information in local regions or domains with arbitrary sizes and shapes, where traditional geometrical measurements fail., 27 pages; 18 figures