Methodology-centered review of molecular modeling, simulation, and prediction of SARS-CoV-2
Kaifu Gao, Rui Wang, Jiahui Chen, Limei Cheng, Jaclyn Frishcosy, Yuta Huzumi, Yuchi Qiu, Tom Schluckbier, Guo-Wei Wei
MMethodology-centered review of molecular modeling,simulation, and prediction of SARS-CoV-2
Kaifu Gao , Rui Wang * , Jiahui Chen , Limei Cheng , Jaclyn Frishcosy ,Yuta Huzumi , Yuchi Qiu , Tom Schluckbier , and Guo-Wei Wei , , † Department of Mathematics,Michigan State University, MI 48824, USA. Clinical Pharmacology and Pharmacometrics,Bristol Myers Squibb, Princeton, NJ 08536, USA Department of Electrical and Computer Engineering,Michigan State University, MI 48824, USA. Department of Biochemistry and Molecular Biology,Michigan State University, MI 48824, USA.February 2, 2021
Abstract
The deadly coronavirus disease 2019 (COVID-19) pandemic caused by severe acute respiratory syn-drome coronavirus 2 (SARS-CoV-2) has gone out of control globally. Despite much effort by scientists,medical experts, healthcare professions, and the society in general, the slow progress on drug discoveryand antibody therapeutic development, the unknown possible side effects of the existing vaccines, and thehigh transmission rate of the SARS-CoV-2, remind us the sad reality that our current understanding of thetransmission, infectivity, and evolution of SARS-CoV-2 is unfortunately very limited. The major limitationis the lack of mechanistic understanding of viral-host cell interactions, the viral regulation of host cell func-tions and immune systems, protein-protein interactions, including antibody-antigen binding, protein-drugbinding, host immune response, etc. This limitation will likely haunt the scientific community for a longtime and have a devastating consequence in combating COVID-19 and other pathogens. Notably, com-pared to the long-cycle, highly cost, and safety-demanding molecular-level experiments, the theoreticaland computational studies are economical, speedy and easy to perform. There exists a tsunami of the lit-erature on molecular modeling, simulation, and prediction of SARS-CoV-2 that has become impossible tofully 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 inthis review. This review will be beneficial to researchers who are look for ways to contribute to SARS-CoV-2studies and those who are assessing the current status in the field.
Key words: COVID-19, SARS-CoV-2, molecular modeling, biophysics, bioinformatics, machine learn-ing, deep learning, network analysis, persistent homology. * Kaifu Gao and Rui Wang contributed equally. † Corresponding author. Email: [email protected] ontents k -nearest neighbors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.4.4 Support vector machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.4.5 Decision trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.4.6 Random forest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.4.7 Gradient boost decision tree (GBDT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.4.8 Artificial neural network (ANN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.4.9 Convolutional neural network (CNN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.4.10 RNN, LSTM, and GRU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.4.11 Machine learning and viral mutations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.5 Mathematical approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.5.1 Network analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.5.1.1 Network based biomolecular structure analysis. . . . . . . . . . . . . . . . . . 382.5.1.2 Network-based drug repurposing. . . . . . . . . . . . . . . . . . . . . . . . . 382.5.2 Flexibility-rigidity index (FRI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.5.3 Topological data analysis (TDA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Introduction
Since its first case was identified in Wuhan, China, in December 2019, coronavirus disease 2019 (COVID-19)caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has expeditiously spread to asmany as 218 countries and territories worldwide, and led to over 100 million confirmed cases and over2 million fatalities as of January 20, 2021. This pandemic has also brought a massive economic recessionglobally.
Figure 1: Confirmed cases all around the world until January 20, 2021. β -coronavirus genus and coronaviridae family, SARS-CoV-2 is an unsegmented positive-sense single-stranded RNA virus with a compact 29,903 nucleotide-long genome and the diameter of eachSARS-CoV-2 virion is about 50-200 nm [128]. In the first 20 years of the 21st century, β -coronaviruses havetriggered three major outbreaks of deadly pneumonia: SARS-CoV (2002), Middle East respiratory syn-drome coronavirus (MERS-CoV) (2012), and SARS-CoV-2 (2019) [441]. Like SARS-CoV and MERS-CoV,SARS-CoV-2 also causes respiratory infections, but at a much higher infection rate [734, 759]. The completegenome of SARS-CoV-2 comprises 15 open reading frames (ORFs), which encode 29 structural and non-structural proteins, as illustrated in Figure 2. The 16 non-structural proteins NSP1-NSP16 get expressed byprotein-coding genes ORF1a and ORF1b, while four canonical 3’ structural proteins: spike (S), envelope(E), membrane (M), and nucleocapsid (N) proteins, as well as accessory factors, are encoded by other fourmajor ORFs, namely ORF2, ORF4, ORF5, and ORF9 (See Figure 2) [294, 481, 497, 512].The viral structure of SARS-CoV-2 can be found in the upper right corner of Figure 3. This structure isformed by the four structural proteins: the N protein holds the RNA genome, and the S, E, and M proteinstogether construct the viral envelope [760]. The studies on SARS-CoV-2 as well as previous SARS-CoV andother coronaviruses have mostly identified the functions of these structural proteins, nonstructural proteinsas well as accessory proteins, which are summarized in Table 1; their 3D structures are also largely known1 SP1 NSP2 NSP3Papain-likeProtease(4,955 - 5,900) NSP4NSP5(10,055 - 10,972)NSP7NSP8NSP9NSP11NSP6 NSP10 NSP12RNA polymeraseRNA-dependent(13,442 - 16,236) Helicase(16,237 - 18,043)NSP14NSP15NSP165’ 3’Spike(21,563 - 25,384)(26,523 - 27,191) (28,274 - 29,533)E M NORF1bORF1a ORF2-ORF102,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000 22,000 24,000 26,000 28,000 29,90313,46813,442 (26,245 - 26,472)NSP13 3a 67a7b8 103b 9c9bAccessory factors
Main Protease
Figure 2: Genomics organization of SARS-CoV-2. E n d o p l a s m i c r e t i c u l u m ( E R ) SARS-CoV-2 ACE2TMPRSS2Nucleocapsid (N)Spike (S)Membrane (M)Envelope (E) 3’ 5’5’ 3’Ribosomepp1a and pp1ab RNA genomeReplicaseGolgiNucleus Translation N i n c y t o p l a s m Transcription R e l e a s e o f v i r a l g e n o m e RNA replication and packingVirus release
SARS-CoV-2 Life Cycle
Mpro/PLpro
New SARS-CoV-2
IIIIII IVVVI
Functional NSPs
SEMN
Figure 3: Six stages of the SARS-CoV-2 life cycle. Stage I : Virus entry. Stage II : Translation of viral replication. Stage III : Replication.Here, NSP12 (RdRp) and NSP13 (helicase) cooperate to perform the replication of the viral genome. Stage IV : Translation of viralstructure proteins. Stage V : Virion assembly. Stage VI : Release of virus. from experiments or predictions, which are shown in Figures 4 and 5.Protein Functions 3D structureavailability2SP1 NSP1 (180 residues) likely inhibits host translation by interacting withthe 40S ribosomal subunit. Its C terminus binds to and obstructs theribosomal mRNA entry tunnel, thereby inhibiting antiviral responsetriggered by innate immunity or interferons. The NSP1-40S ribosomecomplex further induces an endonucleolytic cleavage near the 5’UTRof host mRNAs, targeting them for degradation. By suppressing hostgene expression, NSP1 facilitates efficient viral gene expression in in-fected cells and evasion from host immune response [325]. Experiment(PDB ID: 7k3n,etc.)NSP2 NSP2 (638 residues) may play a role in the modulation of host cell sur-vival signaling pathway by interacting with the host factors, prohibitin1 and prohibitin 2, which are involved in maintaining the functional in-tegrity of the mitochondria and protecting cells from various stresses.It appears that NSP2 could change the intracellular milieu and perturbhost intracellular signaling [153]. Prediction [410]NSP3 (ContainsPLpro) NSP3 (1945 residues) includes the papain-like protease (PLpro) andsome multi-pass membrane proteins. PLpro is responsible for cleavingand releasing NSP1, NSP2, and NSP3; PLpro also possesses a deubiqui-tinating/deISGylating activity and processes both “Lys-48”- and “Lys-63”-linked polyubiquitin chains from cellular substrates. It cleaves pref-erentially ISG15 from substrates in vitro, which can play a role in hostADP-ribosylation by binding ADP-ribose. In addition, NSP3 partici-pates together with NSP4 in the assembly of virally-induced cytoplas-mic double-membrane vesicles necessary for viral replication, and an-tagonizes innate immune induction of type I interferon by blocking thephosphorylation, dimerization and subsequent nuclear translocation ofhost IRF3; it also prevents host NF-kappa-B signaling [54]. Partially avail-able fromexperiments:Residues 1570-1877 (PLpro,PDB ID: 7kol,etc.); Residues819-929 (PDBID: 7kag, etc.);Residues 1024-1192 (PDB ID:6wcf [480], etc.)NSP4 NSP4 (500 residues) is a multi-pass membrane protein. Together withNSP3, it participates in the assembly of virally-induced cytoplasmicdouble-membrane vesicles, which is necessary for viral replication.[615]. Prediction [331]NSP5 (Mpro) NSP5 (306 residues) is the main protease (3CL protease) of the SARS-CoV-2. It takes charge of cleaving and releasing NSP4-NSP16. Addi-tionally, it recognizes substrates containing the core sequence [ILMVF]-Q-—-[SGACN] and is also able to bind an ADP-ribose-1”-phosphate(ADRP). Moreover, it plays a role in NSP maturation [760]. Experiment(PDB ID:5r84 [189],etc.)NSP6 NSP6 (290 residues) is a multi-pass membrane protein, working withNSP3 and NSP4, it induces double-membrane vesicles (autophago-somes) in infected cells from their reticulum endoplasmic. It also limitsthe expansion of these autophagosomes that are no longer able to de-liver viral components to lysosomes [44, 157]. Prediction [331]NSP7 NSP7 (83 residues) plays a role in viral RNA synthesis. It forms a hex-adecamer with NSP8 that may participate in viral replication by actingas a primase. Alternatively, may synthesize substantially longer prod-ucts than oligonucleotide primers [378]. Experiment(PDB ID: 6m5i,etc.)NSP8 NSP8 (198 residues) plays a role in viral RNA synthesis. It forms a hex-adecamer with NSP7 that may participate in viral replication by actingas a primase. Alternatively, it may synthesize substantially longer prod-ucts than oligonucleotide primers [378, 675]. Experiment(PDB ID: 6m5i,etc.)3SP9 NSP9 (113 residues) functions in viral replication as a dimeric ssRNA-binding protein. [675] Experiment(PDB ID: 6w4b,etc.)NSP10 NSP10 (139 residues) plays a pivotal role in viral transcription. It formsa dodecamer and interacts with both NSP14 and NSP16 to stimulatetheir respective 3’-5’ exoribonuclease and 2’-O-methyltransferase activ-ities in viral mRNAs cap methylation [675]. Experiment(PDB ID:6zct [602],etc.)NSP11 NSP11 (13 residues) is a pp1a cleavage product at the NSP10/11 bound-ary. For pp1ab, it is a frameshift product that becomes the N-terminalof NSP12. Its function, if any, is currently unknown [675]. NoNSP12 (RdRp) NSP12 (932 residues) is the RNA-dependent RNA polymerase (RdRp)performing both replication and transcription of the viral genome.Specifically, it catalyzes the synthesis of the RNA strand complemen-tary to a given RNA template. The RdRp of SARS-CoV-2 can be inhib-ited by the nucleoside analogue Remdesivir [675]. Experiment(PDB ID:6m71 [239],etc.)NSP13 (Heli-case) NSP13 (601 residues) is a multifunctional superfamily 1 helicase capa-ble of using both dsDNA and dsRNA as substrates with 5’-3’ polarity.In addition to working with NSP12 in viral genome replication, it isalso involved in viral mRNA capping. It associates with nucleoproteinin membranous complexes [323]. Experiment(PDB ID:5rlh [239],etc.)NSP14 NSP14 (527 residues) possesses two different activities: (1) An exori-bonuclease activity on both ssRNA and dsRNA in a 3’ to 5’ direction; (2)A N7-guanine methyltransferase (viral mRNA capping) activity. It actsas a proofreading exoribonuclease for RNA replication, thereby lower-ing the sensitivity of the virus to RNA mutagens [222]. It always inter-acts with NSP10 [675]. Prediction [410]NSP15 (Nen-doU) NSP15 (346 residues) is the nidoviral RNA uridylate-specific endori-bonuclease (NendoU) that favors the cleavage of RNA at the 3’-ends ofuridylates, loss of NSP15 affects both viral replication and pathogene-sis. It is also required for the evasion of host cell dsRNA sensors [180]. Experiment(PDB ID: 5s72,etc.)NSP16 NSP16 (298 residues) is activated by and interacts with NSP10. Its 2’-O-methyltransferase activity mediates mRNA cap 2’-O-ribose methyla-tion to the 5’-cap structure of viral mRNAs. Since N7-methyl guanosinecap is a prerequisite for binding of NSP16, it plays an essential role inviral mRNAs cap methylation which is essential to evade the immunesystem. It may also work against host cell antiviral sensors [675]. Experiment(PDB ID:6w4h [606],etc.)4RF2 (Spike (S)protein) The S protein (1273 residues) may down-regulate host tetherin (BST2)by lysosomal degradation, thereby counteracting its antiviral activity. Itcan be cleaved into two subunits, S1 and S2. S1 attaches the virion to thecell membrane by interacting with the host receptor, initiating the infec-tion. Binding to human ACE2 receptor and internalization of the virusinto the endosomes of the host cell induces conformational changes inthe S protein. The stalk domain of S contains three hinges, giving thehead unexpected orientational freedom. The S protein uses human TM-PRSS2 for priming in human lung cells, which is an essential step forviral entry. S2 mediates fusion of the virion and cellular membranes byacting as a class I viral fusion protein. Under the current model, theprotein has at least three conformational states: pre-fusion native state,pre-hairpin intermediate state, and post-fusion hairpin state. Duringviral and target cell membrane fusion, the coiled coil regions (heptadrepeats) assume a trimer-of-hairpins structure, positioning the fusionpeptide in close proximity to the C-terminal region of the ectodomain.The formation of this structure appears to drive apposition and subse-quent fusion of viral and target cell membranes. [300]. Experiment(PDB ID:7c2l [137],etc.)ORF3a ORF3a (275 residues) is a multi-pass membrane protein that forms ho-motetrameric potassium sensitive ion channels (viroporin). It upreg-ulates expression of fibrinogen subunits FGA, FGB, and FGG in hostlung epithelial cells, induces apoptosis in cell culture, and downregu-lates the type 1 interferon receptor by inducing serine phosphorylationwithin the IFN alpha-receptor subunit 1 (IFNAR1) degradation motifand increasing IFNAR1 ubiquitination. More importantly, it activatesboth NF-kB and NLRP3 inflammasome and contributes to the genera-tion of the cytokine storm. it may also modulate viral release [667]. Experiment(PDB ID:6xdc [358])ORF3b Along with nucleocapsid protein and ORF6, ORF3b (22 residues) ap-pears to block induction of IFN-I. This 22-residue variant is also presentin SARS-CoV-2-related viral genomes in bats and pangolins [25]. NoORF4 (En-velope (E)protein) The E protein (75 residues) is a single-pass type III membrane proteinplaying a central role in virus morphogenesis and assembly, it acts asa viroporin and self-assembles in host membranes forming pentamericprotein-lipid pores that allow ion transport. It is also involved in theinduction of apoptosis. [628]. Partially avail-able fromexperiment:Residues8-38 (PDBID:7k3g [454])ORF5 (Mem-brane (M)protein) The M protein (222 residues) is the most abundant structural com-ponent of the virion, and very conserved. It mediates morphogene-sis, assembly, and budding of viral particles through the recruitmentof other structural proteins to the ER-Golgi-intermediate compartment(ERGIC). It also interacts with N for RNA packaging into virion [730]. Prediction [331]ORF6 ORF6 (61 residues) appears to be a virulence factor. It disrupts cell nu-clear import complex formation by tethering karyopherin alpha 2 andkaryopherin beta 1 to the membrane. Retention of import factors atthe ER/Golgi membrane leads to a loss of transport into the nucleus,thereby preventing STAT1 nuclear translocation in response to inter-feron signaling and thus blocking the expression of interferon stimu-lated genes (ISGs) that display multiple antiviral activities. [308]. Prediction [410]5RF7a ORF7a (121 residues) is a type I membrane protein that plays a role asan antagonist of bone marrow stromal antigen 2 (BST-2), disrupting itsantiviral effect. As BST-2 tethers virions to the host’s plasma membrane,ORF7a binding inhibits BST-2 glycosylation and interferes with this re-striction activity. ORF7a may suppress small interfering RNA (siRNA)and also may bind to host ITGAL, thereby playing a role in attachmentor modulation of leukocytes. [700]. Partially avail-able fromexperiment:Residues 16-82(PDB ID:6w37)ORF7b ORF7b (43 residues) is a type III integral transmembrane protein in theGolgi apparatus. In SARS-CoV-2, it appears to be a viral attenuationfactor. It may be involved in human infectivity of SARS-CoV-2 [568]. NoORF8 ORF8 (121 residues) might be a luminal ER membrane-associated pro-tein. It may trigger ATF6 activation and affect the unfolded proteinresponse (UPR). Like ORF7b, it may be involved in human infectivityof SARS-CoV-2 [504, 568, 692]. Experiment(PDB ID:7jtl[226], etc.)ORF9a (Nucleo-capsid (N) pro-tein) The N protein (419 residues) packages the positive strand viral genomeRNA into a helical ribonucleocapsid (RNP) and plays a fundamen-tal role during virion assembly through its interactions with the viralgenome and membrane protein M. It also plays an important role inenhancing the efficiency of subgenomic viral RNA transcription as wellas viral replication. It may modulate transforming growth factor-betasignaling by binding host smad3 [497]. Partially avail-able fromexperiments:Residues 41-174 (PDBID:6m3m [347],etc.); Residues247-364 (PDBID:6zco [801],etc.);ORF9b ORF9b (97 residues) plays a role in the inhibition of the host’s innateimmune response by targeting the mitochondrial-associated adapterMAVS. Mechanistically, it usurps the E3 ligase ITCH to trigger thedegradation of MAVS, TRAF3, and TRAF6. In addition, it can causemitochondrial elongation by triggering ubiquitination and proteasomaldegradation of dynamin-like protein 1/DNM1L [651]. Experiment(PDB ID:6z4u)ORF9c ORF9c (70 residues), located in the N coding region, interacts with var-ious host proteins including Sigma receptors, implying involvement inlipid remodeling and the ER stress response. It might also target NF-kBsignaling [262]. NoORF10 ORF10 (38 residues) interacts with factors in the CUL2 RING E3 ligasecomplex and thus may modulate ubiquitination [262]. Prediction [410]With these SARS-CoV-2 proteins, the intracellular viral life cycle of SARS-CoV-2 can be realized [377].This life cycle has six stages as shown in Figure 3. The first stage is the entry of the virus. SARS-CoV-2 entersthe host cell either via endosomes or plasma membrane fusion. In both ways, the S protein of SARS-CoV-2first attaches to the host cell-surface protein, angiotensin-converting enzyme 2 (ACE2). Then, the cell’s pro-tease, transmembrane protease serine 2 (TMPRSS2), cuts and opens the S protein of the virus, exposing afusion peptide in the S2 subunit of the S protein [468]. After fusion, an endosome forms around the virion,separating it from the rest of the host cell. The virion escapes when the pH of the endosome drops or whencathepsin, a host cysteine protease, cleaves it. The virion then releases its RNA into the cell [300]. After theRNA releasing, the polyproteins pp1a and pp1ab are translated. Notably, facilitated by viral Papain-like6 igure 4: 3D conformations of the SARS-CoV-2 nonstructural proteins. protease (PLpro), NSP1, NSP2, NSP3, and the amino terminus of NSP4 from the pp1a and pp1ab are re-leased. Moreover, NSP5-NSP16 are also cleaved proteolytically by the main protease (Mpro) [732]. The nextstage of the life cycle is the replication process, where the NSP12 (RdRp) and NSP13 (helicase) cooperate toperform the replication of the viral genome. Stages IV and V are the translation of viral structural proteins7 igure 5: 3D conformations of the ORF2-ORF10 proteins. and the virion assembly process. In these stages, the structural proteins S, E, and M are translated by ribo-somes and then present on the surface of the endoplasmic reticulum (ER), which will be transported fromthe ER through the golgi apparatus for the preparation of virion assembly. Meanwhile, multiple copies ofN protein package the genomics RNA in cytoplasm, which interacts with the other 3 structural proteins todirect the assembly of the virions. Finally, virions will be secreted from the infected cell through exocytosis.Since the first outbreak of the COVID-19, the raging pandemic caused by SARS-CoV-2 has lasted over ayear. Despite much effort by scientists, medical professions, and the society in general, there is still no effec-tive control, prevention, and cure for the deadly disease at present. The discovery of small-molecular drugsand antibody therapies has been progressing slowly. We do have many promising vaccines, but they mighthave side effects and their full side effects, particularly, long-term side effects, remain unknown. To makethings worse, near 30,000 unique mutations have been recorded for SARS-CoV-2 as shown by Mutation8racker ( https://users.math.msu.edu/users/weig/SARS-CoV-2 Mutation Tracker.html). All of these re-veal a sad reality that our current understanding of life science, virology, epidemiology, and medicine isseverely limited. This limitation hinders our understanding of the transmission, infectivity, and evolutionof SARS-CoV-2. Ultimately, the root of the challenge is the lack of the molecular mechanistic understand-ing of coronavirus RNA proofreading, virus-host cell interactions, antibody-antigen interactions, protein-protein interactions, protein-drug interactions, viral regulation of host cell functions, including autophago-cytosis and apoptosis, and irregular host immune response behavior such as cytokine storm and antibody-dependent enhancement. Molecular-level experiments on SARS-CoV-2 are expensive and time-consuming,and require to take heavy safety measures. However, the advances in computer power, the accumulation ofmolecular data, the availability of artificial intelligence (AI) algorithms, and the development of new math-ematical tools have paved the road for mechanistic understanding from molecular modeling, simulation,and prediction. A gigantic literature for molecular modeling, simulation, and prediction of SARS-CoV-2has been published or available online. It has become impossible for senior exports, not to mention juniorresearchers, to go through this literature at present. Therefore, it is time to present a methodology-centeredreview so that a reader can still grasp the current status of SARS-CoV-2 modeling, simulation, and predic-tion without having to read the entire literature. In this review, we cover the studies of molecular modeling,Monte Carlo (MC) methods, structural bioinformatics, machine learning & deep learning, and mathemati-cal approaches, in the combating of COVID-19. Comments are given in the discussion section, while futureperspectives are presented in the concluding remarks. In the field of molecular modeling, docking is a method to predict the preferred orientation of one moleculeto a second when bound to each other to form a stable complex as shown in Figure 6. Since bindingbehavior plays a vital role in the rational design of drugs, molecular docking, which can provide bindingconformations of ligands to specific binding sites, is one of the most popular methods in structure-baseddrug design [380, 702]. A docking program includes two key components: a scoring function to evaluatethe energies of different conformations and a search algorithm to sample the conformational degrees offreedom and locate the global energy minimum from all the sampled conformations [95]. In addition toregular docking, ensemble docking [37] docks a ligand to an ensemble of receptor conformations (oftengenerated by molecular dynamics simulation) and picks up the optimal binding pose. Molecular dockingis well-established in early-stage drug discovery and is, as a result, widely applied to many SARS-CoV-2proteins.
One important source for SARS-CoV-2 treatment isexisting drugs. Chen et al. [131] implemented a quite extensive drug-repurposing work: they dockedand predicted the binding affinities of 7173 purchasable drugs, 4574 unique compounds as well as theirstereoisomers to the main protease. As a result, disosmin, hesperidin, and MK-3207 with an affinity of-10.1 kcal/mol, were suggested as the most potent inhibitors. Sencanski et al. [633] and Gurung et al. [276]both screened about 1400 FDA (the United States Food and Drug Administration)-approved drugs throughdocking, predicting that dihydroergotamine has a promising affinity (-9.4 kcal/mol). Eleftheriou et al. [199]used docking to evaluate the potency of around 100 approved protease inhibitors and suggested that fal-daprevir has the strongest binding affinity of -11.15 kcal/mol. Many others [40, 164, 233, 280, 304, 335, 407,426, 453, 457, 641, 717, 725, 733] have also docked and repurposed existing drugs against the SARS-CoV-2main protease. 9 igure 6: The molecular docking procedure targeting the SARS-CoV-2 main protease.
Another type of potential inhibitors is natural products. Chandel et al. [399] screened 1000 active phyto-chemicals from Indian medicinal plants by molecular docking. Among them, rhein and aswagandhanolidewere predicted to have binding affinities over -8.0 kcal/mol. Mazzini et al. [472] docked more than 100 nat-ural and nature-inspired products from an in-house library to the main protease, predicting leopolic acid Ato have with the highest affinity, -12.22 kcal/mol. Vijayaraj et al. [728] studied some bioactive compoundsfrom marine resources, suggesting that an ethyl ester (-8.42 kcal/mol) from Marine Sponges Axinella cf.corrugata is the most potent against SARS-CoV-2 among them. Moreover, a variety of natural productsfrom aloe vera, Moroccan medicinal plants, fungal metabolite, millet, tannins, neem leaves, nigella sativa,etc., [1, 2, 92, 165, 205, 261, 360, 361, 486, 487, 496, 532, 595, 618, 621, 638, 663, 689, 698] were also investigated bydocking-based virtual screening.Other works focus on small compounds from other sources. Tsuji et al. [711] virtually screened the com-pounds in ChEMBL database [242] against the main protease, suggesting that the compound CHEMBL1559003with a binding affinity of -10.6 kcal/mol as the most potent. Udrea et al. [713] predicted the binding affini-ties of 15 phenothiazines, reporting the compound SPZ (-10.1 kcal/mol) as the most effective. Ghaleb etal. [251] also studied some pyridine N-oxide compounds, indicating the most potent one with a predictedpIC50 value of 5.294 (about -7.22 kcal/mol). More similar works are described in Refs. [11, 14, 78, 79, 135,136, 240, 406, 433, 490, 546, 719].
Many researchers have analyzed the binding interactions between the Sprotein and human ACE2. For example, Ortega et al. [541] used docking calculations to compare the bind-ing affinities of the SARS-CoV-2 S protein and the SARS-CoV S protein to ACE2. Their results suggestedmore residue interactions are between the SARS-CoV-2 S protein and ACE2, leading to a higher bindingaffinity, which is consistent with recent experimental research [758].More investigations were about drug or compound repurposing. To repurpose existing drugs againstthe SARS-CoV-2 S protein, Miroshnychenko et al. [484] systematically docked 248 drugs to the S proteinand found that amentoflavone and ledipasvir (-8.5 kcal/mol and -8.4 kcal/mol) were the top two inhibitors.Since their binding domains were predicted to be different, the combined use of them to treat SARS-CoV-2was suggested by the authors. The potency of lopinavir and ubrogepant against the S protein was alsoinvestigated [534, 640].For natural products, Subbaiyan et al. [688] performed virtual screening on 12 compounds from indige-nous food additives and herbal constituents. Among them, epigallocatechin gallate was predicted as the10op compound with a binding affinity of -9.2 kcal/mol. Basu et al. [65] revealed that hesperidin had thehighest binding affinity of -8.99 kcal/mol among the 6 phytochemicals from Indian medicinal plants. Othernatural products from tea flavonoids and triterpenoid were also studied against the S protein [263,332,449].Inhibitors from other sources were repurposed to inhibit the S protein as well. For example, Fakihet al. [216] performed docking on dermaseptin-based antiviral peptides. Zegheb et al. [782] evaluatedN-ferrocenylmethyl derivatives against the S-protein. Abo-zeid et al. [5] virtually screened some FDA-approved iron oxide nanoparticles to target the S-protein receptor-binding domain (RBD).
Through docking, Ahmad et al. [12] systematically assessed 7922 approvedor experimental drugs against SARS-CoV-2 RdRp and suggested that Nacartocin has the highest bindingaffinity of -13.943 kcal/mol. Beg et al. [71] screened 70 anti-HIV (human immunodeficiency virus) or anti-HCV (hepatitis C virus) drugs, reporting the top drug paritaprevir with a -10 kcal/mol binding affinity.Aftab et al. [10] studied 10 antiviral drugs and revealed Remdesivir’s docking score was the highest (-14.06kcal/mol). Other RdRp drug-repurposing works include Refs. [200, 296, 501, 560].Lung et al. [443] retrieved 83 traditional Chinese medicinal compounds as well as their similar structuresfrom the ZINC15 database, evaluated their potency against the RdRp by docking, and reported the bindingaffinity of theaflavin (-9.11 kcal/mol) as the highest among them. Singh et al. [662] virtually screenedover 100 phytochemical inhibitors and predicted that withanolide E, with a binding affinity of -9 kcal/mol,was the most potent. Pandeya et al. [552] also investigated some biologically active alkaloids of argemonemexicana.
Through docking, Mohideen et al. [492] found that the binding affinity of thenatural product thymoquinone to the E protein was -9.01 kcal/mol. Borgio et al. [88] screened 23 FDA-approved drugs to target the helicase of SARS-CoV-2 and reported vapreotide with a binding affinity of-11.58 kcal/mol as the most potent.
Maurya et al. [470] assessed phytochemicals and active pharmaco-logical agents present in Indian herbs against 7 different proteins of SARS-CoV-2 (The main protease, Nprotein, NendoU, NSP3, NSP9, and S protein) and human proprotein convertase (furin) through docking.Deshpande et al. [182] also docked 11 antiviral drugs to the main protease, S-protein, PLpro, NSP10, NSP16,and NSP9, and calculated their binding affinities. Nimgampalle et al. [527] virtually screened chloroquine,hydroxychloroquine, and their derivatives against multiple SARS-CoV-2 protein drug targets: the main pro-tease, RdRp, S-protein, ADP-ribose-1 monophosphatase (in NSP3), and NSP9. Da Silva et al. [162] studiedthe potency of essential oil components against the main protease, PLpro, NendoU, ADP-ribose-1 phos-phatase, RdRp, S protein, and human ACE2. Notably, there is a controversy about using human ACE2 as atarget (See Section 2.1.1.6). Some limonoids and triterpenoids were evaluated by Vardhan et al. [722] againstthe main protease, PLpro, S protein, RdRp, and human ACE2. Laksmiani et al. [414] performed docking onsome medicinal plants against the main protease, PLpro, RdRp, human cellular transmembrane proteaseserine 2 (TMPRSS2), and ACE2. Khan et al. [367] tested some dietary molecules by docking against themain protease, S protein, HR2 domain and post fusion core S2 subunit of the S protein, and NendoU. Thu-rakkal et al. [703] docked organosulfur compounds against the main protease, PLpro, S-protein, RdRp, andhelicase. Yu et al. [781], targeting the main protease, PLpro, RdRp, and S protein, evaluated the potency offive FDA-approved drugs and some Chinese traditional drugs.Vijayakumar et al. [726] assessed the potency of natural flavonoids and synthetic indole chalconesagainst the main protease, S protein, and RdRp. On the same set of targets, Parvez et al. [559] studied someplant metabolites, Maurya et al. [469] investigated yashtimadhu (glycyrrhiza glabra) active phytochemi-cals, and Alexpandi et al. [27] simulated quinoline-based inhibitors. Targeting the main protease, RdRp,11nd PLpro, Hosseini et al. [305] calculated some drug candidates; Chowdhury et al. [148] reported that anarsenic-based approved drug darinaparsin had docking binding affinities over -7.0 kcal/mol. Additionally,Iftikhar et al. [316] reported results targeting the main protease, RdRp, and helicase.More works studied the potency of compounds inhibiting two different proteins. Elmezayen et al. [202]virtually screened 4500 approved or experimental drugs against the main protease and human TMPRSS2,finding ZINC000103558522 had the highest binding affinity to the main protease (-12.36 kcal/mol), andZINC000012481889 had the highest binding affinity to the TMPRSS (-12.14 kcal/mol). Chandel et al. [116]repurposed about 2000 FDA-approved compounds targeting S protein and NSP9, reporting that Tegobu-vir was the most potent to S protein (-8.1 kcal/mol) and Conivaptan was the most potent to NSP9 (-8.4kcal/mol). Targeting the main protease and S protein, Narkhede et al. [513], Durdagi et al. [192], andCubuk et al. [159] evaluated tens of existing drugs, Kamaz et al. [344] and Tallei [696] tested some plantproducts, Moreover, Maiti et al. [450] docked Nigellidine to these targets. Targeting the main proteaseand RdRp, Al-Masoudi et al. [20] focused on some antiviral and antimalarial drugs, Rono et al. [604] stud-ied azole derivatives, and Lakshmanan et al. [413] and Suresh et al. [693] investigated Kabasura KudineerChooranam and Maramanjal Kudineer Churnam, respectively. Against the S protein and NenDoU, Sinhaet al. [666] reported that saikosaponin V was potent to both targets.
Some docking studies involved targeting human pro-teins such as the ACE2 [3, 94, 162, 270, 283, 334, 414, 587, 645, 721, 791] and glucose regulated protein 78(GRP78) [548], which are related to SARS-CoV-2 binding. However, according to some reports, it is contro-versial to design SARS-CoV-2 inhibitors targeting human ACE2 or related proteins. ACE2 is an importantenzyme attached to cell membranes in lungs, arteries, heart, kidney, and intestines. It is critical for loweringblood pressure in a human body [355]. It is unclear whether drugs to inhibit ACE2 or related targets aremore beneficial than harmful. Further investigation is needed [217].
Biomolecules are not static. X-ray crystallography and nuclear magnetic resonance (NMR) have alreadyrevealed that even a same molecule can adopt multiple conformations [249, 259]. Conformational changeplays a significant role in biomolecular function, such as enzyme catalytic cycles [234, 238]. While X-raycrystallography and NMR can only provide static structures, MD simulation is a feasible way to investigatebiomolecular conformational changes [303,352]. Furthermore, thanks to high-performance computing plat-forms such as graphical processing units (GPUs), current MD simulation can reveal conformation changesof biomacromolecules such as proteins, DNA, and RNA in the time scale of milliseconds (ms) [648].MD simulation is a commonly used computational method for understanding the physical movementof atoms (or particles) in molecules (see Figure 7). The motions driven by force fields are determined usingNewton’s second law [8]. In MD simulations, the interactions between atoms are described by force fields.Most force fields in chemistry are empirical, which consist of a summation of bonded forces associated withchemical bonds, bond angles, bond dihedrals, and non-bonded forces associated with van der Waals andelectrostatic forces [31]. The functional form of a typical force field such as AMBER looks like [152]: V ( r N ) = (cid:88) bonds k r ( r − r ) + (cid:88) angles k θ ( θ − θ ) + (cid:88) torsions V n [1 + cos( nω i − γ i )]+ N − (cid:88) j =1 N (cid:88) i = j +1 (cid:34) A ij R ij − B ij R ij + q i q j (cid:15)R ij (cid:35) , (1)12 igure 7: The workflow of MD simulations. where k r and k θ are the force constants for bond lengths and bond angles, respectively. Here, r and θ are a bond length and a bond angle, r and θ are the equilibrium bond length and bond angle, ω i is thedihedral angle, V n is the corresponding force constant, n is the multiplicity, and phase angle γ i takes valuesof either ◦ or ◦ . The non-bonded part of the potential is represented by the Lennard-Jones repulsive A ij and attractive B ij terms, Coulomb interactions between partial atomic charges ( q i and q j ). Here, R ij is the distance between atoms i and j . Finally, (cid:15) is the dielectric constant that considers the medium effectthat is not explicitly represented and usually equals 1.0 in a typical solvated environment where solventis represented explicitly. The non-bonded terms are calculated for atom pairs that are either separated bymore than three bonds or not bonded.To tackle systems with an excessive number of atoms, coarse-grained models are also developed. Inthese models, a group of atoms is represented by a “pseudo-atom”, so the number of atoms is largelyreduced [381]. Popular coarse-grained models are the G ¯o model [714], MARTINI force field [459], UNRESforce field [448], et al.Since MD simulations can provide many samplings, one can calculate free energy change between dif-ferent states from these samplings. Typical binding free energy calculation methods based on MD sim-ulations are the molecular mechanics energies combined with Poisson–Boltzmann or generalized Bornand surface area continuum solvation (MM/PBSA and MM/GBSA) [246, 466], free energy perturbation(FEP) [440], thermodynamic integration [685], and metadynamics [412]. Recently, a method that is moreefficient method than normal-mode analysis, called WSAS [737], was developed to estimate the entropiceffect in the free energy calculation. MD simulations can be applied to investi-gate the dynamical properties of SARS-CoV-2 proteins and the interactions between proteins and inhibitors.Multiscale coarse-grained model was employed to understand the behavior of the SARS-CoV-2 virion [780].Multiscale simulations were designed to examine glycan shield effects on drug binding to influenza neu-raminidase [630].
1. The main protease.
Grottesi et al. [268] analyzed 2- µ s MD trajectories of the apo form of the SARS-CoV-2 main protease and indicated that the long loops, which connect domain II and III and provide access13o the binding site and the catalytic dyad, carried out large conformational changes. Bz ´owka et al. [101]applied MD simulations to compare dynamical properties of the SARS-CoV-2 main protease and SARS-CoV main protease, which suggests that the SARS-CoV main protease has a larger binding cavity and moreflexible loops. Yoshino et al. [612] used MD simulations to reveal the key interactions and pharmacophoremodels between the main protease and its inhibitors.
2. The S protein.
Bernardi et al. [76] built a glycosylated molecular model of ACE2-Fc fusion proteinswith the SARS-CoV-2 S protein RBD and used MD simulations to equilibrate it. Veeramachaneni et al. [723]ran 100-ns MD simulations of the complexes of human ACE2 and S protein from SARS-CoV-2 and SARS-CoV. Their simulations showed that the SARS-CoV-2 complex was more stable. Gur et al. [275] carried outsteered MD to simulate the transition between closed and open states of S protein, a semi-open intermediatestate was observed. Han et al. [286] applied MD simulation to design and investigate peptide S-proteininhibitors extracted from ACE2. Oliveira [533] used MD simulation to support his hypothesis that theSARS-CoV-2 S protein can interact with a nAChRs inhibitor. All atom molecular dynamics was used tounderstand the interactions between the S protein and ACE2 [62, 112].
3. Other SARS-CoV-2 proteins.
MD simulations were also used to investigate other SARS-CoV-2proteins’ conformational changes. Henderson et al. [295] performed pH replica-exchange CpHMD sim-ulations to estimate the pKa values of Asp/Glu/His/Cys/Lys sidechains and assessed possible proton-coupled dynamics in SARS-CoV, SARS-CoV-2, and MERS-CoV PLpros. They also suggested a possibleconformational-selection mechanism by which inhibitors bind to the PLpro.
Much effort combines docking and MD sim-ulation. For example, molecule docking predicts binding poses, and MD simulation further optimizes andstabilizes the conformations of complexes. Some researchers rescore the optimized complexes by dockingprograms, or follow an ensemble-docking procedure to dock compounds to multiple conformations of theprotein extracted from MD simulations.An ensemble docking of the SARS-CoV-2 main protease was performed by Sztain et al. [695]. Theydocked almost 72,000 compounds to over 80 conformations of the main protease generated from MD sim-ulations and screened these compounds through the ensemble docking strategy. To obtain extensive con-formational samplings of the main protease, a Gaussian accelerated MD simulation [479] was run. Anotherensemble docking work of the main protease was implemented by Koulgi [387]. They carried out long-timeMD simulations on the apo form of the main protease. Sixteen representative conformations were collectedfrom these MD simulations by clustering analysis and Markov state modeling analysis [142]. Targetingthese 16 conformations, ensemble docking was performed on some FDA-approved drugs and other drugleads, suggesting some potent candidates such as Tobramycin. Additionally, Stoddard et al. [684] dockedinhibitors to two different crystal structures of the main protease. A similar scheme was also applied toRdRp by Elfiky et al. [201]. They extracted 8 conformations from clustering analysis of MD simulation anddocked 31 drugs and other compounds to these conformations of RdRp. Many other investigations focusedon docking and then optimizing by MD simulations.
1. Targeting the main protease.
Odhar et al. [531] applied docking and MD simulation to systemati-cally investigate the binding affinities and interactions of 1615 FDA-approved drugs to the main protease,suggesting some potential repurposed drugs such as Perampanel with a predicted binding affinity of -8.8kcal/mol. Baildya et al. [58] tested Hydroxychloroquine, reporting a binding affinity of -6.3 kcal/mol.Other existing drugs such as lopinavir, oseltamivir, ritonavir, atazanavir, darunavir, tetracyclines, flavio-lin, Hydroxyethylamine Analogs, buriti oil (mauritia flexuosa L.) like inhibitors, etc. were also investigatedspecifically by docking and MD simulations [80,156,176,223,313,340,366,401,404,408,446,502,593,594,655].14nother important inhibitor source is natural products. Following the workflow of ligand docking, MDoptimization, and rescoring, Gentile et al. [248] screened the library of marine natural products (MNP),which includes 14064 marine natural products. The best one, heptafuhalol A, was predicted to have adocking score as high as -18.0 kcal/mol. Khan et al. [368] also investigated some marine products. Qa-mar et al. [715] used docking and MD simulation to screen a medicinal plant library containing 32,297potential anti-viral phytochemicals/traditional Chinese medicinal compounds. Potent inhibitors such as5,7,3´,4´-Tetrahydroxy-2´-(3,3-dimethylallyl) isoflavone with a docking score of -16.35 kcal/mol were pre-dicted. Virtual screening was also performed towards other natural products such as Indian medicinalherbs [147, 318, 393, 472, 564, 592, 715, 716, 776].Other small molecules were also screened to inhibit the SARS-CoV-2 main protease. Ton et al. [705]identified potential main protease inhibitors by docking 1.3 billion compounds, and suggested that com-pound ZINC000541677852 had the highest binding affinity of -11.32 kcal/mol. Jim´enez-Alberto et al. [326]performed docking and MD simulations to test 4384 molecules from the Zinc dataset [683] and some ofthem are FDA-approved drugs. Among them, the best one was Bisoctrizole, which has a docking score of-10.25 kcal/mol. Besides, the prototypical-ketoamide inhibitors, HIV protease inhibitors, Leucoefdin, somenutraceuticals, and other compounds from literature were also studied [68, 109, 382, 429, 437, 659, 686]. No-tably, Mohammad et al. [491] optimized some complexes of the main protease with ligands in the proteindata bank (PDB) and re-scored them by AutoDock Vina. The best PDB structure is 6m2n with a predictedbinding affinity of -8.3 kcal/mol.
2. Targeting the S protein.
Trezza et al. [709] ran docking and MD simulations to identify potential in-hibitors against SARS-CoV-2 S protein from 1582 FDA-approved drugs. Lumacaftor was predicted to havethe highest binding affinity (-9.4 kcal/mol). Moreover, in order to evaluate the binding interactions be-tween the S protein and compounds, steered MD simulations [319] were performed on the top compounds.Bharath et al. [81] and Choudhary et al. [145] screened 4015 and 1280 small compounds, respectively, andpredicted that fytic acid and GR hydrochloride had the highest energies of -10.296 kcal/mol and -11.23kcal/mol. Fantini et al. [218] and Kalathiya et al. [342] also evaluated some potential small moleculesagainst the S protein.Since the RBD of S protein is relatively large, the small-molecule drugs may not efficiently block theentire RBD. The entire RBD of S protein needs to be blocked by peptides [735]. Basit et al. [64] designed atruncated version of ACE2 (tACE2) receptor covering the binding residues; they performed protein-proteindocking and MD simulations to analyze its binding affinity to RBD and complex stability; since the tACE2was predicted to have a higher binding score, it could compete with the wild type of ACE2 for binding toSARS-CoV-2. Baig et al. [57] also identified a potential peptide inhibitor against S protein through dockingand MD simulations. Souza et al. investigated some synthetic peptides using the same method [679].
3. Targeting the RdRp.
RdRp is another important target of SARS-CoV-2. Pokhrel et al. [570] screened1930 FDA-approved drugs, optimized the protein structures by MD simulations, and predicted poses andbinding affinities by molecular docking. As a result, quinupristin was identified as the most potent drugwith a docking score of -12.3 kcal/mol.
4. Targeting the PLpro.
Bosken et al. [91] ran MD simulations to investigate the conformational changeof PLpro and docked inhibitors to the PLpro to reveal binding behaviors.
5. Other targets.
Following the workflow of docking, optimizing the top predictions by MD simula-tions, and redocking, Sharma et al. [644] repurposed 3000 FDA-approved and experimental drugs againstthe 2’-O-methyltransferase in NSP16 of SARS-CoV-2; dihydroergotamine and irinotecan were predicted tobe the best drugs with binding affinities of -9.3 kcal/mol for both. Menezes et al. [170] used MD simulation15o investigate the dynamics of NSP1. More importantly, they screened 8694 approved and experimentaldrugs from DrugBank against NSP1 and predicted that tirilazad was the most potent one. Tazikeh-Lemeskiet al. [701] docked 1516 FDA-approved drugs from DrugBank to the NSP16 and investigated the drug-protein interactions by MD simulation, finding that raltegravir had the best predicted binding affinity (-10.4kcal/mol). Following a similar scheme, Selvaraj et al. [631] screened 22122 Chinese traditional medicinesfrom TCM Database@Taiwan against the NSP14; the best one, TCM57025, had a docking score of -11.486kcal/mol. Tatar et al. [699] also studied the potency of 34 drugs against the N protein.
6. Multiple targets.
In many reports, the same drugs were tested against multiple targets. Dwarkaet al. [194] studied the potency of 14 South African medicinal plants against the main protease, RdRp, andS-protein RBD using docking. They also investigated the dynamics and interactions inside the complexesusing MD simulations. However, no potent inhibitors were found. Through a similar procedure, Adeoye etal. [9] evaluated some clinically approved antiviral drugs against the main protease, PLpro, and S protein.Sinha et al. [665] identified some bioactive natural products from glycyrrhiza glabra targeting the S proteinand NendoU. Ortega et al. [540] and Aouidate et al. [45] repurposed some drugs and small molecules inthe category of histamine type 2 receptor antagonists to inhibit the main protease and RdRp. Ahmed [16]predicted the potency of the Caulerpin and its derivatives against the main protease and S protein. Khanet al. [369] utilized the virtual drug repurposing approach to test some antiviral drugs against the mainprotease and 2/’-O-ribose methyltransferase in NSP16. Some works involved the structural proteins ofSARS-CoV-2. Bhowmik et al. [85] virtually screened more than 200 anti-viral natural compounds and 348anti-viral drugs targeting the E, M, and N proteins responsible for envelope formation and virion assembly.Gentile et al. [247] simulated chloroquine and hydroxychloroquine against the E Protein, NSP10/NSP14complex, and NSP10/NSP16 complex.
7. The human ACE2 target with controversy.
Khelfaoui et al. [374], Marciniec et al. [456], and Gutier-rez et al. [278] performed docking and MD studies targeting the human ACE2. However, as mentioned inSection 2.1.1.6, it is quite controversial to design anti-SARS-CoV-2 drugs targeting ACE2.
To obtain more accuratefree energies, after docking and MD simulation, many works calculated binding free energies based on theMM/PBSA or MM/GBSA methods [409]. The basic idea of MM/PBSA and MM/GBSA is to divide upthe calculation according to the thermodynamic cycle in Figure 8, then evidently, the binding free energy ∆ G bind,solv can be calculated by: ∆ G bind,solv = ∆ G bind,vacuum + ∆ G solv,complex − (∆ G solv,ligand + ∆ G solv,receptor ) . (2)Polar solvation free energies for each of the three states are calculated by either solving the linearizedPoisson Boltzmann (PB) equation in MM/PBSA or generalized Born (GB) equation in MM/GBSA. Moredetail about the PB and GB models can be found in Section 2.1.5. Nonpolar solvation free energy is obtainedby solvent accessible area (SA). ∆ G bind,vacuum is from calculating the average interaction energy betweenreceptor and ligand and taking the entropy change upon binding into account if necessary [466].
1. Targeting the main protease.
Florucci et al. [224] used docking, MD simulations, and MM/PBSAbinding free energy calculations to investigate around 10000 compounds from the DrugBank [755]. Thesecompounds were first screened by docking, and then MD-based MM/PBSA binding free energy calcula-tions were performed on the best 36 compounds. The reported binding data were the consensus of dockingand MM/PBSA prediction and leuprolide was the best one. A very similar work by Ibrahim et al. [315]also screened thousands of compounds from the DrugBank by docking and MM/GBSA MD simulations.16 igure 8: The thermodynamic cycle of the MM/PB(GB)SA calculation.
2. Targeting the S protein.
Both SARS-CoV and SARS-CoV-2 infect humans through the S proteinbinding to the human ACE2. Therefore, many investigations focused on the interaction between the Sprotein and the ACE2. Hassanzadeh et al. [287] used MM/PBSA, and He et al. [291] used MM/GBSA cal-culations to compare the binding affinities of the S proteins from SARS-CoV and SARS-CoV-2 to the humanACE2. Their calculations indicated that the S protein of SARS-CoV-2 bound to ACE2 much more tightlythan that of SARS-CoV. Spinello et al. [680], Bhattacharyay et al. [289], and Armijos et al. [47] investigatedthe mechanism of tight binding of the SARS-CoV-2 S-protein through MD simulations and MM/GBSA orMM/PBSA calculations. Shah et al. [639] and Ou et al. [544] ran some MM/PBSA calculations and foundthat some mutations on the S protein could facilitate stronger interactions with human ACE2.Other two interesting studies by Piplani et al. [569] and by Shen et al. [650] performed MM/PBSAor MM/GBSA calculations to reveal the binding affinities of the SARS-CoV-2 S-protein to the ACE2s fromdifferent species. Their results showed that chimpanzee’s binding affinity was even higher than human, cat,pangolin, dog, monkey, and chimpanzee had a similar affinity to human, which suggested some mammalswere also vulnerable to SARS-CoV-2.Drug repurposing against the S protein was also implemented by MM/GBSA or MM/PBSA. De Oliveiraet al. [174] docked 9091 approved or experimental drugs to the S protein and selected the top 3 to performMM/PBSA calculation, which led to suramin sodium having the highest affinity of -51.07 kcal/mol. Fol-lowing a similar scheme, Romeo et al. [603] repurposed 8770 approved or experimental drugs by dock-ing and MM/GBSA, reporting 31h-phthalocyanine as the most potent (-84.8 kcal/mol). Padhi et al. [547]performed docking and MM/PBSA calculations studies on the inhibition of Arbidol to the RBD/ACE2complex.Some MM/GBSA or MM/PBSA investigations were about the use of natural products against the Sprotein. Pandey et al. [550] used docking and MM/PBSA calculations on Among 11 phytochemicals, sug-gesting that quercetin has the highest affinity (-22.17 kcal/mol).MM/GBSA or MM/PBSA approaches were applied to other compounds against S protein. Sethi etal. [636] performed docking to 330 galectin inhibitors against the S protein and ran MM/GBSA calculationsto some active ones, revealing that ligand No.213 had the highest binding free energy of -54.11 kcal/mol.Rane [589] and Li et al. [427] calculated the potency of all diaryl pyrimidine derivatives and the MERS-CoVreceptor DPP4, respectively.
3. Targeting the RdRp.
Ruan et al. [610] studied 7496 approved or experimental drugs against bothSARS-CoV-2 and SARS-CoV RdRp. They screened by docking and ran MM/GBSA calculations to the topones, suggesting lonafarnib, tegobuvir, olysio, filibuvir, and cepharanthine’s potency to both SARS-CoV-2and SARS-CoV RdRp. Khan et al. [364] screened 6842 South African natural products against RdRp using18ocking, and selected the top 4 to further investigate by MD simulations and MM/GBSA calculations.Their most potent one was Genkwanin 8-C-beta-glucopyranoside with a MM/GBSA binding free energyof -63.695 kcal/mol. By contrast, such energy of an approved SARS-CoV-2 drug, remdesivir, against RdRPwas reported to be -54.406 kcal/mol. Singh et al. [664] also studied 100 natural polyphenols by docking.The leading 8 compounds were used in MD simulations and MM/GBSA calculations, which shows thecompound TF3 being the best (-42.27 kcal/mol). Aktacs et al. [18] used MM/PBSA calculations to showthat CID294642 was a potent RdRp inhibitor. Venkateshan et al. [724] and Ahmad et al. [13] also carried outMM/GBSA or MM/PBSA calculations.
4. Targeting the PLpro.
Kandee et al. [345] repurposed 1697 approved drugs against the PLpro bydocking, and their top 10 were studied by MD simulations and MM/GBSA, with the drug phenformin be-ing their best one (-56.5 kcal/mol). Bosken et al. [91] assessed the potential effectiveness of one naphthalene-based inhibitor, 3k, and one thiopurine inhibitor, 6MP, through docking, MD simulations, and MM/PBSAcalculations.
5. Other targets.
Many MM/GBSA or MM/PBSA investigations focused on the SARS-CoV-2 N pro-tein. For instance, Khan et al. [365] studied the mechanism of RNA recognition by the N-terminal RNA-binding domain of the SARS-CoV-2 N protein as well as mutation-induced binding affinity changes bydocking, MD simulations, and MM/GBSA calculations. Yadav et al. [769] docked 8987 compounds fromAsinex and PubChem databases against the N protein and assessed the potency of the top 10 by MM/GBSA.TMPRSS2 is another attractive target. Some natural products and compounds were repurposed throughdocking, MD simulations, and MM/GBSA calculations against TMPRSS2 [139, 405], suggesting the com-pound neohesperidin as the most potent. Khan et al. [370] docked 123 antiviral drugs to NendoU andfound simeprevir had the highest binding energy. Their MM/PBSA calculations also confirmed this find-ing. Encinar et al. [204] used docking to screen 8696 approved or experimental drugs against NSP16/NSP10protein complex and, through MM/PBSA calculations, discovered that the presence of NSP10 strengthensthe ligand binding to NSP16. Fulbabu Sk et al. [668] performed MM/PBSA simulations to study the bind-ing interactions inside NSP16/NSP10 complex. Vijayan et al. [727] carried out repurposing against NSP16involved 4200 drugs or compounds. their best one predicted from MM-PBSA was Carba-nicotinamide-adenine-dinucleotide. Chandra et al. [117] studied 2895 approved or experimental drugs against the Nen-doU and selected the top 3 compounds from docking results and ran MM/PBSA calculations to these three,finding glisoxepide, with a MM/PBSA binding free energy of -141 kcal/mol, being the most potent one.Dhankhar et al [184] and Parida et al. [555] used MM/PBSA calculations to target 6 different non-structuralproteins of SARS-CoV-2.
6. Multiple targets.
Some researchers screened drugs or compounds against multiple targets of SARS-CoV-2. Gupta et al. [632] docked drug famotidine to the twelve targets of SARS-COV-2 including fourstructural targets: M protein, E protein, S protein, N protein, and eight non-structural targets: the mainprotease and PLpro, NendoU, Helicase, RdRp, NSP14, NSP16, and NSP10. They found famotidine had thehighest docking binding energy of -7.9 kcal/mol with the PLpro, and the MM/PBSA energy was -59.72kcal/mol.Naik et al. [510] screened 3963 natural compounds from the NPASS database (http://bidd.group/NPASS/index.php)against 6 different SARS-CoV-2 targets, namely, the main protease, RdRp, NendoU, helicase, exoribonu-clease in NSP14, and methyltransferase in NSP16. They docked these compounds to these targets andcalculated MM/GBSA binding free energies of the top ones. Quimque et al. [578] studied 97 secondarymetabolites from marine and terrestrial fungi. They screened these compounds against 5 different SARS-CoV-2 targets, i.e., the main protease, S protein, RdRp, PLpro, and NendoU, by docking and MM/PBSAcalculations. Murugan [503] investigated four compounds in A. paniculata targeting four different proteins19n SARS-CoV-2, i.e., the main protease, S protein-ACE2 complex, RdRp, and PLpro through docking, MDsimulations and MM/GBSA, finding that AGP-3 had the potency to all four targets. Alazmi et al. [26]assessed around 100,000 natural compounds against RdRp, NSP4, NSP14, and human ACE2 by dock-ing. Their top compounds were further investigated by MD simulations and MM/PBSA, reporting thatBaicalin was potent against RdRp, NSP4, and NendoU. Kar et al. [349] studied main protease, S protein,and RdRp. Their ligands were natural products from Clerodendrum spp. After docking and rescoring thetop ones by MM/GBSA, these authors found taraxerol being effective to all three targets. Using dockingand MM/GBSA or MM/PBSA calculations, Alajmi et al. [24] and Sasidharan et al. [627] evaluated the po-tency of around 40 compounds, including some existing drugs and protein azurin secreted by the bacteriumpseudomonas aeruginosa as well as its derived peptides, against the main protease, PLpro, and S protein.In a similar way, Mirza et al. [485] repurposed some compounds against the main protease, RdRp, andhelicase. Maroli et al. [458] investigated procyanidin inhibiting the main protease, S protein, and humanACE2.Panda et al. [549] targeted the main protease and S protein; they screened 640 compounds throughdocking and MD simulations and identified PC786 had high docking scores both to the S protein (-11.3kcal/mol) and main protease (-9.3 kcal/mol). Moreover, their MD simulations and MM/PBSA calculationsrevealed the binding of PC786 could change the conformation of the S-protein and weaken the S-protein’sbinding interactions to ACE2. Also targeting the main protease and S protein, Prasanth et al. [576] studied48 isolated compounds from cinnamon by docking and MD-simulation based MM/PBSA calculations, sug-gesting the compounds tenufolin and pavetannin C1 were potent to both the main protease and S protein.Parida et al. [554] also predicted some potential inhibitors against the SARS-CoV-2 main protease and Sprotein from Indian medicinal phytochemicals by MM/PBSA.Gul et al. [269] and Ahmed et al. [15] used docking, MD simulations, and MM/GBSA calculations tosuggest the potency of current drugs against the main protease and RdRp. Targeting the main protease andPLpro, Mitra et al. [488]’s pharmacophore-based virtual screening yielded 6 existing FDA-approved drugsand 12 natural products with promising pharmacophoric features, and through docking, MD simulations,and MM/PBSA calculations, lopinavir and tipranavir being predicted to be the best inhibitors against thetwo proteases. Similarly, Naidoo et al. [509] investigated the potency of cyanobacterial metabolites againstthese two proteases. Chikhale et al. [140] repurposed Indian ginseng against the S protein and NendoU bydocking and MM/GBSA calculation. Borkotoky et al. [89] focused on the M protein and E protein. Dockingand MM/PBSA calculations were performed on the inhibitors from Azadirachta indica (Neem).
Besides MM/PBSA or MM/GBSA,other binding free energy calculation methods such as FEP and metadynamics were also applied to evaluatethe binding affinities of inhibitors to the main protease.
1. FEP.
Wang et al. [748] applied MD simulations and FEP free energy calculations to uncover themechanism of the stronger binding of SARS-CoV-2 S protein to ACE2 than that of SARS-CoV S protein.They compared hydrogen-bonding and hydrophobic interaction networks of SARS-CoV-2 S protein andSARS-CoV S protein to ACE2 and calculated the free energy contribution of each residue mutation fromSARS-CoV to SARS-CoV-2. Ngo et al. [519] first docked about 4600 drugs or compounds to the mainprotease and then, used pull work obtained from the fast pulling of ligand simulation [518] to rescore thetop 35 compounds. They reevaluated the top 3 using FEP free energy calculations, which suggested thatthe inhibitor 11b was the most potent. Zhang et al. [787] docked remdesivir and ATP to RdRp, and usedFEP to calculate the binding free energy, which indicated the binding of remdesivir was about 100 timesstronger than that of ATP, so it could inhibit the ATP polymerization process.20 . Metadynamics.
Namsan et al. [511] docked 16 artificial-intelligence generated compounds by Bung[98] to the main protease, then ran metadynamics to calculate their binding affinity, and predicted somepotential inhibitors.
De Sacho et al. [175] used the G ¯o coarse-grained MD modelto simulate the process of the SARS-CoV-2 S protein RBD binding to the human ACE2, characterized thefree energy landscape, and obtained the free energy barrier between bound and unbound states was about15 kcal/mol. Nguyen et al. [525] also applied the G ¯o coarse-grained model and replica-exchange umbrellasampling MD simulations to compare the binding of SARS-CoV-2 S protein and SARS-CoV S protein to thehuman ACE2, revealing SARS-CoV-2 binding to human ACE2 to be stronger than that of SARS-CoV. Gironet al. [257] studied the interactions between SARS-CoV-2 S protein and some antibodies by coarse-grainedMD simulations.
Gupta [273] first selected 92 potential main-protease inhibitors from FDA-approved drugs by docking, then further evaluated their potency by MDsimulations and MM/PBSA calculations using the hybrid of the ANI deep learning force field [673] and aconventional molecular mechanics force field. Their results suggested that targretin was the most potentdrug against the main protease. Joshi et al. [333] screened compounds by first making use of a deep neuralmodel, and then performed docking and MD simulations to further evaluate them.
Turovnova et al. [712]’s MD simulations revealedthree flexible hinges within the stalk, coined hip, knee, and ankle of the S protein, which were consistentwith their tomographic experiments.
Through MD simulations, Qiao et al. [577] found that themutation on the distal polybasic cleavage sites of the S protein could weaken the binding between the Sprotein and human ACE2, which means these distal polybasic cleavage sites were critical to the binding.Zou et al. [804] also performed virtual alanine scanning mutagenesis by FEP MD simulations to uncoverkey S protein residues in binding to ACE2. Similarly, Ou et al. [545] investigated the interaction impact of Sprotein mutation through MM/PBSA calculations. Dehury et al. [178] compared the interactions of mutatedS proteins and the wild type S protein to ACE2. Haidi [279] mutated the human ACE2 and assessed theimpact on interactions with S protein by MM/GBSA calculations. Sheik et al. [649] studied the impact ofmain protease mutations on its 3D conformation.
Grant et al. [266] ran MD simulations and evaluated the ex-tent to which glycan microheterogeneity could impact epitope exposure of the S protein. Their studiesindicated that glycans shield approximately 40% of the underlying protein surface of the S protein fromepitope exposure. Peele et al. [565] generated more than 30 epitode vaccine candidates originating fromthe S protein by the online servers NetCTL, IEDB, and FNepitope. These epitodes’ tertiary structures werepredicted and also docked to the toll-like receptor 3. MD simulations were run for these complexes andthe immune reactions were simulated. Lizbeth et al. [435] not only predicted some epitodes, but also usedMM/PBSA MD simulations to calculate the binding affinity of the MCH II-epitope complexes, with thehighest one being -1810.9855 kcal/mol. Through docking and MD simulations, De Moura et al. [173] iden-tified epitopes from the S protein that were able to elicit an immune response mediated by the most frequentMHC-I alleles in the Brazilian population. Other similar reports include Refs. [84, 574, 582, 617, 619].Not only epitodes from the S-proteins were investigated, but also epitodes from other targets werestudied. Rahman et al. [581] also researched some epitodes from the S, M, and E proteins. Chauhan etal. [119], Kalita et al. [343], Ranga et al. [590], and [624] studied multiple targets.21 .1.2.10 MD simulation data analysis methods.
One of the popular methods to analyze dynamics char-acteristic in MD simulation is principal component analysis (PCA), which can extract the principal modesof motion from MD simulations [35, 670]. Towards SARS-CoV-2, Kumar et al. [401], Mahmud et al. [447],Islam et al. [318], and Sk et al. [669] applied PCA to reveal the internal motions of the main protease. Raneet al. [589] and Dehury et al. [178] used such analysis to investigate the dynamics of the S protein. Hen-derson et al. [295] and Chandra et al. [117] used PCA to elucidate the motions of the PLpro and NendoU,respectively.Normal mode analysis (NMA) [113] is another way to study protein fluctuations. Bhattacharya et al. [84]applied NMA to display the mobility of the human TLR4/5 protein and SARS-CoV-2 vaccine componentcomplex.
DFT is a computational quantum-mechanics modeling method widely used in computational physics, com-putational chemistry, and computational materials science to investigate the electronic structure of atoms,molecules, and condensed phases [418,557]. Using this theory, the properties of a many-electron system arerepresented by functionals (functions of another function) of the spatially dependent electron density [557].Because of the development of DFT, Walter Kohn won the Nobel Prize in Chemistry in 1998 [384].Bui et al. [97] applied DFT calculations to optimize the silver/bis-silver-lighter tetrylene complex andstudy the molecular orbits, and docked the optimized compounds to the main protease and ACE2, report-ing NHC-Ag-bis has a -16.8 kcal/mol binding affinity to the main protease. Gatfaoui et al. [241], and Hagaret al. [281] also optimized the conformation of 1-Ethylpiperazine-1,4-diium Bis(Nitrate) and some antiviralN-heterocycles, investigated that partial charge distribution as well as hydrogen bond strength by DFT.They docked these compounds to the main protease and studied the interactions between them.
The QM/MM approach is a molecular simulation method that combines the accuracy of QM and the speedof MM: the region of the system in which the chemical process takes place is treated at an appropriate levelof QM. The remainder is described by a MM force field [750]. This approach can be used to study chemicalprocesses in solution and proteins. The Nobel Prize in Chemistry in 2013 was awarded to Arieh Warsheland Michael Levitt for the introduction of QM/MM.Khrenova et al. [375] used QM/MM to simulate the covalent bonds forming between the substrate andCys145 residue of the main protease based on the crystal structure with a PDB ID 6LU7 [329], revealingthe inhibition mechanism of covalent inhibitors. Swiderek et al. [694] studied the covalent bonding ofthe polypeptide Ac-Val-Lys-Leu-Gln-ACC (ACC is the 7-amino-4-carbamoylmethylcoumarin fluorescenttag) to the main protease by QM/MM, suggesting that the free energy barrier is 22.8 kcal/mol. Ramoset al. [586] also performed a QM/MM simulation on the covalent complex of Ac-Ser-Ala-Val-Leu-Gln-Ser-Gly-Phe-NMe and the main protease.
In biomolecular studies, electrostatic interactions are of paramount importance due to their ubiquitous ex-istence in the protein-protein interactions, protein-ligand interactions, amino acid interactions, et al. Elec-trostatics potentials can be calculated using explicit or implicit solvent models as shown in Figure 10. How-ever, including explicit solvent models in free energy calculation is computationally expensive due to itsdetailed description of solvent effect. Implicit solvent models describe the solvent as a dielectric contin-uum, while the solute molecule is modeled by an atomic description [167, 302, 600, 607, 647]. A wide vari-ety of two-scale implicit solvent models has been developed for electrostatic analysis, including Poisson-22oltzmann (PB) [227, 647], generalized Born (GB) [63, 187, 493, 538], and polarized continuum [155, 704]models. GB models are approximations of PB models. GB models are faster but provide only heuristicestimates for electrostatic energies, while PB methods offer more accurate methods for electrostatic analy-sis [63, 120, 133, 338, 537, 600, 798]. − 𝚪 ⊕ ⊕ ⊕ ⊖ ⊖⊖ ⊖⊖ ⊖−− −− + − + + ++ + + 𝛀 𝐒𝐨𝐥𝐯𝐞𝐧𝐭𝛀 𝐒𝐨𝐥𝐮𝐭𝐞 − + + 𝐌𝐨𝐛𝐢𝐥𝐞 𝐢𝐨𝐧𝐬𝜖 𝒓 = 𝜖 𝜖 𝒓 = 𝜖 Figure 9: An illustration of the Poisson-Boltzmann (PB) model, in which the molecular surface Γ separates the computational domaininto the solute region Ω and solvent region Ω . As demonstrated in Fig. 9, the PB model describes the two-scale treatment of the electrostatics withinthe interior domain Ω containing the solute biomolecule with fixed charges and the exterior domain Ω containing the solvent and dissolved ions. The interface Γ separates the biomolecular domain and sol-vent domain. While various surface models are available, the most commonly used ones are the solventexcluded surface or molecular surface.A biomolecule in domain Ω consists of a set of atomic charges q k located at atomic centers r k for k =1 , ..., N c , with N c as the total number of charges. In domain Ω , the charge source density of mobile ions isapproximated by the Boltzmann distribution. For simplicity, a linearized PB model is always applied: − ∇ · (cid:15) ( r ) ∇ φ ( r ) + (cid:15) κ φ ( r ) = N c (cid:88) k =1 q k δ ( r − r k ) , (3)where φ ( r ) is the electrostatic potential, (cid:15) ( r ) is a dielectric constant given by (cid:15) ( r ) = (cid:15) for r ∈ Ω and (cid:15) ( r ) = (cid:15) for r ∈ Ω , and κ is the inverse Debye length representing the ionic effective length. For the PBequation to be well-posed, interface conditions on the molecular surface are needed: φ ( r ) = φ ( r ) , (cid:15) ∂φ ( r ) ∂ n = (cid:15) ∂φ ( r ) ∂ n , r ∈ Γ , (4)where φ and φ are the limit values when approaching the interface from inside or outside the solutedomain, and n is the outward unit normal vector on Γ . The far-field boundary condition for the PB modelis lim | r |→∞ φ ( r ) = 0 . The electrostatic solvation free energy can be obtained from the PB model by ∆ G = 12 N c (cid:88) k =1 q k ( φ ( r k ) − φ ( r k )) (5)where φ ( r k ) is the solution of the PB equation as if there were no solvent-solute interface.The GB model is devised to offer a relatively simple and efficient approach to calculate electrostaticsolvation free energy. However, with an appropriate parametrization, a GB solver can be as accurate as aPB solver [228]. The GB approximation of electrostatic solvation free energy can be expressed as, ∆ G GB ≈ (cid:88) ij ∆ G GB ij = − (cid:16) (cid:15) − (cid:15) (cid:17)
11 + αβ (cid:88) ij q i q j (cid:16) f ij ( r ij , R i , R j ) + αβA (cid:17) , (6)23here R i is the effective Born radius of atom i , r ij is the distance between atoms i and j , β = (cid:15) /(cid:15) , α = 0 . , and A is the electrostatic size of the molecule. The function f ij is given as f ij = (cid:115) r ij + R i R j exp (cid:16) − r ij R i R j (cid:17) . (7)The effective Born radii R i is calculated by the following boundary integral: R − i = (cid:16) − π (cid:73) Γ r − r i | r − r i | · d S (cid:17) / . (8) Figure 10: A electrostatic potential of the SARS-CoV-2 main protease based on the PB model.
Due to its success in describing biomolecular systems, the PB and GB models have attracted a wideattention in both mathematical and biophysical communities [255, 596, 796]. Meanwhile much effort hasbeen given to the development of accurate, efficient, reliable, and robust PB solvers. A large number ofmethods have been proposed in the literature, including the finite difference method (FDM) [330], finiteelement method (FEM) [59], and boundary element method (BEM) [337]. The emblematic solvers in thiscategory are MM-PBSA [738], Delphi [421, 601], ABPS [60, 338], MPIBP [120, 245, 796], CHARM PBEQ [330],and TABIPB [124, 244].PB and GB models have been applied to the SARS-CoV-2 studies including protein-ligand binding andprotein-protein binding energetics. Adaptive Poisson-Boltzmann solver [60,338] is one of the most popularPB solvers. By using it, Su et al. [656], Rosario et al. [605], Amin et al. [38], and Morton et al. [494] calculatedelectrostatic potentials of the S protein and ACE2 complex. Su et al. [656] also calculated that of the mainprotease. Jin et al. [327] and Xi et al. [328] studied human Furin, which is involved in the SARS-CoV-2binding. Zhang et al. [789] calculated the electrostatic potential of SARS-CoV-2 SUD-core dimer. Nerli et al.[517] studied the electrostatic surface potentials of some SARS-CoV-2 antigens. Lu et al. [439] investigatedmultiple other targets. Another popular software is DELPHI [601]. Ali et al. [28] solved the S protein andACE2 complex using it. Moreover, AQUASOL [383] can solve the dipolar nonlinear Poisson-Boltzmann-Langevin equation, Smaoui et al. [672] used AQUASOL to study the S protein RBD.24 .1.6 Gibbs-Helmholtz equation
The Gibbs-Helmholtz equation describes the thermodynamics calculating changes in the Gibbs energy of asystem as a function of temperature. It is a separable differential equation which is given as (cid:18) ∂ (∆ G/T ) ∂T (cid:19) p = − ∆ HT (9)where ∆ G is the change in Gibbs free energy, ∆ H is the enthalpy change, T is the absolute temperature,and p is the constant pressure.In the study of nucelocapsid protein (N-protein) of SARS, it was shown that the N-protein’s maximumconformational stability near pH 9.0, and the oligomer dissociation and protein unfolding occur simultane-ously [444]. In the denaturation of the N-protein by chemicals, the free energy changes ( ∆ G ) of unfoldingat temperature ( T ) is calculated by the solution of Gibbs-Helmholtz equation [96] ∆ G ( T ) = ∆ H m (1 − T /T m ) − ∆ C p [( T m − T ) + T ln( T /T m )] (10)where T m is the transition temperature, ∆ H m is the enthalpy of unfolding at T m , and ∆ C p is the heatcapacity change. The Gibbs free energy, ∆ G ( T ) of unfolding is applied to estimated the protein stability inenduring the denaturants, where high ∆ G ( T ) means the protein might be more stable against denaturant[181]. MC methods are a broad class of computational algorithms that rely on repeated random sampling to ob-tain optimized numerical results. In principle, Monte Carlo methods can be used to solve any problemhaving a probabilistic distribution [392]. When the probability distribution of the variable is parametrized,mathematicians often use a Markov chain Monte Carlo (MCMC) sampler [288]: the central idea is to de-sign a judicious Markov chain model with a prescribed stationary probability distribution. By the ergodictheorem, the stationary distribution is approximated by the empirical measures of the random states of theMCMC sampler.Moreover, Metropolis Monte Carlo methods [478] are a branch of MC methods popularly used in molec-ular modeling. The essential idea is that, if the energy of a trial conformation is lower than or equal to thecurrent energy, it will always be accepted; if the energy of a trial conformation is higher than that of the cur-rent energy, then it will be accepted with a probability determined by the Boltzmann (energy) distribution, P accept ( m → n ) = (cid:40) exp (cid:0) − ∆ U nm kT (cid:1) , if ∆ U nm > , if ∆ U nm ≤ , where m is the current conformation, n is the new conformation, P accept ( m → n ) is the probability to acceptthe new conformation, U nm is the energy difference between n and m , k is the Boltzmann constant, and T is temperature. Therefore, the evolution of molecular conformations can be simulated.There are several aspects of MC applications regarding SARS-CoV-2. Francis et al. [229] performed a MC simulation of ionizing radiation damage tothe SARS-CoV-2 and found that γ -rays produced significant S protein damage, but much less membranedamage. Thus, they proposed γ -rays as a new effective tool to develop inactivated vaccines. Cojutti et al.[151] used a Metropolis MC sampling process to simulate a pharmacokinetic model of HIV drug darunaviragainst SARS-CoV-2. 25 . The main protease. Amamuddy et al. [36] performed coarse-grained MC simulations of the SARS-CoV-2 main protease in the free and ligand-bound forms. Toropov et al. [707] used MC simulations to searchweights of the QSAR model about the main protease inhibitory activity of aromatic disulfide compounds.Sheik et al. [649] investigated mutation-induced conformational changes of the main protease by coarse-grained MC models.
3. The S protein.
Othman et al. [542] ran MC simulations to predict the flexibility of the S protein.Wong et al. [757] assessed the mutation impact on the structure of the S protein via a sequential MC model.Polydorides et al. [571] used MC simulations to collect the S protein mutations that could enhance its bind-ing to ACE2. Amin et al. [38] used MC simulations to sample the protonation states of the amino acids.The generated conformer occupancies based on Boltzmann distributions were used to calculate the elec-trostatic and van der Waals interactions between the SARS-CoV-2 and the ACE2. Bai et al. [55] used a MCproton transfer (MCPT) method to determine the charge configuration of all ionizable residues so that thecoarse-grained free energy of each protein configuration could be obtained. Giron et al. [257] performedcoarse-grained MC simulations to calculate antibodies 80R, CR3022, m396, and F26G19’s binding processesand binding free energies to the S protein. Becerra et al. [69] applied MC simulations to optimize thestructures of mutated S proteins. Huang et al. [309] performed MC simulations to generate some potentialpeptide-based inhibitors against the S protein.
4. Other targets.
Amin et al. [39] built a MC-based QSAR model to study the potency of some in-housemolecules against the PLpro. Cubuk et al. [160] sampled different conformations of the N protein. Pandeyet al. [551] used coarse-grained MC simulations to investigate the structural dynamics of the E proteinat multiple temperatures. Wu et al. [760] applied MC simulations to optimize the structures of the mainprotease, PLpro, and RdRp.
Most investigations focused on the full genome of the SARS-CoV-2. Lai et al. [411], Nie et al. [526], Li etal. [420], Koyama et al. [390], and Khan et al. [364] aimed to investigate the temporal origin, the rate of viralevolution, and the population dynamics of the virus globally using a Bayesian MCMC simulation. Li etal. [425] implemented cross-species gene analysis using the MCMC method, revealing that human SARS-CoV-2 is close to Bat CoV. Nabil et al. [506] employed MC-based phylogenetic analysis to deduce the SARS-CoV-2 gene transmission route among China, Italy, and Spain. Castells et al. [114] performed a MCMCanalysis of complete genome sequences of SAR strains recently isolated in different regions of the world(i.e., Europe, North America, South America, and Southeast Asia). Using MC models, Zehender et al. [783]and Xavier et al. [762] studied SARS-CoV-2 in Italy and the city Minas Gerais of Brazil, respectively. Riceet al. [599] used MC simulations to calculate mutation matrices. Andonegui et al. [42] used MC samplingto estimate relative samples of RNA transcripts. Makhoul et al. [451] carried out MC sampling to simulaterandom polymerase chain reaction (PCR) test.Other works consider the genome for some proteins in SARS-CoV-2. Flores et al. [225] conducted MC-based phylogenetic analysis, suggesting that SARS-CoV-2 S protein resulted from ancestral recombinationbetween the bat-CoV RaTG13 and the pangolin-CoV MP789. Sarkar et al. [626] used a MC procedure to testhomogeneity among the sequence of the E proteins.
The serial interval is defined as the duration between the symptom-onset time of the infector and that of theinfectee. Ali et al. [29] built a MCMC model to estimate the serial interval of SARS-CoV-2, which concludedthat this serial interval was shortened over time by nonpharmaceutical interventions. Peak et al. [563] also26ocused on the serial interval. They studied sequential MC models with different serial intervals. Miller etal. [483] applied an MC simulation to predict the emission rate in one super spreading event. Kucharski etal. [394] ran sequential MC simulations to infer the transmission rate over time in Wuhan, China. Silvermanet al. [658] and Lavezzo et al. [416] used MC models to investigate the prevalence of SARS-CoV-2 in theUS and the Italian municipality Vo’. Fu et al. [231] performed a MC-based approach to estimate dailycumulative numbers of confirmed cases of SARS-CoV-2. Mizumoto et al. [489] used the Hamiltonian MCalgorithm to calculate the probability of being asymptomatic given infection as well as the infection time ofeach individual. Yang et al. [772] built a MC infection model considering age structures.The role of suppression strategies in SARS-CoV-2 transmission was also studied by MC models. Yang etal. [771] focused on the impact of household quarantine on SARS-Cov-2 infection. Chu et al. [149] simulatedthe effect of physical distancing, face masks, and eye protection to prevent person-to-person transmission.Girona et al. [258]’s MC model tried to answer the question: “how long should suppression strategies lastto be effective to avoid quick rebounds in the transmission once interventions are relaxed”.MC models were applied to simulate other aspects of SARS-CoV-2 transmission as well. Ahmed etal. [17] used MC simulations to deduce the number of infected individuals from the viral RNA copy num-bers observed in the waste water. Khalil et al. [362] built an MC model to reveal SARS-CoV-2 infection inpregnancy. Vuorinen et al. [731] modeled aerosol transport and virus exposure with MC simulations indifferent public indoor environments.
Pascual et al. [561] employed a MC model to simulate the SARS-CoV-2 virus replication cycle. Jain etal. [322] used MC simulations to study SARS-CoV-2’s impact on the backlog of orthopedic surgery, whichconcluded that it would take over 2 years to end the cumulative backlog.
The detection and characterization of protein pockets and cavities is a critical issue in molecular biologystudies. Pocket detection algorithms can be classified as grid-based and grid-free approaches [417, 792].Grid-based approaches embed proteins in 3D grids and then search for grid points that satisfy some condi-tions. Grid-free ones include methods based on probe (sphere) or the concepts of Voronoi diagrams. Zhaoet al developed differential geometry and algebraic topology based protein pocket detections using convexhull surface evolution and associated Reeb graph [792].Gervasoni et al. [250] evaluated the performance of the pocket-detecting algorithms Fpocket [417] andPLANTS [385] on 12 different SARS-CoV-2 proteins with an accuracy of 0.97. Manfredonia et al. [455]predicted the 3D structure of SARS-CoV-2 RNA by coarse-grained modeling and detected potential pockets.Boldrini et al. [86] constructed a ACE2 folding pathway through ratchet-and-pawl MD (rMD) [191] and hightemperature MD simulations, identified intermediates, and predicted potential druggable pockets on somelate intermediates. Sheik et al. [649] predicted potential binding pockets of the main protease.
Homology modeling constructs an atomic-resolution model of the “target” protein from its amino acidsequence based on experimental 3D structures of related homologous proteins (the “templates”) [629].Homology modeling relies on identifying one or more known protein structures likely to resemble thestructure of the query sequence, and producing an alignment that maps residues in the query sequence toresidues in the template sequence [143]. 27ecause the 3D experimental structures of SARS-CoV-2 proteins were largely unknown at the earlystage of the epidemic, homology modeling was widely applied to predict the 3D structures of SARS-CoV-2proteins, such as the main protease [4,102,123,326,369,369,482,485,642,740], S protein [56,145,220,284,311,321,373,403,424,430,432,442,541,556,558,643,657,661,687,794], RdRp [10,49,71,200,443,516,609,724,786,787],PLpro [307], E protein [25, 52, 171, 530, 626], N protein [52], and others [75, 88, 108, 127, 161, 188, 297, 369, 431,461, 475, 485, 631, 760, 799].Some human proteins that interact with SARS-CoV-2 were also predicted, such as ACE2 [197], TM-PRSS2 [310, 597, 677], and CD147 [767]. Some 3D structures of vaccine proteins [565, 617] were also built byhomology modeling.
QSAR models refer to regression or classification models to predict the physicochemical, biological, andenvironmental properties of compounds from the knowledge of their chemical structure [264]. In QSARmodeling, the predictors consist of physico-chemical properties and theoretical molecular descriptors ofchemicals; the QSAR response-variable could be a biological activity of the chemicals. Building a QSARmodel includes two steps: first, summarizing a supposed relationship between chemical structures andbiological activity in a data-set of chemicals and then, using QSAR models to predict the activities of newchemicals [608].To identify potential main protease inhibitors, Ghaleb et al. [251] and Acharya et al. [6] applied 3DQSAR models: Ghaleb et al.’s 3D model was based on comparative molecular similarity indices analysis(CoMSIA); Acharya et al.’s 3D model was based on pharmacophores. More works used 2D QSAR models:Alves et al. [34] used the random forest algorithm to build the model; Kumar et al. [406] and Masand etal. [462, 463] used genetic algorithms; Basu et al. [66] used support vector machine; Islam et al. [318], De etal. [169], and As et al. [7] used multiple linear regression; Toropov et al. [707] used linear models. Moreover,Ghost et al. [252] built a Monte Carlo-based classification model.Inhibitors against other targets were also investigated. QSAR models based on multiple linear regres-sion and Monte Carlo classification were constructed by Laskar et al. [415] and Amin et al. [39] againstPLpro. Against the main protease and RdRp, Ahmed et al. [15] built a QSAR model followed partial-least-square regression. Borquaye et al. [90] used multiple linear regression.
The linear regression is one of the basic algorithms in machine learning. It can be used to solve the re-gression problem. We assume the training set is { ( x i , y i ) | x i ∈ R m , y i ∈ R } ni =1 . The predictor is definedas ˆ y ( x ) = w T x + b , (11)where w is the weights, b is the bias, and w T represents the transpose of w . The aim of the linear regressionis to minimize the loss function, which can be defined as L = 12 n n (cid:88) i =1 (ˆ y i − y i ) . (12)As a basic machine learning algorithm, linear regression can be commonly found in the literature relatedto COVID-19 research. In the framework of QSAR [608], to identify potential SARS-CoV-2 main proteaseinhibitors, Toropov et al. [707], Islam et al. [318], De et al. [169], and As et al. [7] used linear or multiplelinear regression methods to build prediction models. Other SARS-CoV-2 targets were also investigated:28gainst papain-like protease, QSAR models based on multiple linear regression were constructed by Laskaret al. [415] against the main protease and RdRp. Ahmed et al. [15]’s QSAR model was based on partial-least-square regression. Borquaye et al. [90] used multiple linear regression.More examples involve applying linear regression to calculate the correlation coefficient and predictdifferent types of dependent variable values. Becerra et al. [69] and Korber et al. [386] calculated infectivityof the SARS-CoV-2 S protein D614G mutation percentage by employing linear regression. In Mckay etal.’s work about vaccine candidates [473], a linear regression was performed between SARS-CoV-2 IgG andviral neutralization. Bunyavanich et al. [99] built linear regression models between ACE2 gene expressionand age. Ma et al. [445] used linear regression to analyze the relationship between serum T:LH ratio andthe clinical characteristics of COVID-19 patients. Jary et al. [324] applied linear models to study the geneevolution of SARS-CoV-2. Logistic regression is an algorithm designed for solving classification problems. Assume the training set is { ( x i , y i ) | x i ∈ R m , y i ∈ Z } ni =1 . The predictor of the logistic regression is ˆ y ( x ) = 11 + e − w T x + b , (13)where w is the weights and b is the bias. The loss function can be defined by L = − n n (cid:88) i =1 [ − y i log (ˆ y i ) − (1 − y i ) log (1 − ˆ y i )] . (14)Ayouba et al. [51] used logistic regression to represent the dynamics of IgG response to the S protein, Nprotein, or both antigens at the same time since symptoms onset. In addition, researchers stated that thepublicly shared CD8 + might be used as a potential biomarker of SARS-CoV-2 infection at high specificityand sensitivity by applying the logistic regression in [419]. k -nearest neighbors The k -nearest neighbors algorithm ( k -NN) is a non-parametric technique proposed by Thomas Cover andP. E. Hart in 1967 [158]. k -NN can be used for solving both regression and classification problems [33], andit is sensitive to the local structure of the data. The algorithm 1 below shows the pseudo code for the k -NN.Different distance metrics can be employed in the k -NN algorithm such as Euclidean distance, Manhattandistance, Minkowski distance, Chebyshev distance, natural log distance, generalized exponential distance,generalized Lorentzian distance, Camberra distance, quadratic distance, and mahalanobis distance.The classifier can be built by using the k -NN algorithm. Granholm et al. [265] used k -NN as a classifier todistinguish the SARS-CoV-2 virus genome from other viruses, bacteria, and eukaryotes. Similarly, Naeemet al. [507] trained a k -NN model to distinguish the SARS-CoV-2 genome from SARS-CoV genome andMERS genome. Moreover, AllerTOP v.2.0 classified allergens and non-allergens based on the k -NN methodwith an accuracy of 88.7% [500]. Furthermore, the k -NN algorithm can be employed to classify the humanprotein sequences of COVID-19 according to country [30]. Stanley et al. [682] classified cells using the k -NNalgorithm. The support vector machine (SVM) was developed by Vapnik and his colleagues, which can be used forboth classification and regression analysis [154, 190]. For the classification problem, assume the training set29 lgorithm 1: k -NN algorithm Input : k : The nearest data points; x : The feature of the training set with shape R n × m ; y : labels with shape R n × ; x (cid:48) : unknown samples with shape R s × m . Output:
The predicted labels of x (cid:48) with shape R s × . for i = 1 to s do Compute the distance d ( x , x (cid:48) i ) with shape n × ;Sort the distance values in ascending order;Choose the top k rows from the sorted array; if Classification then
Assign the label of x (cid:48) i based on the most frequent label of these k rows; endif Regression then
Assign the label of x (cid:48) i based on the average label(value) of these k rows. endend is x = { x , x , · · · , x i , · · · , x n } with x i ∈ R × m , and the label of the training set is y = { y , y , · · · , y i , · · · , y n } ∈ R n × with y i ∈ {− , } . The predictor of the SVM will be ˆ y = w T x + b . Here, w is the weights and b is thebias. If the training set is linearly separable, the aim is to minimize (cid:107) w (cid:107) subject to y i ( w T x i − b ) ≥ . If thetraining set is not linearly separable, then the hinge loss function max(0 , − y i ( w T x i − b )) will be involved.The aim of SVM is to minimize (cid:107) w (cid:107) + λ n (cid:88) i =1 max(0 , − y i ( w T x i − b ) , (15)where λ is the regularization term. For the regression problem, the aim is to minimize (cid:107) w (cid:107) subject to | y i − (cid:104) w , x i (cid:105) − b | ≤ (cid:15) .The SVM mentioned above is a linear classifier. To design a non-linear classifier, the kernel trick isemployed to maximize margin hyper-planes. The feature of the kernel SVM will become k ( x , x ) , wherethe commonly used kernels are the linear kernel k ( x , z ) = x T z , the polynomial kernel defined by k ( x , z ) =( α x T z + r ) d , the radial basis function kernel (RBF) k ( x , z ) = e − ( (cid:107) x − z (cid:107) σ ) µ , and the sigmoid kernel denoted as k ( x , z ) = e − γ x T z .Through SVM models, Basu et al. [66] and Ghosh et al. [252] identified potential main protease in-hibitors. Kowalewski et al. [389] screened near 100,000 FDA-registered chemicals and approved drugs aswell as about 14 million other purchasable chemicals against multiple SARS-CoV-2 targets.Additionally, Dutta et al. [193] predicted a novel peptide analogue of S protein using SVM modelsimplemented by the AVPred antiviral peptide prediction server. Yadav et al. [768], Peele et al. [565], Rahmanet al. [582], Martin et al. [460], and [774] used an SVM-based online server to identify epitopes. In Beg’swork [72], the Ease-MM web server based on the SVM algorithm was applied to predict protein stability.Kumar et al. [398], Kibria et al. [376], Rajput et al. [584], and Chauhan et al. [119] used SVM-based webservers to predict allergenicity of proposed epitopes or vaccines. Decision trees (DTs) are a basic machine method, which is used to perform both classification and regres-sion model by representing the attribute of the data using a flowchart-like structure. Decision trees wereused commonly in diagnosis of COVID-19. In Ref. [46, 341, 528, 749, 779], authors used decision trees in30onjunction with a feature detection model to diagnose COVID-19 from CT scans [46, 341, 749] or chestX-rays [528, 779]. Diagnosis was also done using physical symptom information [543, 800] and demo-graphic information [83, 800] with decision tree models. Decision trees were also used to make predic-tors of case severity of COVID-19, using physical data from infected individuals [50, 498, 573] and usingphysical data in conjunction with demographic data [118] with the intent that the predictors will proveuseful for hospitals’ allocation of resources. Other predictors of case severity were constructed using theclarity of the decision tree algorithm to make conclusions on which factors most influenced case severity[115,121,203,260,292,465,567,706]. Age was found to be a significant factor in predicting an individual case’soutcome [260, 567, 706], as was obesity [292, 567]. Blood data like oxygenation [567], troponin [567, 706],aspartate aminotransferase levels (AST) [706], lymphocyte and neutrophil count [121, 203, 292], procalci-tonin [203, 567], C-reactive protein [203, 567], D-dimer levels [203], and white blood cell count [203] werealso linked to case severity. In Ref. [465], authors used a decision tree model to investigate the benefit orharm of kidney transplantation during the pandemic, concluding that despite the risks, kidney transplan-tation provided survival benefit in most scenarios. Authors in [115] created a case fatality rate regressiontree, from which it was concluded that total number of cases, percentage of people older than 65 years, totalpopulation, doctors per 1000 people, lockdown period, and hospital beds per 1000 people were significantpredictors is case fatality rate. Decision tree models were constructed in order to understand environmentaleffects on COVID-19 spread [272,359] and severity [452]. In Refs. [206,397,598], authors used decision treesto create short term predictors of disease spread and fatalities. The disease genome was classified usingdecision trees, one used to conclude the zoonotic source of Pangolin in [198] and one created to provide areliable option for taxonomic classification [588]. Others used decision trees to evaluate the effectiveness oflockdowns and shelter-in-place orders [23, 718]. In [436], authors used a decision tree model in conjunctionwith a feature detection model to determine if a person is wearing a mask. Decision trees were also usedfor language processing to classify sentiments [637] or information quality [312] in social media posts aboutCOVID-19.
Random Forest (RF) [298] is an ensemble learning method, which is designed to reduce the over-fitting inthe original decision trees. Both classification and regression problems are suitable for random forest mod-els. In Refs. [50, 53, 118, 129, 134, 185, 219, 221, 260, 320, 474, 498, 514, 536, 573, 625, 652, 697, 775], authors usedRandom Forest to predict severity of individual cases of COVID-19 from physical, demographic, or geo-graphic data. From CT images in particular, a number of sources used RF algorithms in order to diagnosea COVID-19 infection more rapidly than the available testing procedures [32, 130, 219, 271, 341, 402, 474, 652,691, 697, 761]. Many authors also used the nature of the Random Forest algorithm to determine which ofthe provided data fields were most important in determining severity or mortality of COVID-19. Age wasfound to be a highly relevant factor in [129,130,185,260,293,614,616,625]. Male gender was associated withhigher risk of mortality in [129,614]. In [130,185,260], C-reactive protein level was determined to be a majorfactor in predicting recovery. Climate was determined to be a factor in COVID-19 spread and severity inRussia in [575], while weather factors were also associated with severity in [452]. Other notable factorswere high population density in [467], D-dimer levels in [130, 428], and other illnesses such as arterial hy-pertension, history of coronary artery disease (CAD), active cancer, atrial fibrillation, dementia and chronickidney disease in [614]. Authors in [67] used RF to predict effectiveness of drugs and other therapeuticagents for treatment of COVID-19. Short term prediction models of disease spread were created usingRandom Forest on environmental predictors in [359, 591, 660]. RF was used to predict cases and deaths indifferent geographic regions; in Russia in [575], in the United States in [751], in a region of Spain in [74], inIran in [572], in Morocco in [206], and worldwide in [777]. The authors in [23, 150, 290] used Random Forestto determine the effectiveness of social distancing and shelter-in-place orders at containing the spread ofthe virus. RF was also used in language processing to determine public opinion and track the propagation31f information on social media, specifically the Chinese Sina-Weibo in [285, 422] and Twitter in [637]. Theeffects on the US stock market by COVID-19 were predicted by RF in [183]. Random Forest was also usedto fill out datasets in [788, 790].
GBDT is a machine learning technique for regression and classification problems, which produces a predic-tion model in the form of an ensemble of decision trees [464]. This ensemble of decision trees is built in astage-wise fashion like other boosting methods. That is, algorithms optimize a cost function over functionspace by iteratively choosing a function that points in the negative gradient direction.Many sources used GBDT in order to diagnose COVID-19 from CT images [354, 785], chest X-rays [402],blood test data [172, 395, 676], or clinical/physical symptoms [654, 802]. In Refs. [61, 100, 111, 118, 177, 207,214, 221, 282, 353, 372, 423, 579, 678, 720, 747, 775, 795], authors used GBDT to create predictors of case sever-ity/mortality, with the intent that the predictors will be used to aid in the decision making for distributinghealth resources. Some authors trained GBDTs to predict case severity and used the nature of the algorithmto determine which data fields most impact the prediction [146, 293, 467, 562, 616, 671, 720, 756, 770, 773, 784,795]. In Refs. [146,293,616,720,756,773,784,795] it was found that age is one of the most important parame-ters for predicting case severity, with [756] finding age as a significant predictor in hospitalization, mortality,and ventilator need. Preexisting issues including hypertension, diabetes, immunosuppression, and respi-ratory illness were linked to case severity in [756,795]. In refs. [146,720,770], lactic dehydrogenase (LDH) aswell as C-reactive protein were important in prediction models. Other parameters included population den-sity in [467,671], measures of oxygenation status in [293], coagulation parameters in [720], male sex in [795],a country’s number of tourists and gross domestic product in [671], socio-economic standing in [562], neu-trophils and lymphocye percentage in [146], country-wise research sentiment and local weather conditionsin [784]. Weather conditions were also linked to COVID-19 spread using a GBDT model in [452]. Gradientboosting was also used to predict cases and deaths in Para-Brazil [708] and worldwide [434]. In [535], au-thors used GBDT to predict which proteins would likely make up an effective vaccine for COVID-19. Theeffectiveness of social distancing measures were studied using GBDT in [179]. In [495], the current spreadand landscape of COVID-19 were assessed by integrating GBDT with lateral flow assays. A predictor forinfection risk in nursing homes was constructed with gradient boosting in [690]. GBDT was employed forlanguage processing in [505, 637] to classify topics/sentiments of social media posts relating to COVID-19.Pandemic inspired lockdowns’ effects on pollution were studied using gradient boosting in [357, 566]. Ef-fects on psychological state among Chinese undergraduates were studied employing GBDT as well [243].Gao et al. [235]’s GBDT model repurposed 8565 approved or experimental drugs targeting the main pro-tease, suggesting some existing drugs could be effective. Wang et al. [743] used topology-based featuresand GBDT models to predict the NSP6 protein stability upon mutation.
Artificial neural network (ANN) is a computational model inspired by the biological neural network thatconstitutes animal brains [132]. ANN can be viewed as a weighted directed graph in which artificial neu-rons can be considered as nodes, and weights can be considered as the links between input and outputnodes. ANN is designed for both regression and classification problems. We assume the training set is x = { x , x , · · · , x i , · · · , x n } with x i ∈ R × m . Here, n is the number of samples, and m represents thenumber of features. The label of the training set is y = { y , y , · · · , y i , · · · , y n } ∈ R n × . There are twomain procedures in the ANN algorithm, the feed-forward and the back-propagation procedures. The feed-forward starts from the input layer to the first hidden layer. We define z = f ( xW + b ) , (16)32here W ∈ R m × h represents the weights from the input layer to the first hidden layer, b ∈ R × h represents the bias from the input layer to the first hidden layer; h is the number of the neurons in the firsthidden layer, and function f represents the activation functions such as ReLu and Sigmoid function. Next,from the first hidden layer to the second hidden layer, we apply a similar function defined as: z = f ( z W + b ) , (17)where W ∈ R h × h and b ∈ R × h . Here, h is the number of neurons in the second hidden layer. Werepeat a similar procedure until we get to the output layer. Our predictor from the last hidden layer to theoutput layer is: ˆ y = z j W j + b j . (18)where W i ∈ R h j × and b j ∈ R × . h j is the number of neurons in the last hidden layer In the ANN. Weuse the cross-entropy loss to describe the cost function, which is defined as L = − n (cid:88) i =1 y i log (ˆ y i ) . (19)The ANN algorithm obtains the prediction via the feed-forward procedure and then minimizes the cross-entropy loss through the back-propagation procedure.The typical ANN application to SARS-CoV-2 is to repurpose existing drugs and compounds or even gen-erate new ones to treat SARS-CoV-2. Ton et al. [705] developed a deep docking (DD) model, which providesfast prediction of docking scores from Glide or any other docking program, hence, enabling structure-basedvirtual screening of billions of purchasable molecules in a short time. The DD model relies on a deep neuralnetwork trained with docking scores of small random samples of molecules extracted from a large databaseto predict the scores of remaining molecules. Karki et al. [351] predicted potential SARS-COV-2 drugs us-ing a deep neural network framework, scale selection network (SSnet). SSnet was trained to predict drugbinding affinity. Beck et al. [70] used a pre-trained deep learning-based drug-target interaction model calledmolecule transformer-drug target interaction (MT-DTI) to identify commercially available drugs that couldact on viral proteins of SARS-CoV-2. The CNN [391] is a specialized type of neural network model originally designed to analyze visual imagery,but it can be also applied to lots of areas. CNN is a superstar of neural networks, since the first successfulCNN was developed in the late 1990s, it has achieved much success in image and video recognition, naturallanguage processing, etc., even in biophysics areas such as protein structure prediction and protein-ligandbinding [103, 106]. The core of CNN is the convolutional layer where its name comes from (see Figure 11).In the context of CNN, convolution is a linear operation that involves the multiplication of a set of weightswith the input. This multiplication is always called a filter or a kernel. Using a filter smaller than the inputis intentional as it allows the same filter to be multiplied by the input array multiple times at different pointson the input. Specifically, the filter is applied systematically to each overlapping part or filter-sized patchof the input data, left to right, top to bottom, which allows the filter an opportunity to discover that featureanywhere in the input.In the antibody and vaccine research, Chen et al. used algebraic-topology based features to build aCNN-GBT hybrid model for predicting mutation-induced binding affinity change, investigating the impactof S protein mutations on the ACE2 [125,741] 27 antibodies (see Figure 12) [122], as well as suggesting somehighly risky ones to vaccine design [123]. In the inhibitor research, Nguyen et al. [522] used algebraic-topology based features and CNN models to predict the potency of ligands from the 137 crystal structuresof the main protease. 33
Pooling &dropout
FlatteningOutput Topological data analysis
Figure 11: The CNN model from Ref. [122].
Critical Assessment of Protein Structure Prediction (CASP) also proved a domain for application ofpowerful CNN methods in protein structure prediction. For example, CNN-based AlphaFold by GoogleDeepmind obtained the highest accuracy in CASP13 [634, 753]. During this epidemic, Deepmind appliedthe AlphaFold to predict the 3D structures of SARS-CoV-2 M protein, PLpro, NSP2, NSP4, NSP6 [331].Meanwhile, the CNN-based C-I-TASSER algorithm developed by the Zhang Lab was implemented to pre-dict as many as 24 SARS-CoV-2 proteins [410].
The recurrent neural network (RNN) is a class of artificial neural network where connections betweennodes form a directed graph along a temporal sequence [611], which allows it to exhibit temporal dynamicbehavior. Derived from the feed-forward neural network, RNN can use its internal state (memory) toprocess variable length sequences of inputs. RNN was originally designed for language processing tasks,but it can also be applied to other circumstances.The long short-term memory (LSTM) shown in Figure 14) and gated recurrent unit (GRU) are two pop-ular variants of RNN. LSTM [299] is designed to avoid the vanishing gradient problem. LSTM is normallyaugmented by recurrent gates called “forget gates”, and so errors can flow backwards through unlimitednumbers of virtual layers unfolded in space. GRU is a gating mechanism in recurrent neural networksintroduced in 2014 [141]. Its performance was found to be similar to that of LSTM. However, as it lacks anoutput gate, its parameters are fewer than LSTM, so it is easier and faster to train.Their application to SARS-CoV-2 includes the following: Hofmarcher et al. [301] utilized “ChemAI” toscreen and rank around one billion molecules from the ZINC database for favourable effects against CoV-2; in more detail, the network is of the type Smiles LSTM [471]. Bung et al. [98] employed RNN-basedgenerative and predictive models for de novo design of new small molecules capable of inhibiting the mainprotease of SARS-CoV-2. The generative network complex [236] is a GRU-based generative model. Gaoet al. [237] used this AI technology to generate some potential main protease inhibitors as illustrated inFigure 15.
In Refs. [72, 178, 277, 317, 622, 623], authors used a variety of different machine learning approaches in orderto predict the effect of given mutations on disease stability or severity. Others utilized machine learningto aid in the phylogenic analysis and geographic modeling [346, 508, 585, 729]. Alam et al. [25] used ma-34
V30 BD23
SR4
RBD S309REGN10987H11-D4REGN10933CB6 RBD RBD4A8 RBDH11-D4
RBD
ACE2BD-629 CR3022CC12.3 RBDB38 RBDMR17 Fab 2-4BD-604 C105
BD-368-2
Nb RBDBD-236 CC12.1 EY6AP2B-2F6COVA2-04 H014RBDCOVA2-39 (a) (b) (c) (d) (e) (f)(g) (h) (i)
NTDNTD
Figure 12: The 3D alignment of the available unique 3D structures of SARS-CoV-2 S protein RBD in binding complexes with 27antibodies as well as ACE2 in Ref. [122]. chine learning approaches to predict Gene Ontology and extrapolate on the features most important inthe ontology prediction. Wang et al. use K -means clustering to cluster the SARS-CoV-2 sequences intodifferent groups based on the single nucleotide polymorphisms (SNP) profiles [743]. Moreover, Huzumiet al. compared the performances of various dimensional reduction algorithms such as PCA, t-SNE, andUMAP, which aims to find a best-suited, stable, and efficient technique to improve the clustering accuracyof SARS-CoV-2 sequences [306]. Networks represent interactions between pairs of units in biomolecular or other systems, such as atomicinteractions, protein-protein interactions, drug-target interactions, disease-protein associations, and drug-disease treatments. The unique characteristics of these networks can be quantified for descriptions andcomparisons of different networks. If considering protein-protein interactions as networks, each descriptor35 ellRNN CellRNN CellRNN a (cid:31) (cid:30) a (cid:31) (cid:30) a (cid:31) T x − (cid:29) a (cid:31) T x (cid:30) y (cid:31) T x (cid:30) y (cid:31) (cid:30) y (cid:31) (cid:30) x (cid:31) (cid:30) x (cid:31) (cid:30) x (cid:31) Tx (cid:30) · · · CellRNN a (cid:31) t − (cid:29) · · · ⊗ ⊕⊗ x (cid:31) t (cid:30) W aa a (cid:31) t − (cid:29) b a tanh softmax ˆ y (cid:31) t (cid:30) a (cid:31) t (cid:30) · · · W ax x (cid:31) t (cid:30) ˆ y (cid:31) t (cid:30) = softmax ( W y aa (cid:31) t (cid:30) + b y ) a (cid:31) t (cid:30) = t anh ( W ax x (cid:31) t + W aa a (cid:31) t − (cid:30) + b a ) a (cid:31) (cid:30) (b)(a) a (cid:31) t (cid:30) W ya b y Figure 13: The workflow of RNN (See Figure 13). (cid:104) t (cid:105) represents the an object at time-step t . x (cid:104) t (cid:105) , y (cid:104) t (cid:105) , and a (cid:104) t (cid:105) denote the input x ,output y , and activation at time-step t , respectively. ˆ y (cid:104) t (cid:105) represents the prediction at time-step t . (a) The forward propagation of RNN.(b) The operations for a single time-step of a RNN cell. W and b represent weights and bias at a specific state. a (cid:31) (cid:30) a (cid:31) (cid:30) a (cid:31) T x − (cid:29) a (cid:31) T x (cid:30) y (cid:31) T x (cid:30) y (cid:31) (cid:30) y (cid:31) (cid:30) x (cid:31) (cid:30) x (cid:31) (cid:30) x (cid:31) Tx (cid:30) · · · a (cid:31) t − (cid:29) · · · x (cid:31) t (cid:30) softmax ˆ y (cid:31) t (cid:30) a (cid:31) t (cid:30) · · · a (cid:31) (cid:30) (b)(a) CellLSTM CellLSTM CellLSTM CellLSTM c (cid:31) (cid:30) c (cid:31) (cid:30) c (cid:31) (cid:30) c (cid:31) T x − (cid:29) c (cid:31) T x (cid:30) c (cid:31) t − (cid:29) (cid:31) forget update tanh output ⊕(cid:31) (cid:31) c (cid:31) t (cid:30) tanh ˜ c (cid:31) t (cid:30) Γ (cid:31) t (cid:30) o Γ (cid:31) t (cid:30) f c (cid:31) t (cid:30) c (cid:31) t (cid:30) a (cid:31) t (cid:30) Γ (cid:31) t (cid:30) f = σ ( W f [ a (cid:31) t − (cid:30) , x (cid:31) t (cid:30) ] + b f ) Γ (cid:31) t (cid:30) u Γ (cid:31) t (cid:30) u = σ ( W u [ a (cid:31) t − (cid:30) , x (cid:31) t (cid:30) ] + b u ) Γ (cid:31) t (cid:30) o = σ ( W o [ a (cid:31) t − (cid:30) , x (cid:31) t (cid:30) ] + b o ) ˜ c (cid:31) t (cid:30) = σ ( W c [ a (cid:31) t − (cid:30) , x (cid:31) t (cid:30) ] + b c ) c (cid:31) t (cid:30) = Γ (cid:31) t (cid:30) f ◦ c (cid:31) t − (cid:30) + Γ (cid:31) t (cid:30) u ◦ ˜ c (cid:31) t − (cid:30) Figure 14: The workflow of LSTM. (cid:104) t (cid:105) represents an object at time-step t . x (cid:104) t (cid:105) , y (cid:104) t (cid:105) , a (cid:104) t (cid:105) , and c (cid:104) t (cid:105) denote the input x , output y ,activation, and cell state at time-step t . respectively. ˆ y (cid:104) t (cid:105) represents the prediction at time-step t . (a) The forward propagation ofLSTM. (b) The operations for a single time-step of a LSTM cell. Γ (cid:104) t (cid:105) f , Γ (cid:104) t (cid:105) i , Γ (cid:104) t (cid:105) o , c (cid:104) t (cid:105) , and ˜ c (cid:104) t (cid:105) denote the forget gate state, update gatestate, output gate state, cell state, and previous cell state at time-step t . W and b represent weights and bias at a specific state, and σ isthe activation function such as tanh. evaluates the network properties and measures how proteins connect. Network heterogeneity.
The network heterogeneity is an index that evaluates the heterogeneity of anetwork on different distributions [208]. The heterogeneity can reflect the distribution of a network ondifferent impacts or compare the heterogeneity of two networks, which is defined as: ρ = N e (cid:88) i =1 N e (cid:88) j = i +1 ( k − / i − k − / j ) , (20)where N e is the number of edges of the network, and k i is the degree of the i -th node, which is the numberof connections that the i -th node has with other nodes. Edge density.
The edge density is defined as D = 2 N e N v ( N v − , (21)36 igure 15: Illustration of the generative network complex [237]. SMILES strings are encoded into latent vector space through a gatedrecurrent neural network (GRU)-based encoder. where N e is the number of edges and N v is the number of vertices. The edge density is also called theaverage degree centrality. For a complete network in which each pair of network vertices is connected, theedge density is equal to one. A non-complete network has an edge density smaller than one. Path length.
The characteristic path length studied the typical separation between two vertices in thenetwork. It was used to study infectious diseases spread in so-called ”small-world” networks [752]. Theshortest path distance d ( i, j ) was defined as the shortest path between the corresponding pairs of vertex i and j . The average path length was defined as: (cid:104) L (cid:105) = 1 N v ( N v − N v (cid:88) i =1 N v (cid:88) j = i +1 d ( i, j ) . (22)For instance, in protein-protein interactions, the path length between two atoms reflects how ACE2 orantibodies connect to RBD. Betweenness centrality
The concept of betweenness centrality illustrates communications in a network[230]. The betweenness centrality of a vertex v k is given as: C b ( v k ) = N v (cid:88) i =1 N v (cid:88) j = i +1 g ij ( v k ) /g ij , (23)and the average betweenness centrality is given as: (cid:104) C b (cid:105) = 1 N v N v (cid:88) k =1 C b ( v k ) , (24)37here g ij ( v k ) is defined as the number of geodesics linking vertex v i and v j that passes v k , and g ij considersall the paths between v i and v j . Eigencentrality.
The eigenvector centrality is the elements of the eigenvector V max with respect to thelargest eigenvalue of the adjacency matrix A of networks [87]. It describes the probability of starting at andreturning to the same point for infinite length walks. Thus, the average eigenvector centrality is, (cid:104) C e (cid:105) = 1 N v N v (cid:88) i =1 e i , (25)where e i are elements of V max , which stands for the average impact spread of vertices beyond its neighbor-hood for an infinite walk. Subgraph centrality.
The following descriptors are built on the exponential of the adjacency matrix, E = e A . The average subgraph centrality is defined as (cid:104) C s (cid:105) = 1 N v N v (cid:88) k =1 E ( k, k ) , (26)which indicates the vertex participating in all subgraphs of the graphs [210, 213]. Subgraph centrality is thesummation of weighted closed walks of all lengths starting and ending at the same node. The long pathlength has a small contribution to the subgraph centrality. Communicability.
Finally, the last two descriptors are average communicability, given as (cid:104) M (cid:105) = 2 N v ( N v − N v (cid:88) i =1 N v (cid:88) j = i +1 E ( i, j ) , (27)and average communicability angle, given as (cid:104) Θ (cid:105) = 2 N v ( N v − N v (cid:88) i =1 N v (cid:88) j = i +1 θ ( i, j ) , (28)where θ ( i, j ) = arccos (cid:16) E ( i,j ) √ E ( i,i ) ,E ( j,j ) (cid:17) . The average communicability measures how much two vertices cancommunicate by using all the possible paths in the network, where the shorter paths have more weightthan the longer paths [211]. The average communicability angle evaluates the efficiency of two verticespassing impacts to each other in the network with all possible paths [210, 212]. Using networks to analyze the structural simi-larities is important to drug repurposing and functional mechanisms. Estrada applied the aforementionednetwork indices to analyze the interaction networks between the SARS-CoV-2 main protease and variousinhibitors [210]. Chen et al. [125] applied a similar strategy to predict binding affinity changes induced bymutations. A variety of studies using the network indexes on protein residue/atom networks followed thesame path [122, 186, 267, 350, 741, 743]. Moreover, Chen et al. employed the network analysis of antibody-antigen complexes on C α atoms in [122] as illustrated in Figure 16. Drug repurposing methods require comparing the uniquefeatures, such as chemical components, or proteomic, metabolomic, or transcriptomic data, of a drug can-didate with existing drugs, diseases, or clinical phenotypes. One idea of drug repurposing is that one drugcurrently working for one disease may also work for other diseases if these diseases share some similar pro-tein targets [138, 356]. Thus, integrated disease-human-drug interactions could form a network with nodes38 igure 16: C α network analysis of three antibody-antigen complexes. Here, circle markers represent antigen (spike protein RBD), andcube markers represent antibody or ACE2. The PDB ID of the three antibody-antigen complexes are 2D0G, 6M0J, and 6W41. The rowsrepresent the FRI rigidity index, betweenness centrality, and subgraph centrality [122]. as drugs, diseases, and proteins, weighted edges referring to interactions between them, e.g., the numberof drugs with a certain treatment. Novel drug usage can be discovered based on shared treatment profilesfrom any disease connections, and the weight between two disease connections determines the possibilityof repurposing drugs [138]. Common pathways between different viruses or diseases are already identi-fied on a large scale [674]. Meanwhile, another way to define drug repurposing is based on the structural39imilarities of two drugs: two drugs may work on the same therapeutic target if the two drugs have similarstructures.Network-based drug repurposing studies have already been performed on SARS-CoV-2. Gordon etal. [262] investigated the protein-protein interaction (PPI) network between SARS-CoV-2 and humans, andidentified 332 high-confidence PPIs between SARS-CoV-2 and human proteins; based on that and consid-ering the features of drugs such as drug status, drug selectivity, drug availability, and the statistical calcu-lations of the protein interactions, they screened drugs targeting the human proteins in the SARS-CoV-2human interactome. Consequently, 29 drugs already approved by USDA, 12 investigational new drugs,and 28 preclinical compounds were identified according to their studies. Zhou et al. [797] studied the an-tiviral drug repurposing methodology targeting SARS-CoV-2; a systematic pharmacology-based networkmedicine platform was implemented to identify the interplay between the virus-host interactome and drugtargets where they investigated the network proximity of SARS-CoV-2 host and drug targets interaction.Based on that, they reported three potential drug combinations. In the study by Sadegh et al. [613], CoVexwas developed for SARS-CoV-2 host interactome exploration and drug (target) identification, which alsoexplored the virus-host interactome and potential drug target; the network was constructed based on PPIs,drug-protein-protein interactions, etc. for repurposing drug candidates. Additionally, Srinivasan et al. [681]developed a network of the comprehensive structural gene and interactome of SARS-CoV-2. Messina etal. [477] investigated host-pathogen interaction model through the PPI network. The flexibility-rigidityindex (FRI) is a geometric graph-based method that utilizes weighted graph edgesto molecular interactions [523, 763]. Multiscale FRI [539], colored (i.e., element-specific) FRI [93] and theiralgebraic graph counterpart [764] have been also proposed. The atomic rigidity index at position r i isdefined as a summation of all the weighted edges around it: ν i ( η ) = N c (cid:48) (cid:88) j =1 e − (cid:0) (cid:107) r i − r j (cid:107) η (cid:1) , (29)where r j are atom positions and N c (cid:48) is the number of atoms in the neighborhood of r i . Here, η is a char-acteristic scale. Element-specific rigidity [93] and molecular rigidity [763] can be obtained by appropriatecollection of atomic rigidity indices.FRI has been applied for protein and nucleic acid flexibility and fluctuation analysis [763] and protein-ligand binding affinity prediction [524]. Protein-protein interactions, such as the elasticity between anti-body and antigen, especially long-range impacts, are studied by calculating the FRI index of the networkconsisting of C α atoms. FRI rigidity index is an important feature for machine learning models to predictthe binding affinity changes on mutations [739] and the protein folding energy changes on mutations [105].Some studies already applied the machine learning models based on FRI index to study the SARS-CoV-2proteins: combining with network analysis, Wang et al. [741, 743] calculated FRI rigidity index and investi-gated the folding stability changes of the S protein (see Figure 17, the definition of subgraph centrality is inthe next section) and other proteins caused by mutations. FRI-based binding affinity change between the Sprotein and human ACE2 due to mutations was also calculated by Chen et al. [122, 125]. Recent years have witnessed a rapid increase in topological data analysis (TDA) and its applications to awide variety of scientific and engineering problems [110, 339]. The main workhorse of TDA is persistenthomology [195, 803], a new branch of algebraic topology. This approach has been applied to characterize40 igure 17: The FRI rigidity index of the SARS-CoV-2 S protein. (a) Illustration of S protein and ACE2 interaction. The RBD is displayedin blue, the ACE2 is given in pink, and mutation D614G is highlighted in red. (b) The difference of FRI rigidity index of the S proteinbetween the network with wild type and the network with mutant type. (c) The difference of the subgraph centrality between thenetwork with wild type and the network with mutant type in Ref. [741]. biomolecular systems [388, 765, 766]. More powerful methods that provide simultaneous topological per-sistence and spectral analysis have been proposed [126, 476, 746]. In algebraic topology, molecular atomscan be treated as k +1 affinely independent points v , v , ... , v k . A simplicial complex, the essential buildingblock, is a finite collection of sets of points K = { σ i } , and σ i is a linear combination of these points in R n ( n ≥ k ). A simplicial complex K is valid if a face τ of a k -simplex σ i of K is also in K , such that τ ⊆ σ i and σ i ∈ K imply τ ∈ K and the non-empty intersection of any two simplices is a face for both. Given a sim-plicial complex K , a k -chain is a finite formal sum of k -simplices; that is, (cid:80) i α i σ ki . The set of all k -chains ofthe simplicial complex K equipped with an algebraic field (typically, Z ) forms an abelian group C k ( K, Z ) .A boundary operator ∂ k : C k → C k − for a k -simplex σ k = { v , v , · · · , v k } are homomorphisms definedas ∂ k σ k = (cid:80) ki =0 ( − i { v , v , · · · , ˆ v i , · · · , v k } , where { v , v , · · · , ˆ v i , · · · , v k } is a ( k − -simplex excluding v i from the vertex set. Consequently, an important property of boundary operator, ∂ k − ∂ k = ∅ , follows fromthat boundaries are boundaryless. Moreover, the k th cycle group Z k = ker ∂ k = { c ∈ C k | ∂ k c = ∅} isdefined to be the kernel of ∂ k , whose elements are called k -cycles; and the k th boundary group is the imageof ∂ k +1 , denoted as B k = im ∂ k +1 = { ∂ k +1 c | c ∈ C k +1 } . The algebraic construction to connect a sequenceof complexes by boundary maps is called a chain complex, · · · ∂ i +1 −→ C i ( X ) ∂ i −→ C i − ( X ) ∂ i − −→ · · · ∂ −→ C ( X ) ∂ −→ C ( X ) ∂ −→ , and the k th homology group is the quotient group defined by H k = Z k /B k . The key property of boundaryoperators implies B k ⊆ Z k ⊆ C k . The Betti numbers are defined by the ranks of k th homology group H k which counts k -dimensional holes. Especially, β = rank( H ) reflects the number of connected components, β = rank( H ) reflects the number of loops, and β = rank( H ) reveals the number of voids or cavities.41ogether, the set of Betti numbers { β , β , β , · · · } indicates the intrinsic topological property of a system.Persistent homology is devised to track the multiscale topological information over different scalesalong a filtration [196]. A filtration of a topology space K is a nested sequence of subspaces { K t } t =0 ,...,m of K such that ∅ = K ⊆ K ⊆ K ⊆ · · · ⊆ K m = K . Moreover, on this complex sequence, we obtain asequence of chain complexes by homomorphisms: C ∗ ( K ) → C ∗ ( K ) → · · · → C ∗ ( K m ) and a homologysequence: H ∗ ( K ) → H ∗ ( K ) → · · · → H ∗ ( K m ) , correspondingly. The p -persistent k th homology groupof K t is defined as H t,pk = Z tk / ( B t + pk (cid:84) Z tk ) , where B t + pk = im ∂ k +1 ( K t + p ) . Intuitively, this homology grouprecords the homology classes of K t that are persistent at least until K t + p . Under the filtration process, thepersistent homology barcodes can be generated. Then, the feature vectors can be constructed from thesesets of intervals for machine learning models [103].Since the first integration of persistent homology and machine learning [104], topology-based approacheshave found much success in biomolecular modeling and prediction [103, 106, 107, 520]. Combined withlarge datasets and machine learning algorithms, TDA is a powerful tool in predicting biomolecular prop-erties such as protein-ligand binding affinity [103, 106] and drug discovery [521]. Features are generatedby constructing complexes on protein atoms. According to the biomolecular properties, complexes are con-structed as an atomic-specific strategy or bipartition graph. For instance, when studying the protein foldingenergy of the ACE2 and SARS-CoV-2 S protein, one can use element-specific and/or site-specific persistenthomology to simplify the structural complexity of protein structure and encode vital biological informationinto topological invariants [103, 743]. Wang et al. [743] applied topology features on the studying of proteinfolding studies on the energy changes on mutations of SARS-CoV-2 NSP6 protein. Moreover, in the com-plex forms in a bipartite graph, the features of protein-protein interaction can be studied where the atoms ofantibody and antigen consist of two disjoint and independent sets. Chen et al. [122] used this idea to predictthe binding free energy changes on mutations of the protein-protein interactions between the S protein andantibodies. Nguyen et al. [522] studied the potency and molecular mechanism of main protease inhibitionfrom 137 crystal structures by integrating mathematics, deep learning methods, and applied persistent ho-mology. Topological data analysis is not only applied to study protein-protein interactions. Chen et al. [125]studied the mutations that strengthened SARS-CoV-2 infectivity where persistent homology played a keyrole in analyzing the interactions between the S protein and human ACE2. Since the outbreak of the COVID-19 epidemics in December 2019, enormous effort has been devoted to thescientific research relating to SARS-CoV-2, leading to significant breakthroughs, such as the developmentof vaccines and experimental determination of protein structures. However, effective drugs and therapiesare still absent. Notably, thanks to the rapid development of high-performance computers, biophysicalmethods, and AI algorithms in recent decades, plenty of theoretical and computational studies were carriedout against SARS-CoV-2. Theoretical and computational studies are significant to combat urgent epidemicssuch as this COVID-19 because they lead to important understandings faster and cheaper [209]. This reviewstrives to summarize the existing SARS-CoV-2 theoretical & computational works and enlighten futureones.Most of the researches covered by this review are about repurposing current drugs or inhibitors to targetSARS-CoV-2 because drug development has been one of the most urgent issues in combating COVID-19.A variety of drug-repurposing approaches has been applied, from molecular docking and MD simulationto machine learning & deep learning, as summarized below. (1) The most straightforward approach ismolecular docking, which provides both binding poses and corresponding scores. (2) In many studies,docking poses were further optimized by MD simulations, and these optimized poses were rescored bydocking programs. (3) More accurate binding free energies can be achieved by MD simulation-based or42ven QM-based calculations, such as MM/PB(GB)SA, free energy perturbation, metadynamics, QM/MM,and DFT. (4) Other than traditional molecular docking and MD simulations, thanks to the developmentof AI, machine learning & deep learning technologies such as GBDT, DNN, and CNN open a new trail todiscover SARS-CoV-2 drugs. With existing drugs as training sets, machine learning & deep learning couldpredict the potency of a large number of potential SARS-CoV-2 inhibitors in a short time [235]. 3D modelsalso provided binding poses [522]. (5) Network-based drug repurposing was also performed to hunt SARS-CoV-2 drugs. The basic idea is that one drug currently curing one disease may also work for other diseasesif sharing some similar protein targets [138, 356]. Thus, integrated disease-human-drug interactions forma network connecting drugs, diseases, and targets. Novel drug usage can be discovered based on sharedtreatment profiles from disease connections. (6) Traditional QSAR approaches were implemented in manycalculations for drug discovery.The magic of AIs is not limited to the repurposing of existing drugs or inhibitors. They also have thepotential to create new drugs [236,754] to combat COVID-19. For example, Bung et al. [98] employed RNN-based networks and Gao et al. [237] used GRU-based generative networks to design new potential mainprotease inhibitors.Since SARS-CoV-2 is an RNA virus, it is quite vulnerable to gene mutation. New variants have al-ready been spotted in some places in the world. Mutations are potentially harmful to the efficacy of vac-cines, drugs, etc. Mutation studies collected in this review include MD based and deep-learning basedapproaches. MD-based mutation studies mainly investigated mutation-induced conformation and bindingaffinity changes such as that between the S protein and human ACE2. The deep-learning models weredesignated to predict mutation-induced binding affinity changes, applied to reveal the mutation impactson the ACE2 and/or antibody binding with the S protein. These impacts are significant to SARS-CoV-2infectivity [125] and antibody therapies [122].Some computational investigations were devoted to vaccine design. MD simulations were employed tosimulate vaccine-related immune reaction, such as the binding of the MCH II-epitope complexes [435].Deep learning was also applied to study mutation impacts on vaccine efficiency. Based on predictedmutation-induced binding affinity changes by their CNN model and frequency of mutations, they sug-gested some hazardous ones [123].SARS-CoV-2 protein structure prediction also plays an important role, especially at the early stage ofthe epidemics when experimental structures were largely unavailable. At this point, besides traditionalhomology modeling, a more fancy solution is the high-level deep learning based models such as Alphafold[331] and C-I-TASSER [410], both making use of deep CNN.
Since the first COVID-19 case was reported in December 2019, this pandemic has gone out of control world-wide. Although scientists around the world have already placed a top priority on SARS-CoV-2 relatedresearches, there is still no effective and specific anti-virus therapies at this point. Moreover, despite theexciting progress on vaccine development, the reasons that caused the side effects, such as allergy reactionsto COVID-19 vaccines, are unknown. Furthermore, whether the newly emergent variants of SARS-CoV-2could make the virus more transmissible, infectious and deadly are also unclear, indicating that our un-derstanding of the infectivity, transmission, and evolution of SARS-CoV-2 is still quite poor. Therefore,providing a literature review for the study of the molecular modeling, simulation, and prediction of SARS-CoV-2 is needed. Since the related literature is huge and varies in quality, we cannot collect all of existingliterature for the topic. However, we try to put forward a methodology-centered review where we empha-size the methods used in various studies. To this end, we gather the existing theoretical and computationalbiophysics studies of SARS-CoV-2 with respect to the aspects such as molecular modeling, machine learn-43ng & deep learning, and mathematical approaches, aiming to provide a comprehensive, systematic, andindispensable component for the understudying of the molecular mechanism of SARS-CoV-2. Our reviewprovides a methodology-centered description of the status on molecular model, simulation, and predictionof SARS-CoV-2.Although the U.S. Food and Drug Administration (FDA) has approved the emergency use of vaccinesfrom Pfizer and Moderna in December 2020, the vaccination rate is still quite low. Even with the promisingnews of the vaccines, COVID-19 as a global health crisis may still last for years before it is fully stoppedglobally.The research on SARS-CoV-2 will also last for many years. It will take researchers many more years tofully understand the molecular mechanism of coronaviruses, such as RNA proofreading, virus-host cell in-teractions, antibody-antigen interactions, protein-protein interactions, protein-drug interactions, and viralregulation of host cell functions. Even if we could control the transmission of SARS-CoV-2 one day in thenear future, newly emergent conronaviruses may still cause similar pandemic outbreaks. Therefore, theconronavirus studies will continue even after the current pandemic is fully under control.Currently, epidemiologists, virologists, biologists, medical scientists, pharmacists, pharmacologists, chemists,biophysicists, mathematicians, computer scientists, and many others are called to the investigation of var-ious aspects of COVID-19 and SARS-CoV-2. This trend of joint effort on COVID-19 investigations willcontinue and be kept the present pandemic.The urgent need for molecular mechanistic understanding of SARS-CoV-2 and COVID-19 will furtherstimulate the development of computational biophysical, artificial intelligent, and advanced mathematicalmethods. The theoretical, computational, and mathematical communities will benefit from this endeavoragainst the pandemic.Year 2020 has witnessed the birth of human mRNA vaccines for the first time — a remarkable accom-plishment in science and technology. Although there are more dark days ahead us, humanity will prevailin a post-COVID-19 world. Science will emerge stronger against all pathogens and diseases in the future.
Acknowledgments
This work was supported in part by NIH grant GM126189, NSF Grants DMS-1721024, DMS-1761320, andIIS1900473, NASA grant 80NSSC21M0023, Michigan Economic Development Corporation, George MasonUniversity award PD45722, Bristol Myers Squibb, and Pfizer. The authors thank The IBM TJ Watson Re-search Center, The COVID-19 High Performance Computing Consortium, NVIDIA, and MSU HPCC forcomputational assistance.
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