Drug repurposing based on a Quantum-Inspired method versus classical fingerprinting uncovers potential antivirals against SARS-CoV-2 including vitamin B12

The COVID-19 pandemic has accelerated the need to identify new therapeutics at pace, including through drug repurposing. We employed a Quadratic Unbounded Binary Optimization (QUBO) model, to search for compounds similar to Remdesivir (RDV), the only antiviral against SARS-CoV-2 currently approved for human use, using a quantum-inspired device. We modelled RDV and compounds present in the DrugBank database as graphs, established the optimal parameters in our algorithm and resolved the Maximum Weighted Independent Set problem within the conflict graph generated. We also employed a traditional Tanimoto fingerprint model. The two methods yielded different lists of compounds, with some overlap. While GS-6620 was the top compound predicted by both models, the QUBO model predicted BMS-986094 as second best. The Tanimoto model predicted different forms of cobalamin, also known as vitamin B12. We then determined the half maximal inhibitory concentration (IC50) values in cell culture models of SARS-CoV-2 infection and assessed cytotoxicity. Lastly, we demonstrated efficacy against several variants including SARS-CoV-2 Strain England 2 (England 02/2020/407073), B.1.1.7 (Alpha), B.1.351 (Beta) and B.1.617.2 (Delta). Our data reveal that BMS-986094 and different forms of vitamin B12 are effective at inhibiting replication of all these variants of SARS-CoV-2. While BMS-986094 can cause secondary effects in humans as established by phase II trials, these findings suggest that vitamin B12 deserves consideration as a SARS-CoV-2 antiviral, particularly given its extended use and lack of toxicity in humans, and its availability and affordability. Our screening method can be employed in future searches for novel pharmacologic inhibitors, thus providing an approach for accelerating drug deployment.

repositioning, repurposing, re-tasking, re-profiling or drug rescue is the process by which 55 approved drugs are employed to treat a disease they were not initially intended/designed for. 56 The main strategies are based on known pharmacological side-effects (e.g. Viagra [5]), library 57 drug screening in vitro or computational approaches. The latter offers an advantage as processes 58 can be modelled and investigated in silico, which allows for higher throughput than wet lab 59 experiments. Virtual screening can be based on genetic information about the disease 60 mechanisms, similarity with other diseases for which the drug is intended for, biological 61 pathways that are common and/or known to be affected by certain drugs, or molecular 62 modelling. Within the latter, molecular docking is perhaps the most common, where structures 63 of targets are screened against libraries of compounds that will fit or dock into relevant sites [6]. 64 65 . CC-BY 4.0 International license made available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprint this version posted August 10, 2021. The solution was a map that indicated the value 1 or 0 to every binary variable, meaning its 169 presence or not in the independent set, respectively. Considering we also knew the map 170 between each binary variable and the vertices from their respective molecules, we were able to 171 calculate which atoms were similar and which were not. We employed a set of 100 instances for the preliminary experimentation to configure our 176 algorithm. This set is described by Franco et al [21] and includes 100 pairs of molecules 177 annotated by 143 experts that contain the SMILES (simplified molecular-input line-entry system, 178 a line annotation that encodes molecular structures) for both molecules, the percentage of 179 experts who determined they are similar and the percentage of experts who determined they 180 are not similar. We assumed that if a percentage of experts annotated similarity between a pair 181 of molecules, then that pair of molecules have a similarity value of that percentage of experts. 182 We then tested the influence of different parameters that configure weights and thresholds to 183 build the conflict graph within the algorithm (Wsim, Minsim, Wedges). We also tested the 184 parameter that configures the similarity value. 185 186 Wsim is a similarity measure between two vertices that is tested against Minsim. Since other 187 variables involved in this calculation, such as vertices_similarity and edges_similarity, are in the 188 range [0, 1], we need to maintain the similarity measure of Wsim in that same range. However, 189 we do not want to add the extreme values 0 and 1, as they represent similarity only among 190 vertices (value 1) or edges (value 0). We therefore tested values for Wsim within [0.1, 0.9] in steps 191 . CC-BY 4.0 International license made available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprint this version posted August 10, 2021. combinations. The quality of the solutions was calculated as the Maximum Error (ME) of the 205 similarity measure given by the QUBO model compared against the similarity measure given by 206 the experts for each pair of molecules, averaged over all the results for each value of each 207 parameter. We used the ME as a metric since it captures the worst-case error between the value 208 given by the model and the value given by the experts. We thus considered the value that 209 minimized the ME for each parameter for the final model. For each parameter we report a 210 summary of the quality of the solutions considering the value of the parameters (Tables 1-4 for Table 4 shows the results for the parameter, for which the best ME is 0. The higher the value 220 of , the higher the divergence, since the measure gives more weight to the maximum value of 221 similarity. Thus, we selected 0.5 as the value for our algorithm, calculating then the similarity 222 between two molecules as the average between the maximum and minimum values of similarity 223 given by the model. (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprint this version posted August 10, 2021.   . CC-BY 4.0 International license made available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprint this version posted August 10, 2021.

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Assessment of IC50 and cytotoxicity of predicted compounds 264
We then evaluated the possible antiviral effects of the top predicted molecules by both 265 methods. We did not assess GS-6620 as previous work has determined its lack of efficacy against 266 SARS-CoV-2 [24]. We therefore assessed the antiviral effects of cobamamide (CB) and BMS and 267 compared these with RDV in Vero E6 cells. Cells were incubated with serial dilutions of the 268 compounds, infected with SARS-CoV-2 (England 02/2020/407073 isolate) and assessed for viral 269 replication by plaque assay as well as cytotoxicity.

BMS-986094 and several forms of vitamin B12 inhibit SARS-CoV-2 replication 283
We then assessed concentrations closest to their corresponding IC50 in both Vero E6 cells as well 284 as Caco-2 cells, a human cell line permissive to SARS-CoV-2 infection. In addition to cobamamide, 285 we also examined other forms of naturally occurring vitamin B12, namely methylcobalamin 286     supernatants was quantified by plaque assay using Vero E6 cells. Data are mean ± s.d.; **P < 0.01, ***P < 0.001, 332 ****P < 0.0001, ordinary one-way ANOVA with Dunnett's multiple comparisons test. 333 334 . CC-BY 4.0 International license made available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprint this version posted August 10, 2021.  (Figure 1a). We demonstrated how both 339 approaches identified compounds that showed antiviral properties in vitro in two cell culture 340 models (Figures 2-5). Our QUBO model rendered BMS-986094 as the second-best candidate 341 (Table 5) vertices and the other one given by the similarity of their respective edges. Thus, we weigh those 520 values differently in order to get a measure of similarity. If that measure value is higher than the 521 minimum established value of similarity (Step 9), we add some weight to the final weight 522 depending on the similarity of the edges (Step 10). If the vertices belong to a ring (Step 11), we 523 also multiply this final value of weight by the number of elements in Step 12. Therefore, we 524 consider rings heavier than atoms in our weigh method. In Step 14, we add the pair of vertices 525 with their respective weight to the conflict graph as a new node. 526 527 When this process was finished, we needed to construct the edges among the vertices in the 528 conflict graph. For every pair of vertices, we checked in Step 22 if they needed to be linked by 529 an edge. We first checked they were not in the conflict graph yet and that the edge was feasible. 530 Feasibility here means that the atoms/rings belonging to the first molecule are linked in the 531 same way as the atoms/rings belonging to the second molecule are linked. If all the conditions 532 were met, we calculated in Step 23 a weight for the edge. Finally, in Step 24 we added an edge 533 . CC-BY 4.0 International license made available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprint this version posted August 10, 2021.
Where # is a binary variable that is equal to 1 if the vertex is included in the independent set 543 and 0 otherwise, # is the weight associated to that vertex from the conflict graph, #% is the 544 weight associated to the vertices and , ) is the set of vertices from the conflict graph and ) 545 is the set of edges of the conflict graph. 546 547 The first part of that expression minimizes the weights of the selected vertices from the conflict 548 graph (the objective function) and the second part of the expression penalizes the infeasible 549 assignments (the constraint). Building the model is trivial given the conflict graph. Since we had 550 weights for each vertex as well as for each edge, the only thing we needed was to generate a 551 map between vertices and binary variables for the model. 552

Similarity measurement 554
We used the same metric as in[38] for our similarity measurement: 555 556 . CC-BY 4.0 International license made available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprint this version posted August 10, 2021.
Where * and + are the original graphs from the molecules, | ) * | and | ) + | denote the number 559 of unique vertices of * and + in the independent set of the conflict graph, | * | and | + | denote 560 the number of vertices from * and + , and is a parameter to tune the result. 561 562 Depending on the perspective, we have two different values of similarity: the similarity of * 563 respect to + and the similarity of + respect to * . Those values might be different depending 564 on the number of similar vertices and the size of the graphs. Thus, this metric gives a value that 565 mixes the contribution of each graph to the solution of the problem, and we were able to give 566 more weight to one similarity value or the other one depending on the value of . 567

568
We also took into account that if the two values of similarity given by this measure (the minimum 569 and the maximum ones) were very different, we considered the similarity as the minimum value. 570 This high difference usually comes from two molecules very different in size, so we took the 571 minimum value of similarity, which in this case corresponds to the bigger molecule. We set this 572 when the maximum value is equal to or higher than the minimum one by its 50%. 573 574

Configuration of the algorithm, similarity search and graphical representation 575
We implemented our algorithms in Python 3, which were run on an Intel Core i5 with 1.9 GHz 576 and 8 GB of RAM with Microsoft Windows 10 OS for every part except for solving the 577 mathematical model, for which we used Digital Annealer. 578 579 . CC-BY 4.0 International license made available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprint this version posted August 10, 2021. The IC50 value was defined as the drug concentration at which there was a 50% decrease in the 627 titre of supernatant virus. Data were analysed using Prism 9.0 (GraphPad), and IC50 values were 628 calculated by nonlinear regression analysis using the dose-response (variable slope) equation. 629 630 . CC-BY 4.0 International license made available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprint this version posted August 10, 2021. ; https://doi.org/10.1101/2021.06.25.449609 doi: bioRxiv preprint