Predicting the outcomes of treatment to eradicate the latent reservoir for HIV-1
Alison L. Hill, Daniel I. S. Rosenbloom, Feng Fu, Martin A. Nowak, Robert F. Siliciano
PPredicting the outcomes of treatment to eradicate the latent reservoir forHIV-1
Alison L. Hill ∗ , Daniel I. S. Rosenbloom ∗ , Feng Fu , Martin A. Nowak , and Robert F. Siliciano † Program for Evolutionary Dynamics, Department of Mathematics,Department of Organismic and Evolutionary Biology, Harvard University,Cambridge, MA 02138, USA Biophysics Program and Harvard-MIT Division of Health Sciences and Technology, Harvard University, Cambridge, MA 02138, USA Department of Biomedical Informatics, Columbia University Medical Center, New York, NY 10032, USA Institute of Integrative Biology, ETH Zurich, 8092 Zurich, Switzerland Department of Medicine, Johns Hopkins University School of Medicine and Howard Hughes Medical Institute, Baltimore, MD 21205, USA ∗ These authors contributed equally to the manuscript † To whom correspondence should be addressed: [email protected]
Abstract
Massive research efforts are now underway to develop acure for HIV infection, allowing patients to discontinue lifelongcombination antiretroviral therapy (ART). New latency-reversingagents (LRAs) may be able to purge the persistent reservoir oflatent virus in resting memory CD4 + T cells, but the degree ofreservoir reduction needed for cure remains unknown. Here weuse a stochastic model of infection dynamics to estimate the effi-cacy of LRA needed to prevent viral rebound after ART interrup-tion. We incorporate clinical data to estimate population-level pa-rameter distributions and outcomes. Our findings suggest that ap-proximately 2,000-fold reductions are required to permit a major-ity of patients to interrupt ART for one year without rebound andthat rebound may occur suddenly after multiple years. Greaterthan 10,000-fold reductions may be required to prevent reboundaltogether. Our results predict large variation in rebound timesfollowing LRA therapy, which will complicate clinical manage-ment. This model provides benchmarks for moving LRAs fromthe lab to the clinic and can aid in the design and interpretationof clinical trials. These results also apply to other interventionsto reduce the latent reservoir and can explain the observed returnof viremia after months of apparent cure in recent bone marrowtransplant recipients and an immediately-treated neonate.
Significance Statement
HIV infection cannot be cured by current antiretroviral drugs,due to the presence of long-lived latently-infected cells. Newanti-latency drugs are being tested in clinical trials, but majorunknowns remain. It is unclear how much latent virus must beeliminated for a cure, which remains difficult to answer empiri-cally due to few case studies and limited sensitivity of viral reser-voir assays. In this paper, we introduce a mathematical modelof HIV dynamics to calculate the likelihood and timing of viralrebound following anti-latency treatment. We derive predictionsfor the required efficacy of anti-latency drugs, and demonstratethat rebound times may be highly variable and occur after yearsof remission. These results will aid in designing and interpretingHIV cure studies.
Introduction
The latent reservoir (LR) for HIV-1 is a population of long-lived resting memory CD4 + T cells with integrated HIV-1DNA [1]. After establishment during acute infection [2], it in-creases to − cells and then remains stable. As only repli-cating virus is targeted by antiretroviral therapy (ART), latentlyinfected cells persist even after years of effective treatment [3; 4].Cellular activation leads to virus production and, if treatment isinterrupted, viremia rebounds within weeks [5]. Several molec-ular mechanisms maintain latency, including epigenetic modifi-cations, transcriptional interference from host genes, and the ab-sence of activated transcription factors [6; 7; 8; 9].Major efforts are underway to identify pharmacologic agentsthat reverse latency by triggering the expression of HIV-1 genesin latently infected cells, with the hope that cell death from vi-ral cytopathic effects or cytolytic immune responses follows, re-ducing the size of the LR [10; 11]. Collectively called latency-reversing agents (LRAs), these drugs include histone deacetylaseinhibitors [12; 13; 14], protein kinase C activators [15; 16; 17;18], and the bromodomain inhibitor JQ1 [19; 20; 21]. WhileLRAs are the subject of intense research, it is unclear how muchthe LR must be reduced to enable patients to safely discontinueART.The feasibility of reservoir reduction as a method of HIV-1 cureis supported by case studies of stem-cell transplantation [22; 23]and, more recently, early treatment initiation [24; 25], which haveallowed patients to interrupt treatment for months or years with-out viral rebound. The dramatic reductions in reservoir size ac-companying these strategies stands in stark contrast to the actionsof current LRAs, which induce only a fraction of latent virus invitro [26; 27] and have not produced a measurable decrease in LRsize in vivo [12; 13; 28]. It unclear how patient outcomes dependon reservoir reduction between these extremes, nor even whethera reduction that falls short of those achieved with stem-cell trans-plantation will bring any clinical benefit. LRA research needs toaddress the question: how low must we go ?In the absence of clinical data, mechanistic mathematical mod-els can serve as a framework to predict results of novel interven-tions and plan clinical trials. When results do become available,the models can be tested and refined. Mathematical models have1 a r X i v : . [ q - b i o . P E ] A ug ells remaining in LR Dynamics of each cell N LR q N LR Initial LR size LRA ART -3 -2 -1 0 1 210 -6 -4 -2 L R s i z e ( vs . o r i g i na l ) Rebound? Clearance? -3 -2 -1 0 1 210 -2 P l a s m a H I V - RN A ( c op i e s / m l ) Rebound time Residual viremia 200 c/ml Rebound? Clearance? ba Figure 1:
Schematic of LRA treatment and stochastic model of reboundfollowing interruption of ART. a) Proposed treatment protocol, illustratingpossible viral load and size of LR before and after LRA therapy. WhenART is started, viral load decreases rapidly and may fall below the limit ofdetection. The LR is established early in infection (not shown) and decaysvery slowly over time. When LRA is administered, the LR declines. Afterdiscontinuation of ART, the infection may be cleared, or viremia may even-tually rebound. b) LRA efficacy is defined by the parameter q , the fractionof the LR remaining after therapy, which determines the initial conditionsof the model. The stochastic model of viral dynamics following interrup-tion of ART and LRA tracks both latently infected resting CD4 + T cells(rectangles) and productively infected CD4 + T cells (ovals). Each arrowrepresents an event that occurs in the model. Alternate models consider-ing homeostatic proliferation and turnover of the LR are discussed in theMethods and Supplementary Methods. Viral rebound occurs if at leastone remaining cell survives long enough to activate and produce a chainof infection events leading to detectable infection (plasma HIV-1 RNA >
200 c ml − ). a long tradition of informing HIV-1 research and have been par-ticularly useful in understanding HIV-1 treatment. Previous mod-els have explained the multi-phasic decay of viremia during an-tiretroviral therapy [29], the initial seeding of the LR during acuteinfection [30], the limited inflow to the LR during treatment [31],the dynamics of viral blips [32], and the contributions of the LRto drug resistance [33]. No model has yet been offered to describethe effect of LRAs. Here we present a novel modeling frameworkto predict the degree of reservoir reduction needed to prevent vi-ral rebound following ART interruption. The model can be usedto estimate the probability that cure is achieved, or, barring thatoutcome, to estimate the length of time following treatment inter-ruption before viral rebound occurs (Fig. 1a). Results
Determination of key viral dynamic parameters governingpatient outcomes
We employ a stochastic model of HIV-1 reservoir dynamicsand rebound that, in its simplest form, tracks two cell types: pro- ductively infected activated CD4 + T cells and latently infectedresting CD4 + T cells (Fig. 1b). A latently infected cell can eitheractivate or die, each with a particular rate constant. An activelyinfected cell can produce virions, resulting in the active infectionof some number of other cells, or it can die from other causeswithout producing virions that infect other cells; in the latter case,cytotyoxic T lymphocyte (CTL) killing, errors in viral reversetranscription, or other problems upstream of virion productionmay prevent further infection. The model only tracks the initialstages of viral rebound, when target cells are not yet limited. Afull description is provided in the Methods and SupplementaryMethods.The initial conditions for the dynamic model depend on thenumber of latently infected cells left after LRA therapy. LRAefficacy is defined by the fraction q of the LR that remains fol-lowing treatment. The model tracks each latent and active cellto determine whether viral rebound occurs, and if so, how longit takes. Importantly, no single activated cell is guaranteed tore-establish the infection, as it may die prior to infecting othercells. Even if it does infect others, those cells likewise may dieprior to completing further infection. This possibility is a gen-eral property of stochastic models, and the specific value for theestablishment probability depends on the rates at which infectionand death events occur. Our goal is to calculate the probabilitythat at least one of the infected cells remaining after therapy es-capes extinction and causes viral rebound, and if so, how long ittakes. If all cells die, then rebound never occurs and a cure isachieved. As the model only describes events after completionof LRA therapy, our results are independent of the therapy pro-tocol or mechanism of action. Using both stochastic simulationsand theoretical analysis of this model, we find that the probabilityand timing of rebound relies on four key parameters: the decayrate of the LR in the absence of viral replication ( δ ), the rate atwhich the LR produces actively infected cells ( A ), the probabil-ity that any one activated cell will produce a rebounding infectionbefore its lineage dies ( P Est ), and the net growth rate of the in-fection once restarted ( r ). Estimates of these four parameters areprovided in Table 1 and Supplementary Fig.1. After therapy, therate at which the LR produces actively infected cells is reducedto qA . The probability that an individual successfully clears theinfection is: P Clr ( q ) ≈ e − qAP Est /δ . (1)The expression qAP Est /δ approximates the expected number offated-to-establish cells that will ever exit from the LR, explainingthe Poisson form of this expression. In the Supplementary Meth-ods, we provide the full derivation, as well as a formula (Eq. S8)for the probability that rebound occurs a given number of daysfollowing treatment interruption (a function of δ , A , P Est , r , andefficacy q ). Of note, the initial size of the reservoir itself is not in-cluded among these parameters: while it factors into both A (theproduct of the pre-LRA reservoir size and the per-cell activationrate), and q (the ratio of post-LRA to pre-LRA reservoir size), itdoes not independently influence outcomes. Both of these formu-las provide an excellent match to explicit simulation of the model(Fig. 2). The key assumption required for the analysis is that r greatly exceeds δ ; since viral doubling times during rebound are2easured on the order of a few days, while LR decay is measuredon the order of many months or years, this assumption is expectedto hold. Likelihood-based inference can therefore proceed by ef-ficient computation of rebound probabilities (using equation S8),rather than by time-consuming stochastic simulation.Outcomes depend only on the four parameters above even inmore complex models of viral dynamics including other featuresof T cell biology and the HIV lifecycle (Supplementary Meth-ods). Alternate models studied include explicit tracking of freevirus with varying burst sizes, an “eclipse phase” during which aninfected cell produces no virus, proliferation of cells upon reacti-vation, maintenance of the LR by homeostatic proliferation, andeither a constant or Poisson-distributed number of infected cellsproduced by each cell (Supplementary Figs. 2-7). If prolifera-tion of latently infected cells is subject to high variability, e.g., by“bursts” of proliferation, then rebound time and cure probabilityincrease slightly beyond the predictions of the basic model (Sup-plementary Figs. 6 and 7). No other modification to the modelaltered outcomes. Outcomes of LRA therapy therefore are likelyto be insensitive to details of the viral lifecycle; accordingly, fewparameters must be estimated to predict outcomes. cba Time after stopping treatment % pa t i en t s w i t h s upp r e ss ed V L LRA log-efficacy R ebound t i m e ( da ys ) LRA log-efficacy P r ob . c l ea r an c e Figure 2:
Clearance probabilities and rebound times following LRA ther-apy predicted from model using point estimates for the parameters (Ta-ble 1). “LRA log-efficacy” is the number of orders of magnitude by whichthe latent reservoir size is reduced following LRA therapy ( − log ( q ) ). a)Probability that the LR is cleared by LRA. Clearance occurs if all cells inthe LR die before a reactivating lineage leads to viral rebound. b) Medianviral rebound times (logarithmic scale), among patients who do not clearthe infection. c) Survival curves (Kaplan-Meier plots) show the percent-age of patients who have not yet experienced viral rebound, plotted as afunction of the time (logarithmic scale) after treatment interruption. Solidlines represent simulations, and circles represent approximations from thebranching process calculation. All simulations included to patientswith identical viral dynamic parameter values. Predicted prospects for eradicating infection or delaying timeto rebound
Using best estimates of parameters derived from previously re-ported data (Table 1), we can explore the likely outcomes of in-terventions that reduce the latent reservoir. The best outcome ofLRA therapy, short of complete and immediate eradication, is thatso few latently infected cells survive that none reactivate and starta resurgent infection during the patient’s lifespan. In this case,LRA has essentially cleared the infection and a cure is achieved.We simulated the model to predict the relationship between LRAefficacy and clearance (Fig. 2a). We find that the reservoir mustbe reduced , -fold before half of patients are predicted to clear the infection.If LRA therapy fails to clear the infection, the next-best out-come is extension of the time until rebound, defined as plasmaHIV-1 RNA ≥
200 c ml − . We computed the relationship be-tween LRA efficacy and median time until rebound among pa-tients who do not clear the infection (Fig. 2b). Roughly a 2,000-fold reduction in the reservoir size is needed for median reboundtimes of 1 year. Only modest ( ∼ -fold) increases in median re-bound time are predicted for up to 100-fold reductions in LR size.In this range, the rebound time is independent of latent cell lifes-pan (decay rate δ ) and is driven mainly by the reactivation rate ( A )and the infection growth rate ( r ). The curve inflects upward (ona log scale) at ≈ growth-limited regime . If the reservoir is small (large re-duction), the dominant component is instead the expected waitingtime until activation of the first cell fated to establish a reboundinglineage; the system is in an activation-limited regime . Since wait-ing time is roughly exponentially distributed, times to rebound inthis regime can vary widely among patients on the same therapy,even with identical values of the underlying parameters.Survival curves, plotting the fraction of simulated patientsmaintaining virologic suppression over time, demonstrate the ex-treme interpatient variability and long follow-up times requiredfor LRA therapy (Fig. 2c). For less than 100-fold reductionsin LR size, simulated patients uniformly rebound within a fewmonths, since rebound dynamics are not in the activation-limitedregime. If therapy decreases LR size , -fold, then ∼
55% ofpatients are predicted to delay rebound for at least six months.However, of these patients, 47% suffer rebound in the followingsix months. Higher reservoir reductions lead to clearance in manypatients. In others, rebound may still occur after years of apparentcure, posing a challenge for patient management.Earlier work suggested a shorter reservoir half-life of 6 months[37], indicating that dramatic decreases in LR size would occurafter 5 or more years of suppressive ART even in the absenceof LRA therapy. We consider the prospects for HIV eradicationor long treatment interruptions with this faster reservoir decayrate (Fig. 3b). In this optimistic scenario, only 1,500-fold reduc-tions are needed for half of patients to clear the LR, and reboundbecomes highly unlikely after a few years. Alternatively, in aworst-case scenario where latent cell death is perfectly balancedby homeostatic proliferation such that the reservoir does not de-cay at all ( δ = 0 ), much higher efficacies are needed to achievebeneficial patient outcomes (Fig. 3c). Setting treatment goals with uncertainty considerations
We conducted a full uncertainty analysis of the model, by si-multaneously varying all parameters over their entire ranges (Ta-ble 1, Supplementary Fig. 1). For each simulated patient, val-ues for the three parameters δ , A , and r were sampled indepen-3 arameter Symbol Estimation Method Source Best Estimate DistributionLR decay rate δ Long-term ART (cid:0) δ = ln(2) /τ / (cid:1) [3; 4] . × − d − δ ∼ N (5 . , . × − d − LR exit rate A Viral rebound afterART interruption [5; 34] 57 cells d − log ( A ) ∼ N (1 . , . Growth rate r − log ( r ) ∼ N ( − . , . Establishment probability P Est
Population geneticmodeling [35; 36] 0.069 (composite distribution;see Methods)
Table 1:
Estimated values for the key parameters of the stochastic viral dynamics modelNotation X ∼ N ( µ, σ ) means that X is a random variable drawn from a normal distribution with mean µ and standard deviation σ . a I II III % pa t i en t s s upp r e ss ed Time after stopping treatment10 days 100 days 3 years 30 yearsLRA log-efficacy R ebound t i m e ( da ys ) P r ob . c l ea r an c e b % pa t i en t s s upp r e ss ed Time after stopping treatment10 days 100 days 3 years 30 yearsLRA log-efficacy R ebound t i m e ( da ys ) P r ob . c l ea r an c e c % pa t i en t s s upp r e ss ed Time after stopping treatment10 days 100 days 3 years 30 yearsLRA log-efficacy R ebound t i m e ( da ys ) P r ob . c l ea r an c e Figure 3:
Predicted LRA therapy outcomes, accounting for un-certainty in patient parameter values. a) Full uncertainty analysiswhere all viral dynamics parameters are sampled for each patientfrom the distributions provided in Table 1. b) A best-case scenariowhere the reservoir half-life is only 6 months ( δ = 3 . × − d − ).All patients have the same underlying viral dynamic parameters,otherwise given by the point estimates in Table 1. c) A worst-casescenario where the reservoir does not decay because cell deathis balanced by homeostatic proliferation ( δ = 0 ). I) Probabilitythat the LR is cleared by LRA. Clearance occurs if all cells in theLR die before a reactivating lineage leads to viral rebound. “LRAlog-efficacy” is the number of orders of magnitude by which the la-tent reservoir size is reduced following LRA therapy ( − log ( q ) ).II) Median viral rebound times (logarithmic scale), among patientswho do not clear the infection. III) Survival curves (Kaplan-Meierplots) show the percentage of patients who have not yet experi-enced viral rebound, plotted as a function of the time (logarithmicscale) after treatment interruption. All simulations included to patients. dently from their respective distributions, while P Est was sam-pled from a conditional distribution that depends on r (see Meth-ods). Results for this simulated cohort are similar to those for thepoint estimates, with greater interpatient variation in outcomes(Fig. 3a). This variation makes the survival curves less steep:cure is slightly more likely at low efficacy, but slightly less likelyat high efficacy. As expected from Equation (1), cure is morelikely for patients with lower A or P Est values and higher δ val-ues. If therapy provides only 10–100-fold LR reductions, a subsetof patients may delay rebound for several months.Using these cohort-level predictions, we can set efficacy goalsfor the reservoir reduction needed to achieve a particular like-lihood of a desired patient outcome. Fig. 4 provides the targetLRA efficacies for which 50% of patients are predicted to re-main rebound-free for a specified interruption time. Reductionsof under 10-fold afford patients only a few weeks to a month offtreatment without rebound. For one-year interruptions, a 1,000–3,000-fold reduction is needed. To achieve the goal of eradication(cure) a 4-log reduction is required. This value increases to 4.8logs to cure 75% of patients, and to 5.8 logs for 95% of patients. Model applications and comparison to data
Current ability to test the model against clinical data is limitedboth by the dynamic range of assays measuring LR size and bythe low efficacy of investigational LRA treatments. Yet we cancompare our predictions to results observed for non-LRA-basedinterventions that lead to smaller LR size and prolonged treat-ment interruptions (Fig. 4). A 2010 study of early ART initiators who eventually underwent treatment interruption found a singlepatient with LR size approximately 1,500-fold lower than a typ-ical patient (0.0064 infectious units per million resting CD4 + Tcells, versus an average of 1 per million) in whom rebound wasdelayed until 50 days off treatment [38]. The well-known ‘Berlinpatient’ [22] has remained off treatment following a stem-celltransplant since 2008, and a comprehensive analysis of his vi-ral reservoirs found HIV DNA levels at least log decrease inviral reservoirs [23]; they have since both rebounded, at approxi-mately 3 and 8 months post-interruption. In the case of the ‘Mis-sissippi baby’, infection was discovered and treated within 30hours of birth, and ART continued until interruption at around18 months. Virus remained undetectable for 27 months, when vi-ral rebound occurred, assuming the accuracy of widely reportedclaims [40]. At the time of treatment cessation, the LR size waslikely at least 300-fold lower than that of a typical adult (basedon less than 0.017 infectious units per million resting CD4+ Tcells at age 30 months [41], and scaled on a weight basis rel-ative to adults). These few available cases demonstrate that ourmodel is not inconsistent with current knowledge. When survivalcurves for larger cohorts become available, Bayesian methods canbe used to update estimates in Table 1 and reduce uncertainty offuture predictions.4 wk 1 mth 3 mths 1 yr 10 yrs Lifetime0123456 Treatment interruption goal T a r ge t L R A l og - e ff i c a cy C. Bo.1 Bo.2 Be.Mi.
Figure 4:
Efficacies required for successful LRA therapy. The target LRAlog-efficacy is the treatment level (in terms of log-reduction in latent reser-voir size) for which at least 50% of patients still have suppressed viral loadafter a given treatment interruption length (blue line). Shaded ranges showthe results for the middle 50% (dark gray) and 90% (light gray) of patients.“Lifetime” means the LR is cleared. Annotations on the curve representdata points for case studies describing large reservoir reductions and ob-serving rebound times after ART interruption. From left to right, they rep-resent a case of early ART initiation in an adult (the “Chun patient” (C.)[38]), two cases of hematopoietic stem cell transplant with wild-type donorcells (the two Boston patients (Bo.1 and Bo.2) [23]), a case of early ARTinitiation in an infant (the Mississippi baby (Mi.) [41], assuming, as re-cently reported, rebound after 27 months), and a case of hematopoieticstem cell transplant with ∆
32 CCR5 donor cells (the Berlin patient (Be.)[22; 39]). For the Chun patient, the annotations represent the maximumlikelihood estimate for LR reduction (diamond), as well as 95% confidenceintervals (vertical bar). For the Boston and Berlin patients, vertical arrowsindicate that only a lower bound on treatment efficacy is known (LR sizewas below the detection limit) and that the true value may extend further inthe direction shown. For the Berlin patient, the horizontal arrow indicatesthat rebound time is at least five years (rebound has not yet occurred).
Discussion
Our model is the first to quantify the required efficacy oflatency-reversing agents for HIV-1 and set goals for therapy. Fora wide range of parameters, we find that therapies must reduce theLR by at least two orders of magnitude to meaningfully increasethe time to rebound after ART interruption (upward inflection inFigs. 2b, 3II), and that reductions of approximately four ordersof magnitude are needed for half of patients to clear the infec-tion (Figs. 3a, 4). Standard deviations in rebound times of manymonths are expected, owing to substantial variation in reactiva-tion times after effective LRA therapy brings the infection to anactivation-limited regime. While the efficacy required for thesebeneficial outcomes is likely beyond the reach of current drugs,our results permit some optimism: we show for the first time thatreactivation of all cells in the reservoir is not necessary for cessa-tion of ART. This is because some cells in the LR will die beforereactivating or, following activation, will fail to produce a chainof infection events leading to rebound. On a more cautionarynote, the wide distribution in reactivation times necessitates care-ful monitoring of patients, as rebound may occur even after longperiods of viral suppression.Even without any reservoir reduction, variation in infection pa-rameters and chance activation together predict delays in reboundof at least two months in a small minority of patients (Fig. 4), consistent with ART interruption trials such as SPARTAC [42].More detailed (and possibly more speculative) models includingspecific immune responses may be needed to explain multi-yearpost-treatment control, such as found in the VISCONTI cohort[24].Our analysis characterizing the required efficacy of LRA ther-apy does not rely on the specific mechanism of action of thesedrugs, only the amount by which they reduce the reservoir. Wehave assumed that, after ART/LRA therapy ends, cell activationand death rates return to baseline. We have also assumed that thereservoir is a homogeneous population with constant activationand death rates. The presence of reservoir compartments with dif-ferent levels of LRA penetration does not alter our results, as theyare stated in terms of total reservoir reduction. If, however, thesecompartments vary in activation or death rates [43], or if dynam-ics of activated cells depends on their source compartment, thenour model may need to be modified. Moreover if spatial popu-lation structure affects viral replication, viral dynamics above thedetection limit (from which we estimated parameters r and A )may not correspond straightforwardly to the infection/death ratesin early infection, due to local limitations in target cell density[44]. Spatial restrictions on viral transmission may be particu-larly important in densely packed lymphoid tissue [45]. In theabsence of clear understanding of multiple compartments consti-tuting the LR, we have considered the simplest scenario whichmay fit future LRA therapy outcomes.Throughout this paper, we assume that combination ART issufficiently effective so that viral replication alone cannot sustainthe infection after all latent virus is cleared. Studies of treat-ment intensification [46; 47], of viral evolution during ART[48; 49], and of in vitro antiviral efficacy [50; 51] all supportthis assumption. Moreover, HIV persistence is widely believedto result solely from the long lifespan or proliferative ability oflatently infected cells [3; 52]. If this assumption is violated,e.g., by the presence of long-lived drug-protected compartments[45; 53; 54], then any curative strategy predicated solely on la-tency reversal would be futile.Our model also highlights the importance of measuring spe-cific parameters describing latency and infection dynamics. De-spite the field’s focus on measuring latent reservoir size with in-creasing accuracy [55], our results suggest that the rate at whichlatently infected cells activate — and the fraction of these thatare expected to establish a rebounding infection — are more pre-dictive of LRA outcomes. Among all parameters that determineoutcome, the establishment probability is least understood, as itcannot be measured from viral load dynamics above the limit ofdetection. Simply because an integrated provirus is replication-competent and transcriptionally active does not mean that it will initiate a growing infection: as with all population dynamics,chance events dominate early stages of infection growth [56; 57].HIV-1 transcription is itself a stochastic process, governed byfluctuating concentrations of early gene products [58]. Sensi-tive assays of viral outgrowth may pave the way toward under-standing the importance of these chance events to early infec-tion; for instance, fluorescent imaging studies of adenovirus haveshown that a large majority of in vitro infections seeded by single5roductively infected cells die out early, before rapid growth andplaque formation can occur [57]. Similar experiments with HIVare underway in our laboratory and may help refine parameterestimates. Keeping other parameters constant, assuming a worst-case (highest) value for the establishment probability raises thereservoir reductions required for cure or a desired extended re-bound time by 0.8 logs. Regardless of the exact probability, thestochastic nature of HIV-1 activation and infection dynamics im-plies that even similarly situated patients may experience diver-gent responses to LRA.The model can also advise aspects of trial design for LRAs.Survival curves computed from equation S8 can be used to pre-dict the probability that a patient is cured, given that they havebeen off treatment without rebound for a known period. As fre-quent viral load testing for years of post-interruption monitoringis not feasible, it may be helpful to choose sampling timepointsbased on the expected distribution of rebound times. Trial designis complicated by the fact that LRA treatment efficacy is unknownif post-treatment LR size is below the detection limit. By consid-ering prior knowledge about viral dynamics parameters and therange of possible treatment efficacies, the model may estimateoutcomes even in the presence of uncertainty.To date, laboratory and clinical studies of investigational LRAshave generally found weak potential for reservoir reduction —up to one log-reduction in vitro and less in vivo [12; 26; 59].We predict that much higher efficacy will be required for eradi-cation, which may be achieved by multiple rounds of LRA ther-apy, a combination of therapies, or development of therapies towhich a greater fraction of the LR is susceptible. While we havefocused on LRA therapy, our findings also serve to interpret in-fection eradication or delays in rebound caused by early treat-ment [24; 25; 60] or stem cell transplantation [22; 23], both ofwhich also reduce the latent reservoir. In both of these cases,however, additional immunological dynamics likely play a ma-jor role and will need to be incorporated into future models.We believe that these modeling efforts will provide a quantita-tive framework for interpreting clinical trials of any reservoir-reduction strategy. Methods
Basic stochastic model
The basic model of reservoir dynamics and rebound tracks twocell types: productively infected activated CD4 + T cells, and la-tently infected resting CD4 + T cells. The model can be describedformally as a two-type branching process, in which four types ofevents can occur (Fig. 1): Z → Y ... rate constant: aZ → ∅ ... rate constant: d z Y → cY ... rate constant: b × p λ ( c ) Y → ∅ ... rate constant: d (2)In this notation Y and Z represent individual actively or latentlyinfected cells, respectively, ∅ represents no cells, and the arrowsrepresent one type of cell becoming the other type. A latentlyinfected cell can either activate (at rate a ) or die (at rate d z ). An actively infected cell can either die (at rate d ) or produce a col-lection of virions (at rate b ) that results in the infection of c othercells, where c is a Poisson-distributed random variable with pa-rameter λ , p λ ( c ) = (exp( − λ ) λ c ) / ( c !) . After an infection event,the original cell dies.Each event occur independently within a large, constant targetcell population. As the model does not include limitations on vi-ral growth, it describes only the initial stages of viral rebound.Since clinical rebound thresholds (plasma HIV RNA >
50 – 200c ml − ) are well below typical setpoints ( – c ml − ), thismodel suffices to analyze rebound following LRA therapy andART interruption. We do not explicitly track free virus, but as-sume it to be proportional to the number of infected cells. Thisassumption is valid because rates governing production of andclearance of free virus greatly exceed other rates, allowing a sep-aration of time scales. As we are not interested in blips or otherintraday viral dynamics, this assumption does not influence ourresults. A method for calculating the proportionality between freevirus and infected cells is provided in the Supplementary Meth-ods.The growth rate of the infection is r = b ( λ − − d . Thetotal death rate of infected cells is d y = b + d , and the basicreproductive ratio (mean offspring number for a single infectedcell) is R = bλ/ ( b + d ) . The establishment probability P Est is the solution to R (cid:0) − e − λP Est (cid:1) − λP Est = 0 . The total LRdecay rate in the absence of viral replication is ∆ = a + d z . Ifthere are Z cells in the latent reservoir, then the number of cellsreactivating per day is A = Z a .Analysis of the model to determine the four key pa-rameters ( δ , A , r , P Est
Parameter estimation
The half-life of latently infected cells has been estimated to beapproximately τ / = 44 months [3; 4]. The resulting value of δ = ln(2) /τ / is centered at . × − d − , and we construct adistribution of values based on ref. [3] . This value represents the net rate of LR decay during suppressive therapy, considering ac-tivation, death, homeostatic proliferation, and (presumably rare)events where activated CD4 + T cells re-enter a memory state.The net infection growth rate r describes the rate of exponen-tial increase in viral load once infection has been reseeded. TheLR reactivation rate A is the number of cells exiting the LR perday, before reservoir-reducing therapy. A and r were jointly es-timated from the dynamics of viral load during treatment inter-ruption trials in which there was no additional reservoir-reducingintervention [5; 34]; in particular, infection growth immediatelyfollowing rebound is sensitive to r , while the time to rebound issensitive to A . In the absence of reservoir reduction, observedrebound dynamics are insensitive to P Est , and so this parameterwas instead estimated from population genetic models [35; 36]that relate observed rates of selective sweeps and emergence ofdrug resistance to variance in the viral offspring distribution (seeSupplementary Methods).6 imulation of the model
We use the Gillespie algorithm to track the number of latentlyand actively infected cells in a continuous time stochastic process.The initial number of latent cells is Z (0) ∼ Binomial ( N LR , q ) ,where N LR is the pre-treatment reservoir size and q is the effi-cacy of LRA treatment (fraction of cells remaining). The initialnumber of actively infected cells Y (0) is then chosen from a Pois-son distribution with parameter a Z (0) /d y (corresponding to theimmigration-death equilibrium of the branching process). Thesimulation proceeds until the number of actively infected cellsreaches the threshold for clinical detection given by a viral loadof 200 c ml − (equivalent to Y = 3 × cells total) or until noactive or latent cells remain. Because stochastic effects are impor-tant only for small Y , we switch to faster deterministic numericalintegration when Y reaches a level where extinction probabilityis very low ( < − ). For each q value we perform to simulations.Simulations are seeded with values of the key parameters ( δ , A , r , P Est ), which may be either the point estimates or random num-bers sampled from the distributions in Table 1. We then back outvalues of the model-specific parameters that are consistent withthe sampled key parameters. In general, we use a pre-therapyLR size of N LR = 10 cells to get a = A/N LR . We then have d z = δ − a . As detailed in the Supplementary Methods, sam-pling P Est requires first sampling the variance-to-mean ratio ofthe viral offspring distribution ( ρ ). Then using r and ρ along with d y = d + b = 1 day − , we can get λ , b , d , and P Est . Consis-tent with our generating function analysis, we find that the spe-cific values assumed for N LR and d y do not influence the results.For simulating other models, any other parameter assumptionsare listed in the corresponding supplementary figure captions. Acknowledgements
We thank Y.-C. Ho, S. A. Rabi, L. Shan, and G. Laird forinsightful discussions and for sharing data, and we thank A.Perelson for helpful comments on an earlier version of thismanuscript. This work was supported by the Martin DelaneyCARE and DARE Collaboratories (NIH grants AI096113 and1U19AI096109), by an ARCHE Grant from the American Foun-dation for AIDS Research (amFAR 108165-50-RGRL), by theJohns Hopkins Center for AIDS Research, and by the HowardHughes Medical Institute. MAN was supported by the JohnTempleton Foundation. FF was funded by a European ResearchCouncil Advanced Grant (PBDR 268540). ALH and DISR weresupported by a Bill & Melinda Gates Foundation Grand Chal-lenges Explorations Grant (OPP1044503).
References [1] Chun, T. W., et al.
Quantification of latent tissue reservoirs andtotal body viral load in HIV-1 infection.
Nature (6629), 183–188 (1997).[2] Chun, T. W., et al.
Early establishment of a pool of latently in-fected, resting CD4(+) T cells during primary HIV-1 infection.
Proc. Natl. Acad. Sci. USA (15), 8869–8873 (1998).[3] Siliciano, J. D., et al. Long-term follow-up studies confirm thestability of the latent reservoir for HIV-1 in resting CD4+ T cells.
Nat. Med. (6), 727–728 (2003). [4] Archin, N. M., et al. Measuring HIV latency over time: Reservoirstability and assessing interventions. In , 406 (CROI, Boston, MA,2014).[5] Ruiz, L., et al.
Structured treatment interruption in chronicallyHIV-1 infected patients after long-term viral suppression.
AIDS (4), 397 (2000).[6] Marsden, M. D. & Zack, J. A. Establishment and maintenanceof HIV latency: model systems and opportunities for intervention. Future Virol (1), 97–109 (2010).[7] Hakre, S., Chavez, L., Shirakawa, K., & Verdin, E. Epigenetic reg-ulation of HIV latency. Curr. Opin. HIV AIDS (1), 19–24 (2011).[8] Mbonye, U. & Karn, J. Control of HIV latency by epigenetic andnon-epigenetic mechanisms. Curr HIV Res. (8), 554–567 (2011).[9] Ruelas, D. S. & Greene, W. C. An integrated overview of HIV-1latency. Cell (3), 519–529 (2013).[10] Choudhary, S. K. & Margolis, D. M. Curing HIV: pharmacologicapproaches to target HIV-1 latency.
Ann. Rev. Pharmacol. Toxicol. (1), 397–418 (2011).[11] Durand, C. M., Blankson, J. N., & Siliciano, R. F. Developingstrategies for HIV-1 eradication. Trends Immunol (11), 554–562(2012).[12] Archin, N. M., et al. Antiretroviral intensification and valproic acidlack sustained effect on residual HIV-1 viremia or resting CD4+cell infection.
PLoS ONE (2), e9390 (2010).[13] Archin, N. M., et al. Administration of vorinostat disrupts HIV-1 latency in patients on antiretroviral therapy.
Nature (7408),482–485 (2012).[14] Shirakawa, K., Chavez, L., Hakre, S., Calvanese, V., & Verdin,E. Reactivation of latent HIV by histone deacetylase inhibitors.
Trends Microbiol (6), 277–285 (2013).[15] Korin, Y. D., Brooks, D. G., Brown, S., Korotzer, A., & Zack, J. A.Effects of prostratin on T-cell activation and human immunodefi-ciency virus latency. J Virol (16), 8118–8123 (2002).[16] Williams, S. A., et al. Prostratin antagonizes HIV latency by acti-vating NF-kappaB.
J. Biol Chem (40), 42008–42017 (2004).[17] Mehla, R., et al.
Bryostatin modulates latent HIV-1 infection viaPKC and AMPK signaling but inhibits acute infection in a receptorindependent manner.
PloS ONE (6), e11160 (2010).[18] DeChristopher, B. A., et al. Designed, synthetically accessiblebryostatin analogues potently induce activation of latent HIV reser-voirs in vitro.
Nat Chem (9), 705–710 (2012).[19] Bartholomeeusen, K., Xiang, Y., Fujinaga, K., & Peterlin, B. M.Bromodomain and extra-terminal (BET) bromodomain inhibitionactivate transcription via transient release of positive transcriptionelongation factor b (p-TEFb) from 7SK small nuclear ribonucleo-protein. J. Biol Chem (43), 36609–36616 (2012).[20] Zhu, J., et al.
Reactivation of latent HIV-1 by inhibition of BRD4.
Cell Rep. (4), 807–816 (2012).[21] Boehm, D., et al. BET bromodomain-targeting compounds reac-tivate HIV from latency via a tat-independent mechanism.
CellCycle (3), 452–462 (2013).[22] H¨utter, G., et al. Long-term control of HIV by CCR5Delta32/Delta32 stem-cell transplantation.
New Engl J Med (7), 692–698 (2009). PMID: 19213682.[23] Henrich, T. J., et al.
Antiretroviral-free HIV-1 remission and vi-ral rebound after allogeneic stem cell transplantation: Report of 2cases.
Ann Int Med , July (2014).[24] S´aez-Ciri´on, A., et al.
Post-treatment HIV-1 controllers with along-term virological remission after the interruption of early initi-ated antiretroviral therapy ANRS VISCONTI study.
PLoS Pathog (3), e1003211 (2013). PMID: 23516360.[25] Persaud, D., et al. Absence of detectable HIV-1 viremia after treat-ment cessation in an infant.
New Engl J Med (19), 1828–1835(2013). PMID: 24152233.[26] Cillo, A. R., et al.
Quantification of HIV-1 latency reversal in rest-ing CD4+ t cells from patients on suppressive antiretroviral ther-apy.
Proc. Natl. Acad. Sci. USA (19), 70787083 (2014).[27] Bullen, C. K., Laird, G. M., Durand, C. M., Siliciano, J. D., &Siliciano, R. F. New ex vivo approaches distinguish effective andineffective single agents for reversing HIV-1 latency in vivo.
Na-ture Medicine (4), 425–429, April (2014).[28] Spivak, A. M., et al. A pilot study assessing the safety and latency-reversing activity of disulfiram in HIV-1Infected adults on an-tiretroviral therapy.
Clin Infect Dis (6), 883–890 (2014). PMID:24336828.[29] Perelson, A. S., et al. Decay characteristics of HIV-1-infected com-partments during combination therapy.
Nature (6629), 188–191(1997).[30] Archin, N. M., et al.
Immediate antiviral therapy appears to restrictresting CD4+ cell HIV-1 infection without accelerating the decayof latent infection.
Proc. Natl. Acad. Sci. USA (24), 9523–9528(2012).[31] Sedaghat, A. R., Siliciano, J. D., Brennan, T. P., Wilke, C. O., &Siliciano, R. F. Limits on replenishment of the resting CD4+ T cellreservoir for HIV in patients on HAART.
PLoS Pathog (8), e122(2007).[32] Conway, J. M. & Coombs, D. A stochastic model of latently in-fected cell reactivation and viral blip generation in treated HIV pa-tients. PLoS Comput Biol (4), e1002033 (2011).[33] Rosenbloom, D. I. S., Hill, A. L., Rabi, S. A., Siliciano, R. F., &Nowak, M. A. Antiretroviral dynamics determines HIV evolutionand predicts therapy outcome. Nat. Med. (9), 1378–1385 (2012).[34] Luo, R., Piovoso, M. J., Martinez-Picado, J., & Zurakowski, R.HIV model parameter estimates from interruption trial data includ-ing drug efficacy and reservoir dynamics. PLoS ONE (7), e40198(2012).[35] Pennings, P. S. Standing genetic variation and the evolution of drugresistance in HIV. PLoS Comput Biol (6), e1002527 (2012).[36] Pennings, P. S., Kryazhimskiy, S., & Wakeley, J. Loss and recoveryof genetic diversity in adapting populations of HIV. PLoS Genetics (1), e1004000 (2014).[37] Zhang, L., et al. Quantifying residual HIV-1 replication in pa-tients receiving combination antiretroviral therapy.
New Engl JMed (21), 1605–1613 (1999). PMID: 10341272.[38] Chun, T.-W., et al.
Rebound of plasma viremia following cessa-tion of antiretroviral therapy despite profoundly low levels of HIVreservoir: implications for eradication.
AIDS (18), 2803–2808(2010). PMID: 20962613 PMCID: PMC3154092.[39] Yukl, S. A., et al. Challenges in detecting HIV persistence duringpotentially curative interventions: A study of the Berlin Patient.
PLoS Pathog (5), e1003347 (2013).[40] Ledford, H. HIV rebound dashes hope of cure. Nature , July(2014).[41] Persaud, D., et al.
Very early combination antiretroviral therapy inperinatal HIV infection: Two case studies. In , 75LB (CROI, Boston,MA, 2014).[42] St¨ohr, W., et al.
Duration of HIV-1 viral suppression on cessationof antiretroviral therapy in primary infection correlates with timeon therapy.
PloS ONE (10), e78287 (2013).[43] Buz´on, M. J., et al. HIV-1 persistence in CD4(+) T cells with stem cell-like properties.
Nat Med (2), 139–142 (2014).[44] Strain, M. C., Richman, D. D., Wong, J. K., & Levine, H. Spa-tiotemporal dynamics of HIV propagation. J Theor Biol (1),85–96, September (2002).[45] Cardozo, E. F., Luo, R., Piovoso, M. J., & Zurakowski, R. Spatialmodeling of HIV cryptic viremia and 2-LTR formation during ral-tegravir intensification.
Journal of Theoretical Biology , 61–69,March (2014).[46] Gandhi, R. T., et al.
The effect of raltegravir intensification onlow-level residual viremia in HIV-Infected patients on antiretro-viral therapy: A randomized controlled trial.
PLoS Med (8),e1000321, August (2010).[47] Dinoso, J. B., et al. Treatment intensification does not reduce resid-ual HIV-1 viremia in patients on highly active antiretroviral ther-apy.
Proc. Natl. Acad. Sci. USA (23), 9403 (2009).[48] Kieffer, T. L., et al.
Genotypic analysis of HIV-1 drug resistance atthe limit of detection: virus production without evolution in treatedadults with undetectable HIV loads.
J Infect Dis (8), 1452–1465, April (2004).[49] Joos, B., et al.
HIV rebounds from latently infected cells, ratherthan from continuing low-level replication.
Proc. Natl. Acad. Sci.USA (43), 16725–16730, October (2008).[50] Shen, L., et al.
Dose-response curve slope sets class-specific limitson inhibitory potential of anti-HIV drugs.
Nat. Med. (7), 762–766 (2008).[51] Jilek, B. L., et al. A quantitative basis for antiretroviral therapy forHIV-1 infection.
Nat Med (3), 446–451, February (2012).[52] Chomont, N., et al. HIV reservoir size and persistence are drivenby t cell survival and homeostatic proliferation.
Nat Med (8),893–900 (2009).[53] Luo, R., et al. Modelling HIV-1 2-LTR dynamics following ralte-gravir intensification.
J Roy Soc Interface (84), July (2013).[54] Fletcher, C. V., et al. Persistent HIV-1 replication is associated withlower antiretroviral drug concentrations in lymphatic tissues.
Proc.Natl. Acad. Sci. USA (6), 2307–2312, February (2014). PMID:24469825 PMCID: PMC3926074.[55] Ho, Y.-C., et al.
Replication-competent noninduced proviruses inthe latent reservoir increase barrier to HIV-1 cure.
Cell (3),540–551 (2013). PMID: 24243014.[56] Pearson, J. E., Krapivsky, P., & Perelson, A. S. Stochastic theory ofearly viral infection: Continuous versus burst production of virions.
PLoS Comput Biol (2), e1001058 (2011).[57] Hofacre, A., Wodarz, D., Komarova, N. L., & Fan, H. Early in-fection and spread of a conditionally replicating adenovirus underconditions of plaque formation. Virology (1), 89–96 (2012).PMID: 22192628.[58] Singh, A. & Weinberger, L. S. Stochastic gene expression as amolecular switch for viral latency.
Curr Opin in Microbiol (4),460–466 (2009).[59] Xing, S., et al. Disulfiram reactivates latent HIV-1 in a bcl-2-transduced primary CD4+ T cell model without inducing globalT cell activation.
J. Virol. (12), 6060–6064 (2011).[60] Strain, M. C., et al. Effect of treatment, during primary infection,on establishment and clearance of cellular reservoirs of HIV-1.
J.Infect. Dis. (9), 1410–1418 (2005).(9), 1410–1418 (2005).