COVID-19 and SARS-CoV-2. Modeling the present, looking at the future.

Since December 2019 the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) has produced an outbreak of pulmonary disease which has soon become a global pandemic, known as COronaVIrus Disease-19 (COVID-19). The new coronavirus shares about 82% of its genome with the one which produced the 2003 outbreak (SARS CoV-1). Both coronaviruses also share the same cellular receptor, which is the angiotensin-converting enzyme 2 (ACE2) one. In spite of these similarities, the new coronavirus has expanded more widely, more faster and more lethally than the previous one. Many researchers across the disciplines have used diverse modeling tools to analyze the impact of this pandemic at global and local scales. This includes a wide range of approaches - deterministic, data-driven, stochastic, agent-based, and their combinations - to forecast the progression of the epidemic as well as the effects of non-pharmaceutical interventions to stop or mitigate its impact on the world population. The physical complexities of modern society need to be captured by these models. This includes the many ways of social contacts - (multiplex) social contact networks, (multilayers) transport systems, metapopulations, etc. - that may act as a framework for the virus propagation. But modeling not only plays a fundamental role in analyzing and forecasting epidemiological variables, but it also plays an important role in helping to find cures for the disease and in preventing contagion by means of new vaccines. The necessity for answering swiftly and effectively the questions: could existing drugs work against SARS CoV-2? and can new vaccines be developed in time? demands the use of physical modeling of proteins, protein-inhibitors interactions, virtual screening of drugs against virus targets, predicting immunogenicity of small peptides, modeling vaccinomics and vaccine design, to mention just a few. Here, we review these three main areas of modeling research against SARS CoV-2 and COVID-19: (1) epidemiology; (2) drug repurposing; and (3) vaccine design. Therefore, we compile the most relevant existing literature about modeling strategies against the virus to help modelers to navigate this fast-growing literature. We also keep an eye on future outbreaks, where the modelers can find the most relevant strategies used in an emergency situation as the current one to help in fighting future pandemics.

Loss of structural balance in stock markets.

We use rank correlations as distance functions to establish the interconnectivity between stock returns, building weighted signed networks for the stocks of seven European countries, the US and Japan. We establish the theoretical relationship between the level of balance in a network and stock predictability, studying its evolution from 2005 to the third quarter of 2020. We find a clear balance-unbalance transition for six of the nine countries, following the August 2011 Black Monday in the US, when the Economic Policy Uncertainty index for this country reached its highest monthly level before the COVID-19 crisis. This sudden loss of balance is mainly caused by a reorganization of the market networks triggered by a group of low capitalization stocks belonging to the non-financial sector. After the transition, the stocks of companies in these groups become all negatively correlated between them and with most of the rest of the stocks in the market. The implied change in the network topology is directly related to a decrease in stock predictability, a finding with novel important implications for asset allocation and portfolio hedging strategies.

Cascading from SARS-CoV-2 to Parkinson's Disease through Protein-Protein Interactions.

Extensive extrapulmonary damages in a dozen of organs/systems, including the central nervous system (CNS), are reported in patients of the coronavirus disease 2019 (COVID-19). Three cases of Parkinson's disease (PD) have been reported as a direct consequence of COVID-19. In spite of the scarce data for establishing a definitive link between COVID-19 and PD, some hypotheses have been proposed to explain the cases reported. They, however, do not fit well with the clinical findings reported for COVID-19 patients, in general, and for the PD cases reported, in particular. Given the importance of this potential connection, we present here a molecular-level mechanistic hypothesis that explains well these findings and will serve to explore the potential CNS damage in COVID-19 patients. The model explaining the cascade effects from COVID-19 to CNS is developed by using bioinformatic tools. It includes the post-translational modification of host proteins in the lungs by viral proteins, the transport of modified host proteins via exosomes out the lungs, and the disruption of protein-protein interaction in the CNS by these modified host proteins. Our hypothesis is supported by finding 44 proteins significantly expressed in the CNS which are associated with PD and whose interactions can be perturbed by 24 host proteins significantly expressed in the lungs. These 24 perturbators are found to interact with viral proteins and to form part of the cargoes of exosomes in human tissues. The joint set of perturbators and PD-vulnerable proteins form a tightly connected network with significantly more connections than expected by selecting a random cluster of proteins of similar size from the human proteome. The molecular-level mechanistic hypothesis presented here provides several routes for the cascading of effects from the lungs of COVID-19 patients to PD. In particular, the disruption of autophagy/ubiquitination processes appears as an important mechanism that triggers the generation of large amounts of exosomes containing perturbators in their cargo, which would insult several PD-vulnerable proteins, potentially triggering Parkinsonism in COVID-19 patients.

Protein-driven mechanism of multiorgan damage in COVID-19.

We propose a new plausible mechanism by mean of which SARS-CoV-2 produces extrapulmonary damages in severe COVID-19 patients. The mechanism consist on the existence of vulnerable proteins (VPs), which are (i) mainly expressed outside the lungs; (ii) their perturbations is known to produce human diseases; and (iii) can be perturbed directly or indirectly by SARS-CoV-2 proteins. These VPs are perturbed by other proteins, which are: (i) mainly expressed in the lungs, (ii) are targeted directly by SARS-CoV-2 proteins, (iii) can navigate outside the lungs as cargo of extracellular vesicles (EVs); and (iv) can activate VPs via subdiffusive processes inside the target organ. Using bioinformatic tools and mathematical modeling we identifies 26 VPs and their 38 perturbators, which predict extracellular damages in the immunologic endocrine, cardiovascular, circulatory, lymphatic, musculoskeletal, neurologic, dermatologic, hepatic, gastrointestinal, and metabolic systems, as well as in the eyes. The identification of these VPs and their perturbators allow us to identify 27 existing drugs which are candidates to be repurposed for treating extrapulmonary damage in severe COVID-19 patients. After removal of drugs having undesirable drug-drug interactions we select 7 drugs and one natural product: apabetalone, romidepsin, silmitasertib, ozanezumab, procaine, azacitidine, amlexanox, volociximab, and ellagic acid, whose combinations can palliate the organs and systems found to be damaged by COVID-19. We found that at least 4 drugs are needed to treat all the multiorgan damages, for instance: the combination of romidepsin, silmitasertib, apabetalone and azacitidine.

Fractional diffusion on the human proteome as an alternative to the multi-organ damage of SARS-CoV-2.

The coronavirus 2019 (COVID-19) respiratory disease is caused by the novel coronavirus SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2), which uses the enzyme ACE2 to enter human cells. This disease is characterized by important damage at a multi-organ level, partially due to the abundant expression of ACE2 in practically all human tissues. However, not every organ in which ACE2 is abundant is affected by SARS-CoV-2, which suggests the existence of other multi-organ routes for transmitting the perturbations produced by the virus. We consider here diffusive processes through the protein-protein interaction (PPI) network of proteins targeted by SARS-CoV-2 as an alternative route. We found a subdiffusive regime that allows the propagation of virus perturbations through the PPI network at a significant rate. By following the main subdiffusive routes across the PPI network, we identify proteins mainly expressed in the heart, cerebral cortex, thymus, testis, lymph node, kidney, among others of the organs reported to be affected by COVID-19.

Fractional-Order Susceptible-Infected Model: Definition and Applications to the Study of COVID-19 Main Protease.

We propose a model for the transmission of perturbations across the amino acids of a protein represented as an interaction network. The dynamics consists of a Susceptible-Infected (SI) model based on the Caputo fractional-order derivative. We find an upper bound to the analytical solution of this model which represents the worse-case scenario on the propagation of perturbations across a protein residue network. This upper bound is expressed in terms of Mittag-Leffler functions of the adjacency matrix of the network of inter-amino acids interactions. We then apply this model to the analysis of the propagation of perturbations produced by inhibitors of the main protease of SARS CoV-2. We find that the perturbations produced by strong inhibitors of the protease are propagated far away from the binding site, confirming the long-range nature of intra-protein communication. On the contrary, the weakest inhibitors only transmit their perturbations across a close environment around the binding site. These findings may help to the design of drug candidates against this new coronavirus.

Topological analysis of SARS CoV-2 main protease.

There is an urgent necessity of effective medication against severe acute respiratory syndrome coronavirus 2 (SARS CoV-2), which is producing the COVID-19 pandemic across the world. Its main protease (Mpro) represents an attractive pharmacological target due to its involvement in essential viral functions. The crystal structure of free Mpro shows a large structural resemblance with the main protease of SARS CoV (nowadays known as SARS CoV-1). Here, we report that average SARS CoV-2 Mpro is 1900% more sensitive than SARS CoV-1 Mpro in transmitting tiny structural changes across the whole protein through long-range interactions. The largest sensitivity of Mpro to structural perturbations is located exactly around the catalytic site Cys-145 and coincides with the binding site of strong inhibitors. These findings, based on a simplified representation of the protein as a residue network, may help in designing potent inhibitors of SARS CoV-2 Mpro.