SAveRUNNER algorithm requires in input a list of drug targets and a list of disease genes to evaluate the extent to which a given drug can repositioned to treat a given disease.
In the present study, disease-associated genes were downloaded from Phenopedia 19 , which provides a disease-centered view of genetic association studies; whereas drug-target associations were obtained from DrugBank 20 , which collects huge amount of drug-related data, recently enabling the discovery and repurposing of a relevant number of existing drugs to treat rare and newly identified diseases 6, 14 (Figure 1a) .
We tested the performance of SAveRUNNER on a panel of 14 diseases that have been found to be related to COVID-19 for genetic similarity, comorbidity, or for their association to drugs with the potential to shorten the recovery time for seriously ill COVID-19 patients. Thus, we included Severe Acute Respiratory Syndrome (SARS) since it is caused by the coronavirus with the highest nucleotide sequence identity with SARS-CoV-2 16, 21 . Unlike COVID-19, for which there is still a partial knowledge of its associated disease genes, SARS has been widely studied and a reliable list of the its molecular determinants is available in the most common databases of human genetic associations 19 . Yet, we comprehended cardiovascular diseases, diabetes and hypertension, whose comorbidity in COVID-19 patients is well documented 22, 23 . In addition, we included other viral infections (i.e., malaria, HIV and Ebola) and immune disorders (i.e., rheumatoid arthritis), since drugs that have been authorized for their treatment (i.e., chloroquine/hydroxychloroquine, lopinavir/ritonavir, remdesivir, and tocilizumab, respectively) are being investigated worldwide for their potential to treat coronavirus disease (COVID-19) 7, 9, [24] [25] [26] [27] [28] [29] [30] .
For what concerns drug-target associations, we assembled target information for a total of 1875 FDAapproved drugs. In addition, we considered in our input list of drug targets also the combination of remdesivir with other four antiviral agents, i.e. hydroxycloriquine, chloriquine, lopinavir, and ritonavir (referred as "5-cocktail"), as well as the combination of two of them, i.e. lopinavir and ritonavir (referred as "kaletra"), whose antiviral action against coronavirus infections has been demonstrated both in vitro and in vivo studies 31, 32 . In fact, despite significant progress in the COVID-19 management pointing to remdesivir as the most promising therapeutic candidate, the mortality remains high, indicating that treatment with an antiviral drug alone is not likely to be sufficient and combinations of antiviral agents should be evaluated by future strategies to improve patient outcomes in COVID-19 10 .
The complete lists of the analyzed diseases and drugs are provided in Supplementary Table 1. The rationale behind SAveRUNNER algorithm lies on the hypothesis that, for a drug to be effective against a specific disease, its associated targets (drug module) and the disease-specific associated genes (disease module) should be nearby in the human interactome 14 (Figure 1b) . To quantify the vicinity between drug and disease modules, SAveRUNNER implements a novel network similarity measure:
where p is the network proximity measure defined in 14 :
that represents the average shortest path length between drug targets in the drug module and the nearest disease genes in the disease module ; is the quality cluster score; is ( ); and are the steepness and the midpoint of ( ), respectively (see Materials and Methods). To assess the statistical significance of this new defined network-based similarity measure, SAveRUNNER applies a degreepreserving randomization procedure, expecting a p-value ≤ 0.05 for proximal drug and disease modules.
The novelty of our approach resides in having implemented a procedure to prioritize the predicted off-label drug indications for a given disease (see Materials and Methods section). This prioritization procedure exploits a clustering analysis to reward associations between drugs and diseases belonging to the same network cluster, based on the assumption that if a drug and a disease group together is more likely that the drug can be effectively repurposed for that disease. In this sense, we say that drugs and disease that are members of the same group (cluster), are more similar to each other than to members of other groups (clusters).
SAveRUNNER algorithm releases as output a weighted bipartite drug-disease network, in which one set of nodes corresponds to drugs and the other one corresponds to diseases. A link between a drug and a disease occurs if the corresponding drug targets and disease genes are nearby in the interactome more than expected by chance (p-value ≤ 0.05) and the weight of their interaction corresponds to the new defined network-based similarity measure. In this study, the final drug-disease network was composed of a total of 1682 nodes (i.e., 14 diseases associated to 1668 drugs) and 7177 edges.
This drug-disease network was naturally rendered as a matrix reporting the 14 diseases on the rows, and the 1668 drugs on the columns (Figure 2 ), labeled with their original medical indication according to the Therapeutic Target Database (TTD). Each matrix cell was colored according to the corresponding similarity value of a given drug-disease pair: shades of yellow denote drug-associated targets more proximal (high similarity) to the disease-associated genes in the human interactome, whereas shades of blue denote drug targets more distal (low similarity) to the disease genes ( Figure 2 ).
For elucidating drugs/diseases relatedness in terms of network similarity, we computed a hierarchical biclustering on the drug-disease similarity matrix. This analysis pointed out two main disease clusters: one including SARS, RDS, multiple sclerosis, rheumatoid arthritis, malaria, and viral infection diseases (magenta box in Figure 2 ); the other one including cardiovascular diseases and their risk factors, i.e., diabetes mellitus and hypertension (green box in Figure 2 ).
As proof of validity of SAveRUNNER, among the predicted drug-disease associations, we found several already known associations. For example, tocilizumab, interferon-beta 1a/b, chloroquine/ hydroxychloroquine, lopinavir/ritonavir, resulted to be significantly associated (p-value ≤ 0.05) with the diseases for which they were approved (i.e. rheumatoid arthritis, multiple sclerosis, malaria, and HIV infection, respectively).
In total, we found 41 host proteins associated with SARS-CoV and their specific subnetwork within the human interactome is shown in Figure 3a .
By mapping the known drug-target network into the SARS-CoV-host interactome, we revealed that 21 out of 41 (51%, light blue nodes in Figure 3a) (Figure 3b ), mirroring the enrichment results found for the total 41 SARS-CoV-associated disease genes (Figure 3c ).
The high druggability of SARS-CoV-host interactome and the relevance of the pathways in which the 21 druggable SARS-CoV-associated disease genes are involved strongly supports a drug repurposing strategy for potential treatment of COVID-19, by specifically targeting cellular proteins associated with SARS.
The remaining 20 non-targetable SARS-CoV-associated disease genes include proteins (e.g., CD14, IFNA1, IFNB1, IL4, IL10, CCL5) having key roles in the immune-inflammatory response to viral infection as well.
This strongly supports a network-based view of drug action, according to which most disease phenotypes are difficult to reverse through the use of a single "magic bullet", that is, an intervention that affects a single node in the network and encourages to inspect all the molecules that are situated in the neighborhood of the targetable proteins, leading to also detect possible side-effects 12 .
In total, SAveRUNNER identified 282 repurposable drugs that were significantly associated (p-value ≤ 0.05) with the SARS-CoV infection (Supplementary Table 2 ). Figure 4a illustrates a sketch of SARS drugdisease network in which SARS is connected to the other analyzed diseases via the high-confidence predicted drugs (with their original medical indications) that could be repurposed for potential SARS fighting. This network is composed of two independent sets of nodes: one set corresponds to 13 diseases (i.e., SARS and the other 12 diseases sharing at least one drug with SARS) represented as red circles and whose size scales with their degree; the other one corresponds to the 66 FDA-approved non-SARS drugs for which known therapeutic indications were available from TTD or to the drugs combination proposed as new potential medical indication, colored accordingly. Two nodes of the two independent sets were connected whether the network similarity of the drug targets and disease genes in the human interactome was statistically significant (p-value ≤ 0.05).
Looking at Figure 4a , it clearly emerges that there exist several candidate repurposable drugs for treatment of SARS. Among them, we pointed out the 5-cocktail (adjusted similarity = 0.89, p-value = 0.036) that appeared as a promising candidate for targeting SARS showing a quite high network similarity.
In total, among the candidate repurposable drugs for SARS with an already known medical indication, we found 16 drugs indicated for hypertension treatment, including enalapril which is also the top potential anti- hydroxycloriquine (adjusted similarity = 0.51, p-value = 1.85 10 -6 ); and 2 drugs for influenza ( Figure 4b ).
By analyzing the distribution of all the known medical indications associated to the drugs shared between SARS infection and each analyzed disease, hypertension-and cardiac-associated drugs appeared as highly frequent drugs, followed by rheumatoid arthritis-and respiratory disease-associated ones ( Figure 4c ). This findings appear in accordance with the fact that patients with SARS-CoV-2 infection also showed potential hypertension and cardiac injuries, including arrhythmia and myocardial dysfunction 22, 23, 33, 34 . This could be owed to the disruption of the subtle balance between angiotensin-converting enzyme 1 (ACE1) and
angiotensin-converting enzyme 2 (ACE2), identified as functional receptor of both SARS-CoV/SARS-CoV-2 for host cell entry 35 and normally devoted to present various cardiovascular protective effects 33 .
In order to validate the 282 anti-SARS repurposable drugs predicted by SAveRUNNER, we performed a gene set enrichment analysis (GSEA) as in 16 , by using transcriptome data of SARS-CoV infected cells as gene signature for SARS. The gene expression data of drug-treated human cell lines from the Connectivity Map (CMAP) database were exploited to obtain drug signatures and thus to calculate a GSEA score for each drug as an indication of in-silico validation. In particular, for each SARS dataset, we selected drugs with a score > 0 in order to focus on those drugs able to have a potential treatment effect on genes that are hallmark for that phenotype. The assigned GSEA score, ranging from 0 to 2, corresponded to the number of datasets satisfying this criterion for a specific drug.
The GSEA analysis validated a total of 61 out the 282 candidate drugs to be repositioned against SARS infection, including 26 with a GSEA score of 2 and 35 with a GSEA score equal to 1 (Supplementary Table   2 ).
In this study, we focused on SARS disease, which is caused by the coronavirus having the higher genetic similarity with SARS-CoV-2 16, 21 and for which the specific disease genes are known. Conversely, given the novelty of the new coronavirus COVID-19 in the spectrum of human disease, the knowledge of the COVID-19-associated genes is far from completeness. However, a study has been recently published, where the authors identified 332 human proteins interacting with 26 SARS-CoV-2 proteins by using affinity purification mass spectrometry 36 . Although the authors verified that these proteins were preferentially highly expressed in lung tissue (typical environment where the virus causes a major damage), this study has been carried out on human HEK293T kidney cells that does not represent the primary physiological site of infection.
For a more generalizable understanding of human coronaviruses infection, we completed our analysis by applying SAveRUNNER on these the 332 human proteins preliminarily associated to SARS-CoV-2. The obtained results are encouraging and appears in accordance with the analysis carried out on SARS-CoV.
Indeed, by performing a hierarchical clustering on the network of predicted drug-disease associations, we found COVID-19 in the same cluster of SARS, RDS, multiple sclerosis, rheumatoid arthritis, malaria, and viral infection diseases (Figure 5a ). This is in accordance with recent studies that are attempting to repurpose, for COVID-19 treatment, drugs approved to treat other viral infections such as influenza, malaria, HIV, and Ebola or immune-related disorders, such as rheumatoid arthritis and multiple sclerosis 9, [24] [25] [26] 28, 29, 37 .
The list of network-predicted drugs potentially able to treat SARS-CoV-2 infection contains a total of 98 drugs, including 54 (i.e., 55%) COVID-19 specific and 44 (i.e., 45%) in common with the 282 candidate repurposing candidates shared between SARS-CoV-2 an SARS-CoV is also reflected in the result of the greedy clustering algorithm implemented by SAveRUNNER, which places COVID-19 and SARS together in the cluster with the highest quality cluster score.
We then investigated whether the network-predicted repurposable drugs could counteract the gene expression perturbations caused by SARS-CoV-2, i.e. if they could up-regulate genes down-regulated by the infection or viceversa. To verify that, we performed the GSEA analysis by using, as COVID-19 gene signature, the 120 differentially expressed genes in SARS-CoV-2-infected A549 cells reported in 38 and, as drug signatures, the gene expression data of drug-treated human cell lines from the CMAP database 39 .
Interestingly, this analysis revealed that 24 out of 98 candidate drugs to be repositioned for COVID-19 treatment achieved the highest GSEA score. In particular, 14 of them, encompassing lopinavir, were included in the 54 specific-SARS-CoV-2 predicted drugs (Supplementary Table 2 and Figure 5b ).
In a recent study 18 , the authors exploited the new knowledge of SARS-CoV-2 host interactome 36 and integrated several network-based drug repurposing strategies to prioritize 81 promising repurposing candidates against COVID-19. The overlap between these 81 repurposable drugs and the 98 ones predicted by SAveRUNNER is of 5 drugs, i.e. isoniazid, lopinavir, romidepsin, sulfinpyrazone, tadalafil.
In order to predict potential comorbidity patterns among all the diseases analyzed in this study, for each disease module corresponding to the 15 analyzed disorders, we computed the non-Euclidean separation distance, which measures the modules' overlap 40 :
where ( , ) is the network proximity defined as:
and ( , ) is the shortest distance between disease gene of module and disease gene of module . A positive value for the separation measure indicates that two disease modules are topologically well-separated in the human interactome, whereas a negative value for the separation measure indicates that two disease modules are located in the same network neighborhood and thus overlap.
We found that SARS-CoV disease module directly overlapped with RDS and Influenza disease modules (s < 0) and appeared to be closest to Malaria (smallest s) followed by cardiomyopathies. (Figure 6a ). On the other hand, by using SARS-CoV-2 disease genes, we found that the COVID-19 disease module did not directly overlap with any disease module here analyzed ( Figure 6b ). However, among the closest diseases (smallest s), we found cardiovascular diseases (i.e., cardiomyopathies, arrhythmia, heart arrest), whose comorbidity in COVID-19 patients has been already discussed 22, 23 .
In the last few years, several computational network-based methods have been proposed to predict direct drug-disease associations for drug repositioning [41] [42] [43] [44] [45] [46] . Among them, the MBiRW algorithm adopts adopted an effective mechanism to measure similarity for drugs and diseases and applied a Bi-Random walk (BiRW) algorithm to predict potential new indications for existing drugs 46 . This methodology has been shown to outperform other well-known network-based prediction methods 15, 47, 48 in correctly predicting true drugdisease associations. These captivating results prompted us to implement a BiRW-based algorithm (see Materials and Methods) against which we compared the performance of SAveRUNNER.
The effectiveness of the drug-disease predictions provided by BiRW and SAveRUNNER were evaluated and compared in terms of Receiver Operating Characteristic (ROC) probability curves with their corresponding Area Under the Curve (AUC) (see Materials and Methods). In particular, we found that SAveRUNNER yielded over 70% accuracy (AUC = 0.73) for identifying well-known drug-disease relationships and overcame the one obtained by the BiRW-based algorithm (AUC = 0.59). In other words, there is 73% chance that SAveRUNNER algorithm will be able to distinguish between positive class (known drug-disease associations) and negative class (unknown drug-disease associations) against the 59% of the BiRW-based algorithm.
Thus far, no proven effective therapies for the novel coronavirus disease COVID-19 exist and the majority of available data are based on expert opinions and anecdotal experiences 49 reports from China suggest that chloroquine has shown a superiority in reducing both the severity and the duration of clinical disease without significant adverse events in almost one hundred patients 26, 51, 52 . In light of this results, an expert consensus group in China has recommended chloroquine for COVID-19 treatment 26 .
Hydroxychloroquine (brand name plaquenil) is an analogue of chloroquine, which was demonstrated to be much less toxic than chloroquine in animals and with similar in vitro efficacy on SARS-CoV-2 25, 27 Lopinavir/ritonavir (brand name kaletra) is a well-known protease inhibitor, which has been widely used for many years for the treatment of HIV infection. Compared to remdesivir, lopinavir/ritonavir has the advantage that it is widely available and has an established toxicity and drug-drug interactions profile. Its One of the most promising monoclonal antibodies under investigation for the management of COVID-19 is tocilizumab (TCZ). Specifically, TCZ is an anti-human IL-6 receptor monoclonal antibody that inhibits signal transduction by binding sIL-6R and mIL-6R. Currently, TCZ is licensed for the treatment of adult patients with moderately to severely active rheumatoid arthritis, but several studies in China showed a possible correlation of massive inflammation and severe lung damage on the rapid evolution of fatal pneumonia. Indeed, in COVID-19 patients, significant differences in IL-6 plasmatic levels were observed at different stage of disease with a higher expression in severe cases 37 . Despite the lack of clinical trials on TCZ efficacy and safety for COVID-19 treatment, "off-label" TCZ has been used as potential treatment strategy in severe and critical COVID-19 patients. Currently, in Italy a multicenter study on the efficacy and tolerability of tocilizumab in the treatment of patients with COVID-19 pneumonia is ongoing.
Another remarkable candidate for the treatment of COVID-19 is LMWH, with the aim to improve the coagulation dysfunction of COVID-19. Really, during the course of SARS-CoV-2 infection, an increased incidence of acute pulmonary embolism episodes was detected. These were often COVID-19 patients with risk factors for embolism, increased D-dimer and deterioration of general conditions and respiratory failure.
Recently, Tong N. et al. 53 showed that anticoagulant therapy mainly with LMWH appears to be associated with better prognosis in severe COVID-19 patients meeting criteria of the sepsis-induced coagulopathy score or with markedly elevated D-dimer. However, its efficacy remains to be validated in large clinical trials.
Interestingly, LMWH seems exert anti-inflammatory effects by reducing IL-6 and increasing lymphocyte %, so that the potential of LMWH could be to mitigate cytokine storm in severe COVID-19 patients.
To complete the clinical landscape of potential adjunctive therapy for COVID-19, we mention also the use of convalescent plasma or hyperimmune immunoglobulins obtained from recovered patients 57 . The rationale for this treatment is that antibodies from recovered patients may help the immune clearance of SARS-CoV-2.
In conclusion, several drugs demonstrate in vitro activity against SARS-CoV-2. Of these, several repurposed Currently, randomized clinical trials have not proven that any of these drugs are undoubtedly effective.
In this study, we developed a novel network-based algorithm for drug repurposing, called SAveRUNNER, with the aim to offer a promising framework to efficiently screen potential novel indications for currently marketed drugs against COVID-19.
Our findings, in accordance with several recent works 14, 16, 58 , suggested that the discovery of efficacious repurposable drugs (or drug combinations) could benefit from the exploration of the relationship between drug targets and the disease genes in the human interactome. The novelty of SAveRUNNER relies on the definition of a new network-based similarity measure, which quantifies the vicinity between drug and disease modules and considers the drug-disease network modular structure to reward predicted associations between drugs and diseases that are located in the same network neighborhoods.
Focusing on SARS disease, which is caused by the coronavirus having the higher genetic similarity with SARS-CoV-2 16, 21 and for which the specific disease genes are known, we identified 282 candidate repurposable drugs. Among them, we recovered some of the most rumored off-label drugs, like chloroquine, hydroxycloriquine, tocilizumab, and heparin. While lopinavir/ritonavir and remdesivir were not found to be significantly associated with SARS, their combination together with chloroquine and hydroxycloriquine (here referred as 5-cocktail) was predicted as a promising anti-SARS-CoV repurposable drug.
Although all the 282 repurposable drugs predicted by SAveRUNNER warrant to be explored, a prioritization of these drugs according to the decreasing value of their network similarity value with SARS may offer the possibility to maximize the efficiency of subsequent experimental screening and clinical trial validation. This does not mean that drugs located at a lower-ranking have no potential efficacy or must be a priori excluded from further exploration.
Thus, we found that the 95 th percentile of the similarity values distribution includes ACE-inhibitors (i.e., 
As indication of in-silico validation of the 282 candidate repurposable drugs predicted by SAveRUNNER,
we performed a GSEA analysis that allowed to investigate whether these repositioning candidates have potential treatment effect against SARS-CoV infection. The GSEA analysis validated a total of 61 out the 282 anti-SARS repurposable drugs. Among the drugs achieving highest GSEA scores, we found some of the ACE-inhibitors above-mentioned (i.e., enalapril, benazepril, quinapril, fosinopril, rescinnamine) as well as ACE-inhibitors with multiple targets (i.e., perindopril, captopril, moexipril, ramipril), and chloroquine.
In addition, this analysis came up other interesting but less obvious drugs falling far outside antiviral use such as ruxolitinib, lovastatin, and a group of H1-antihistamines (i.e., loratadine, fexofenadine, levocetirizine, desloratadine, clemastine, ketotifen, diphenhydramine, cetirizine).
Ruxolitinib is a potent and selective Janus-Associated Kinase (JAK) inhibitor approved for treatment of myelofibrosis, but thanks to its powerful anti-inflammatory effect, it could be likely to be effective against the consequences of the elevated levels of cytokines typically observed in patients with COVID-19 68, 69 .
Lovastatin is widely prescribed to reduce the levels cholesterol in the blood and prevent cardiovascular diseases. Experimental evidence suggested that statin-induced reduction of cholesterol in the plasma membrane results in lower viral titers and failure to internalize the virus 70 .
H1-antihistamines are mostly used to treat allergic reactions, but they potentially could have beneficial antiinflammatory effects on immune dysregulation during COVID 19 infection. Indeed, histamine is a biologically active substance that potentiates the inflammatory and immune responses of the body, regulates physiological function in the gut, and acts as a neurotransmitter.
Notably, among the repurposable drugs against SARS-CoV and SARS-CoV-2 both predicted by SAveRUNNER and validated by GSEA analysis, we found 10 common off-label drugs, encompassing ACE inhibitors (i.e., enalapril, and quinapril) and antihistamines (i.e., cetirizine and fexofenadine). Moreover, among repurposable drugs validated by the GSEA analysis as potential treatment effect against SARS-CoV-2 infection, we found the protease inhibitor lopinavir.
Moving beyond the "one drug, one target" vision prompted us to explore all the molecules that are situated in the interactome neighborhood of the drugs targetable proteins, which may be altered by the drug activity as well as may cause side-effects ( Figure 7) .
We interestingly observe that all drug subnetworks include genes involved in the immune-inflammatory Some drugs are characterized by highly complex interaction networks, whereas others, like the case of remdesivir, seem to have a poorly connected substructure. However, it is worth noting that the observed network complexity does not scale with the potential drug effectiveness. The lack of interactions may be likely ascribable both to the current incompleteness of the human interactome and to the shortage of drugtarget information. As in the case of remdesivir, which being designed to target specifically virus proteins, little is known about its human targetable proteins, leading to a less wired subgraph. This is not the case of the heparin subnetwork (Figure 7f) , where the highly complexity in its interaction network perfectly matches its versatile role of anticoagulant, anti-inflammatory, and antiviral drug turning out in a strong multifactorial impact in the new human coronavirus 55 
The human protein-protein interactome was downloaded from the Supplementary Data of 14 
Disease-associated genes were downloaded from Phenopedia 19 , which provides a disease-centered view of genetic association studies collecting by the online Human Genome Epidemiology (HuGE) encyclopedia 78 .
The updated version of Phenopedia (released 27-04-2020) collects gene associations for 3,255 diseases.
Among them, we selected a panel of 14 diseases of interest with their associated genes (Supplementary Table   1 ).
Drug-target interactions were acquired from DrugBank 20 , which is a comprehensive, freely accessible, online database containing information on drugs and drug targets. 80 database. In particular, for remdesivir (an anti-virus drug designed to target specifically virus proteins), we extracted its human target information from TTD.
The known drug medical indications were obtained from TTD 79 , whose last version was released on 11 Nov
SAveRUNNER (Searching off-lAbel dRUg aNd NEtwoRk) is a network-based algorithm for drug repurposing that, taking as input a list of drug targets and disease genes, constructs a drug-disease network with predicted drug-disease associations by performing the steps that will be next discussed (Figure 8 ).
In order to investigate the extent to which disease and drug modules are close in the human interactome, SAveRUNNER implements the network-based proximity measure defined as 14 :
which is the average shortest path length between drug targets in the drug module and the nearest disease genes in the disease module (Figure 1b) . To evaluate the statistical significance of the observed network proximity between the two modules and , SAveRUNNER builds a reference distance distribution corresponding to the expected distance between two randomly selected groups of proteins with the same size and degree distribution of the original sets of disease proteins and drug targets in the human interactome.
This procedure is repeated 1,000 times and the z statistics, together with the corresponding p-value, is computed by using the mean and the standard deviation of the reference distance distribution.
Step 2: Computation of network similarity
The network proximity measure is then translated in a similarity measure assuming values in the range [0-1]:
where null similarity means that the corresponding disease and drug modules are very distal in the human interactome (i.e., is maximum); whereas maximum similarity means that the corresponding disease and drug modules are very proximal in the human interactome (i.e., equal to zero).
In order to filter out statistically insignificant drug-disease associations, a significance level for the p-values is set. It means that, given a disease A and a drug b, if the p-value associated to their distance in the human interactome is smaller of the chosen significance level, the probability that the off-label drug b would be effective for this disease A is greater than expected by chance. In our analysis, predicted drug-disease associations with a p-value ≤ 0.05 were selected.
Next, SAveRUNNER performs a cluster analysis to detect groups of drugs and diseases in such a way that members in the same group (cluster) are more similar to each other than to those in other groups (clusters).
To do that, SAveRUNNER exploits a cluster detection algorithm based on the greedy optimization of the network modularity 81 . Specifically, modularity measures the strength of network division into clusters, i.e.
networks with high modularity have dense connections between the nodes within clusters but sparse connections between nodes in different clusters. The greedy clustering algorithm was adopted in view of its good performance and high speed in detecting community structure from very large networks 81 . The quality of each cluster is evaluated by SAveRUNNER by computing the following quality cluster ( ) score:
where denotes the total weight of edges within the cluster, denotes the total weight of edges connecting this cluster to the rest of network, and is a penalty term which considers the node density within the cluster.
Step 5: Adjustment of network similarity
The quality cluster score serves to reward associations between drugs and diseases belonging to the same cluster, based on the assumption that if a drug and a disease group together is more likely that the drug can be effectively repurposed for that disease. In this sense, we say that drug and the disease that are members of the same cluster tend to be "more similar" and this translates into the following adjustment for the similarity:
Thus, whether two nodes fall in the same cluster their similarity value increases by a factor proportional to the score of the cluster which they belong; otherwise whether two nodes do not fall in the same cluster is set to zero and their similarity value does not change.
Step 6: Normalization of network similarity
To bound the similarity measure defined in Eq. 1 to values that monotonically increase from 0 to 1, SAveRUNNER performed a normalization procedure by applying the following sigmoid function:
where is the adjusted similarity measure (Eq. 1), d is the sigmoid midpoint (i.e., the value at which the function approaches to 0.5), c is the sigmoid steepness. We set = max ( ) 2 and = 10.
At the end of this step, SAveRUNNER offers a list of predicted/prioritized associations between drugs and diseases as a weighted bipartite drug-disease network, in which one set of nodes corresponds to drugs and the other one corresponds to diseases. A link between a drug and a disease occurs if the corresponding drug targets and disease genes are nearby in the interactome more than expected by chance (p-value ≤ 0.05) and
the weight of their interaction corresponds to the adjusted and normalized similarity value.
The effectiveness of predicted drug-disease associations provided by the SAveRUNNER algorithm was evaluated in terms of the Receiver Operating Characteristic (ROC) probability curve analysis. The drugdisease associations were ranked according to increasing p-values and a "real association" was assigned according to TTD information: 1 if the predicted drug-disease association is known, 0 otherwise. For a specified p-value threshold, the true positive rate (i.e., sensitivity) was calculated as the fraction of known associations that are correctly predicted, while the false positive rate (i.e., 1-specificity) was computed as the fraction of unknown associations that are predicted. The ROC probability curve was drawn based on these measures at different thresholds and the corresponding Area Under the Curve (AUC) was computed. Higher the AUC, better the algorithm is at distinguishing between two classes (i.e., known drug-disease associations versus unknown drug-disease associations).
Inspired by an already existing algorithm of drug repurposing called MBiRW 46 , we exploited a Bi-Random walk-based (BiRW) approach to infer potential reuse for existing drugs. We started from the known drugdisease associations available on the TTD 19 (Figure 9a ).
In analogy with 46 , the matrices and were adjusted based on the known drug-disease associations.
The underlying hypothesis is that drug (disease) pairs, whose similarity value is greater of what expected by chance, are more likely to share common diseases (drugs).
From the adjusted matrix , a weighted drug similarity network was built, in which nodes are the approved drugs and an edge occurs between two nodes if they share at least one target gene, with a weight given by the corresponding element of the matrix . Likewise, from the adjusted matrix , a weighted disease similarity network was built, in which nodes are the diseases, and an edge occurs between two diseases if they share at least one disease gene, with a weight given by the corresponding element of the matrix .
Next, new drug-disease associations were predicted through an iterative random walk process on drug and disease similarity networks, simultaneously. Denoting with the parameters and the walks in the drug network (left walks) and in the disease network (right walks), the bi-random walk can be described by the following equations:
where 0 denotes the drug-disease association at = 0 (matrix ), while and represent the predicted drug-disease associations at iteration starting from left or right, respectively. The hypothesis behind is that an association between a drug R1 and a disease D1 can be added following these two avenues ( Figure 9b ):
1. a random walker starts from a random vertex R1 of the drug similarity network and in each step walks to one of the neighboring vertices (for instance R2, with a known or previously predicted association with D1) with a probability proportional to the weight of the edge traversed (i.e., the corresponding element of ) 2. a random walker starts from a random vertex D1 of the disease similarity network and in each step walks to one of the neighboring vertices (for instance D2, with a known or previously predicted association with R1) with a probability proportional to the weight of the edge traversed (i.e., the corresponding element of )
In both cases, the existence of a known association between a drug R1 and a disease D1 has been considered with a probability (1 − α). Then, in each step of the iteration process, the predicted drug-disease associations matrix is given by the mean between and .
Finally, a bipartite drug-disease network was constructed consisting of two sets of nodes: one set corresponding to all disease, the other set corresponding to all approved drugs. An edge between a drug and a disease occurs if an association is already known or has been predicted among them.
The performance of BiRW-based algorithm in predicting new drug-disease associations was evaluated through a tenfold cross validation 46 . This is a technique to investigate the predictive power of an algorithm by partitioning the original sample into a training and test set. In particular, the tenfold cross-validation consists of randomly partitioning the original sample (in our case the drug-disease associations) into 10 equal size subsamples. Of the 10 subsamples, a single subsample is retained as test set and the remaining 9
subsamples are used as training set. The cross-validation process is then repeated for 10 iterations so that each of the 10 subsamples is used exactly once as the test set.
The results of each iteration were evaluated in terms of ROC probability curves. In particular, each time, the predicted drug-disease associations were ranked according to the similarity score estimated by the BiRWbased algorithm (i.e., the corresponding element of matrix ) and the N top-ranked drug-disease associations were selected to be evaluated by the ROC curve analysis, where N is the length of the test set.
It's worth to stress that, in each cross-validation trial, we didn't use the information about the known drugdisease associations for the test set that were put to zero at first iteration of the bi-random walk process.
Then, the ROC curve is constructed for different values of a specified threshold, where a true drug-disease association was considered as correctly predicted if the estimated similarity score of this association was higher than the specified threshold. The results of the ROC curve analysis obtained for each iteration were averaged to obtain a mean ROC curve and the corresponding Area Under the Curve (AUC) was calculated.
Higher the AUC, better the algorithm is at distinguishing between two classes (i.e., known drug-disease associations versus unknown drug-disease associations).
Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analysis aiming to evaluate functional pathways of SARS-CoV-associated disease genes was performed by using R statistical software and the package clusterProfiler 82 . P-values were adjusted with the false discovery rate (FDR) method and a threshold equal to 0.05 was set to identify functional annotations significantly enriched amongst the selected gene lists.
In order to test whether the selected anti-SARS repurposable drugs can counteract the gene expression perturbations caused by the virus, (i.e., whether they down-regulate genes up-regulated by the virus or vice versa), we performed a gene set enrichment analysis (GSEA) as in 16 . We first collected gene expression datasets of hosts infected SARS-CoV available through the GEO public repository. In particular:
transcriptome data of SARS-CoV-infected samples from patient's peripheral blood (GSE1739) and Calu-3 cells (GSE33267). To define differentially expressed genes, we selected adjusted p-values less than 0.05 and 0.01 for GSE1739 and GSE33267 dataset, respectively. These differentially expressed genes were used as Network-predicted repurposable drugs for SARS (along rows) with their TTD classification (along columns). In the plot, circles are scaled and colored according to the adjusted similarity measure, increasing from light purple (low similarity) to dark purple (high similarity). The barplot placed on the top reports the total number of candidate repurposable drugs for SARS grouped and colored according to TTD classification. (c) Common drugs between SARS and other diseases. For each analyzed disease, the barplot reports the total number of drugs shared with SARS grouped and colored according to TTD classification. The statistically significant (p-value ≤ 0.05) network adjusted similarity values are clustered according to rows (diseases) and columns (drugs) by a complete linkage hierarchical clustering algorithm and by using the Euclidean distance as distance metric.
Heatmap color key denotes the adjusted similarity between drug targets and disease genes in the human interactome, increasing from blue (less similar) to yellow (more similar). Drugs are colored according to the Therapeutic Target , heparin (f), ACE-inhibitors (g-h), ruxolitinib (i), and H1-antistamines (l). Each subnetwork was designed to point out the shortest paths from drug targets and SARS disease genes in the human interactome. In each subnetwork, disease genes specifically targeted by each drug are marked with a yellow star; major histocompatibility complex of class I (MCH-I) and pro-inflammatory cytokines shared by all drug networks are marked with an orange and a green circle, respectively. Legend: red circles refer to SARS disease genes, blue squares refer to drug targets, red squares refer to SARS disease genes that are also drug targets, violet circles refer to the first nearest neighbors (that are not disease genes) of the drug targets in the human interactome. Anti-ACE drugs of panel (g) refer to enalapril, trandolapril, fosinopril, benazepril, cilazapril, zofenopril, spirapril, rescinnamine, and quinapril. H1-anistamines of panel (l) refer to fexofenadine, levocetirizine, desloratadine, clemastine, cetirizine. , and weights are either the proximity or similarity measure; (4-6) compute the normalized adjusted similarity measure to correct the weights of the drug-disease network and to prioritize the predicted drug-disease associations. Legend: QC is the quality cluster score; is the total weight of edges within each cluster; is the total weight of edges connecting each cluster to the rest of network; P is the node density within each cluster; c and d parameters are the sigmoid steepness and midpoint, respectively. 