key: cord-0878963-rbvpwe90
authors: Castle, Brian T.; Dock, Carissa; Hemmat, Mahya; Kline, Susan; Tignanelli, Christopher; Rajasingham, Radha; Masopust, David; Provenzano, Paolo; Langlois, Ryan; Schacker, Timothy; Haase, Ashley; Odde, David J.
title: Biophysical modeling of the SARS-CoV-2 viral cycle reveals ideal antiviral targets
date: 2020-05-23
journal: bioRxiv
DOI: 10.1101/2020.05.22.111237
sha: 9051a7a196366057e11ca654565ac0675fe84eab
doc_id: 878963
cord_uid: rbvpwe90

Effective therapies for COVID-19 are urgently needed. Presently there are more than 800 COVID-19 clinical trials globally, many with drug combinations, resulting in an empirical process with an enormous number of possible combinations. To identify the most promising potential therapies, we developed a biophysical model for the SARS-CoV-2 viral cycle and performed a sensitivity analysis for individual model parameters and all possible pairwise parameter changes (162 = 256 possibilities). We found that model-predicted virion production is fairly insensitive to changes in viral entry, assembly, and release parameters, but highly sensitive to some viral transcription and translation parameters. Furthermore, we found a cooperative benefit to pairwise targeting of transcription and translation, predicting that combined targeting of these processes will be especially effective in inhibiting viral production.

The ongoing global pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has resulted in more than 4 million confirmed cases and 300,000 deaths worldwide (1). The most common symptoms of the illness caused by SARS-CoV-2, COVID-19, include fever, cough and fatigue (2) . The clinical presentation can range from asymptomatic to fatal, with severe cases rapidly progressing to pneumonia, acute respiratory distress syndrome (ARDS), and organ failure (3) . There is currently no vaccine for the disease, and development could take 12 to 18 months (4). Therefore, there exists a critical need for effective therapeutic interventions to minimize the transmission and severity of SARS-CoV-2.

Despite increased expenditures on research and development, less than one out of every ten therapeutic drugs that enter phase I clinical trials eventually gains FDA approval (5) . To accelerate the development process for COVID-19, the initial focus has been on repurposing approved drugs and biologics. However, owing to the large number of possible therapeutics, and the need for rapid testing, there has not been extensive preclinical testing on SARS-CoV-2 specifically. While these therapeutics have been deployed in combinations of two, three, or four in more than 800 clinical trials globally (6) , it is not clear which drugs, possibly in combination with others, would, in principle, be most effective. For other RNA viruses, such as HIV, single therapies have not been successful as a result of the virus' ability to rapidly evolve and develop resistance to antivirals (7) , thus driving the need for combination therapies (8) . With more than 100 distinct agents currently in trials to treat COVID-19, even a two drug combination has over 10,000 possible combinations that could be tried, raising the question of how to rationally focus clinical trials on the single agents and combinations that are most likely to be effective.

Biophysical modeling has the potential to help rationally guide the development of therapeutic interventions for SARS-CoV-2 by identifying key model parameters for effective targeting. In addition, modeling can potentially be used to identify combination therapies, predict clinical trial outcomes, stratify patients, and identify potential source(s) of variable patient-to-patient outcomes. Here we present a biophysical model for the SARS-CoV-2 viral cycle and identify the single and combination parameters with the highest sensitivity, representing the ideal targets for therapeutic intervention to inhibit virus production.

The biophysical model of the SARS-CoV-2 viral life cycle was constructed based on SARS-CoV literature that included processes underlying viral entry, genome transcription, genome translation, virion assembly, and virion release ( Fig. 1 ; reviewed in (9, 10) ). Mass action and chemical rate equations were used to mathematically describe the system using an approach similar to that taken previously to model the life cycle of other viral systems (reviewed in (11) ; see Materials and Methods), and the resulting series of ordinary differential equations solved numerically. As an initial condition we assumed that a single virion was bound to the surface of an individual cell, which was then internalized to initiate the replication cycle. As data specific to the viral cycle to SARS-CoV-2 are limited, we primarily used experimental observations from SARS-CoV to inform model assumptions and parameterization (Table 1) . We assume that it is reasonable to use SARS-CoV data based on the high degree of genomic similarity between the two viruses (12) (13) (14) . Using the base parameter values, the model reproduces viral production on a timescale and of a quantity consistent with experimental observations (Fig. 2) . Importantly, the model reproduces a number of experimental observations without parameter adjustment ( Fig. 2B) ; for example, the model naturally predicts that ~10% of the RNA will be negative sense ( Fig. 2) . Based on this, we conclude that the model provides a suitable tool to identify points of interest for therapeutic intervention, i.e. those parameters and the associated subprocesses that are particularly sensitive to perturbation.

To assess these points of interest in the viral cycle, we performed a sensitivity analysis for each parameter by systematically increasing and decreasing their values from baseline by up to three orders of magnitude (1000-fold) while holding all other parameters constant (Fig. 3) .

Parameters specific to virion stoichiometry or RNA segment length were ignored in this analysis as they are likely difficult to target clinically. Using the viral cycle time tcycle, defined as the time to produce 1000 virions, as a readout of viral replication rate, we examined viral production as a function of individual parameter values. We found that parameter perturbation resulted in a variety of responses, ranging from insensitive to highly sensitive ( Fig. 3A-C) . As seen in Figure   3D , viral production was most sensitive to perturbation of many, but not all, parameters related to genome transcription and translation. Parameters related to viral entry, packaging, and release were comparably insensitive to changes from the base values (Fig. 3D ). While it is theoretically possible to inhibit viral production via targeting of these insensitive parameters, it is necessary to achieve a high level of inhibition compared to those that exhibit high sensitivity ( Fig. S1 ). For example, parameters specific to viral entry and packaging required 100-1000x level of inhibition in order to influence viral production (Figs. 3D and S1A, C), while parameters specific to replication completely inhibited viral production after only a 10x effect (Figs. 3D and S1B). Based on these observations, we conclude that transcription and translation represent high sensitivity targets for therapeutic inhibition.

Due to the ability to rapidly evolve, viral diseases are often treated with combination therapies.

While an exhaustive combinatorial analysis is difficult or impossible to conduct experimentally due to time and resource limitations, it can quickly be implemented in silico. To identify potential combinations that could cooperate to inhibit viral production in the model, we performed a pairwise sensitivity analysis of the model parameters. Parameter pairs were either coordinately increased or decreased from their base value and then scored based on the results (see Materials and Methods). To score parameter combinations we defined a sensitivity (S) and range (R) value (Fig. 4A ), similar to our previous approach for another biophysical model (15) .

The sensitivity S is a measure of how viral production scales with changes to the base parameter values, while R is a measure of the magnitude of perturbation necessary to produce a maximal effect. Ideally, interventional therapies would have a strong effect (large S) with minimal perturbation (small R). Therefore, we scored parameter pairs by dividing the resulting S value by the value of R (S/R). As seen in Figures 4B and S2 , several parameter combinations completely eliminated viral production with only a <10-fold effect. Similar to the single parameter sensitivity analysis, parameters related to transcription and translation once again emerged as the highest sensitivity targets; the highest scores were parameter combinations specific to the host ribosomes and the viral RNA-dependent RNA polymerase (RdRp). Other noteworthy pairs, which completely eliminated viral production, were the rate of proteolytic cleavage of pp1a/1ab by the main protease (kCleav) and the half-life of pp1a/1ab (hpp1) paired with the binding rate of the RdRp ( !" #$#% ). Interestingly, the majority of high scoring combinations were not simply the result of targeting two high sensitivity parameters, but rather resulted from cooperating effects between the two parameters ( Fig. 4C ). Based on these results, we conclude combination targeting of transcription and translation can lead to enhanced effects on viral production, beyond targeting each individually.

Overall, our modeling of the SARS-CoV-2 life cycle, parameterized using published SARS-CoV literature, shows that theoretically there are opportunities for therapeutic interventions that significantly inhibit the viral cycle. In particular, the sensitivity analysis identified several parameters in the middle of the viral cycle, specific to genome transcription and translation, that present the best opportunities for inhibiting viral production. By comparison, parameters specific to viral entry, virion assembly, and virion release were less sensitive and therefore are less promising as targets for inhibiting viral production. The model further identifies potential combination targets that would cooperatively inhibit viral production. For example, the combined effects of targeting both the stepping rate of the host ribosome, &'(% #)* , and the binding rate of RdRp, !" #$#% , may halt the viral cycle even with modest 10X effects. Such a pairwise analysis would be difficult to exhaustively test experimentally, especially in the clinic, since there are 16 2 = 256 possible combinations.

In addition to identifying novel target opportunities within the viral cycle, biophysical modeling may also provide insight into current and emerging therapeutic approaches. Several existing antiviral drugs are being evaluated for their efficacy in treating COVID-19 (16) . It is interesting to note that remdesivir, which was recently approved for emergency use in the U.S. and Japan, acts to disrupt genome transcription by interfering with the viral RdRp (17, 18) , and thus is one example of a therapeutic intervention that interferes with an area of high sensitivity identified by the model. By contrast, hydroxychloroquine, which inhibits viral entry by increasing endosomal pH and affecting terminal glycosylation of the ACE2 receptor (19) , is predicted by the model to be less likely to be effective since drugs that act on viral entry would require exceptionally high suppression to achieve appreciable effects on viral production. Viral entry inhibitors have been used to treat HIV (20) and influenza (21) , therefore it may yet be feasible to target viral entry.

Additionally, we note that therapeutics predicted to be less effective in the viral cycle model, may have potent effects elsewhere in disease progression, e.g. in the immune response. Thus, ineffectiveness in inhibiting viral production does not preclude therapeutic effectiveness overall. regulators of Sigma1 and Sigma2 receptors. Based on our modeling, we predict that therapeutic targeting of the Sigma1 and 2 receptors is not likely to be effective as it would presumably interfere with the virion assembly and release steps, which are relatively insensitive (Fig. 3D ).

By contrast, we predict that targeting protein translation is more likely to be effective due to the high sensitivity of viral cycle time to translation-associated parameters (Fig. 3D ). Everything else being equal, the model predicts that transcription inhibition combined with translation inhibition would be an especially effective combination ( Fig. 4B-C) . Altogether, our model provides a framework for understanding viral cycle dynamics and identifying the therapeutic opportunities that are most likely to be effective in inhibiting viral production. 

The authors thank David Largaespada and Jonathan Sachs for helpful discussions. interests. Data and materials availability: All computer code developed in this manuscript will be made available upon reasonable request to the corresponding author.

The system of ODEs describing the viral cycle was solved using the ode15s solver in Matlab (R2019a; The Mathworks, Natick, MA).

Upon initialization the model is assumed to have a single viral particle (SARS-CoV-2) bound to angiotensin-converting enzyme 2 (ACE2) on the cell membrane (SCoV2-ACE2). SARS-CoV-2 is internalized into endosomes as the spike protein is cleaved by transmembrane protease, serine 2 (TMPRSS2) at a first order-rate (kTMP). 

After the full-length genomic RNA (gRNA) is released and uncoated, host ribosomes bind to open reading frames to begin translation of pp1a and pp1ab. In each instance, transcription and translation is modeled as a multistep process (Figure 1; inset) , similar to that outlined in (26).

Initial binding of the enzyme (Ribosome or RNA-dependent RNA polymerase) to its respective substrate (RNA) is assumed to be irreversible and is the product of the second-order association rate (kon) and the concentrations of the enzyme and its substrate.

ii.

The enzyme completes the primer sequence at rate kPrime, which is determined by the stepping rate of the respective enzyme (kStep) and the length of the primer sequence (l); kPrime = kStep/l. This first step is fast (~0.5-1 s), and once completed the substrate is released such that multiple enzymes can bind to a single strand of RNA. The actively polymerizing translation or transcription complex (T-SE) then continues through the elongation process.

For each active T-SE, the rate of termination (kTerm) is proportional to the length (l) of the sequence and the stepping rate; kTerm = kStep/l. Upon termination, the enzyme unbinds from the substrate and the product is released.

For the specific example of translating pp1a/1ab by the host ribosomes, this multistep process results in the following equations

(Eq. 5) (Eq. 14)

Here, r is the fraction of transcription complexes producing full-length gRNA as opposed to sgRNA. sgRNA is produced at a faster rate due to the shorter sequence length such that where p0 is the baseline value of the specific parameter.

Pairwise sensitivity analysis was performed using a similar approach to that described in (15) Doing so assured higher scores were assigned to those combinations exhibiting high sensitivity over a small range of values, the ideal characteristic for targets of therapeutic intervention.

Individually, some parameters are insensitive while others are highly sensitive ( Figure 3A-C) .

Therefore, we sought to assess whether high-scoring pairwise combinations were simply the combined effects of two sensitive parameters or if there was some amount of cooperativity occurring when both were targeted. We approximated parameter cooperativity as the difference between the pairwise score and the sum of the individual scores according to

Thus, cooperative pairs will have a positive value according to Eq. 40, while those that are anticooperative will have a negative value.

To simulate the effects of a small molecule inhibitor on individual parameters we scaled individual parameters (p) according to a Hill-function Tables: Table 1 S Length of N structural protein 420 aa (12, 14) [ ] a Total ribosome concentration in the cell 4 μM

Fit to the total number of virions (29), constrained approximating ~10 6 total ribosomes and a host cell volume of ~1000 μm 3 (30, 37) 

Coronavirus disease (COVID-19) Highlights

Epidemiological and clinical characteristics of 99 cases of 2019 novel coronavirus pneumonia in Wuhan, China: a descriptive study

Clinical course and outcomes of critically ill patients with SARS-CoV-2 pneumonia in Wuhan, China: a single-centered, retrospective, observational study

SARS-CoV-2 Vaccines: Status Report

The Current Status of Drug Discovery and Development as Originated in United States Academia: The Influence of Industrial and Academic Collaboration on Drug Discovery and Development

In-vitro resistance to zidovudine and alpha-interferon in HIV-1 isolates from patients: Correlations with treatment duration and response

Treatment with Indinavir, Zidovudine, and Lamivudine in Adults with Human Immunodeficiency Virus Infection and Prior Antiretroviral Therapy

Molecular biology of severe acute respiratory syndrome coronavirus

Human Coronavirus: Host-Pathogen Interaction

Kinetic Modeling of

Sars-cov-2 (Covid-19) by the numbers

A pneumonia outbreak associated with a new coronavirus of probable bat origin

Analysis of therapeutic targets for SARS-CoV-2 and discovery of potential drugs by computational methods

Determinants of Maximal Force Transmission in a Motor-Clutch Model of Cell Traction in a Compliant Microenvironment

Remdesivir and chloroquine effectively inhibit the recently emerged novel coronavirus (2019-nCoV) in vitro

Broad-spectrum antiviral GS-5734 inhibits both epidemic and zoonotic coronaviruses

Coronavirus susceptibility to the antiviral remdesivir (GS-5734) is mediated by the viral polymerase and the proofreading exoribonuclease

Chloroquine is a potent inhibitor of SARS coronavirus infection and spread

HIV entry inhibitors

Prophylaxis and Treatment of Influenza