The main international guidelines indicate DTG/3TC therapy as one of the preferred regimens for people living with HIV (PLWH), due to its observed efficacy in randomized clinical trials. However, information in real-life cohorts is relatively scarce for first-line use.st, 2020. Virological failure (VF) was defined as 2 consecutive HIV RNA viral load (VL) >50 copies/mL.A retrospective multicenter study of adult PLWH starting DTG+3TC as a first-line regimen before January 31135 participants were included. Treatment was started without knowing baseline drug resistance testing (bDRT) results in 71.9% of cases, with baseline resistance mutations being later confirmed in 17 patients (12.6%), two of them with presence of M184V mutation. Effectiveness at week 48 was 85.2% (CI95%: 78.1–90.7%) (ITT missing = failure [M = F]) and 96.6% (CI 95%: 91.6–99.1%) . Six patients (4.4%) discontinued treatment. One developed not confirmed VF after discontinuing treatment due to poor adherence; no resistance-associated mutations emerged. Three discontinued treatments due to central nervous system side effects (2.2%), and two due to a medical decision after determining the M184V mutation in bDRT. Finally, 14 (10.4%) were lost to follow-up, most of them due to the COVID-19 pandemic.In a real-life multicenter cohort of ART-naïve PLWH, treatment initiation with DTG + 3TC showed high effectiveness and favorable safety results, comparable to those of randomized clinical trials, without treatment-emergent resistance being observed through week 48. Starting treatment before receiving the results of baseline drug resistance testing did not have an impact on the regimen’s effectiveness. The main international HIV/AIDS treatment guidelines recommend offering antiretroviral treatment (ART) to all people living with HIV (PLWH) as soon as possible. Although classic ART initiation regimens generally contain two nucleoside reverse transcriptase inhibitors (NRTIs) as core therapy, plus a third major agent –3, in reAlthough the emergence and development of combination antiretroviral treatment has improved life expectancy for PLWH, with HIV itself becoming a chronic infection, it has also given rise to an increased incidence of HIV-associated comorbidities, including serious non-AIDS events (SNAEs) –9. As thIn this context, DTG/3TC therapy is currently recommended as one of the preferred treatments for PLWH. However, information in real-life cohorts is still scarce. Our aim is to evaluate the effectiveness and tolerability of DTG/3TC in treatment-naïve adult PLWH from a a multicenter real-life cohort.st, 2020, were included. Patients taking DTG and 3TC as separate pills or DTG/3TC as a single-tablet regimen were included.We carried out an observational, two-phase, multicenter study across eight centers in Spain. The first phase was a retrospective cohort with 48-week follow-up from initiation of treatment (second phase will continue a prospective follow-up to 96 weeks). All ART-naïve adult PLWH who initiated DTG+3TC as first line ART regimen in the participant centers before January 31Baseline demographic data, such as gender, country of origin, age, risk factors for HIV infection, and baseline HIV-related data such as CD4+ cell count, CD4/CD8 ratio, HIV-1 RNA viral load, genotypic drug resistance testing and other biochemical parameters including lipid profile and hepatic and renal function were collected. Follow-up visits after therapy initiation included appointments at 4, 12, 24 and 48 weeks .). An additional per-protocol analysis was performed excluding those participants who were lost to follow-up and those changing therapy due to the presence of M184V mutation. Virological failure (VF) was defined as two consecutive HIV RNA >50 copies/mL. As Spanish national guidelines allows starting ART without having the results of baseline HIV genotype testing, we recorded the proportion of patients who started ART without this result according to routine clinical practice at each hospital [Adverse events (AEs) registered at the follow-up visits were recorded. The primary endpoint was the proportion of participants with viral suppression (HIV RNA <50 copies/mL) at week 48, using an intention to treat (ITT) analysis considering missed cases  as failures , and the study was registered at ClinicalTrials.gov (NCT04638686). Data for the study were collected retrospectively from patients’ medical records, anonymized, and entered into an on-line electronic database. All research was carried out in accordance with the right to privacy, as stipulated in the Organic Regulation (EU) 2016/679 of the European Parliament and of the Council of April 27, 2016 on data protection (GDPR), on the protection of personal data, and the Declaration of Helsinki. A waiver of consent (for retrospective follow-up) from the Ethics Committee was granted as only de-identified data were extracted from clinical records.Categorical variables were presented as frequencies and were compared using Fisher’s exact test or Pearson’s chi-squared test as appropriate; continuous variables were presented as mean and standard deviation or median and interquartile range (IQR) and were compared using the Student’s t test or the Mann-Whitney U test. Comparisons between baseline and follow-up variables were performed with the Wilcoxon signed-rank test. All statistical analyses were performed using IBM SPSS version 20 and a significance level of .05.This data has been previously partial communicated in XII Spanish HIV Conference in 2021 .3 (3 with < 200 cells/mm3). Thirty-eight (28%) of them had occasionally taken recreational drugs, while 14% reported practicing chemsex.One hundred and thirty-five participants were included. Baseline characteristics are described in Treatment was started before receiving the results of baseline drug resistance testing (bDRT) in 71.9% of cases, with baseline resistance mutations posteriorly confirmed in 17 (12.6%), two of them with a M184V mutation. In one other case, an integrase inhibitor resistance-associated mutation (RAM) (G163K) was present, although this mutation does not appear to reduce susceptibility to DTG. A total of five bDRTs showed nucleoside RAMs , 12 non-nucleoside RAMs  and one, a protease inhibitor RAM (82C) . TreatmeEffectiveness at week 48 was 85.2%  and 96.6%  in the ITT (M = F) and in the per-protocol analysis respectively The proportion of participants with plasma HIV-1 RNA <50 copies/ml through week 48 by ITT (M = F) analysis is illustrated in The median time from diagnosis to treatment initiation was six weeks (IQR: 3–14). The median CD4+ and CD4/CD8 T-cell ratio increase was 256 cells/mm3 (IQR 157–463 cells/mm3) and 0.28 (IQR 0.10–0.50) respectively, and the median decrease in the estimated glomerular filtration rate was 11.7 ml/min (IQR 5–24.8 ml/min), with all values remaining above 70 mL/min. There were no significant changes in the lipid profile.3, all of whom continued treatment with DTG/3TC at week 48. All patients with more than 100,000 copies/mL continued treatment with DTG/ 3TC at week 48 except two who were lost to follow-up.In the stratified analysis by age, gender, baseline HIV-1 viral load and CD4+ cell count we observed several differences, although without statistical significance . Only thOur findings reflect a high effectiveness and good safety profile for DTG/3TC as initial therapy of PLWH up to week 48 analysis. These results are similar to those observed in randomized clinical trials (GEMINI I and II studies) . Only onTo the best of our knowledge, the few similar cohorts reported in the literature –21 show It is important to note that 72% of the participants in our cohort started treatment before receiving baseline drug resistance testing results. We can only compare these figures with those from the recently reported STAT study , 27, ThiThe only case which we have considered virological failure was a patient who stopped treatment of her own accord, with a single viral load > 200 copies/mL observed prior to changing therapy. After receiving other therapies, this patient resumed treatment with DTG/3TC, without further lack of optimal adherence, maintaining good HIV-1 viral load control. This finding is consistent with the high barrier to resistance of dolutegravir plus lamivudine observed in phase III randomized controlled clinical trials, where only one case of virological failure has been reported, with treatment-emergent resistance associated with poor adherence to medication .Adverse events were all mild and very infrequent, as reported in other studies. However, due the retrospective design of the cohort, only those adverse events that cause discontinuation of the therapy have been consistently registered, and other adverse events could be underreported.3 to draw conclusions in this subgroup .Stratified analyses in patients with HIV-1 viral load >100,000 copies/mL  do not show significant differences, maintaining similar or higher effectiveness rates than those with viral loads <100,000 copies/mL. These data is similar to those reported in randomized clinical trials and reflect that treatment with DTG/3TC maintains maximum levels of effectiveness even in this setting. Stratified analyses by gender, age and CD4+ level did not show significant differences, although there were too few patients with CD4+ cell counts <200 cell/mmOur study has some limitations. First, the retrospective nature of the study inherently leads to a certain risk of loss of information and channeling bias in the characteristics of patients who start this new kind of therapy. However, as all the participants initiating DTG+3TC as first therapy were included, our cohort reflects the actual group of patients who are starting this treatment in a real-life scenario. A second limitation concerns the loss of participants due to the COVID-19 pandemic. Also, the limited number of participants in the stratified analysis does not permit statistically significant conclusions to be drawn in these scenarios. Another limitation is that our study is a single arm cohort and we do not have the context information when comparing it with a control group. Despite this limitation, we have discussed our results comparing with those of most publications, either randomized clinical trials and cohort studies, and our results endorse the data found by other authors.Despite these limitations, we believe that our work adds some very novel data to the current literature on the use of DTG/3TC therapy in ART-naïve patients. To our knowledge, it is the first multicenter cohort to describe real-life 48-week follow-up data in this setting, in addition to being the largest cohort of treatment-naïve adult patients treated with DTG/3TC outside of randomized clinical trials, and including patients before having baseline drug resistance testing results. We did not observe differences among subgroups . However, the number of them included does not allow us to determine significant differences. Further studies are needed to confirm our results in these underrepresented subgroups, as those with lower CD4+ counts or very high viral loads. It is also necessary to confirm the long-term efficacy and tolerability of the regimen outside of randomized clinical trials.In a real-life multicenter cohort of ART-naïve PLWH, treatment initiation with DTG+3TC showed high effectiveness and safety, similar to that of randomized clinical trials, without treatment-emergent resistance at 48 weeks. Starting treatment without the results of the baseline drug resistance test did not have an impact on the regimen’s effectiveness.A waiver of consent from the Ethics Committee was granted as only de-identified data were extracted from the medical records. Approval was obtained from the institutional research ethics committee . All research was performed in accordance with the General Data Protection Regulation (GDPR) Regulation (EU) 2016/679 of the European Parliament and of the Council of 27 April 2016 on the protection of natural persons with regard to the processing of personal data  and the Declaration of Helsinki.S1 Graphical abstract(TIFF)Click here for additional data file.


Infusion of broadly neutralizing antibodies (bNAbs) has shown promise as an alternative to anti-retroviral therapy against HIV. A key challenge is to suppress viral escape, which is more effectively achieved with a combination of bNAbs. Here, we propose a computational approach to predict the efficacy of a bNAb therapy based on the population genetics of HIV escape, which we parametrize using high-throughput HIV sequence data from bNAb-naive patients. By quantifying the mutational target size and the fitness cost of HIV-1 escape from bNAbs, we predict the distribution of rebound times in three clinical trials. We show that a cocktail of three bNAbs is necessary to effectively suppress viral escape, and predict the optimal composition of such bNAb cocktail. Our results offer a rational therapy design for HIV, and show how genetic data can be used to predict treatment outcomes and design new approaches to pathogenic control. As a rehe virus . Specifihe virus .Recent studies have used bNAb therapies to curb infections by the Simian immunodeficiency virus (SHIV) in non-human primates , and HIVThe principle behind combination therapy with either drugs or antibodies is clear: It is harder for a pathogen population to acquire resistance against multiple treatment targets simultaneously than to acquiring resistance against each target separately. But deciding on combination therapy means navigating an enormous number of possible treatment options.Experimental data from neutralization assays against pseudo-viruses together with modeling and machine learning techniques have been used to statistically characterize the efficacy of bNAbs and their combinations against different variants of HIV . Using tTo characterize viral escape, mechanistic models, partly inspired by previous work on HIV escape from the anti-retro viral therapy (ART), have been developed to explain the dynamics of viremia in patients, following passive infusion of bNAbs. By making a fit to the trial data, these models are used to infer parameters related to the efficacy of a bNAb in clearing virions, reducing viral load and infectivity, and also to infer the characteristics of the HIV and the T-cell populations, such as the initial viral population size, the death rates of uninfected and infected T-cells, and the number of virions released by an infected T-cell . These dEvolution of the HIV-1 population is another key factor to consider in modeling the dynamics and escape of viruses in response to therapy. Studies on population genetics of HIV-1 have found rapid intra-patient evolution and turnover of the virus  and haveIn this study, we present a coarse-grained evolutionary model of viral response to bNAb infusion that uses genetic data of HIV-1 in untreated patient to predict bNAb therapy outcome by characterizing the chances of viral escape from a given bNAb in patients. Specifically, we develop a statistical inference framework that uses the high throughput longitudinal survey of viral sequences collected from 11 ART-naive patients over about 10 years of infection  to charaOur prediction for the viral rebound time in response to a bNAb relies on only a few patient-specific parameters (i.e. the genetic diversity of patients prior to treatment), and is primarily done based on the inferred genetic parameters from the deep sequencing of HIV-1 populations in a separate cohort of ART-naive patient. Therefore, our model could be used to guide therapy trial design with bNAbs against which viral escape variants are previously characterized. To this end, we use our approach to assess a broader panel of nine bNAbs, for which escape sites can be identified from prior deep mutational scanning experiments , to charrebound time—a key quantity that characterizes treatment efficacy within a patient. Although the details of the viremia dynamics, especially at beginning and at the end of the therapy, may be complex  neutral genetic diversity of the viral population, (ii) the mutational target size for escape from the bNAb , and (iii) the intrinsic fitness associated with such mutations. Although viremia traces in clinical trials and growth experiments can be used to model the escape dynamics , they doThe neutral genetic diversity ous work , find thous work .Our inference indicates that the neutral diversity grows over the course of an infection in untreated HIV-1 patients from Methods, . We use We define the mutational target size for escape from a bNAb as the number of trajectories that connect the susceptible codon to codons associated with escape variants, weighed by their probability of occurrences (Methods). The connecting paths with only single nucleotide transitions or transversions dominate the escape and can be represented as connected graphs shown in  variant , Methodsf0. We assume that fitness cost associated with escape mutations are additive and background-independent so the fitness of a variant Since bNAbs target highly conserved regions of the virus, we expect HIV-1 escape mutations to be intrinsically deleterious for the virus , and incInterestingly, we observe the escape variants against different bNAbs to be circulating in the HIV-1 populations from the cohort of ART- and bNAb-naive patients . We use ent from , P on HIV-1 subject to 9 different bNAbs from  3BNC117 , we simuInterestingly, we infer that escape from mono-therapies is almost certain and a combination of at least three antibodies is necessary to limit the probability of early rebound (<56 days) to below 1% . When coThe fitness-limited versus the mutation-limited strategies have different implications for the design of combination cocktails. The small mutational target size of 10E8 makes it the best candidate antibody for mono-therapy among the antibodies we consider because the escape variants against this antibody are less likely to circulate in a patient’s serum prior to treatment. However, in combination, 10E8 appears less often in top ranked therapies than PGT151. PGT151 is unremarkable on its own because of a relatively large target size, but the high cost of escape makes it especially promising in combination therapies. Overall, fitness-limited bNAbs like PGT151 are more effective against high diversity viral populations, while mutation-limited bNAbs such as 10E8 are more effective against low diversity viral populations. Indeed, the best ranked therapy, namely the combination of PG9, PGT151, and VRC01, combines antibodies that target different regions of the virus and also have both types of fitness- and mutation-limited strategies for coverage against the full variability of viral diversities found in pre-treatment individuals  participEscape from bNAbs in multivalent therapy is also influenced by the non-independence of escape pathways. Several of the bNAbs (e.g. 10–1074 and PG121) in this study target the same  epitopes and escape from them is mediated by the same mutations. The sharing of mutational pathways invalidates the assumption of independence and may make our predictions too optimistic. However, the best performing antibody combinations in HIV therapy with passive bNAb infusion has become a promising alternative to anti-retroviral drugs for suppressing and preventing the disease in patients without a need for daily administration. The current obstacle is the frequent escape of the virus seen in mono- and even combination bNAb therapy trials . The keyHere, we have proposed a computational approach to predict the efficacy of a bNAb therapy trial based on population genetics of HIV escape, which we parametrize using high-throughput HIV-1 sequence data collected from a separate cohort of bNAb-naive patients . SpecifiOne key measure of success for a bNAb trial is the suppression of early viral rebound. Our model can accurately predict the rebound times of HIV-1 subject to three distinct therapies , based oCombination therapy with more than two bnAbs (or drugs in ART) has long been shown to be more effective in suppressing early viral rebound, both in theory and practice . In addiThe statistical agreement between our coarse-grained model and the observed distribution of the viral rebound times in trials  implies One strategy to achieve a longer term treatment success is by combining bNAb therapy with ART. One main advantage of bNAb therapy is the fact that it can be administered once every few months, in contrast to ART, which should be taken daily and missing a dose could lead to viral rebound. Although multivalent bNAb therapy reduces the chances of short-term viral escape, viral escape remains a real obstacle for longer term success of a treatment with bNAbs. Alternatively, (fewer) bNAbs can be administered in combination with ART , whereby50 neutralization during treatments, the details of T-cell dynamics during infection . One reason for this discrepancy may be related to the distinct genetic composition of viruses in the two approaches. DMS experiments characterize HIV escape by introducing mutations on a single genetic background  e.g. th, whereasIt should be noted that our analysis in Our approach showcases that, when feasible, combining high-throughput genetic data with ecological and population genetics models can have surprisingly broad applicability, and their interpretability can shed light into the complex dynamics of pathogens subject to therapy. Application of similar methods to therapy design to curb the escape of cancer tumors against immune- or chemo-therapy, the resistance in bacteria against antibiotics, or the escape of seasonal influenza against vaccination is a promising avenue for future work. However, we expect that more sophisticated methods for inferring fitness from evolutionary trajectories may be necessary to capture the dynamical response of these populations.https://github.com/StatPhysBio/HIVTreatmentOptimization  data was obtained from Patient 4 and patient 7 were excluded from the original analysis done in All patients were infected with clade B of HIV, except for patient 6 (clade C), and patient 1 (clade 01_AE). We assessed the robustness of our inference to exclusion of these patients from our analysis in Effect of genomic linkage on the inference of selection. Overall, our inference was not strongly affected by this choice (Model robustness 2 templates of amplicon were associated with the fragments of the envelope (env) protein For our analysis we considered only data reported in single nucleotide polymorphism (SNP) counts. The number of raw SNP counts are the result of amplification and must be converted into estimates for the number of pre-amplification template fragments. Zanini et. al. reported that on average about 10env protein. We use a combination of methods to identify the escape variants for a given bNAb. First, we use deep mutational scanning (DMS) data of HIV-1 in the presence of a bNAb from The starting point for our analysis of HIV response to a given a bNAb is the description of the escape-mediating amino acids in the HIV Escape variants in DMS data are identified as those which are strongly selected for only in the presence of a bNAb. Specifically, we identify escape variants as those which show 3-logs-change in their frequency in the presence versus absence of a bNAb. DMS data reflects in vitro escape in cell culture. However, some of these variants may not be viable in vivo. To identify the reasonable candidates of escape in vivo, we limit our set to the variants that are also observed in the circulating viral strains of untreated HIV-1 patients from Our analysis of DMS data results in a set of escape mediating amino acids for 10–1074 that is consistent with the escape variants that emerge in response to the bNAb trial . One reaFor the CD4 binding site antibodies 3BNC117 and VRC01, we used additional data to call the escape variants. For 3BNC117, we used a combination of trial-patient sequences , that isThe concentration of viral RNA copies in blood serum is a delayed reflection of the total viral population size Here,  rebound , which eWe use with rate parameter set by the model value of the viral multiplicity Np(t) . We use ormation  and defixp, and the decay rate Here, t time t , given tNote that the viremia measurements have a minimum sensitivity threshold of 20 RNA copies per ml. We treat the data points below the threshold of detection as missing data and if The fitted viremia curves for patients enrolled in the three bNAb trials under consideration are shown in To encode for different viral variants, we specify a coarse-grained phenotypic model, where a viral strain of type We define an individual-based stochastic birth-death model  to captuWe assume that a viral strain of type a for a given variant a, defined as the growth rate of the virus in the absence of neutralizing antibody or competition. Since bNAbs target highly vulnerable regions of the virus, we expect that HIV-1 escape mutations to be in trinsically deleterious for the virus and to confer a fitness cost relative to the susceptible viral variants prior to the infusion of bNAbs. Assuming that fitness cost of escape is additive across sites and background-independent, we can express the fitness of a variant as , where Δ is the cost associated with the presence of an escape mutation at site of variant .We specify an intrinsic fitness fWe assume that growth is self-limiting via a competition for host T-cells. This competition enforces a carrying capacity, which sets the steady-state population size The net growth rate of a variant Because the absolute magnitude of This leads to the following equations for the birth and the death rates:In the presence of an antibody, birth is effectively halted for susceptible variants, resulting in birth and death rate for a susceptible variant so that the susceptible phenotype decays at rate We assume that mutations occur independently at each site,na is the number of type where Of special interest for our analysis is the steady-state density of frequencies, which we use to describe the initial state of the population (before treatment) and to infer selection intensity. In the steady state, the population is fluctuating around carrying capacity ribution  with modf1 is the intrinsic fitness of the variant of interest, f0 is the fitness of the competing variant, where where The logistic dynamics describing a patient’s viremia over time in ni resistant variants of type Using the standard birth-death process generating function theory xi, we can convolve the extinction probability in ni resistant variants from To characterize the probability of extinction for a population of size Using the expressions for the growth in the absence of competition, To treat the full viral dynamics including mutations, and transient competition effects, we can exactly simulate the viral dynamics defined by our individual based model. Below are the key steps in this simulation.At the starting point, we set the population size (i.e. the carrying capacity in the simulations) The input to our procedure is a list of antibodies for which we specify (i) the escape mediating sites for each antibody, and the (invariant) quantities describing (ii) the site-specific cost of escape xi from the stationary distribution We assume that at the start of the simulation, populations are in the steady state and that the potential escape sites are at linkage equilibrium. The approximate linkage equilibrium assumption is justified since the distance between these escape sites along the HIV-1 genome is greater than the characteristic recombination length scale he virus . As a reTo sample from the stationary distribution itself, we define a novel Gibbs-sampling procedure  for gene|σ,θ,θ†) . To charHere, We use these conditional distributions to define a joint Gibbs sampler for n factor , which ifi and escape status; see Algorithm 3 (Appendix 5).We use a Gillespie algorithm to simulate the evolutionary process, where we break up the reaction calculation into two parts: randomly choosing a viral strain We set the intrinsic growth rate (fitness) of the wild-type virus, in the absence of competition to be he virus . We infea curves  in the t/θtv=7.8 . We use Generally, the trial patients show viral populations with larger neutral diversity at the start of the trial compared to the patients enrolled in the high-throughput study of It should be noted that the value of The total rate of birth and death events led to λ . We set asticity . We set Previous work has indicated an order of magnitude difference between the rate of transitions (mutations within a nucleotide class) and transversions (out-class mutations) in HIV . TherefoConsider the set of sequences sampled from a patient’s viral population at a particular time. Two neutral alleles that are linked by a symmetric mutational process env protein, the maximum-likelihood estimator for the transition diversity To estimate the transition diversity, we only use twofold synonymous sites, and treat each site independently but with a shared diversity parameter In In a similar way, the likelihood for the transversion The factor of 2 in the argument of the likelihood accounts for the multiplicity of mutational pathways, e.g. from a Using this likelihood approach, we can infer the neutral diversities /θtv=7.8 . In Figu/μtv=5.6 , which icodon substitution graph.The nucleotide triplets which encode for amino acids at an escape site undergo substitutions which can change the amino acid type and create an escape variant. The changes in the state of an amino acid codon can be modeled as a Markov jump process and can be visualized as a weighted graph where the nodes represent codon states, and edges represent single nucleotide substitutions linking two codon states . In our The codon states can be clustered into three distinct classes: (i) codons which are fatal The mutational target size is determined by the density of paths from the wild-type The functions When discussing the mutational target size of escape from a given bNAb, we refer to the total mutation rate from the susceptible (wild type) to the escape variant as,where the sum runs over all the mediating escape sites Here, we develop an approximate likelihood approach to infer the selection ratio We assume that the probability to sample |σ,θ,θ†) , governeHere,  Peq(x) . It shou Peq(x) . AlthougWe will use the probability density in where the constant factors (const.) are independent of selection, and We use data collected across all time points and from all patients to infer reliable estimates for selection strengths. However, allele frequencies are correlated across time points within patients , and thuwhere Gag and the env proteins of HIV-1 from their prevalences across sequences sampled from different patients||P(t|ξ)). Specifically, we use nq quantiles of the observed data x(i) ~ Q to partition the space of observations into discrete outcomesAlgorithm 5 (Appendix 5) defines the procedure that we use to estimate the Hellinger distance where To simulate data for this analysis, we generate Here, ReboundDisparity is the function defined by Algorithm 5 (Appendix 5); see Given the reservoir-corrected estimate of the diversity For a given bNAb, we draw the selection factor at each of the escape mediating sites from the corresponding Bayesian posterior on The elements of the matrix For each patient in our simulated trial, we then draw diversity These parameters are then used to initialize the state of an HIV population within a patient according to (Appendix 5), and to determine the absolute rates in Algorithm 3 (Appendix 5) for the population evolution according to 1days-1 . The carxt is above 0.8; see Algorithm 3 (Appendix 5). After We evolve a population through time until 56 days have elapsed since treatment, or until the escape fraction relative to the carrying capacity The resulting distribution for rebound times are shown as model predictions in 4 simulated patients. The interdecile quantiles (0.1–0.9) of early rebound (lt56 days) probability over 200 values of scaled selection coefficients Rebound times generated in this fashion were also used to estimate the probability of late rebound to characterize the efficacy of a given bNAb in curbing viral rebound. The probability of late rebound was estimated from 10In our inference of selection , we assuTo test the limits on the validity of our inference procedure, we applied it to in silico populations generated by full-genome forward-time simulations  in the presence and absence of recombination. To do so, we considered an ensemble of ten patients with 100 genomes sampled at 10 time points, and used two diversity parameters ent data .One relevant scenario to consider is the impact of other selected sites in the genome on the distribution of alleles at the escape mediating sites against bNAbs. The sites under a strong constant selection are likely to be already fixed (or at a high a frequency) at their favorable state in the population. However, the strong selection on a large fraction of antigenic sites can be thought as time-varying, due to the changing pressure imposed by the immune system or therapy. To capture this effect, we simulated whole genome evolution in which linked sites were under strong selection  for the selection values The reason that selective sweeps of linked beneficial mutations have only minor effects on our inference of selection for the escape mediating sites is two-fold: First, the primary mechanism by which selective sweeps change the strength of selection at linked sites is via a reduction in the effective population size The second reason for the robustness of our selection inference to linkage is due to the fact that a beneficial allele in a linked locus can appear on a genetic background with or without a susceptible variant, leading to the rise of either variants in the population. As a results, the impact of such hitchhiking remains a secondary issue in inference of selection at the escape sites, for which an ensemble of populations from different patients with distinct evolutionary histories of HIV-1are used.To infer the selection effect of mutations from the longitudinal deep sequencing data of where We find that both of these approaches result in similar posteriors for selection In ibutions  comparedibutions . Here, wRecall that the optimal reservoir factor  in data . We can We can then determine the p-value by estimating the quantile of the observed test statistic sis ξ0=1 . Specifiwhere therwise . The obswise  feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.Our editorial process produces two outputs: (i) Decision letter after peer review:eLife. Your article has been reviewed by 3 peer reviewers, including Kayla Sprenger as Reviewing Editor and Reviewer #1, and the evaluation has been overseen by Miles Davenport as the Senior Editor.Thank you for submitting your article "Design of an optimal combination therapy with broadly neutralizing antibodies to suppress HIV-1" for consideration by The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.Essential revisions:1) The text should be modified to more clearly convey the novelty of the current work, and to better place the current work within the context of the existing literature on bnAb therapy design both from an experimental and computational perspective. Specifically, the conceptual advances that this work offers in terms of methodology and/or success in therapy design over past studies should be made more clear, and additional citations/discussion of existing literature is warranted.For example, combination therapy with more than two bnAbs vs. fewer has long been shown to be more effective in suppressing early rebound. A suggestion is to note this fact and discuss the benefits of clinical corroboration of the model's results – i.e., that this corroboration provides a basis for using the model to interrogate new bnAbs (for which DMS data is available), and/or the combinatorial explosion of higher order cocktails for which we cannot possibly test all combinations.2) Related to the above note, the non-independence of bnAbs is an important point that should be discussed/acknowledged as a potential shortcoming of the model.3) As presented, the deep mutational scanning data is not convincing in its ability to fully characterize the spectrum of escape mutations, given the typical inability of DMS data to probe the low-frequency variants that primarily mediate rebound. More work needs to be done here to ensure/make clear that the predictive power of the approach is strong in this regard.4) More discussion should be focused around specific use cases of the work. Particularly, since the framework is most predictive for early rebound times, it should be emphasized that the results from this work would best translate to, e.g., the design of short term suppressive treatments, rather than therapy efficacy over longer timescales, which would require a more complete characterization.5) More discussion of how the predicted fitness costs compare to the older fitness landscape work would be useful context in the discussion.Reviewer #1 (Recommendations for the authors):General comments/questions:In the Abstract (and Discussion), it is stated that bnAbs may serve as an alternative strategy to antiretroviral therapy against HIV, yet in the Introduction it is stated that augmenting antiretroviral therapy with bnAbs may be a fruitful strategy against HIV. Perhaps highlight the more promising approach of the two for consistency?Line 52 states that prior work on designing bnAb therapies did not consider viral dynamics, yet the following sentence appears to give theoretical examples of just this ("dynamics of viremia"). Was the first sentence referring to prior experimental work?In general, I find the paragraph in the Introduction between lines 52-72 to be a bit unfocused; what are the authors wishing to communicate here? Specifically, regarding lines 58-72, it seems like one could skip straight from line 57 to 73 and it would flow just as well.Line 93: are the authors referring to cancer cells, or cancer-causing pathogens? Do such extensive longitudinal sequence datasets also exist for resistant bacteria and cancer-causing pathogens as for HIV, that would enable translation of this approach to those settings?Line 106-107, Equation 1 appears to model the virus population size as a function of time (N(t)), rather than the rebound time explicitly (perhaps reword slightly?).Line 119: in defining the actual rebound time, T=-γ^-1*logx, it would seem that this is a constant, since γ is a constant, and x is also an inferred constant. If this is correct, why is equation 1 needed? Likely, I am just missing something here!Line 135: it might be helpful to talk more physically about what is meant by the 'birth' and 'death' of a variant (variant completely dies out? Or the variant population declines as a result of bnAb infusion?). Does a single amino acid mutation move a variant a to another type b?Line 155: Is not the mutation rate of HIV well known already? Is the rate inferred by the authors in line with past estimates?-1 vs. 3 days-1 for susceptible viruses, or "slowest process"?Line 156-157: The authors state that the 'fastest process in the dynamics…is the growth rate of susceptible viruses". Should this not say 'resistant viruses", since γ = 1/3 daysLine 174: "mutational target size" is not very intuitive for me. I know it is defined later on lines 211-213, but perhaps this can be summarized or stated more intuitively here, as well as in the Discussion?Lines 178-182: the authors propose to infer mutation and fitness characteristics of escape-mediating HIV variants via sequence data. Work out of Arup Chakraborty's lab at MIT comes to mind on developing HIV fitness landscapes. Would this not offer the same information for parameterizing the birth-death model? Perhaps the potential relevance/connection between those past works and the current work could be briefly discussed.In the section on 'Diversity of the viral population', it seems counterintuitive to me that characterizing only synonymous mutations as a measure of neutral genetic diversity would allow one to determine the 'chance to observe a rare  mutation' (line 185), since this implies a change in the amino acid sequence of the protein. I must not be thinking about this correctly; can the authors please clarify this for me?Lines 222-223: The footprint of a bnAb is often larger than the actual epitope, which may contain both variable and conserved sites . Thus, bnAbs must bind to both residue types. Given this, why do the authors expect HIV escape mutations to be intrinsically deleterious for the virus (implying they occur mostly at conserved sites), vs. occurring at the nearby variable sites that bnAbs also contact? For example, the following paper, https://www.pnas.org/content/115/4/E564, states that "Even for the relatively "conserved" CD4 binding-site region, only mutations at some residues are predicted to incur large fitness costs upon mutations."Line 314: what do the authors classify as 'early rebound'? Below 56 days?Line 330-332: the first part of this statement makes sense to me , but I am not certain about the second part. Wouldn't fitness-limiting and mutation-limiting bnAbs be equally good against low-diversity viral populations?Lines 378-379: Might it be possible for the authors to speculate on how the exclusion of the dynamics of Ab concentration and IC50 neutralization during treatments could affect their results/conclusions?Reviewer #2 (Recommendations for the authors):In Appendix 1, the authors might consider coloring the resistant and susceptible amino acid identities based on the data source . Essential revisions:1) The text should be modified to more clearly convey the novelty of the current work, and to better place the current work within the context of the existing literature on bnAb therapy design both from an experimental and computational perspective. Specifically, the conceptual advances that this work offers in terms of methodology and/or success in therapy design over past studies should be made more clear, and additional citations/discussion of existing literature is warranted.For example, combination therapy with more than two bnAbs vs. fewer has long been shown to be more effective in suppressing early rebound. A suggestion is to note this fact and discuss the benefits of clinical corroboration of the model's results – i.e., that this corroboration provides a basis for using the model to interrogate new bnAbs (for which DMS data is available), and/or the combinatorial explosion of higher order cocktails for which we cannot possibly test all combinations.We thank the reviewers for this comment. We have now reorganized and extended the introduction and the discussion to better reflect prior work in both fitness inference and therapy optimization.In the introduction, we elaborate on various modeling and experimental approaches for bNAb mono and combo therapy design, and describe how our approach is distinguished from the existing work. We have made the following changes in the introduction:“We discuss the modeling and machine learning techniques trained on experimental data from neutralization assays against pseudo-viruses to characterize the efficacy of bNAbs and their combinations against different variants of HIV [R1–R3]. These modeling approaches to optimization view the infection as a static collection of viral strains to be neutralized as opposed to an actively evolving population. We then discuss the mechanistic models that have been developed to explain the dynamics of viremia in patients following passive infusion of bNAbs [R4–R9]. These detailed models use trial data to fit parameters in relation to a bNAb’s efficacy in clearing virions, reducing viral load, etc. These detailed mechanistic models cannot easily generalize from one trial to another in order to predict the efficacy of a new bNAb mono- or combination therapy. We describe how evolution of the HIV population is another key factor to consider in modeling the dynamics of viremia in response to therapy with ART or bNAb. We then present our approach as a coarse-grained evolutionary model of viral response to bNAb infusion that uses genetic data of HIV-1 in untreated patients to predict bNAb therapy outcome by characterizing the chances of viral escape from a given bNAb. Although our model does not accurately reproduce the detailed dynamics of viremia in each patient and lacks the mechanistic insight of richer models proposed previously, it can accurately predict the distribution of viral rebound times in response to passive bNAb infusions – a key measure of efficacy for a bNAb therapy trial. We then emphasize that our prediction for the viral rebound time in response to a bNAb relies on only a few patient-specific parameters , and is primarily done based on the inferred genetic parameters from the deep sequencing of HIV-1 populations in a separate cohort of ART-naive patient. Therefore, we argue that our model could be used to guide therapy trial design by identifying optimal combinations of bNAbs to suppress evolutionary escape of HIV-1 in patients.”In the Discussion we have added the reviewer’s suggestion to the text to argue how our approach can be used to identify combo therapies. From the Discussion section (lines 419-426):“Combination therapy with more than two bNAbs (or drugs in ART) has long been shown to be more effective in suppressing early HIV rebound, both in theory and practice . In addition to corroborating this conclusion quantitatively, we provide a method for assessing new bNAbs for which escape mutations are known. Our method can be understood as a tool to navigate the combinatorial explosion of higher order cocktails for which we cannot possibly test all combinations. By assessing the evolvability of resistance against different combinations we can identify the best therapies to target for clinical trial. Specifically, we show that to suppress the chance of viral rebound to below 1%, we show that a combo-therapy with 3 bNAbs with a mixture of mutation- and selection-limited strategies that target different regions of the viral envelope is necessary. Such combination can counter the full variation of viral diversity observed in patients. We found that PG9, PG151, and VRC01, which respectively target V2 loop, Interface, and CD4 binding site of HIV envelope, form an optimal combination for a 3-bNAb therapy to limit HIV-1 escape in patients infected with clade B of the virus.”2) Related to the above note, the non-independence of bnAbs is an important point that should be discussed/acknowledged as a potential shortcoming of the model.We thank the reviewers for pointing this out. Indeed, using bNAbs that target the same  epitopes in a therapy could lead to physical interference during neutralization, and in those cases the assumption of independence can well be violated. The sharing of mutational pathways invalidates the assumption of independence and may make our predictions too optimistic. Still, our model correctly finds that escape from combinations of bNAbs that target the same epitope is easier due to the fewer necessary mutations. We have now expanded our discussions on this matter in the manuscript:From section Devising optimal bNAb therapy cocktails in the main text (lines 375-386):“Escape from bNAbs in multivalent therapy is also influenced by the non-independence of escape pathways. Several of the bNAbs (e.g. 10-1074 and PG121) in this study target the same  epitopes and escape from them is mediated by the same mutations. The sharing of mutational pathways invalidates the assumption of independence and may make our predictions too optimistic. However, the best performing antibody combinations in Figure 4C target multiple epitopes to reduce the chances of collective escape. Therefore, the assumptions of independent fitness effects and independent mutational pathways in this case are not consequential for the main predictions of our model . in vitro data shown in [R13] suggest that additive and independent effects are the norm, but that small but consistent synergistic effects may imply that our assumption of site-wise independence is conservative. More data on HIV escape from combinations of bNAbs would be informative for further modeling efforts and relevant for long-term therapy design.”3) As presented, the deep mutational scanning data is not convincing in its ability to fully characterize the spectrum of escape mutations, given the typical inability of DMS data to probe the low-frequency variants that primarily mediate rebound. More work needs to be done here to ensure/make clear that the predictive power of the approach is strong in this regard.We agree with the reviewers that the utility and limitations of the DMS data should be more clearly demonstrated. We have included a new Appendix  to compare predictions of rebound time distributions when identifying escape sites from the DMS data versus the trial data. We performed this comparison for the 10-1074 bNAb for which we have access to both the DMS and the trial data. We also included an analysis for a new therapy trial dataset with the PGT121 bNAb [R9]; in the previous version of this manuscript we only had access to the DMS data to characterize escape against PGT121. We should note that two other trial datasets are available for the 3BNC117 and VRC01 bNAbs. However, both of these bNAbs target the CD4 binding site of the env protein and, as noted in the manuscript, the DMS experiments in the presence of these bNAbs are very noisy and cannot be used to reliably identify the escape sites; see Appendix 4 for details.In addition, we have included a discussion on this matter in the Methods section Model robustness, subsection Robustness of rebound time predictions to methods of identifying escape mutations (lines 1104-1121):“Our predictions rely on identifying escape variants against each bNAb, either based on in-vivo trial data and patient surveillance, or in-vitro DMS assays. To test the sensitivity of our results to these methods, we compare the predictions of rebound time distributions when identifying escape sites from the DMS data versus the trial data. In Appendix 4 we perform this comparison for the 10-1074 and the PGT121 bNAbs; we do not include the 3BNC117 bNAb in this analysis since it targets the CD4 binding site of HIV-1and the DMS data is unreliable for identifying escape variants against it. As shown in Appendix 4-Figure 1, both trial-inferred and DMS-inferred escape sites result in good predictions for rebound time distributions. However, its appears that using the DMS-inferred escape sites could lead to a more optimistic prediction for treatment success . This inconsistency may be due to the fact that DMS data is collected in-vitro, and other biological factors could be influencing the in-vivo escape patterns. Moreover, the differences in the genetic composition of the HIV-1strains circulating in patients enrolled in trials and the strains used for the DMS experiments could lead to different epistatic interactions that can enhance or reduce the chances of escape. For a systematic understanding of these differences and limitations, more experiments would be necessary. Nonetheless, DMS data can provides baseline to gauge the efficacy of different bNAbs for therapy and further in-vivo investigation.”We have also included a paragraph in the Discussion section, Limitations subsection on this point (lines 472490):“Our predictions are limited by our ability to identify the escape variants for each bNAb, either based on the in-vivo trial data and patient surveillance, or in-vitro assays such as DMS experiments. In Appendix 4 we compare the accuracy of our predictions for the rebound time distributions of HIV using DMS-inferred versus trial-inferred escape variants against the 10-1074 and the PGT121 bNAbs, and we find good agreements between the two approaches in both cases. However, it should be noted that identifying escape variants from DMS experiments lead to a more optimistic prediction for treatment success during the first 8 weeks of trials . One reason for this discrepancy may be related to the distinct genetic composition of viruses in the two approaches. DMS experiments characterize HIV escape by introducing mutations on a single genetic background [R14–R16] (e.g. the HIV-1 strain BF520.W14M.C2 in [R14]), whereas clinical data contain diverse populations of viruses between and within individuals. It is more likely for diverse viral populations to contain variants in which positive epistasis between escape mutations and the background genome is present. Therefore, it is reasonable to expect that genetic data originating in clinical trials show more pathways of escape, resulting in a faster viral rebound following bNAb infusion. Nevertheless, DMS experiments are less costly for identifying escape variants compared to trials, and they provide a baseline to assess the efficacy of different bNAbs for therapy and further in-vivo investigations. More experiments would be necessary for a more systematic understanding of the limitations of each approach.”4) More discussion should be focused around specific use cases of the work. Particularly, since the framework is most predictive for early rebound times, it should be emphasized that the results from this work would best translate to, e.g., the design of short term suppressive treatments, rather than therapy efficacy over longer timescales, which would require a more complete characterization.We agree with the reviewers that we should emphasize the utility of our approach in designing short-term treatments, which we have included in the Discussion section. We have also added a discussion about combining ART and bNAb therapy for longer term treatments.From the Discussion section (lines 433-455):“The statistical agreement between our coarse-grained model and the observed distribution of the rebound times  implies that many of the mechanistic details are of secondary importance in predicting viral escape. Nonetheless, our approach falls short of reproducing the detailed characteristics of viremia traces in patients, especially at very short or very long times, during which the dynamics of T-cell response or the decay of bNAbs could play a role [R17–R19]. The relationship between the short-term suppression of the virus, which is the focus of this analysis, and the long-term treatment success is complicated by reestablishment of HIV from the latent reservoirs and different modes of intra-host HIV evolution .One strategy to achieve a longer term treatment success is by combining bNAb therapy with ART. One main advantage of bNAb therapy is the fact that it can be administered once every few months, in contrast to ART, which should be taken daily and missing a dose could lead to viral rebound. Although multivalent bNAb therapy reduces the chances of short-term viral escape, viral escape remains a real obstacle for longer term success of a treatment with bNAbs. Alternatively, (fewer) bNAbs can be administered in combination with ART , whereby ART could lower the replication rate of the HIV population, reducing the viral diversity and the chances of viral escape. Specifically, we can expect that emergence and establishment of rare  escape variants against bNAbs to be less likely in ART+ patients, which suggests that fitness-limited bNAbs should be more effective in conjunction with ART. Still, more data would be necessary to understand the longterm efficacy of such augmented therapy, and specifically the role of viral reservoirs in this context. A modeling approach could then shed light on how ART administration and bNAb therapy could be combined to efficiently achieve viral suppression.”Moreover, we also discuss aspects of therapy optimization (e.g. safety) that must be considered when identifying the most promising therapy.From the Discussion section (lines 491-498):“It should be noted that our analysis in [figure 4c (antibody ranking)] only focuses on one aspect of therapy optimization, i.e., the suppression of escape. Other factors, including potency  and half-life of the bNAb, or the patient’s tolerance of bNAbs at different dosage should also be taken into account for therapy design. For example, the bNAb 10E8, which we identified as of the most promising mono-therapy candidates in Figure 4, is shown to be poorly tolerated by patients with short half-life [R24], making it undesirable for therapy purposes. Thus, the bNAb candidates shown in Figure 4C should be taken as a guideline to be complemented with further assessment of efficacy and safety for therapy design.”5) More discussion of how the predicted fitness costs compare to the older fitness landscape work would be useful context in the discussion.We thank the reviewers for pointing this out to us. We have included a comparison of our approach to other fitness inference work in the Methods section, Inference of selection for escape mutations against each bNAb (lines 902-919):“Prior work has also inferred the fitness effect of mutations in HIV, but our approach differs in important aspects. For instance, maximum entropy models have been used to infer the preference of different amino acids in the Gag and the env proteins of HIV-1 from their prevalences across sequences sampled from different patients . The inferred preference values can explain the in-vitro growth rate (fitness) of the associated viral strains, especially for sites that are relatively conserved and are not the drivers of antigenic evolution in HIV-1. However, further modeling would be needed to quantitively map these inferred amino acid preferences onto population genetics measures that can be used to characterize the evolutionary dynamics of an HIV population. Other work has used longitudinal HIV-1 sequence data to infer selection and to characterize the role of selective sweeps due to immune pressure, genetic hitchhiking and recombination in the turnover of HIV-1 populations within patients [R27–R30]. In contrast, our work focuses on the expected composition of the population in a viremic patient prior to the start of treatment as opposed to the history of a viral population. Our approach uses a self-consistent formalism for inference of the population genetics parameters (e.g. population diversity and selection strength) and for the evolutionary simulations used to predict outcomes. Therefore, we can directly interpret the fitted parameters in terms of both the viral dynamics and the pre-treatment state of HIV-1 populations within patients.”Reviewer #1 (Recommendations for the authors):General comments/questions:In the Abstract (and Discussion), it is stated that bnAbs may serve as an alternative strategy to antiretroviral therapy against HIV, yet in the Introduction it is stated that augmenting antiretroviral therapy with bnAbs may be a fruitful strategy against HIV. Perhaps highlight the more promising approach of the two for consistency?We thank the reviewer for pointing out this inconsistency to us. We have now included a paragraph in the Discussion section about augmenting ART with bNAb Therapy (lines 442-455):“One strategy to achieve a longer term treatment success is by combining bNAb therapy with ART. One main advantage of bNAb therapy is the fact that it can be administered once every few months, in contrast to ART, which should be taken daily and missing a dose could lead to viral rebound. Although multivalent bNAb therapy reduces the chances of short-term viral escape, viral escape remains a real obstacle for longer term success of a treatment with bNAbs. Alternatively, (fewer) bNAbs can be administered in combination with ART , whereby ART could lower the replication rate of the HIV population, reducing the viral diversity and the chances of viral escape. Specifically, we can expect that emergence and establishment of rare  escape variants against bNAbs to be less likely in ART+ patients, which suggests that fitness-limited bNAbs should be more effective in conjunction with ART. Still, more data would be necessary to understand the longterm efficacy of such augmented therapy, and specifically the role of viral reservoirs in this context. A modeling approach could then shed light on how ART administration and bNAb therapy could be combined to efficiently achieve viral suppression.”Line 52 states that prior work on designing bnAb therapies did not consider viral dynamics, yet the following sentence appears to give theoretical examples of just this ("dynamics of viremia"). Was the first sentence referring to prior experimental work?We have fully restructured and extended the introduction in response to the Q #1, from essential revisions. We have also extended the paragraph that the reviewer is referring to: we have now separate discussions on the experimental work to measure the breadth of bNAbs for optimal therapy design without modeling the dynamics of viremia, and the mechanistic modeling and theoretical work to describe the details of the viremia dynamics in trial data. We believe these modifications have clarified the points conveyed in the introduction; see the response to Q#1 from essential revisions and the marked changes in the introduction.In general, I find the paragraph in the Introduction between lines 52-72 to be a bit unfocused; what are the authors wishing to communicate here? Specifically, regarding lines 58-72, it seems like one could skip straight from line 57 to 73 and it would flow just as well.We thank the reviewer for pointing this out and apologize for the confusing text. As noted in response Q #1 from essential revisions, we have restructured the Introduction to address this point.Line 93: are the authors referring to cancer cells, or cancer-causing pathogens? Do such extensive longitudinal sequence datasets also exist for resistant bacteria and cancer-causing pathogens as for HIV, that would enable translation of this approach to those settings?We clarified the language and explicitly mention “cancer tumor cells” in the manuscript.Still, the reviewer’s question about cancer-causing pathogens is very interesting. There are various longitudinal studies for hepatitis C virus (HCV). The evolutionary rate of HCV is also comparable to that of HIV [R31]. Moreover, there is growing evidence that  broadly neutralizing antibodies play an important role in immune-mediated control of hepatitis C virus (HCV) infection [R32]. Therefore it is likely that our modeling approach would be of relevance for therapy design against HCV. We have now added the example of HCV in the introduction.Longitudinal data for HBV and HPV (two other cancer-causing pathogens) are more limited, but it would be interesting to collect and study such data.Line 106-107, Equation 1 appears to model the virus population size as a function of time (N(t)), rather than the rebound time explicitly (perhaps reword slightly?).Line 119: in defining the actual rebound time, T=-γ^-1*logx, it would seem that this is a constant, since γ is a constant, and x is also an inferred constant. If this is correct, why is equation 1 needed? Likely, I am just missing something here!The reviewer is correct that equation 1 is the viral population size over time N(t). Specifically, this equation refers to the total viral population without reference to type, in the continuous deterministic limit (i.e. ignoring the noise terms in equation 2.) of the stochastic individual-based model. We simulate treatment outcomes using the full stochastic birth-death model, but we use this deterministic limit to analyze observed trajectories of patient viremia. Fitting N(t) is the basis for measuring the characteristic rebound time T and then for connecting the rebound time to the initial frequency of resistant variants x. This quantity is patient-specific—it is a single number characterizing the patient’s viremic response to treatment, but it varies from patient to patient. We have added clarifying wording and added patient-indicating subscripts to the parameters to make this clear (lines145-147):“The maximum-likelihood fits of N(t) to the viremia measurements in Figure 3—figure supplement 1-3 specifies the initial resistant fraction xp and thus the rebound time Tp in each patient p, which in this simple model, is given by Tp = −γ−1 logxp.”Line 135: it might be helpful to talk more physically about what is meant by the 'birth' and 'death' of a variant (variant completely dies out? Or the variant population declines as a result of bnAb infusion?). Does a single amino acid mutation move a variant a to another type b?As an individual-based model, it is not birth and death of a variant, but rather birth and death of an individual member of a variant class . We have modified the language in the section Model: Stochastic evolutionary dynamics of HIV subject to bNAb therapy to clarify when we are describing the dynamics for individual virions (lines 164-169):“At each generation, a virus with phenotype a can undergo one of three processes: birth, death and mutation to another type b, with rates βa, δa, and µa→b, respectively . The net growth rate of the viral subpopulation with phenotype a is the birth rate minus the death rate, γa = βa − δa . The total rate of events (birth and death) per virion λ = βi +δi modulates the amount of stochasticity in this birth-death process, which we assume to be constant across phenotypic variants.”Regarding “Does a single amino acid mutation move a variant a to another type b?”: The amino acids at each site are grouped into two categories: susceptible and resistant. Replacing a susceptible amino acid with a resistant amino acid changes the type and fitness of the virus, but if the substitution replace an amino acid with another from the same category, the type of the virus is unchanged. Note that furthermore, a change of type does not necessarily move a virus between the susceptible and resistant classes. A virus is resistant to a given therapy if it has at least one escape mutation against each antibody, for all antibodies in a given therapy; see figure 1E for the details regarding the mutational model.Line 155: Is not the mutation rate of HIV well known already? Is the rate inferred by the authors in line with past estimates?The reviewer is correct that the mutation rates are known, both in-vitro and in-vivo. We were interested in the transition/transversion ratio as it manifests in formulation of the frequency spectrum . This ratio, rather than mutation rate itself, is necessary to model the frequency distribution of resistant viruses. We compare the result of our analysis to the estimate from [R33] in Methods  and find it in agreement. Nonetheless, for consistency, we used our likelihood estimates for the transition/transversion ratio in our further analysis, since we measured this ratio using the standing variation in untreated patients, and that our model is concerned with how mutational processes maintain resistant variants in steady state (standing variation) of a population. In [R33] and elsewhere, mutation rates are often measured using the divergence along a lineage over time.-1 vs. 3 days-1 for susceptible viruses, or "slowest process"?Line 156-157: The authors state that the 'fastest process in the dynamics…is the growth rate of susceptible viruses". Should this not say 'resistant viruses", since γ = 1/3 daysThe reviewer is correct, and we have fixed the typo.Line 174: "mutational target size" is not very intuitive for me. I know it is defined later on lines 211-213, but perhaps this can be summarized or stated more intuitively here, as well as in the Discussion?We have added a brief intuitive description at this line (now lines 204-205):“The mutational target size for escape from the bNAb  …”Lines 178-182: the authors propose to infer mutation and fitness characteristics of escape-mediating HIV variants via sequence data. Work out of Arup Chakraborty's lab at MIT comes to mind on developing HIV fitness landscapes. Would this not offer the same information for parameterizing the birth-death model? Perhaps the potential relevance/connection between those past works and the current work could be briefly discussed.We thank the reviewer for pointing this out to us. Please see our response to Q#5 from the essential revisions.In the section on 'Diversity of the viral population', it seems counterintuitive to me that characterizing only synonymous mutations as a measure of neutral genetic diversity would allow one to determine the 'chance to observe a rare  mutation' (line 185), since this implies a change in the amino acid sequence of the protein. I must not be thinking about this correctly; can the authors please clarify this for me?The reviewer is right in that neutral diversity alone is not enough to determine the “chance to observe a rare (e.g. resistant) mutation.” The neutral diversity is only part of our larger model that also includes the mutational targets size and the fitness effects. We have made the wording of this section more precise (lines 216-218):“The neutral genetic diversity θ = 2Nkµ/λ  is an observable that relates to key population genetics parameters, i.e., the per-nucleotide mutation rate µ, the population carrying capacity Nk, and the total number of events per virus in the birth-death process λ, which determines the noise amplitude in the evolutionary dynamics (Methods). Nk and λ together determine the effective population size Ne = Nk/λ.”To further clarify why neutral diversity is important for the inference of the non-synonomous substitution frequency: Note that the transition-mediated diversity θts = 2Neµts, is proportional to the effective population size Ne = Nk/λ with a fixed, known timescale µts. Because the value of Ne is shared across synonymous and non-synonymous sites, we can achieve higher statistical precision by determining Ne through θts using the synonymous sites, and then independently fitting the fitness differences from the frequency of non-synonymous substitutions.Lines 222-223: The footprint of a bnAb is often larger than the actual epitope, which may contain both variable and conserved sites . Thus, bnAbs must bind to both residue types. Given this, why do the authors expect HIV escape mutations to be intrinsically deleterious for the virus (implying they occur mostly at conserved sites), vs. occurring at the nearby variable sites that bnAbs also contact? For example, the following paper, https://www.pnas.org/content/115/4/E564, states that "Even for the relatively "conserved" CD4 binding-site region, only mutations at some residues are predicted to incur large fitness costs upon mutations."Yes, the variable regions mediate escape. However even the variable regions are not completely free from stabilizing fitness. We see that the distribution of amino acids at the escape sites we identify have much reduced entropy compared to the most diverse regions of env, the so-called hyper-variable regions . There must therefore be stabilizing selection at these escape sites, reducing the amino-acid distribution entropy. At the same time, we agree that the strength of this selection need not be large. Note the selection we infer is only strong compared to mutation, and the relative fitness costs on absolute growth rate are generally not observable in the lab (perhaps 1% of the wild-type growth rates.)The intrinsic fitness cost is not assumed, it is determined from the frequency data. It is possible for the inference process to return zero or even negative fitness costs and to include such costs in the simulation. However, it is certainly true that for a bNAb to be broad, escape must be rare. It is this feature which means that our fitness inference (which depends on observed frequencies) is generally expected to return a positive fitness cost of escape . Otherwise escape alleles would be too common in sera and neutralization panels to be identified as broad in the first place. Therefore, our inferred valued cost values are consistent with this picture.Line 314: what do the authors classify as 'early rebound'? Below 56 days?Yes, we have clarified this term in the manuscript now. Early rebound refers to any rebound time occurring within 56 days of the start of therapy.Line 330-332: the first part of this statement makes sense to me , but I am not certain about the second part. Wouldn't fitness-limiting and mutation-limiting bnAbs be equally good against low-diversity viral populations?In the limit of very low diversity, the effect of selection is very weak since selection can act only on the circulating alleles. Therefore, the frequencies of resistant variants are determined by the mutational target size of each variant, irrespective of the fitness cost. It is therefore more advantageous to use a mutation-limiting antibody against a low-diversity viral population, rather than a selection-limiting antibody.Lines 378-379: Might it be possible for the authors to speculate on how the exclusion of the dynamics of Ab concentration and IC50 neutralization during treatments could affect their results/conclusions?We thank the reviewer for bringing up this interesting point. We have now added a new appendix (Appendix 3) discussing the impact of incomplete neutralization on viral rebound. We have also added language in the Discussion section, Limitations :In our model of viral escape, we neglect the possibility of incomplete escape of the virus due to the reduced neutralization efficacy of bNAbs as their concentrations decay during trials. In Appendix 3, we show that this simplifying assumption is valid as long as the IC50 is not the same order of magnitude as the initial dosage concentration of the infused bNAb. Notably, the data from therapy trials used in this study fall into the regime for which we can neglect the impact of incomplete neutralization . However, taking into account the dependence of viral fitness on bNAb concentration and its neutralization efficacy, as in the model proposed by [R34], could improve the long-term predictive power of our approach.Moreover, in Appendix 3 we explore the effects of incomplete neutralization on rebound trajectories. As we show in Appendix 3-Figure 1, if an antibody has an IC50 against the viral variant which is an order of magnitude above the initial antibody concentration, the viral dynamics very closely follows the idealized “escaped” trajectory . On the other hand, for an IC50 an order of magnitude below the initial concentration, the viral dynamics behave similarly to a completely neutralized virus, with a late rebound (later than 8 weeks). We found that the most important effect of incomplete neutralization on the dynamics of viremia occurs when the antibody has an IC50 against a resistant variant that is roughly of similar magnitude to the initial bNAb concentration in a patient’s serum; see Appendix 3-Figure 1. In Appendix 3-Figure 2 we show the distribution of IC50 and the initial bNAb concentration from the 10-1074 trial [R35] to see how often we would expect IC50 and initial concentration to be of the same order of magnitude. We find that the IC50 values in this trial are much lower (higher) for susceptible (resistant) variants compared to the initial bNAb concentration in all patients. Therefore, our simplified model assuming that a viral variant is either fully resistant or susceptible to a bNAb  is a reasonable approach for capturing the statistics of treatment failure at the concentrations tested in these trials. Nonetheless, developing a genotype-to-neutralization model such as the ones in  may allow for a more nuanced approach to characterize neutralization in future work.Reviewer #2 (Recommendations for the authors):In Appendix 1, the authors might consider coloring the resistant and susceptible amino acid identities based on the data source .We hope the added section on DMS comparison (the new Appendix 4) clarifies this since it covers the cases where sites are called by more than one method.References:[R1] Wagh K, Bhattacharya T, Williamson C, Robles A, Bayne M, et al. (2016) Optimal Combinations of Broadly Neutralizing Antibodies for Prevention and Treatment of HIV-1 Clade C Infection. 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Follow-up INSTI drug resistance testing could not confirm DTG resistance. Even though DTG resistance was detected at one time point, the viral load continued to decline  regimen consisting of tenofovir disoproxil fumarate (TDF), emtricitabine (FTC) and efavirenz (EFV). Initial poor adherence to treatment and virologic failure was reported for 2012–2015 , and due to concerns of having possibly acquired resistance to this regimen, treatment was empirically switched according to national guidelines to lamivudine (3TC), zidovudine (AZT) and lopinavir/ritonavir (LPV/r). He remained on this regimen with his family practitioner from 2015 until early 2018, when he was referred back to our hospital for persistently high HIV viral loads. He admitted to poor adherence secondary to LPV/r-associated diarrhoea, and was subsequently switched to 3TC, AZT and DTG. Patient clinical data and treatment history are shown in  decline  despite  decline . All samwww.hanc.info/labs/labresources/procedures/Pages/pbmcSop.aspx). Cell-associated DNA and RNA were isolated from PBMCs and viral RNA was isolated from plasma as reported by Hong et al.10 Single genome amplification products covering the p6-protease-reverse transcriptase (p6PrRT) region were generated and Sanger sequencing was performed as described previously.11 Additionally, single genome amplicons covering the entire polymerase region were analysed for drug resistance mutations. Population and single genome nucleotide sequences were analysed for drug resistance mutations.PBMCs were isolated from freshly collected whole blood ethylenediaminetetraacetic acid specimens according to the HIV/AIDS Network Coordination Cross-Network Peripheral Blood Mononuclear Cell Processing Standard Operating Procedure , S2 (plasma RNA) and S3  indicate drug resistance mutation M184V .Mutations N155K and R263K were only detected once in S3 and were confirmed with single genome sequencing . Drug reAt the time INSTI resistance was definitively confirmed, the patient’s HIV viral load had already declined to 50 copies/mL. After much discussion with the patient, the patient elected to continue on his current regimen (rather than switch to a non-DTG-based regimen) with regular HIV viral load monitoring.15 Moreover CD4+ cell recovery and associated improved cytotoxic T-cell responses could have contributed to immune reconstitution to HIV and resulting viral load decline.We report a patient with viral load suppression despite a mixed viral population that includes INSTI-resistant variants with N155H and R263K. The patient was treatment experienced but INSTI naïve when initiated on a DTG-based regimen. DTG-resistant mutations N155H and R263K were first detected 24 months after DTG initiation; however, despite this the HIV-1 viral load continued decline to 50 copies/mL after 42 months. It is unclear why the DTG-resistant variants did not outcompete DTG-susceptible variants, but the low viral fitness could have contributed. Mutations R263K, M184V and K65R are all associated with decreased viral fitness and here occurred on the same viral variant. The slow but continued viral load decline could be due to the remaining activity and hyper-susceptibility to AZT, in the presence of the M184V and K65R mutations.17 The factors associated with DTG resistance are poorly understood. Whereas DTG resistance when used in first-line therapy is exceedingly rare, it is not unusual when DTG is administered to treatment-experienced patients,6 even when previously INSTI naïve. It is interesting that six of the nine cases of treatment-experienced, INSTI-naïve cases in the NADIA study1 with drug resistance received the same regimen as this patient, albeit that in our case this was given as a third-line regimen in contrast to NADIA where the patients received DTG in second-line treatment. Reported clinical risk factors associated with emergence of DTG resistance include poor treatment adherence, drug interactions and HIV factors such as a high baseline viral load.6 In this case we report good adherence but the high viral load (> 100 000 copies/mL) prior to DTG initiation could be a contributing risk factor, even though INSTI resistance was only detected after 24 months. The combination of N155H and R263K is associated with virologic failure on DTG-based regimens,19 in spite of the fitness cost of R263K.7 Even though N155H partially compensates for the R263K viral fitness cost, development of compensatory mutations to the N155H, R263K strain may be unlikely or slow despite drug pressure.20 No additional risk factors were identified in this case.Although previously thought to be rare, several cases of virological failure as a result of DTG resistance in INSTI-naïve patients have been described.22 Random unannounced drug concentration testing on various occasions suggest that intermittent adherence is an unlikely cause of the viraemia. Both compartmentalised replication and clonal viraemia could explain the relatively high viral load for an extended period of time. We investigated clonal viraemia in this case as described by Halvas et al.,11 but we were not able to find a matching proviral clone to the monotypic plasma virus population (data not shown); further investigation could be performed to shed light on this.The presence of DTG resistance only partially explains the viraemia in this patient but offers no clarity on the susceptible sub-population. The detectable viraemia could be the result of intermittent adherence or compartmentalised replication or clonal viraemia.This case report provides further evidence that DTG is not impervious to drug resistance, especially when used in treatment-experienced patients. It also suggests that patients with DTG resistance may not present with immediate viral rebound due to the fitness cost of mutations and could present with delayed viral load suppression or low-level viraemia. It is not known whether this patient’s HIV viral load will continue to remain low or whether additional compensatory mutations might allow the drug-resistant variant to regain fitness resulting in rebound. Continued vigilance is required when using DTG in treatment-experienced patients and sensitive drug resistance assays may be needed to detect drug resistance at low viral load levels.