Early exposure to broadly neutralizing antibodies may trigger a dynamical switch from progressive disease to lasting control of SHIV infection

Antiretroviral therapy (ART) for HIV-1 infection is life-long. Stopping therapy typically leads to the reignition of infection and progressive disease. In a major breakthrough, recent studies have shown that early initiation of ART can lead to sustained post-treatment control of viremia, raising hopes of long-term HIV-1 remission. ART, however, elicits post-treatment control in a small fraction of individuals treated. Strikingly, passive immunization with broadly neutralizing antibodies (bNAbs) of HIV-1 early in infection was found recently to elicit long-term control in a majority of SHIV-infected macaques, suggesting that HIV-1 remission may be more widely achievable. The mechanisms underlying the control elicited by bNAb therapy, however, remain unclear. Untreated infection typically leads to progressive disease. We hypothesized that viremic control represents an alternative but rarely realized outcome of the infection and that early bNAb therapy triggers a dynamical switch to this outcome. To test this hypothesis, we constructed a model of viral dynamics with bNAb therapy and applied it to analyse clinical data. The model fit quantitatively the complex longitudinal viral load data from macaques that achieved lasting control. The model predicted, consistently with our hypothesis, that the underlying system exhibited bistability, indicating two potential outcomes of infection. The first had high viremia, weak cytotoxic effector responses, and high effector exhaustion, marking progressive disease. The second had low viremia, strong effector responses, and low effector exhaustion, indicating lasting viremic control. Further, model predictions suggest that early bNAb therapy elicited lasting control via pleiotropic effects. bNAb therapy lowers viremia, which would also limit immune exhaustion. Simultaneously, it can improve effector stimulation via cross-presentation. Consequently, viremia may resurge post-therapy, but would encounter a primed effector population and eventually get controlled. ART suppresses viremia but does not enhance effector stimulation, explaining its limited ability to elicit post-treatment control relative to bNAb therapy.

Steady state analysis of the model indicates two outcomes of the infection: chronic infection with high viremia that marks progressive disease (red filled square), typically realized in the absence of treatment, and viremic control (blue filled square), a switch to which is orchestrated by early bNAb therapy. 87 To test whether the model accurately captured the underlying dynamics of infection and the influence 88 of bNAbs, we applied it to describe the viral load changes reported in Nishimura et al. 10 where 3 The viral dynamics during and post bNAb therapy was complex and could be divided into the 104 following phases (Figure 2). Viremia dropped post the acute infection peak to undetectable levels 105 (< 10 2 copies/mL), due to bNAb administration, where it remained until the administered bNAb level 106 in circulation declined to a point where its ability to control viremia was lost (Phase I in Figure 2a).

107
Viremia then resurged to an elevated level (∼ 10 5 copies/mL), well above the acute infection peak 108 (< 10 4 copies/mL), but subsequently declined spontaneously to a low (10 2 − 10 3 copies/mL) level certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not this version posted January 18, 2020. Fig. 2 Model fits viral dynamics in responder macaques. Model fits (blue lines) to viral load data10 (symbols) from the 10 controller macaques, shown in individual panels. Empty symbols mark measurements showing undetectable viremia and filled symbols above detection. The latter were used for fitting and the former censored. Black dashed lines in all panels indicate the viral load detection limit (100 RNA copies/mL). The corresponding bNAb concentration dynamics are in Figure 3. In all panels, phase I (yellow) marks the duration when bNAbs are present in circulation, phase II (green) the viremic resurgence post the clearance of bNAbs, phase III (blue) the ensuing viremic control, and, where relevant, phase IV (pink), in two parts, the disruption of this control using anti-CD8α and anti-CD8β Abs, respectively. For the macaque MVJ, we demonstrate the loss of viral control that occurs when effector depletion levels are increased (magenta line), as is observed with the macaque DFIK. The digitized data used for the fitting is available as a supplementary excel file (Database.xlsx). In all cases, predictions without bNAb therapy are included for comparison (red lines). Parameter values used are in Tables 1 and S1. Macaques DEWP, MVJ, DFFX, DFKX, and DFIK were inoculated intrarectally and DEWL and MAF intravenously with 1000 TCID50 (50% tissue culture infective dose) of SHIVAD8-EO virus. DEMR, DEBA, and DEHW received 100 TCID 50 intravenously.   certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not this version posted January 18, 2020. ; https://doi.org/10.1101/548727 doi: bioRxiv preprint  Table S2. lowing bNAb therapy as well as CD8 depletion, that lasting control observed with early bNAb therapy 122 was a distinct steady state of the system. This hypothesis of bistability, or the existence of two distinct  Tables 1 and 2. Bifurcation diagrams for other parameters are shown in Figure S1. To indicate the two steady states for given parameter values, we use red and blue filled squares, certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

Early, short-term bNAb therapy switches the outcome to viremic control via pleiotropic effects
When a new infection occurs, viremia rises significantly during the acute infection phase and achieves 136 high levels typically before an adaptive effector response is mounted. 36 The effector response thus    Tables 1  and S1). The corresponding dynamics of (c,d) the effector response and (e,f) the level of effector exhaustion. The phases are color coded as in Figure 2. Red lines in all panels indicate model predictions with the same parameter values but in the absence of bNAb therapy. Our model predicts thus that bNAb therapy switches disease dynamics from reaching the high viremic, disease progressive state to the state of viremic control. Black dashed lines in (a,b) indicate the viral load detection limit (100 RNA copies/mL).
Our model also predicts that early bNAb therapy drove the infection to the state of lasting viremic 143 control (blue lines in Figure 6), in agreement with the observations in Nishimura et al. 10 . Further, our 144 model predicts that pleiotropic effects of bNAbs were involved in orchestrating this transition: During 145 14 certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not this version posted January 18, 2020. ; https://doi.org/10.1101/548727 doi: bioRxiv preprint acute infection, bNAbs suppressed the viremic peak by enhancing viral clearance. The lower viremia Our analysis suggests, thus, that the rapid clearance of the virus, which lowered viremia and reversed effector exhaustion, together with increased antigen uptake, which led to enhanced effector stimula-175 tion, resulted in the lasting control of viremia elicited by early, short-term bNAb therapy. progression with low (red) initial effector numbers (E * (0)). All other parameters are the same as those that yield the best-fit to the macaque DEHW (Table S1).

177
If ART were used instead of bNAbs, for a duration equivalent to the time over which the administered 178 bNAbs were in circulation, viral load quickly became undetectable during treatment in our model but certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not this version posted January 18, 2020. ; https://doi.org/10.1101/548727 doi: bioRxiv preprint of the size of the latent reservoir in post treatment control with ART 18 . The primed effector population following bNAb therapy, in contrast, drove the system to viremic control in our model. Because of their 188 pleiotropic effects, bNAbs would thus have a significant advantage over ART, explaining their much 189 higher success rate in achieving lasting control.  Tables 1 and S1. Efficacy of ART is assumed to be ε = 0.8.) The duration of ART is shown as a grey region. The black dashed lines in (a) indicates the viral load detection limit (100 RNA copies/mL).

191
The recent success of passive immunization with bNAbs in eliciting functional cure of HIV-1 infection  Our study is thus conservative in its assessment of the influence of bNAbs. We did not consider data certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

251
Model equations 252 We constructed the following equations to describe the viral dynamics depicted schematically in Figure   253 1.
Here, uninfected target CD4 + T cells, T , are produced at the rate λ T , die at the per capita rate d T , certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not this version posted January 18, 2020. at the maximal rate ξ , with the half-maximal parameter q c and Hill coefficient n. The level of exhaus-294 tion, Q, increases with antigen level at the maximal rate κ and with the half-maximal parameter φ 2 .

295
Exhaustion is reversed with the rate constant d q . effectors are lost at the per capita rate d E . We note 296 that E is a measure of the effective effector pool, consisting of activated NK cells and SHIV-specific 297 CTLs, and factoring in the overall level of exhaustion, Q. E is thus not to be viewed as a cell count. of HIV 18 , also shows bistability but could not fit the present data with bNAb therapy ( Figure S4 and 301   Table S5). Similarly, variants of our model without the Hill coefficient, i.e., n=1 18 ( Figure S5 and Ta-302 ble S6), and with a Hill coefficient of n=3 19 ( Figure S6 and Table S7), or without an explicit effector 303 response ( Figure S7 and Table S8) could not fit the data. We also fit the viral load data by letting k E 304 vary. The model fits ( Figure S8 and Table S9) were comparable to the main model ( Figure 2) but with 305 higher AIC (Table 3). certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not this version posted January 18, 2020. ; https://doi.org/10.1101/548727 doi: bioRxiv preprint and γδ T cells. Nishimura et al. 10 also administered anti-CD8β antibodies to some macaques, which presumably only depleted CD8 + T cells. To describe the resulting changes in viremia, we assumed 322 that the depleting effects of anti-CD8α and anti-CD8β antibodies started at time points θ α and θ β , 323 respectively, at which points we reduced the effector populations by fractions ζ α and ζ β . Further, 324 we assumed that anti-CD8α antibodies neutralized all host effector functions, which we modelled by 325 setting m = 0 for a duration θ m representing the residence time of the depleting antibodies.

326
The procedures for solving the above model equations, parameter estimation, and data fitting are 327 described next. All the data employed for fitting was obtained by digitizing the data published in   331 For ease of solution and parameter estimation, we rescaled Eqs. 1-8 in the main text using the quan-332 tities in Eqs. 9 and 10 and obtained an equivalent model with fewer parameters (Eqs. 11-18). bNAb 333 concentrations, A 1 and A 2 , and viral load, V , were not scaled because they were used for fitting data.

Solution of model equations
23 certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not this version posted January 18, 2020. ; https://doi.org/10.1101/548727 doi: bioRxiv preprint certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not this version posted January 18, 2020. ; https://doi.org/10.1101/548727 doi: bioRxiv preprint k E was fixed (Table 3). Here, we therefore chose a model with fixed k E and conservatively set k E = 0.1 day -1 . (Note that the k E here represents the effective expansion of all effectors and not CTLs alone, 360 which may have a higher expansion rate. 18 ) We set the Hill coefficient for exhaustion, n = 4, following 361 studies that recognize underlying non-linearities 18,19 and because smaller integral values of n did not 362 yield good fits (see below). Further, we set φ 1 = φ 2 = φ following earlier studies 19 and because fitting 363 them as separate variables yielded best-fit values that were close, φ 1 ∼ 2.1 × 10 −5 and φ 2 ∼ 5.7 × 10 −5 , 364 but with a higher AIC (Table 3). 365 We divided the remaining parameters into two sets, ϑ = {β , m * , p * , f * , φ * , d E , ξ , V (0), Vol 1 , Vol 2 , 366 k 1 , k 2 , K} and ρ = {ω 1 , ω 2 , η 1 , η 2 }, the former assumed to follow log-normal and the latter logit-367 normal distributions, respectively. To estimate these parameters, we employed a population-based 368 fitting approach using non-linear mixed effects (NLME) models to jointly fit the log plasma viral load 369 (both treated and untreated animals) and antibody concentrations of the ten responder macaques  Briefly, the parameters for all the individual macaques were assumed to be sampled from a common 375 population distribution, and the aim of the fitting exercise was to obtain estimates for the mean and 376 variance of this distribution for each parameter. For each macaque i, parameters ϑ i were estimated 377 assuming underlying log-normal distributions of the form: where µ is the set of the population means and ψ i ∼ N(0, σ ) are normally distributed 'random effects' 379 whose variances are to be estimated. Similarly, parameters ρ i for macaque i were estimated assuming 380 underlying logit-normal distributions of the form: 25 certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not this version posted January 18, 2020. ; https://doi.org/10.1101/548727 doi: bioRxiv preprint where ρ min i and ρ max i are the minimum and maximum allowed values for parameters in ρ i . The latter 382 limits were set so that ω 1 , ω 2 ∈ [0, 5], and η 1 , η 2 ∈ [0.01 − 7] day -1 , expected from the 1 week dosing 383 interval employed. To account for measurement errors in observed viral loads and bNAb levels (y(t)), 384 we defined a 'combined error' model such that y(t) is normally distributed around a true value (y * (t)) 385 as described by the following equation: 386 y(t) = y * (t) + (a + b y * (t)) ψ y (t), ψ y ∼ N(0, 1) where a is the constant error term and b is the error term proportional to the true value, y * (t).

387
All fitting except CD8 depletion was performed using Monolix software version 2019R1 (www.
where bNAb pharmacodynamics (A 1 and A 2 ) remain as before (Eqs. S9 and S10). Again, the model  Effector proliferation rate. Lastly, we checked whether a varying effector proliferation rate (k E in Eq.

455
14) made a difference to the model fits to viral load data. The fits ( Figure S8) were not better than 456 those obtained with our main model by fixing k E = 0.1 day -1 (Figure 2), but had higher AIC (Table 3). 457 29 certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not this version posted January 18, 2020. ; https://doi.org/10.1101/548727 doi: bioRxiv preprint certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.