key: cord-0782260-uy4qtu4k
authors: Conway, J. M.; Abel zur Wiesch, P.
title: Remdesivir to treat COVID-19: can dosing be optimized?
date: 2021-06-18
journal: nan
DOI: 10.1101/2021.06.16.21258981
sha: 7ff708c906d71717d859e7ad8c97f6aeae018a66
doc_id: 782260
cord_uid: uy4qtu4k

The antiviral remdesivir has been approved by regulatory bodies such as EMA and FDA for the treatment of COVID-19. However, its efficacy is debated and toxicity concerns might limit the therapeutic range of this drug. Computational models that aid in balancing efficacy and toxicity would be of great help. Parametrizing models is difficult because the prodrug remdesivir is metabolized to its active form (RDV-TP) upon cell entry, which complicates dose-activity relationships. Here, we employ a computational model that allows predicting drug efficacy based on the binding affinity of RDV-TP for its target polymerase in SARS-CoV-2. We identify an optimal infusion rate to maximize remdesivir efficacy. We also assess drug efficacy in suppressing both wild-type and resistant strains, and thereby selection of resistance. Our results differ from predictions using prodrug dose-response curves (pseudo-EC50s). We expect that reaching 90% inhibition (EC90) is insufficient to suppress SARS-CoV-2 in lungs. While standard dosing mildly inhibits viral polymerase and therefore likely reduces morbidity, we also expect selection for resistant mutants for most realistic parameter ranges. To increase efficacy and safeguard against resistance, we recommend continuing remdesivir use with companion antivirals and/or with dosing regimens that substantially increase the levels of RDV-TP.

In November 2020, the first ACTT-1 study results were released showing that the 28 antiviral drug remdesivir (commercial name Veklury) had some efficacy in treating 29 COVID-19, specifically in shortening the time to recovery in adults who were 30 hospitalized with COVID-19 and had evidence of lower respiratory tract infection [1] . 31 It was mid-pandemic and as there were, at the time, no therapeutic agents shown to be 32 efficacious against COVID-19, study results were very welcome news. Remdesivir had 33 already been granted emergency usage approval by large organizations such as the 34 European Medical Association (EMA)[2] and the US Food and Drug Administration 35 (FDA) [3] . This approval was granted based largely on evidence that remdesivir 36 successfully prevented disease in rhesus macaques infected with Middle East 37 respiratory syndrome coronavirus (MERS-CoV), which is closely related to SARS-CoV-38 2, the virus associated with COVID-19 [4] and preliminary results ACTT study results 39 showing remdesivir accelerated recovery from advanced COVID-19 [5] . 40 It is precisely due to these high level of resistance that adamantanes are no longer recommended for 96 treatment of influenza A [29] . 97 Already there is documentation of emergent RDV resistant SARS-CoV-2 in an immunocompromised 98 patient being treated with RDV for . This observation matches expectations from in vitro 99 studies [31, 32] . Specifically, RDV inhibits the SARS-CoV-2 RNA-dependent RNA polymerase (RdRp, 100 encoded by nsp12-nsp7-nsp8), and mutations in RdRp can decrease sensitivity to RDV. What is most 101 troubling is that, in vitro, these mutations leave viral fitness largely unaffected [31] [32] [33] . Thus as we will 102 show, resistance can easily be selected for by some RDV drug regimen. While at this time there is limited 103 concern that resistant strains will transmit or become dominant, as is the case for amantadane-resistant 104 strains of influenza A, since RDV is administered in hospital only, acquired RDV resistance of SARS-CoV-105 2 in a host can limit the capacity of RDV to accelerate viral clearance and improve clinical outcomes. 106 In the following, we describe our model of PK and PD of RDV and its intracellular active metabolite 107 RDV-TP. Referencing estimates for rates of viral replication in the lower respiratory tract (LRT) and upper 108 respiratory tract (URT) [34] , we show efficacy of current treatment regimen. Note that since we parametrize 109 our model using PK parameters from plasma rather than tissues [25] , our results represent a best-case-110 scenario. We then derive from our model an optimal dosing rate and show that at this rate, one can achieve 111 RDV-TP concentrations sufficient to fully suppress spread within the LRT, but not the URT. We therefore 112 conclude that RDV will serve best as a companion therapy. Finally we show the importance of careful 113 dosing by demonstrating our model predictions on the broad regime of drug regimen that will select for 114 RDV resistant variants. 115

2.1 Pharmacokinetic model 117

We develop a PK model to describe the distribution in the body of the remdesivir (RDV) prodrug and 118 its active triphosphate metabolite GS-443902, (RDV-TP) parametrized using data from Humeniuk et al. 119 (2020) [15]. We focus on these two components because the metabolic pathway leading from extracellular 120 RDV to intracellular RDV-TP is not yet confirmed [15] [16] [17] . However, there is consensus that intracellular 121 RDV-TP is the active form of the drug [16] [17] [18] .

122 Examination of the available data suggests nonlinear behavior. Notably, RDV shows biphasic decay, 123 with a rapid drop in concentration following termination of RDV infusion. Further, reportedly the half-life 124 of RDV-TP in PBMCs varies with dose size and duration of infusion, as does the peak concentration (note 125 that, to our knowledge, there is no available longitudinal data on GS-443902). We are therefore motivated 126 to develop a nonlinear model to describe their dynamics. The model equations are given in equation (1), 127 where R represents the concentration of remdesivir (RDV) in plasma, P in the periphery, and A represents 128 the intracellular concentration of the active metabolite RDV-TP. 129

(1) 131

Remdesivir is infused at a constant rate with duration , where is the infusion 133 duration. We model the short infusion using a Heaviside function, 134 135 RDV in plasma, R, diffuses to the periphery at rate , returns from the periphery at rate k, and is 136 eliminated at rate . RDV in the periphery, P, returns is eliminated at rate . RDV in plasma, R, is also 137 absorbed into cells and converted through a series of reactions to the active metabolite A. In absence of 138 definitive reactions and longitudinal data on intermittent steps, we model this process using a Hill function 139 with rate d and Hill coefficient 2. A is eliminated linearly at rate and nonlinearly at rate , again 140 modeled with a Hill function with Hill coefficient 2. 141 d R dt

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We estimate model parameters using the Nelder-Mead algorithm as implemented by the "optim" 142 function in R. Specifically we use longitudinal RDV concentration measurements in the plasma following 143 single-dose administration ([15] , Figure 1 and Figure 2 ) in addition to PBMC pharmacokinetic parameters 144 ( , Cmax, C24, and t1/2) of RDV-TP in the single-ascending-dose study in Humeniuk et al. [15] . 145 Parameter estimates are provided in Table 1 and details on the fitting are provided in Supplementary 146 Materials Text S1. We show how our model fits compare with the data in Figure 1 and Supplementary 147 Materials Figure S1 and Table S1 . . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

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The parameters β and k also implicitly include the transition with apparent volumes since the ODEs represent 164 dynamics of drug concentrations. That is, k=(drug transport rate)*Vp/Vr.

To the best of our knowledge, the IC50 or EC50 of RDV-TP has never been determined experimentally. 168 We therefore assume that the production of new virions is inversely proportional to the number of occupied 169 binding sites in the viral target, the polymerases producing a nascent RNA chain. The half-life of 170 intracellular RDV-TP is very long, such that the binding should be in equilibrium and the equilibrium 171 binding constant KD is sufficient to calculate target occupancy. In the absence of other data, we use the 172 predicted KD as derived via the binding energy from molecular modeling studies (KD=3.6µM, [35] ). In HCV, 173 the directly measured IC50 of RDV-TP was close to this value (5.6 µM) [36] . Importantly, we here define the 174 target as all potential insertion sites where RDV-TP could integrate into the nascent RNA chain and thereby disrupts 175 the production of a functional viral genome. In reality this process is very complicated [36] . Here, we use a very 176 simplified approach to be able to work with the available data-for more complicated approaches, we do not have enough 177 reliable parameter measurements yet. Thus, we assume that the antiviral efficacy of RDV-TP is at its EC50 when 178 the intracellular concentration is exactly at the KD. (2) 183 184 where [RDV-TP] is the concentration of RDV-TP and KD the affinity as described above. As stated 185 above, we assume here that the production rate of new virions, is inversely proportional to foccupied . In 186 standard models of viral within-host dynamics, R0, the number of new cells an infected cell infects, is 187 proportional to the viral production rate [37] . We therefore assume that the effective viral reproductive 188 number depending on the drug concentration, Rd, depends on R0 and the amount of free target:

189 190 Note: The parameters β and k also implicitly include the transition with apparent volumes since the ODEs represent dynamics of drug concentration. That is, k=(drug transport rate)*Vp/Vr.

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The copyright holder for this preprint this version posted June 18, 2021. Resistant strains have a lower effective affinity, either because mutations lead to reduced binding, or 199 because excision repair removes RDV-TP from the nascent RNA chain. Since the affinity constant KD is 200 inversely correlated to affinity, the effective KD,res of the resistant strain must be larger than the one for the 201 wild-type, KD,wt. This results in a lower target occupancy for the resistant than the wt strain at the same 202 concentrations of RDV-TP ( Figure 2a Wild Type 224 225 This means that less drug is needed when KD becomes small (and therefore drug-target affinity large), 226 and more drug is needed when R0 rises (and therefore the virus replicates more).

227 The minimal effective concentration for resistant strains is given by 228 229

(6) 230 231 The latter is also the highest dose that still selects for resistance, i.e. the upper limit of the resistance-232 selection window in Figure 2b . 

While the dose-response curve of RDV-TP has never been measured in vitro, there are several 250 publications that investigated the dose-response relationship and EC50 of the parent drug remdesivir in 251 vitro as measured by the inhibition of viral production. This has also been referred to as a "pseudo-EC50" 252 because it does not reflect the molecular mechanism of action. Additionally, remdesivir is thermally 253 unstable and rapidly degraded at 37 °C [38] , such that the initial remdesivir concentration is not suitable 254 for obtaining an EC50. As a validation step, we set out to investigate whether our PK model (that describes 255 the metabolization of RDV to RDV-TP and cell entry) together with our PD model can reproduce realistic 256 estimates for the pseudo-EC50 (Figure 2 and Supplementary Materials Figure S2 ). It is important to note 257 that our PK model was fitted to RDV-TP levels in PBMCs, which are not primary targets for SARS-CoV-2 258 but a proxy for intracellular concentrations because they can be easily obtained. Also, EC50s and RDV-TP 259 content strongly depend on the cell type [39] . However, our estimate of 0.17 µM is well within the range of 260 reported pseudo-EC50 values of 0.01 µM in isolated human epithelial airway cells, 0.28 µM in Calu cells 261 and 1.65 µM or 0.77 µM in Vero E6 cells [39, 40] . 262

3. Figure 3a illustrates the pharmacokinetics of RDV and 270 

Our results thus indicate that the standard dosing regimen of RDV fails to suppress viral replication 282 in either the URT or LRT. In fact, it lowers the viral production rate by an average of ~70%, where at least 283 88% would be necessary to suppress viral replication in the URT in an average patient. However, our 284 results also indicate the RDV is not entirely ineffective, it is only dosed suboptimally. 285 286

Using our nonlinear model equation (1), we can predict an RDV dosing rate that would approximately 288 maximize the intracellular active metabolite RDV-TP, thereby maximizing efficacy of RDV. RDV data [15] 289 ( Figure 1a&b) shows that plasma RDV achieves steady-state rapidly after initiating the infusion, and decays 290 very rapidly after the infusion ends. We therefore use the RDV steady-state from equation (1), , to then 291 maximize the amount of RDV ultimately converted to RDV-TP, , as a function of the dosing 292 rate . Details are provided in the Supplementary Materials Text S1. Thus we predict with our 293 model that a dosing rate of approximately 168 mg/h maximizes intracellular RDV-TP, thereby maximizing 294 the efficacy of RDV therapy for COVID-19. Thus for example, if we a 1-hour infusion is planned, a total 295 dose of approximately 168 mg should maximize the drug efficacy, while for 2-hour infusion or 30-minute 296 infusions, total doses of approximately 336 mg or 84 mg, respectively, would maximize RDV drug efficacy. 297 In the following, we use this optimal infusion rate (rounding both duration and dosing) to explore the 298 efficacy of several dosing regimens. 299 300

Our results indicate that RDV is currently underdosed. We therefore set out to investigate the highest 302 daily dose tested in phase I studies, 225 mg, infused at an optimal rate (80 min). Again, we assess a 5 day 303 treatment regimen. We find (Figure 4 ) that this dosing regimen performs better. However, viral replication 304 would also in this case only be suppressed in the URT at peak concentrations. In the LRT, the necessary 305 concentration would never been reached. 

To the best of our knowledge, it is currently unclear whether RDV toxicity is mediated by RDV itself 316 or any of its metabolites, and whether this toxicity is correlated to peak concentrations, average exposure 317 or time that the concentration exceeds a certain threshold. In addition to hepatotoxicity, side effects that 318 peak during the time of infusion have been described [41] . This might hint that RDV toxicity is driven by 319 is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 18, 2021. ; peak RDV concentrations in plasma. If this was true, one could keep the peak concentration of RDV in 320 plasma constant but maximize intracellular RDV-TP concentration by extending the infusion time. Here, 321 we investigate which RDV doses infused at an optimal rate would allow viral suppression in the upper 322 and lower respiratory tract, respectively. We find that 500 mg infused over 3 h would suppress viral 323 replication in the upper respiratory tract (Figure 4 c,d,e & f) . For suppressing viral replication in the lower 324 respiratory tract, 1350 mg RDV would have to be infused overnight (8 h). 325 At this time point, it is entirely unclear whether RDV toxicity is indeed mediated by peak plasma 326 concentrations and whether such dosing regimens would be safe. However, our results do indicate that 327 RDV therapy could be further optimized if safe and calls both for dose ranging studies and clarification 328 which metabolites contribute to toxicity. 329 330

As mentioned in the introduction, a mutation conferring mild resistance (2.5x increased EC50) was 332 described emerged in a remdesivir-treated patient [31] [32] [33] . This mutation did not carry a detectable fitness 333 cost. If this mutant has no fitness costs in all relevant environments in the host and during transmission, 334 we would expect it to arise quite frequently in remdesivir treated patients and ultimately to spread between 335 patients, irrespective of mitigation strategies. Resistance mutations without fitness costs in vitro have been 336 described in other anti-infectives [42] , but frequently they do not spread epidemiologically, hinting at 337 fitness costs in vivo and/or during transmission. Mutations conferring higher levels of resistance to 338 remdesivir but a significant (but unspecified) fitness cost in vitro have been described already before the 339 pandemic in the very closely related MERS virus [43] . Generally, spontaneous resistance mutations can 340 lower the efficacy of antiviral polymerase inhibitors up to 20x [44] . When resistant mutants carry a fitness 341 cost, their spread can more easily be mitigated. A useful concept for this is avoiding drug concentrations 342 in the resistance selection window (see methods section 2.3). The resistance selection window describes 343 antiviral concentrations which are high enough that the resistant virus spreads better within host, but low 344 enough that the resistant virus is not eradicated, i.e. antiviral concentrations that select for resistance. Figure 345 5 illustrates this concept with arbitrary resistance mutations that carry a 20% fitness cost and have a 5x or 346 20x reduced susceptibility to remdesivir, either because of reduced drug-target affinity or because of 347 increased excision repair (the latter would increase the drug-target dissociation rate). 

Although there are case reports of resistance, we do not have a good overview of potential RDV-357 resistant mutations. We therefore first assess the minimal fitness with which newly emerging resistant 358 mutants can be selected for (equation 8) with a range of reduced drug-target binding. Figure 6a . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 18, 2021.

that for within-host R0 larger than two, resistance mutations may carry more than 50% fitness costs and yet 360 can be theoretically selected for. This means that there are drug concentrations that are able to select for 361 resistance, even if it is a very narrow concentration range just below the minimal effective concentration 362 for the resistant strain. Importantly, R0 is likely much larger than 2, it has been estimated to be 8.5 (7). The x-axis shows the 370 parameter kres, which describes the factor by which drug-target binding is decreased by a resistance mutation, the y-371 axis the relative fitness. In this work, we developed a PK/PD model that allows predicting the treatment efficacy of remdesivir, 384 which is currently the only approved antiviral to treat COVID-19 patients. In contrast to earlier work, our 385 model is built on clinical data from phase I rather than extrapolated to human patients from preclinical 386 murine data. Our model predicts that remdesivir treatment efficacy could be substantially improved by i) 387 optimizing the infusion rate and ii) increasing the overall dose. 388 Typical pharmacodynamic models rely on fitting empirical sigmoidal dose-response curves to data 389 obtained in vitro. For remdesivir, this approach is difficult, because remdesivir is a prodrug and has to be 390 converted to its active form, RDV-TP upon cell entry [36] . Furthermore, remdesivir is very unstable and 391 rapidly decays at temperatures used in cell culture (37 °C), such that over the time course of an experiment 392 (15-48 h), only a miniscule fraction of the originally used drug concentration is left [38] . Thus, the measured 393 EC50s from cell culture have also been termed "pseudo-EC50s" [45] . It is difficult to use these pseudo-EC50s 394 directly in PK-PD models because remdesivir does not follow the same thermal degradation in vivo (rather, 395 remdesivir decay is described by a pharmacokinetic model) and because diffusion barriers and the 396 necessary metabolic steps of drug activation complicate the relationship between extracellular remdesivir 397 and intracellular RDV-TP. Thus, using only plasma remdesivir levels coupled to this pseudo-EC50 will 398 likely give inaccurate results. Therefore, we employ a pharmacokinetic model to predict the intracellular 399 concentration of RDV-TP and then use RDV-TP target engagement calculated based on a predicted affinity 400 constant from structural studies [35] . Although this approach makes multiple assumptions, we find that 401 our model accurately predicts EC50s measured in cell culture using extracellularly supplied initial 402 remdesivir concentrations. . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 18, 2021. ;

However, the EC50 alone is not enough to predict optimal therapy, since it might be necessary to 404 achieve very high levels (not only half-maximal) to suppress viral spread within host. A typical target 405 would be achieving 90% viral suppression (EC90). Here, we use the speed with which SARS-CoV-2 spreads 406 through the body (within-host R0) to determine how much viral replication has to be suppressed to clear 407 the virus. While we expect that the EC90 is sufficient in the upper respiratory tract where the virus spreads 408 less quickly, we expect that 96.5% target binding and therefore viral suppression are needed to inhibit viral 409 replication in the lower respiratory tract. 410 Based on our pharmacokinetic model, which is calibrated to RDV-TP concentrations in blood (PBMC) 411 and not lung tissue, we expect that the current standard dosing regimen fails to suppress viral replication 412 in both the upper and the lower respiratory tract. Lung tissue concentrations are likely even lower, such 413 that our estimates are conservative [25] . 414 Nevertheless, our results do not indicate that remdesivir is ineffective, they indicate that the current 415 dosing has room for improvement if toxicity allows. This is in line with clinical trials that report a shorter 416 time to recovery [1, 46] , newer meta-analyses that support a slightly reduced mortality [7] and recent 417 findings that the viral load declines more quickly in patients receiving remdesivir [11] . We therefore would 418 like to argue for more dose-ranging and dose-fractionation trials. To minimize toxicity, it would also be 419 important to understand whether remdesvir itself or any of its metabolites drive toxicity, and whether this 420 toxicity correlates best with peak concentrations (Cmax) or average exposure (AUC). 421 Remdesivir resistance mutations have been characterized both clinically and experimentally. 422 Unfortunately, one mutation conferring mild resistance does not carry any fitness cost in vitro [31] [32] [33] . 423 Moreover, our model predicts that the current standard regimen strongly selects for resistance to 424 remdesivir for a vast majority of the credible parameter space. We would therefore argue for increasing 425 efforts to find potential resistance mutations in patients treated with remdesivir. Combining remdesivir 426 with one or more other antivirals would not only improve outcome, it likely would also reduce resistance 427 evolution [19] [20] [21] [22] [23] . This might be especially important if remdesivir is used as a template to design new 428 compounds with increased efficacy [47] . Resistance against older, less effective anti-infectives often 429 provides a stepping stone to resistance against improved but similar compounds [48] .

430 Taken together, our work indicates that remdesivir is expected to be mildly effective and therefore a 431 useful companion drug in COVID-19 treatment. However, dosing should be improved and/or antiviral 432 companion drugs should be employed to safeguard against resistance. 433

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Classic Reaction Kinetics Can Explain Complex Patterns of Antibiotic Action

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