key: cord-0673322-2p1xtlm3
authors: Wang, Rui; Chen, Jiahui; Gao, Kaifu; Wei, Guo-Wei
title: Vaccine-escape and fast-growing mutations in the United Kingdom, the United States, Singapore, Spain, South Africa, and other COVID-19-devastated countries
date: 2021-03-14
journal: nan
DOI: nan
sha: a4c57d304fae0071b1bb3ce7a28af1229ae4f89e
doc_id: 673322
cord_uid: 2p1xtlm3

Recently, the SARS-CoV-2 variants from the United Kingdom (UK), South Africa, and Brazil have received much attention for their increased infectivity, potentially high virulence, and possible threats to existing vaccines and antibody therapies. The question remains if there are other more infectious variants transmitted around the world. We carry out a large-scale study of 252,874 SARS-CoV-2 genome isolates from patients to identify many other rapidly growing mutations on the spike (S) protein receptor-binding domain (RDB). We reveal that 88 out of 95 significant mutations that were observed more than 10 times strengthen the binding between the RBD and the host angiotensin-converting enzyme 2 (ACE2), indicating the virus evolves toward more infectious variants. In particular, we discover new fast-growing RBD mutations N439K, L452R, S477N, S477R, and N501T that also enhance the RBD and ACE2 binding. We further unveil that mutation N501Y involved in United Kingdom (UK), South Africa, and Brazil variants may moderately weaken the binding between the RBD and many known antibodies, while mutations E484K and K417N found in South Africa and Brazilian variants can potentially disrupt the binding between the RDB and many known antibodies. Among three newly identified fast-growing RBD mutations, L452R, which is now known as part of the California variant B.1.427, and N501T are able to effectively weaken the binding of many known antibodies with the RBD. Finally, we hypothesize that RBD mutations that can simultaneously make SARS-CoV-2 more infectious and disrupt the existing antibodies, called vaccine escape mutations, will pose an imminent threat to the current crop of vaccines. A list of most likely vaccine escape mutations is given, including N501Y, L452R, E484K, N501T, S494P, and K417N.

Up to February 19, 2021 , coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has taken 2,438,287 lives and infected 109,969,891 people according to the data from World Health Organization (WHO). The first complete SARS-CoV-2 genome sequence was deposited to the GenBank (Access number: NC 045512.2) on January 5, 2020. Thereafter, new SARS-Cov-2 genome sequences were accumulated rapidly at the GenBank and GISAID, which laid the foundations for analyzing the SARS-CoV-2 mutations, virulence, pathogenicity, antigenicity, and transmissibility. A complete SARS-CoV-2 genome is an unsegmented positive-sense single-stranded RNA virus, which encodes 29 structural and non-structural proteins (NSPs) by its 29,903 nucleotides. NSPs play vital roles in RNA replication, while structure proteins form the viral particle. There are four structural proteins on SARS-CoV-2, namely, spike (S), envelope (E), membrane (M), and nucleocapsid (N) proteins [9, 17, 18, 20] . Among them, the S protein with 1273 residues of SARS-CoV-2 has drawn much attention due to its critic role in viral infection and the development of vaccines and antibody drugs.

The SARS-CoV-2 enters the host cell by interacting between its S protein and the host angiotensinconverting enzyme 2 (ACE2), primed by host transmembrane protease, serine 2 (TMPRSS2) [10] . Such a process initiates the response from the host adaptive immune system, which generates antibodies to combat the invading virus. Therefore, the S protein of SARS-CoV-2 has become a target in the development of antibody therapies and vaccines. A major concern is what are the potential impacts of S protein mutations on viral infectivity, the existing vaccines, and antibody therapies.

The most well-known mechanism of mutations is the random genetic drift, which plays a role in the processes of transcription, translation, replication, etc. Compared with DNA viruses, RNA viruses are more prone to random mutations. Unlike other RNA viruses, such as influenza, SARS-CoV-2 has a genetic proofreading mechanism regulated by NSP14 and NSP12 (a.k.a RNA-dependent RNA polymerase) [6, 28] , which enables SARS-CoV-2 to have a higher fidelity in its replication. However, the host gene editing was found to be the major source for existing SARS-CoV-2 mutations [38] , counting for 65% of reported mutations. Therefore, the worldwide transmission of COVID-19 provides SARS-CoV-2 an abundant opportunity to experience fast mutations. Another important mechanism for SARS-CoV-2 evolution is natural selection, which makes the virus more infectious while less virulent, in general [8, 27] .

It has been established that the infectivity of different viral variants in host cells is proportional to the binding free energy (BFE) between the RBD of each variant and the ACE2 [10, 14, 24, 32, 35] . Based on such a principle, it has been reported that mutations on the S protein have strengthened SARS-CoV-2 infectivity [3] . Whereas, virulent can be a result of mutations on many SARS-CoV-2 proteins. The widely spread asymptomatic COVID-19 infection and transmission can be a result of mutation-induced virulent changes [37] . mutations occurred since May 2020 were predicted as the most likely mutations in our work published online last May [3] . We also predicted a list of 625 unlikely RBD mutations [3] and currently, none of them has ever been observed. Recently, our TopNetTree model has been trained on SARS-CoV-2 datasets to accurately predict the S protein and ACE2 or antibody binding free energy changes induced by mutations [2] . A total of 31 disruptive mutations on S protein RBD has been reported as the potential mutations that would most likely disrupt the binding of S protein and essentially all the known SARS-CoV-2 antibodies had they ever occurred [2] . Therefore, tracking the growth rate of existing mutations on S protein RBD enables us to monitor the mutations that may impact the efficacy of the existing vaccines and antibody drugs. The study of fast-growing mutations also enables us to understand the SARS-CoV-2 evolutionary tendency and eventually predict future mutations.

The objective of this work is to track the fast-growing RBD mutations in pandemic-devastated countries and to analyze its evolutionary tendency around the world based on one of the most comprehensive data sets involving 252,874 SARS-CoV-2 genome sequences shown in the Mutation Tracker ( https://users.ma th.msu.edu/users/weig/SARS-CoV-2 Mutation Tracker.html). We found 5,420 unique single mutations on the S protein and among them, 825 occurred on the RBD. In terms of protein sequence, 95 of 506 nondegenerate mutations on the RBD were observed more than 10 times in the database and are regarded as significant mutations. We show that in addition to N501Y, E484K, and K417N, the mutations in the UK, South Africa, and Brazil(ian) variants, N439K, L452R, S477N, S477R, and N501T are also fast-growing mutations in 30 pandemic-devastated countries in the past few months. Using the TopNetTree model [2, 36] , we discover that 88 out of 95 significant mutations on the RBD are associated with the BFE strengthening of the binding of the RBD and ACE2 complex, resulting in more infectious SARS-CoV-2 variants. Considering mutation occurrence probability and ability to disrupt antibodies, we identify vaccine escape and vaccine weakening RBD mutations. The present finding suggests that S protein RBD mutations, in general, make the virus more infectious and are disruptive to the existing vaccines and antibody drugs.

Driven by natural selection, random genetic drift, gene editing, host immune responses, etc [8, 27] , viruses constantly evolve through mutations, which create genetic diversity and generates new variants. To have a good understanding of how the mutation will affect the infectivity, transmission, and virulence of SARS-CoV-2, it will be of great importance to study the mutations on SARS-CoV-2, particularly the S protein and the RBD, over a long time period. Therefore, in this work, we mainly focus on the mutations in S protein and S protein RBD. Here, a total of 27,390 unique single mutations has been decoded from 252,874 complete SARS-CoV-2 genome sequences. Table 1 shows the distribution of 12 single-nucleotide polymorphism (SNP) types among 5,420 unique mutations and 650,852 non-unique mutations on the S gene of SARS-CoV-2 worldwide. Symbols N U , N NU , R U , and R NU represent the number of unique mutations, the number of non-unique mutations, the ratio of 12 SNP types among unique mutation, and the ratio of 12 SNP types among non-unique mutations, respectively. It can be seen that A>G and C>T have a higher ratio in both unique and non-unique cases, which may be related to the host immune response via APOBEC and ADAR gene editing as reported in [38] . Moreover, T>C has the highest mutation ratios among unique mutations. However, the ratio of T>C mutations among the non-unique mutations is not very high, indicating that T>C mutations do not commonly occur in the population. Table 2 shows the distribution of 12 SNP types among 825 unique mutations and 50,291 non-unique mutations on the spike RBD gene sequence of SARS-CoV-2 worldwide. To be noticed, compared to Table 1 , Figure 1 is the 2D amino acid sequence alignment for the S protein RBD of SARS-CoV-2, Bat-SL-RaTG13, Pangolin-CoV, SARS-CoV, and Bat-SL-BM48-31. It can be seen that residues R346, N354, K417, N438, N440, S443, K444, V445, K458, N460, T478, S494, Q495, and Q498 located on the S protein RBD is not conservative, while the other residues are relatively conservative among different species.

The RBD is located on the S1 domain of the S protein, which plays a vital role in binding with the human ACE2 to get entry into host cells. The mutations that are detected on the RBD may affect the binding process and lead to the BFE changes. In this section, we apply the TopNetTree model [2] to predict the mutationinduced BFE changes of RBD and ACE2. Figure 2 illustrates the predicted BFE changes for S protein and human ACE2 induced by single-site mutations on the RBD. Here, only significant mutations with frequencies being greater than 10 will be considered. The bar plot of mutations with frequencies smaller than 10 can be found in the Supporting Information. In this figure, a total of 95 significant mutations are displayed. Among them, 7 mutations induced the negative BFE changes, while the other 88 mutations are bindingstrengthening mutations. Mutation T478K has the largest BFE changes which are nearly 1 kcal/mol. To be noted, the residue T478 is not conservative among different species as illustrated in Figure 1 . The S477N, N501Y, and N439K mutations are the top 3 significant mutations. Among them, the N501Y mutation has a relatively high BFE change of 0.55 kcal/mol. Moreover, the frequency and predicted BFE changes are both at a high level for mutations L452R, N501T, Y508H. Figure 3 shows the 3D structure of SARS-CoV-2 S protein RBD bound with ACE2. Here, we mark 6 mutations with either high frequency or high BFE changes. The blue and red colors represent the mutations that have positive and negative BFE changes, respectively. The darker the color is, the larger the absolute value of BFE changes is. Figure 3 : The 3D structure of SARS-CoV-2 S protein RBD bound with ACE2 (PDB ID: 6M0J). We choose blue and red colors to mark the binding-strengthening and binding-weakening mutations, respectively. Vaccine escape mutations described in Table 4 are labeled.

As reported early [2] , nearly 71% mutations on the S protein RDB will weaken the binding of S protein and antibodies, while 64.9% mutations on the RBD will strengthen the binding of S protein and ACE2, suggesting that these mutations may potentially enhance the infectivity of SARS-CoV-2. A total of 31 mutations on RBD are reported to significantly weaken the binding of the S protein and most of 51 SARS-CoV-2 antibodies, indicating that these mutations may make the existing vaccine less effective. Such mutations are called the antibody disrupting mutations, which are listed in Table 3 . Notably, most antibody disrupting mutations have negative BFE changes, suggesting that they will make the SARS-CoV-2 less infectious and thus, will not frequently occur due to the natural selection. As a result, many of them may not be able to evade the existing vaccines in a population. We hypothesize that RBD mutations that can simultaneously strengthen the infectivity and disrupt the binding between the S protein and existing antibodies will pose imminent threats to the current crop of vaccines. In other word, vaccine escape (VE) mutations are both fast-growing and antibody disrupting. We also define vaccine weakening (VW) as those fast-growing mutations that will moderately weaken the binding of the S protein and many existing antibodies. Based on the fast-growing RBD mutations detected since the beginning of 2021, we predict a list of vaccine escape, vaccine weakening RBD mutations in Table 4 . Fast growing RBD mutation that do not significantly weaken most antibody bindings are presented in Table 4 . It is of great importance to track not only the ACE2-binding-strengthening RBD mutations but also the antibody-binding-weakening RBD mutations. 

In this section, we extract the 30 countries with the highest number of SNP profiles and analyze their mutations on S protein RBD, as illustrated in Table 5 . We can see that the BFE changes of S protein and ACE2 induced by mutations on the RBD are mostly positive, suggesting that the binding of ACE2 and S protein will be potentially strengthened in these 30 countries. This indicates that SARS-CoV-2 becomes more infectious, driven by most mutations on the receptor-binding domain.

Tracking the binding-strengthening mutations will play a vital role in the development of anti-virus Emirates  1581  21  80  21  0  Sweden  1302  18  326  18  0  Singapore  1268  16  66  15  1  Brazil  1244  14  207  12  2  Russia  1060  22  68  20  2  Norway  1021  13  196  13  0  Portugal  947  14  90  13  1  Chile  888  2  2  2  0  Ireland  877  11  191  11  0  South Africa  851  20  84  17  3  Japan  713  2  2  2  0  Austria  705  10  84  9  1  Israel  693  19  117  19  0  Mexico  593  10  83  10  0  China  565  6  12  5  1 drugs, antibody drugs, and vaccines. Therefore, we calculate the growth ratio of mutations on the RBD on a 10-day average, aiming to monitor the binding-strengthening mutations that have rapid growth over time. Figure 4 illustrates the log growth ratio and log frequency of mutations on the S protein RBD in the United Kingdom on a 10-day average. The blue and red colors respectively represent the positive and negative BFE changes induced by a specific mutation, and the purple color represents the log frequency of a specific mutation. The darker the color is, the higher the log growth ratio/log frequency will be. For a better view, please check the HTML file in our Supporting Information. From Figure 4 , we can see that the N501Y mutation with a positive BFE change have a relatively high growth ratio since early September 2020, which consist with the news that a new strain B.1.1.7 (also known as 20I/501Y.V1) in the United Kingdom has the potential to increase the pandemic trajectory [7] . Moreover, mutations V367F, E484K, N355D, and S373L with positive BFE changes also have a relatively higher mutation ratio since early 2021, indicating that these four mutations may strengthen the binding of ACE2 and the S protein RBD, and potentially increase the infectivity of SARS-CoV-2. Reported in Ref. [2] , mutation E484K may dramatically disruptive effects on Figure 4 : The log growth ratio and log frequency of mutations on S protein RBD in the United Kingdom. The blue and red colors respectively represent the binding-strengthening and binding-weakening mutations on RBD. The darker blue/red means the bindingstrengthening/binding-weakening mutations with a higher growth ratio in a specific 10-day period. The darker purple represents the mutation with a higher log frequency. Figure 5 illustrates the log growth ratio and log frequency of mutations on S protein RBD in the United States on a 10-day average. Similar to the United Kingdom, the N501Y, E484K recently have a high log growth rate. Additionally, the binding-strengthening mutations T385I, N439K, S477R, and L452R also have a high log growth ratio since late 2020. To be noted, L452R had been reported as the key mutation that linked to COVID-19 outbreaks in California on January 17, 2021 [42] . Figure 6 tracks the fast-growing mutations in Denmark. Binding-strengthening mutation L452R has a fast-growing tendency since December 8, 2020. Binding-strengthening mutation S477N has a high growth ratio from late July to early December. Mutation S477R that induced the positive BFE changes has a very rapid growth between November 28, 2020, to December 08, 2020, while the number of S447R mutations has recently not increased rapidly. The number of the binding-strengthening mutation N439K keeps a high growth rate since early August. However, the increasing rate of the N439K mutation slows down recently. As first reported in the United Kingdom, the N501Y mutation also has a fast-growing tendency since early December 2020, making the SARS-CoV-2 more infectious. A similar pattern can also be observed in Netherlands, Switzerland, Norway, and Sweden. Moreover, as shown in Figure 7 , three binding-strengthening mutations have a rapid growth since late December 2020: V367F, T478K, and P479S. Scientists and researchers worldwide should keep tracking these three mutations in the following months.

Unlike the mutations in the United Kingdom, United States, and Denmark, the only binding-strengthening mutation in India is N440K, which has a relatively high frequency. Although the A530S mutation introduces the positive BFE changes with the highest frequency, the growth rate quite low after early October 2020 (See Figure 8) . Singapore also has the binding-strengthening mutations E484K, N501Y, S477N, and L452R, as those found in other countries. Moreover, one binding-strengthening mutation N440K with a high frequency has a relatively high growth rate since 2021 (See Figure 9 ). T478K  F456Y  A520S  V395I  E484Q  V367F  K444R  P384L  N354K  D427Y  T430I  R457K  T478A  N501Y  Y508H  N439K  A411S  I418V  G446D  Q493L  R346K  N450K  A352S  A411T  F490S  E484K  E406Q  S459F  P479H  S477N  R357K  E471A  Y453F  F374L  T470I  H519Q  N501K  Y489H  N331S  L335F  S375F  S477R  L452R  P499H  A352V  Y451H  S371T  T470N  L390I  A419S  G504C  A520V  E465G  D427N  R346I  P527S  K378N  R466K  E406D  S514Y K417T I434M Figure 5 : The log growth ratio and log frequency of mutations on S protein RBD in the United States. The blue and red colors respectively represent the binding-strengthening and binding-weakening mutations on RBD. The darker blue/red means the bindingstrengthening/binding-weakening mutations with a higher growth ratio in a specific 10-day period. The darker purple represents the mutation with a higher log frequency. L452R  N450K  A522S  S477N  Y453F  Q493L  S477R  A522V  S494P  N439K  V367A  A520S  Y508H  R346S  G446V  Q414K  G482S  S459Y  I468V  A344S  G413W  T385I  P337L  K444R  V367F  V445F  V483L  L335F  P384L  L517F  Y369C  N501Y  P330L  F490L  L452M  V382L  I410V  N501T  P463S  F490S  S373L  I472L  T478I  N440K  A411T  A522P  L425V  R346I  S494L  P330S  A475V  R408I  P384S  E471Q  A352V  S459F  L455F  A372T  N437S  F490Y  N501S  S477I  A348S  V483F  V512I  I434V  E484K  N481Y  L335S  I472V  L390F  T478K  A372P  K417N  S477G  S373A  A411S  S469L  N354K  A372V  E484D Figure 6 : The log growth ratio and log frequency of mutations on S protein RBD in the Denmark. The blue and red colors respectively represent the binding-strengthening and binding-weakening mutations on RBD. The darker blue/red means the bindingstrengthening/binding-weakening mutations with a higher growth ratio in a specific 10-day period. The darker purple represents the mutation with a higher log frequency.

Brazil sampled a branch of the B.1.1.28 lineage called P.1 variant (also known as 20J/501Y.V3) [21] . This variant contains three mutations in the S protein RBD: K417T, E484K, and N501Y. All of them are all the binding-strengthening mutations with a fast growth rate since late December 2020, as illustrated in Figure 10 . The binding-strengthening mutations in Russia are S477N, A522S, T385I, and E484K. All of them have a high frequency and a fast growth ratio since September 2020 (See Figure 11 ). Figure 7 : The log growth ratio and log frequency of mutations on S protein RBD in the Netherlands. The blue and red colors respectively represent the binding-strengthening and binding-weakening mutations on RBD. The darker blue/red means the bindingstrengthening/binding-weakening mutations with a higher growth ratio in a specific 10-day period. The darker purple represents the mutation with a higher log frequency. Figure 8 : The log growth ratio and log frequency of mutations on S protein RBD in India. The blue and red colors respectively represent the binding-strengthening and binding-weakening mutations on RBD. The darker blue/red means the bindingstrengthening/binding-weakening mutations with a higher growth ratio in a specific 10-day period. The darker purple represents the mutation with a higher log frequency.

The B.1.351 lineage (also known as 20H/501Y.V2) first identified in Nelson Mandela Bay, South Africa, which can be traced back to the beginning of October 2020, has become a predominant variant in South Africa. From Figure 12 , we can see that mutations F480S, N501Y, K417N, and E484K have a rapid growing tendency since the beginning of October 2020. Moreover, these four mutations are all the bindingstrengthening mutations with a very high frequency, which consistent with the finding of the B. Figure 9 : The log growth ratio and log frequency of mutations on S protein RBD in Singapore. The blue and red colors respectively represent the binding-strengthening and binding-weakening mutations on RBD. The darker blue/red means the bindingstrengthening/binding-weakening mutations with a higher growth ratio in a specific 10-day period. The darker purple represents the mutation with a higher log frequency. Figure 10 : The log growth ratio and log frequency of mutations on S protein RBD in Brazil. The blue and red colors respectively represent the binding-strengthening and binding-weakening mutations on RBD. The darker blue/red means the bindingstrengthening/binding-weakening mutations with a higher growth ratio in a specific 10-day period. The darker purple represents the mutation with a higher log frequency.

eage. This indicates that the predicted BFE changes of S protein and ACE2 from our TopNetTree model are reliable.

From analyzing the SNP profiles in Mexico, we notice that 6 binding-strengthening mutations have a rapid growth since late October 2020. They are L452R, S477N, T478K, S494P Figure 11 : The log growth ratio and log frequency of mutations on S protein RBD in Russia. The blue and red colors respectively represent the binding-strengthening and binding-weakening mutations on RBD. The darker blue/red means the bindingstrengthening/binding-weakening mutations with a higher growth ratio in a specific 10-day period. The darker purple represents the mutation with a higher log frequency. Figure 12 : The log growth ratio and log frequency of mutations on S protein RBD in South Africa. The blue and red colors respectively represent the binding-strengthening and binding-weakening mutations on RBD. The darker blue/red means the bindingstrengthening/binding-weakening mutations with a higher growth ratio in a specific 10-day period. The darker purple represents the mutation with a higher log frequency.

them, T478K has the highest growth ratio since late October 2020, indicating that T478K may potentially make the SARS-CoV-2 more transmissible and infectious. Figure 13 : The log growth ratio and log frequency of mutations on S protein RBD in Mexico. The blue and red colors respectively represent the binding-strengthening and binding-weakening mutations on RBD. The darker blue/red means the bindingstrengthening/binding-weakening mutations with a higher growth ratio in a specific 10-day period. The darker purple represents the mutation with a higher log frequency.

The BFE changes following 506 non-degenerate mutations on the S protein RBD are presented in Figures Figures 4-13 , shows that, in addition to well-known mutations E484K, K417N, and N501Y, mutations N439K, L452R, S477N, S477R, and N501T are also the binding-strengthening mutations that have a high growth ratio recently with high frequency. Tracking the growth ratio tendency on a 10-day average for a long time enables us to detect the mutations that may strengthen the binding of S protein and ACE2, which will guide the development of vaccines and antibody therapies. Based on our early model of mutation impacts on antibodies [2] , we found that the E484K mutation may cause a dramatically disruptive effect on antibodies such as H11-D4, P2B-2F6, Fab 2-4, H11-H4, COVA2-39, BD368-2, VH binder, S2M11, S2H13, CV07-270, P2C-1A3, P17, etc [2] , which is consistent with the finding that E484K may affect neutralization by some polyclonal and monoclonal antibodies [25, 39] . Mutation N501Y could weaken antibodies B38, CC12.1, VH binder, S309 S2H12 S304, NAB, C1A-B12, C1A-F10, and STE90-C11 [2] . Mutation N501Y could weaken antibodies B38, SR4, CC12.1, DB-604, S309 S2H12 S304, NABC1A-B12, etc. Both E484 and N501 are coil residues on the RBD. Similarly, mutation K417N, which is a helix-residue of the RBD, could weaken antibodies B38, CB6, CV30, CC12.3, COVA2-04, BD-604, BD-236, NAB, P2C-1F11, C1A-B12, C1A-B3, C1A-F10, and C1A-C2, [2] . It is interesting to understand whether newly identified fast-growing mutations N439K, L452R, and S477R are also disruptive to vaccines and antibodies. By checking the results reported early [2] , we note that mutation L452R may make antibodies H11-D4, P2B-2F6, SR4, MR17, MR17-K99Y, H11-H4, BD-368-2, CV07-270, and Fabs 298 52 ineffective. However, mutation N439K is not as disruptive as E484K, K417N, N501Y, and N501T. It may weaken the binding of antibody SR4. S477N can slightly weaken antibodies DB23 and CV07-250. Finally, mutation S477R may even enhance the binding of most antibodies to the RBD.

The first complete SARS-CoV-2 genome sequence was released on the GenBank ((Access number: NC 045512.2)) on January 5, 2020, by Zhang's group at Fudan University [40] . Since then, the rapid increment of the complete genome sequences is kept depositing to the GISAID database [29] . In this work, a total of 252,874 complete SARS-CoV-2 genome sequences with high coverage and exact submission date are downloaded from the GISAID database [29] ( https://www.gisaid.org/) as of February 19, 2021. We take the NC 045512.2 as the reference genome, and the multiple sequence alignment (MSA) will be applied by the Clustal Omega [30] with default parameters, which results in 252,874 SNP profiles.

Assume we have N SNP profiles, which have a total of M n non-unique mutations and M u unique mutations (M u ≤ M n ). Let ∆N i be the number of the increment of a particular mutation during the ith 10-day period, and N i be the total number of a particular mutation.

Let the number of a particular mutation in the jth day of the ith 10-day period to be N j i , where 1 ≤ i ≤ 10. Let the ∆N i = N 10 i − N 1 i be the number of the increment of a particular mutation during the ith 10-day period. Then the growth rate of a particular mutation in the ith 10-day period will be defined as

Moreover, the natural logarithm growth rate of a particular mutation in the ith 10-day period will be defined as LR i j = log(R i j + 1).

Mutation-induced protein-protein binding free energy (BFE) changes are an important approach for understanding the impact of mutations on protein-protein interactions (PPIs) and viral infectivity [13] . A variety of advanced methods has been developed [13, 26] . The topology-based network tree (TopNetTree) model [3, 36] is applied to predict mutation-induced BFE changes of PPIs in this work. TopNetTree model was implemented by integrating the topological representation and network tree (NetTree) to predict the BFE changes (∆∆G) of PPIs following mutations [36] . The structural complexity of protein-protein complexes is simplified by algebraic topology [1, 4, 41] and is represented as the vital biological information in terms of topological invariants. NetTree integrates the advantages of convolutional neural networks (CNN) and gradient-boosting trees (GBT), such that CNN is treated as an intermediate model that converts vectorized element-and site-specific persistent homology features into a higher-level abstract feature, and GBT uses the upstream features and other biochemistry features for prediction. The performance test of tenfold cross-validation on the dataset (SKEMPI 2.0 [11] ) was carried out using gradient boosted regression tree (GBRTs). The errors with the SKEMPI2.0 dataset are 0.85 in terms of Pearson correlation coefficient (R p ) and 1.11 kcal/mol in terms of the root mean square error (RMSE) [36] .

The TopNetTree model is trained by several important training sets. The most important dataset which provides the information for binding free energy changes upon mutations in the SKEMPI 2.0 dataset [11] . The SKEMPI 2.0 is an updated version of the SKEMPI database, which contains new mutations and data from other three databases: AB-Bind [31] , PROXiMATE [12] , and dbMPIKT [16] . There are 7,085 elements including single-and multi-point mutations in SKEMPI 2.0. 4,169 variants in 319 different protein complexes are filtered as single-point mutations are used for TopNetTree model training. Moreover, SARS-CoV-2 related datasets are also included to improve the prediction accuracy after a label transformation. They are all deep mutation enrichment ratio data, mutational scanning data of ACE2 binding to the receptor-binding domain (RBD) of the S protein [23] , mutational scanning data of RBD binding to ACE2 [15, 33] , and mutational scanning data of RBD binding to CTC-445.2 and of CTC-445.2 binding to the RBD [15] . Note the training datasets used in the validation in the main text does not include the test dataset, which the mutational data scanning data of RBD binding to CTC-445.2.

Persistent homology, a branch of algebraic topology, is a powerful method for simplifying the structural complexity of macromolecules [1, 4, 41] . To construct topological data analysis on protein-protein interactions, we first preset the constructions for a PPI complex into various subsets.

A m : atoms of the mutation sites.

A mn (r): atoms in the neighborhood of the mutation site within a cut-off distance r.

A Ab (r): antibody atoms within r of the binding site.

A Ag (r): antigen atoms within r of the binding site.

A ele (E): atoms in the system that has atoms of element type E. The distance matrix is specially designed such that it excludes the interactions between the atoms form the same set. For interactions between atoms a i and a j in set A and/or set B, the modified distance is defined as

where D e (a i , a j ) is the Euclidian distance between a i and a j .

In algebraic topology, molecular atoms of different can be constructed as points presented by v 0 , v 1 , v 2 , ..., v k as k +1 affinely independent points in simplicial complex. A simplicial complex is a finite collection of sets of points K = {σ i }, and σ i are called linear combinations of these points in R n (n ≥ k). To construct a simplicial complex, the Vietoris-Rips (VR) complex and alpha complex, which are widely used for point clouds, are applied in this model [4] . The boundary operator for a k-simplex would transfer a k-simplex to a k − 1-simplex. Consequently, the algebraic construction to connect a sequence of complexes by boundary maps is called a chain complex

and the kth homology group is the quotient group defined by

Then the Betti numbers are defined by the ranks of kth homology group H k which counts k-dimensional invariants, especially, β 0 = rank(H 0 ) reflects the number of connected components, β 1 = rank(H 1 ) reflects the number of loops, and β 2 = rank(H 2 ) reveals the number of voids or cavities. Together, the set of Betti numbers {β 0 , β 1 , β 2 , · · · } indicates the intrinsic topological property of a system. Persistent homology is devised to track the multiscale topological information over different scales along a filtration [4] and is significantly important for constructing feature vectors for the machine learning method. Features generated by binned barcode vectorization can reflect the strength of atom bonds, van der Waals interactions, and can be easily incorporated into a CNN, which captures and discriminates local patterns. Another method of vectorization is to get the statistics of bar lengths, birth values, and death values, such as sum, maximum, minimum, mean, and standard derivation. This method is applied to vectorize Betti-1 (H 1 ) and Betti-2 (H 2 ) barcodes obtained from alpha complex filtration based on the fact that higher-dimensional barcodes are sparser than H 0 barcodes.

It is very challenging to predict binding affinity changes following mutation for PPIs due to the complex dataset and 3D structures. A hybrid machine learning algorithm that integrates a CNN and GBT is designed to overcome difficulties, such that partial topologically simplified descriptions are converted into concise features by the CNN module and a GBT module is trained on the whole feature set for a robust predictor with effective control of overfitting [36] . The gradient boosting tree (GBT) method produces a prediction model as an ensemble method which is a class of machine learning algorithms. It builds a popular module for regression and classification problems from weak learners. By the assumption that the individual learners are likely to make different mistakes, the method using a summation of the weak learners to eliminate the overall error. Furthermore, a decision tree is added to the ensemble depending on the current prediction error on the training dataset. Therefore, this method (a topology-based GBT or TopGBT) is relatively robust against hyperparameter tuning and overfitting, especially for a moderate number of features. The GBT is shown for its robustness against overfitting, good performance for moderately small data sizes, and model interpretability. The current work uses the package provided by scikit-learn (v 0.23.0) [22] . A supervised CNN model with the PPI ∆∆G as labels is trained for extracting high-level features from H 0 barcodes. Once the model is set up, the flatten layer neural outputs of CNN are feed into a GBT model to rank their importance. Based on the importance, an ordered subset of CNN-trained features is combined with features constructed from high-dimensional topological barcodes, H 1 and H 2 into the final GBT model.

Understanding the evolution trend of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and estimating its threats to the existing vaccines and antibody drugs are of paramount importance to the current battle against coronavirus disease 2019 (COVID- 19) . To this end, we carry out a unique analysis of mutations on the spike (S) protein receptor-binding domain (RBD). Our study is based on comprehensive 252,874 SARS-CoV-2 genome isolates recorded on the Mutation Tracker ( https://users.math.msu.edu/use rs/weig/SARS-CoV-2 Mutation Tracker.html). There are 5,420 unique single mutations and 650,852 nonunique mutations on the S protein gene. Therefore, an average genome sample has 2.6 mutations on the S protein but new samples have increasingly more mutations. In terms of the protein sequence, 535 missense mutations and 506 non-degenerate mutations occurred on the RBD. However, most of these RBD mutations have a relatively low frequency, leaving 95 significant mutations that have been detected more than 10 times in the database. We track fast-growing (FG) RBD mutations in 30 pandemic-devastated countries, including the UK, the US, Singapore, Spain, South Africa, Brazil, etc. To avoid random low-frequency mutations, we pursue this task by analyzing the 10-day growth rate of 95 significant RBD mutations. We show that three fast-growing mutations N439K, L452R, S477N, S477R, and N501T in addition to all known infectious variants containing N501Y, E484K, and K417N, deserve the world's attention.

Additionally, we reveal that 92.6% (88 out of 95) significant mutations on the RBD strengthen the RBD binding with the host angiotensin-converting enzyme 2 (ACE2), based on a cutting-edge topology-based neural network tree (TopNetTree) model trained on SARS-CoV-2 experimental datasets [2, 36] . More specifically, we found that mutations N501Y, E484K, and K417N in the United Kingdom (UK), South Africa, or Brazil variants as well as mutations N439K, L452R, S477N, S477R, and N501T are all associated with the enhancement of the BFE of the S protein and ACE2, confirming the earlier speculation. This result suggests that SARS-CoV-2 has evolved into more infectious strains due to the wide-spread transmission.

Finally, the early finding shows that more 70% mutations would weaken the efficacy of known antibodies [2] . We report that rapidly growing mutations E484K, K417N, and L452R are more likely to disrupt existing vaccines and many antibody drugs, while mutations N501Y and N501T can also be disruptive, but mutations N439K, V367F, and S477R are not as disruptive as other rapidly growing ones. We have predicted vaccine escape mutations that are not only fast-growing but also can disrupt many existing vaccines. We have also identified vaccine weakening mutations as fast-growing RBD mutations that will weaken the binding between the S protein and many existing antibodies. A list of vaccine escape and vaccine weakening RBD mutations are predicted. We unveil that regulated by host gene editing, viral proofreading, random genetic drift, and natural selection, the mutations on the S protein RBD tend to disrupt the existing antibodies and vaccines and increase the transmission and infectivity of SARS-CoV-2.

The SARS-CoV-2 SNP data in the world is available at Mutation Tracker. The SARS-CoV-2 S protein RBD SNP data in 30 countries can be downloaded from the Supplementary Data. The TopNetTree model is available at TopNetTree. The related training datasets are described in Section 3.3.3.

The supporting information is available for S1 BFE changes following 506 non-degenerate mutations on the S protein RBD. Figure S6 - Figure S25 plot the log growth ratio and log frequency of mutations on S protein RBD in the Australia, Austria, Belgium, Canada, Chile, China, France, Germany, Iceland, Ireland, Israel, Italy, Japan, Luxembourg, Norway, Portugal, Spain, Sweden, Switzerland, and the United Arab Emirates.

Topology and data

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

Mutations strengthened SARS-CoV-2 infectivity

Topological persistence and simplification

Genomic characterisation of an emergent sars-cov-2 lineage in manaus: preliminary findings

Structural and molecular basis of mismatch correction and ribavirin excision from coronavirus RNA

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Making sense of mutation: what D614G means for the COVID-19 pandemic remains unclear

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SARS-CoV-2 cell entry depends on ACE2 and TMPRSS2 and is blocked by a clinically proven protease inhibitor

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Proximate: a database of mutant protein-protein complex thermodynamics and kinetics

Saambe-seq: a sequencebased method for predicting mutation effect on protein-protein binding affinity

Bats are natural reservoirs of SARS-like coronaviruses

De novo design of potent and resilient hace2 decoys to neutralize sarscov-2

dbmpikt: a database of kinetic and thermodynamic mutant protein interactions

Characterization of accessory genes in coronavirus genomes

Sarscov-2 n protein antagonizes type i interferon signaling by suppressing phosphorylation and nuclear translocation of stat1 and stat2

Detection of b. 1.351 sars-cov-2 variant strain-zambia

Insights into sars-cov-2 genome, structure, evolution, pathogenesis and therapies: Structural genomics approach

Sars-cov-2 reinfection by the new variant of concern (voc) p. 1 in amazonas, brazil. virological. org

Scikit-learn: Machine learning in python

The sequence of human ace2 is suboptimal for binding the s spike protein of sars coronavirus 2

Identification of two critical amino acid residues of the severe acute respiratory syndrome coronavirus spike protein for its variation in zoonotic tropism transition via a double substitution strategy

Spike e484k mutation in the first sars-cov-2 reinfection case confirmed in brazil

mcsm-ppi2: predicting the effects of mutations on protein-protein interactions

Mechanisms of viral mutation

Insights into RNA synthesis, capping, and proofreading mechanisms of SARS-coronavirus

GISAID: Global initiative on sharing all influenza data-from vision to reality

Clustal omega, accurate alignment of very large numbers of sequences

AB-Bind: antibody binding mutational database for computational affinity predictions

Cross-host evolution of severe acute respiratory syndrome coronavirus in palm civet and human

Deep mutational scanning of sars-cov-2 receptor binding domain reveals constraints on folding and ace2 binding

Emergence of a new sars-cov-2 variant in the uk

Structure, function, and antigenicity of the SARS-CoV-2 spike glycoprotein

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

Decoding asymptomatic covid-19 infection and transmission. The journal of physical chemistry letters

Host immune response driving SARS-CoV-2 evolution

Escape from neutralizing antibodies by sars-cov-2 spike protein variants

A new coronavirus associated with human respiratory disease in China

Persistent homology analysis of protein structure, flexibility, and folding. International journal for numerical methods in biomedical engineering

Emergence of a novel sarscov-2 strain in southern california, usa. medRxiv