Thresholds for postrebound SHIV control after CCR5 geneedited autologous hematopoietic cell transplantation
Abstract
Autologous, CCR5 geneedited hematopoietic stem and progenitor cell (HSPC) transplantation is a promising strategy for achieving HIV remission. However, only a fraction of HSPCs can be edited ex vivo to provide protection against infection. To project the thresholds of CCR5edition necessary for HIV remission, we developed a mathematical model that recapitulates blood T cell reconstitution and plasma simianHIV (SHIV) dynamics from SHIV1157ipd3N4infected pigtailed macaques that underwent autologous transplantation with CCR5 gene editing. The model predicts that viral control can be obtained following analytical treatment interruption (ATI) when: (1) transplanted HSPCs are at least fivefold higher than residual endogenous HSPCs after total body irradiation and (2) the fraction of protected HSPCs in the transplant achieves a threshold (76–94%) sufficient to overcome transplantationdependent loss of SHIV immunity. Under these conditions, if ATI is withheld until transplanted genemodified cells engraft and reconstitute to a steady state, spontaneous viral control is projected to occur.
Introduction
The major obstacle to HIV1 eradication is a latent reservoir of longlived, infected cells (Chun et al., 1997; Chun et al., 1995; Finzi et al., 1997). Cure strategies aim to eliminate all infected cells or permanently prevent viral reactivation from latency. The only two known cases of HIV cure, the ‘Berlin Patient’ and ‘London Patient’, resulted from allogeneic hematopoietic stem cell (HSC) transplant with homozygous CCR5Δ32 donor cells (Allers et al., 2011; Hütter et al., 2009; Gupta et al., 2019; Gupta et al., 2020), a mutation that makes cells resistant to CCR5tropic HIV1. The Berlin Patient was diagnosed with HIV in 1995 and received total body irradiation and alloHSC transplantation for the treatment of his acute myeloid leukemia in 2007 and 2008. On the day of his first transplantation, antiretroviral therapy (ART) was interrupted, and HIV viremia never returned (Allers et al., 2011; Hütter et al., 2009; Peterson and Kiem, 2019). In 2019, an HIV1 remission for more than 18 months was reported in the London Patient as part of the IciSTEM cohort (Gupta et al., 2019). The London Patient underwent one alloHSC transplantation for treatment of Hodgkin Lymphoma in 2016, but with a less aggressive conditioning compared to the Berlin patient without irradiation (Gupta et al., 2019). This individual stopped ART 17 months after transplantation and as of March, 2020 his viremia remains suppressed, representing a possible case of HIV1 cure (Gupta et al., 2020). The success of the alloHSC transplantation is likely multifactorial—in part attributable to HIV resistance of the transplanted cells, the conditioning regimen that facilitates engraftment and eliminates infected cells, graftversushost effect against residual infected cells, and immunosuppressive therapies for graftversushost disease (Henrich et al., 2016; Henrich et al., 2014; Henrich et al., 2013; Salgado et al., 2018).
We are interested in recapitulating this method of cure but with reduced toxicity. Specifically, we are investigating the use of autologous transplantation following ex vivo inactivation of the CCR5 gene with geneediting (Tebas, 2014; Peterson et al., 2016). This procedure is safe and feasible in pigtail macaques infected with simianHIV (SHIV) (Peterson et al., 2016; Peterson et al., 2017; Peterson et al., 2018) and is currently being investigated in a Phase I clinical trial in suppressed, HIV1infected humans (NCT02500849). Also, this approach is more broadly applicable because an allogeneic CCR5negative donor is not needed. However, current data suggests that protocols do not achieve sufficient fractions of genetically modified HIVresistant hematopoietic stem and progenitor cells (HSPCs). In contrast, in allogeneic transplant, nearly 100% of circulating immune cells after engraftment consist of donorderived CCR5Δ32 cells. This leads to a key question: what threshold percentage of CCR5edited, autologous HSPCs is necessary for the cure/longterm remission observed in the Berlin and London patients?
To answer this question, we developed a mathematical model that predicts the minimum threshold of genemodified cells necessary for functional cure. First, we modeled the kinetics of CD4^{+}CCR5^{+}, CD4^{+} CCR5^{}, and CD8^{+} T cell reconstitution after autologous transplantation. Then, we modeled SHIV kinetics during acute infection and rebound following ATI to identify the degree of loss of antiHIV cytolytic immunity following transplantation as presented before but including some additional data (Peterson et al., 2017; Reeves et al., 2017). Finally, we applied our models to predict the proportion of genemodified cells, the dose of these cells relative to the intensity of the preparative conditioning regimen (total body irradiation, TBI), and the levels of SHIVspecific immunity required to maintain virus remission following ATI. Results from this threepart modeling approach support strategies that (1) increase stem cell dose, (2) enhance potency of conditioning regimen to reduce the number of endogenous HSPCs that compete with transplanted CCR5edited HSPCs, (3) increase the fraction of genemodified SHIVresistant cells, (4) extend periods between HSPC transplantation and ATI with tracking of CCR5 cell recovery and/or (5) augment antiHIV immunity to achieve sustained HIV remission.
Results
Study design and mathematical modeling
We analyzed data from 22 juvenile pigtailed macaques that were intravenously challenged with 9500 TCID50 SHIV1157ipd3N4 (SHIVC) (Figure 1A). After 6 months of infection, the macaques received combination ART that included tenofovir (PMPA), emtricitabine (FTC), and raltegravir (RAL). When on ART, 17/22 received total body irradiation (TBI) followed by the transplantation of autologous HSPCs with (n = 12) or without (n = 5) CCR5 gene editing (ΔCCR5 and WT groups, respectively). A control group (n = 5) did not receive TBI or HSPC transplantation. 14 of the animals underwent ATI approximately 1 year after ART initiation. The remaining eight animals were necropsied at an earlier time relative to the other animals’ ATI (see Materials and methods for details).
To analyze the data and estimate thresholds for viral control under this approach, we used ordinary differential equation models. We performed multistage modeling (Figure 1B). First, we modeled the kinetics of CD4^{+} and CD8^{+} T cell subsets after autologous HSPC infusion following transplant and before ATI, assuming that ART suppression decouples SHIVdynamics from cellular dynamics. After validation of the firststage model, we introduced a secondstage of modeling to (1) explain virus and T cell kinetics during primary infection and ATI and to (2) identify the degree of loss of antiHIV cytolytic immunity due to the preparative conditioning. Then, we used the final validated model to project SHIV kinetics assuming different transplantation conditions.
CD4^{+}CCR5^{+} and CD8^{+} T cells recover more rapidly than CD4^{+}CCR5^{} T cells after HSPC transplantation
We analyzed the kinetics of peripheral blood CD4^{+}CCR5^{+} and CD4^{+}CCR5^{} T cells, and total, T_{naive}, T_{CM}, and T_{EM} CD8^{+} T cells in macaques after HSPC transplantation.
In untransplanted controls, levels of CD4^{+} and CD8^{+} T cells oscillated around a persistent set point (blue datapoints in Figure 2A). Also, CD4^{+} CCR5^{+} T cell levels were ~100 cells/μL and were uniformly lower than the CD4^{+}CCR5^{} T counts (each ~1000 cells/μL) (Figure 2—figure supplement 1A). Finally, total CD8^{+} T cell levels in the control group were ~1400 cells/μL with a greater contribution from T_{EM} (73%) than T_{N}+T_{CM} (27%) (based on median values, Figure 2—figure supplement 1).
In the transplant groups, postTBI levels of CD4^{+}CCR5^{+}, CD4^{+}CCR5^{}, and CD8^{+} T cells were significantly lower than in the control group but expanded at different rates during the following weeks (Figure 2A–C). The levels of CD4^{+}CCR5^{+} T cells started at 1–10 cells/μL and reconstituted to levels similar to the control group over 5–10 weeks (Figure 2A–B). CD4^{+}CCR5^{} T cells remained at higher levels (~100 cells/μL) than CD4^{+}CCR5^{+} T cells after TBI but expanded more slowly and did not reach the values of the control group after 25 weeks (Figure 2A–B). The CD4^{+}CCR5^{+} T cell compartment expanded eightfold more rapidly than the CD4^{+}CCR5^{} compartment (p=0.008, paired MannWhitney test, Figure 2C). CD8^{+} T cells decreased to levels between 10 and 100 cells/μL after TBI but recovered to levels just below the control group in 5 weeks (Figure 2A–B); CD8^{+} T cells recovered as rapidly as the CD4^{+}CCR5^{+} population (Figure 2C).
Overall, these results show that after transplantation CD4^{+}CCR5^{+} and CD8^{+} T cells recover faster than CD4^{+}CCR5^{} cells. This suggests that each cell subset may have different and/or complementary mechanisms that drive their expansion. To explore these mechanisms, we analyzed the data with a mechanistic mathematical model of cellular dynamics.
Lymphopeniainduced proliferation drives early CD4^{+}CCR5^{+} and CD8^{+} T cell reconstitution after HSPC transplantation
To identify the main drivers of T cell reconstitution after transplant, we developed a mathematical model that considered plausible mechanisms underlying reconstitution of distinct T cell subsets following autologous transplantation (Figure 3A). We assumed that T cell reconstitution may have two main drivers: (1) lymphopeniainduced proliferation of mature cells that persist through myeloablative TBI (Jameson, 2002; Schluns et al., 2002; Schluns et al., 2000; Goldrath et al., 2004; Voehringer et al., 2008) and (2) differentiation from naive cells from progenitors in the thymus (from transplanted CD34^{+} HSPCs (Douek et al., 2000; Douek et al., 1998) or residual endogenous CD34^{+} HSPCs that persist following TBI) and further differentiation to an activated effector state (Voehringer et al., 2008; Bender et al., 1999; Kieper and Jameson, 1999; Sallusto et al., 2004; Le Saout et al., 2008; Sprent and Surh, 2011). We also assumed the infused product dose $D$ contains a fraction ${f}_{p}$ of transplanted, geneedited HSPCs that do not express CCR5 (see Figure 3—source data 1 for individual values of $D$ and ${f}_{p}$). Thus, in our model, ΔCCR5genemodified CD4^{+} T cells differentiating from these modified HSPCs are a subset of the total CD4^{+}CCR5^{} cell compartment (Figure 3A).

Figure 3—source code 1
 https://cdn.elifesciences.org/articles/57646/elife57646fig3code1v1.zip

Figure 3—source code 2
 https://cdn.elifesciences.org/articles/57646/elife57646fig3code2v1.zip

Figure 3—source data 1
 https://cdn.elifesciences.org/articles/57646/elife57646fig3data1v1.docx

Figure 3—source data 2
 https://cdn.elifesciences.org/articles/57646/elife57646fig3data2v1.docx

Figure 3—source data 3
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Figure 3—source data 4
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Figure 3—source data 5
 https://cdn.elifesciences.org/articles/57646/elife57646fig3data5v1.zip
We built 24 versions of the model by assuming that one or multiple mechanisms are absent, or by assuming certain mechanisms have equivalent or differing kinetics (Figure 3—source data 2). Using model selection theory, we identified the most parsimonious model that reproduced the data (schematic in Figure 3A without reddashed lines). The best model predictions for each cell subset using maximum likelihood estimates of the population parameters (Figure 3—source data 3) are presented in Figure 3B. Individual fits are visualized in Figure 3—figure supplement 1–3 and parameter estimates are collected in Figure 3—source data 4.
Model selection illuminated several likely biological phenomena: (1) CD4^{+}CCR5^{+} T cell reconstitution after transplant is determined by cell proliferation and to a minor degree by upregulation of CCR5 (Figure 3C); (2) CD4^{+}CCR5^{} T cell expansion is driven primarily by new naive cells from the thymus and to a lesser extent by CCR5 downregulation (Figure 3C); and (3) thymic export is not significantly different for CD4^{+} or CD8^{+} T cells (Figure 3—source data 2). However, model selection could not distinguish between the two models where ΔCCR5genemodified CD4^{+} T cells have the kinetics of both nonmodified CD4^{+}CCR5^{+} and CD4^{+}CCR5^{} versus only the kinetics of nonmodified CD4^{+}CCR5^{} (i.e. having compartment N_{p}_{2} or not in Figure 3A). Regardless, these two best models were identical in all other respects (Figure 3—source datas 2 and 3).
This firststage modeling suggested additional testable biological predictions. First, the estimated CD4^{+}CCR5^{+} T cell proliferation rate (~0.1/day) far exceeds the estimated CCR5 upregulation (~0.004/day) and thymic export rates (~0.002/day). Therefore, 1 month after transplantation, the total concentration of CD4^{+}CCR5^{+} T cells generated by proliferation is predicted to be 40fold higher than the concentration generated by upregulation of CCR5 (Figure 3C). Second, the CD8^{+} T_{EM} cells comprise the majority of the total CD8^{+} T cell compartment (Figure 3B) with a proliferation rate up to 10fold higher than the CD8^{+} T_{CM} cell differentiation rate (Figure 3—figure supplement 4). In this way, CD8^{+} T cells follow a similar pattern to CD4^{+}CCR5^{+} T cells (Figure 3B).
In summary, following autologous HSPC transplant: (1) thymic export and downregulation of CCR5 drive a modest expansion of CD4^{+}CCR5^{} T cells, whereas (2) rapid lymphopeniainduced proliferation after TBI is the main driver for CD4^{+}CCR5^{+} and CD8^{+} T cell expansion, which are derived from both the transplanted HSPC product and residual endogenous cells that persisted through the myeloablative conditioning regimen.
Plasma virus and blood CD4^{+}CCR5^{+} dynamics are heterogenous among transplanted, SHIVinfected animals
To build a mathematical model for the virus and T cell dynamics, we analyzed plasma viral load kinetics and CD4^{+}CCR5^{+}/CCR5^{} T cell subset dynamics after ATI with respect to kinetics preART (Peterson et al., 2017; Reeves et al., 2017). Figure 4A presents the plasma viral loads and the blood CD4^{+}CCR5^{+} and CD4^{+}CCR5^{} T cell kinetics before and after transplantation in the three groups.
We calculated the ratio of the viral load at necropsy versus at initiation of ART (Figure 4B) and the ratio of the nadir and median viral load after ATI versus preART (Figure 4C–D). In general, the viral burden after ATI compared to preART was slightly lower for the control group. However, for transplanted animals the viral load changes were heterogeneous, having much higher ratios for the wildtype (WT) group and slightly higher for CCR5edited (ΔCCR5) group. For the three computed ratios, the viral load change after ATI was between 10 and 100fold for the wildtype group (Figure 4B–D).
During ATI, CD4^{+}CCR5^{+} T cells declined heterogeneously in the transplanted groups (Figure 4A), but CD4^{+}CCR5^{+} T cell nadirs in the transplanted groups were consistently lower than those of control animals whose CD4^{+}CCR5^{+} T cell levels did not decrease (Figure 4—figure supplement 1A). On the other hand, blood CD4^{+}CCR5^{} T cell levels decreased to a similar nadir in all groups during ATI (Figure 4A and Figure 4—figure supplement 1B).
To summarize, SHIV viral load and CD4^{+}CCR5^{+} dynamics are heterogeneous among transplanted animals. Higher ATI versus preART viral load ratios in transplanted animals suggest that transplantation affects the host response against SHIVreplication, but this damage to host response may be mitigated somewhat when transplantation includes CCR5edition.
A reduction in SHIVspecific immunity leads to higher viral rebound set points following ATI in transplanted animals
We simultaneously analyzed the viral and T cell subset data using mechanistic mathematical models in order to recapitulate the heterogeneity of plasma viral load and CD4^{+}CCR5^{+} T cell kinetics and how transplantation may modify the immune response during ATI compared to the preART stage. We extended our T cell reconstitution model to include SHIV infection of CD4^{+}CCR5^{+} T cells (Figure 5A and Methods) and used this secondstage model to analyze virus and T cell dynamics during primary SHIVinfection, ART, transplant, and ATI.

Figure 5—source code 1
 https://cdn.elifesciences.org/articles/57646/elife57646fig5code1v1.zip

Figure 5—source code 2
 https://cdn.elifesciences.org/articles/57646/elife57646fig5code2v1.zip

Figure 5—source code 3
 https://cdn.elifesciences.org/articles/57646/elife57646fig5code3v1.zip

Figure 5—source data 1
 https://cdn.elifesciences.org/articles/57646/elife57646fig5data1v1.docx

Figure 5—source data 2
 https://cdn.elifesciences.org/articles/57646/elife57646fig5data2v1.docx

Figure 5—source data 3
 https://cdn.elifesciences.org/articles/57646/elife57646fig5data3v1.docx

Figure 5—source data 4
 https://cdn.elifesciences.org/articles/57646/elife57646fig5data4v1.zip
Again, following model selection theory based on AIC, we compared six mechanistic models and found a parsimonious model to explain the data (Figure 5A, Figure 5—source data 1). This model simultaneously recapitulates plasma viral load and the kinetics of CD4^{+} CCR5^{+} and CCR5^{} T cells as shown in Figure 5B and Figure 5—figure supplements 1–3 with corresponding estimated parameters in Figure 5—source datas 2 and 3. In the best fitting model, parameters related to immune response against infection: the SHIVspecific CD8^{+} T cell proliferation (${\omega}_{8}$), saturation (${I}_{50}$), and death rates (${d}_{h}$) were different during ATI and the preART stage (see Figure 5—source data 1; Reeves et al., 2017). SHIVspecific CD8^{+} effector cells reduce virus production rather than killing infected cells (Elemans et al., 2011; Klatt et al., 2010; Wong et al., 2010), possibly by secretion of HIVantiviral factors (Shridhar et al., 2014; Blazek et al., 2016; Zhang et al., 2002)—not explicitly included in the model. The model also suggests that infection enhances upregulation of CD4^{+}CCR5^{} T cells. This upregulation transiently reduces the CD4^{+}CCR5^{} compartment and replenishes CD4^{+}CCR5^{+} T cells after ATI (Douek et al., 2003; Okoye et al., 2007; Okoye et al., 2012). Finally, in this model, some of the ΔCCR5genemodified CD4^{+} T cells also have kinetics similar to nonmodified CD4^{+}CCR5^{+} cells (i.e. it includes the compartment N_{p}_{2} as in Figure 5A), whereas this was not able to be differentiated in the firststage modeling.
We used our model to compute the SHIVspecific CD8^{+} T cell turnover rates after ATI and during preART as measures of SHIVspecific immunity ($SI$) for each stage, that is, $S{I}_{ATI}=\frac{{\omega}_{8}^{ATI}}{{d}_{h}^{ATI}}$ and $S{I}_{preART}=\frac{{\omega}_{8}^{preART}}{{d}_{h}^{preART}}$, respectively. We found that the SHIV immunity ATI/preART ratio $\left(\frac{S{I}_{ATI}}{S{I}_{preART}}\right)$ correlated negatively with the ATI/preART ratio of the observed nadir and median viral loads (Figure 5C–D). In this sense, the viral burden increase during ATI (viral burden ratio >1) in animals in the transplant groups might be due to the underlying loss of the immune response to the virus ($\frac{S{I}_{ATI}}{S{I}_{preART}}<1$, Figure 5C–D). Similarly, decrease in viral burden during ATI (viral burden ratio <1) in animals in control and ΔCCR5 groups might be due immune response memory or its recovery, respectively ($\frac{S{I}_{ATI}}{S{I}_{preART}}>1$, Figure 5C–D).
In conclusion, we developed a secondstage model that simultaneously recapitulates viral and T cell dynamics from SHIVinfected animals receiving autologous HSPC transplantation. The model suggests that transplant may reduce host Tcell immunity resulting in higher viral loads after ATI compared to the preART stage. However, SHIV immunity might be recovered if CCR5 disruption is added in the transplant resulting in lower viral loads after ATI.
PostATI viral control requires a large HSPC dose containing a high fraction of CCR5edited cells
An important advantage of our model is the ability to calculate the conditions required for postATI viral control (viral load set point <30 copies/ml) after CCR5edited autologous transplant. To this end, we used our secondstage model to approximate an effective reproductive ratio ${R}_{eff}$ to describe the ability of the virus to sustain infection after ATI in transplanted animals (see Materials and methods):
Here, ${f}_{p}$ describes the fraction of protected HSPCs in the transplant product, $D$ the dose or total number of infused HSPCs, and ${P}_{r}$ the number of residual endogenous HSPCs after conditioning (variable $P$ at time of transplant, Figure 3A). ${R}_{T}$ is the approximate number of new infections caused by one infected cell after T cell complete reconstitution postconditioning as defined in Equation 4 (see Materials and methods) and is inversely related to the antiSHIV immune response at the time of ATI. PostATI viral control depends on the fraction of protected HSPCs in the body immediately after transplant that are protected from SHIV infection, or $\left(\frac{{f}_{p}D}{D+{P}_{r}}\right)$.
To estimate the values of ${f}_{p}$, $D$, and ${P}_{r}$ needed for viral control, we first estimated ${R}_{T}$ for each animal based on individual parameter estimates pertaining to SHIV virulence and antiSHIV immunity. We then simulated the model for each animal using varying values of f_{p} from zero to one (0–100% CCR5edited HSPCs), values of $D$ from 10^{6} to 10^{9} HSPCs, and values of ${P}_{r}$ from zero to 10^{7} HSPCs. As an illustration, Figure 6A depicts projections of the model for ΔCCR5transplanted animal A11219 for a range of values of ${f}_{p}$ when $D={10}^{7}$ HSPCs/kg and ${P}_{r}=6\times {10}^{6}$ HSPCs. When ${f}_{p}$, $D$ and ${P}_{r}$ resulted in ${R}_{eff}\ge 1$, plasma virus was not controlled following viral rebound postATI. When ${R}_{eff}$ < 1, postrebound control was observed, but only at weeks 40–60 postATI, following an initial decrease in viral loads beginning 30–40 weeks after ATI. In this case, postrebound control occurred concomitantly with ΔCCR5 CD4^{+} T cell complete reconstitution relative to nonedited CCR5^{+/} CD4^{+} T cells (Figure 6B). Lower values of ${R}_{eff}$ resulted in earlier postrebound control (earliest ~40 weeks).

Figure 6—source code 1
 https://cdn.elifesciences.org/articles/57646/elife57646fig6code1v1.zip

Figure 6—source code 2
 https://cdn.elifesciences.org/articles/57646/elife57646fig6code2v1.zip

Figure 6—source data 1
 https://cdn.elifesciences.org/articles/57646/elife57646fig6data1v1.zip
Indeed, for all animals, posttreatment control occurred when values of ${f}_{p}$, $D$, and ${P}_{r}$ resulted in ${R}_{eff}<1$ (Figure 6—figure supplement 1). Model predictions for animal A11200 demonstrate that regardless of the fraction of protected HSPCs in the transplant (${f}_{p}$), viral control is possible only when the ratio of HSPCs in the transplant to the residual endogenous HSPCs in the body postTBI ($D:{P}_{r}$) is above 5 (Figure 6C). Moreover, if the ratio $D:{P}_{r}$ is greater than 5, the minimum fraction of protected cells required is 76%, and further increasing $D:{P}_{r}$ does not decrease ${f}_{p}$ significantly. From all transplanted animals we found that the minimum fraction of protected cells in the transplant ${f}_{p}$ varied from 76% to 94% and was positively correlated with a weaker antiSHIV immune response of the given animal defined by ${R}_{T}$ (Figure 6D and Figure 6—figure supplement 2). This is consistent with Equation 1 as ${R}_{eff}\approx {R}_{T}\left(1{f}_{p}\right)$ when $D\gg {P}_{r}$. ${R}_{T}$ varied from 4 to 16 across animals using individual parameter estimates in Figure 5—source data 3. The required levels for ${f}_{p}$ are lower in the context of more intense antiSHIV immunologic pressure and lower viral strength. This result argues for strategies that (1) augment antiSHIV immunity despite conditioning (lower ${R}_{T}$ using SHIVspecific CAR T cells, therapeutic vaccination, etc.), (2) increase the stem cell dose relative to the residual endogenous stem cells ($D:{P}_{r}$) after transplant—perhaps by enhancing potency of the conditioning regimen, and (3) increase the fraction of genemodified, SHIVresistant cells $\left({f}_{p}\right)$.
Based on the observation that viral control occurred when CD4^{+} T cell subsets approached a steady state in the simulations (Figure 6A–B), we simulated the model again to determine whether viral control might occur faster if ATI was postponed at a time when more mature, protected cells have expanded. As an illustration, we simulated animal A11219 under conditions that lead to viral control: ${f}_{p}=0.95$, $D={10}^{8}$ HSPCs and ${P}_{r}={10}^{7}$ HSPCs with ATI occurring at 3, 14, 25, or 37 weeks after transplantation. Indeed, time to postATI viral control (shaded areas in Figure 7A) decreased as time to ATI was extended after transplant and as the difference between CD4^{+}CCR5^{} cell density at ATI and its expected set point decreased (shaded areas in Figure 7B). In this case, ΔCCR5 CD4^{+} T cells comprised the majority of the CD4^{+}CCR5^{} T cell compartment (Figure 7B). Further, we simulated increasing times of ATI using parameter estimates for all transplanted animals but under conditions that lead to viral control (${f}_{p}>0.95$, $D={10}^{8}$ HSPCs and ${P}_{r}={10}^{7}$ HSPCs). The model predicted the same decreasing pattern with times between transplant and ATI required to avoid viral rebound from 20 to 60 weeks (Figure 7C). This timeframe allowed all animals to achieve viral control due to CD4^{+}CCR5^{} cell densities at ATI exceeding 60–90% of the ultimate steady state value (Figure 7D). As in Figure 7B for all animals ΔCCR5 CD4^{+} T cells comprised the majority of the CD4^{+}CCR5^{} T cell compartment.
In summary, our model predicts that postATI viral control during autologous HSPC transplantation is obtained when (1) the transplanted HSPC dose is significantly higher than the residual endogenous HSPCs that persist through myeloablative conditioning (in this case TBI) and (2) the fraction of protected (i.e. CCR5edited) HSPCs in the transplant $\left({f}_{p}\right)$ is sufficiently high to outcompete cells susceptible to infection and disrupt ongoing cycles of viral replication. Spontaneous postrebound control occurs after CCR5^{} CD4^{+} T cells achieve a steady state approximately 1year after transplantation. Hence, our model suggests that, under the two described conditions, prolonging time to ATI (at least 1year posttransplantation) may increase the likelihood of rapid viral control postATI. Moreover, specifically tracking CD4^{+}CCR5^{} (or CCR5edited CD4^{+}) T cell growth and waiting for steadystate could be used as a surrogate for the decision to undergo ATI.
Discussion
Here we introduce a datavalidated mathematical model that, to our knowledge, is the first to simultaneously recapitulate viral loads as well as CD4^{+} and CD8^{+} T cell subset counts in a macaque model of suppressed HIV1 infection. In addition, our model is the first to describe dynamics of CCR5^{+} and CCR5^{} T cells within the CD4 compartment. We performed extensive, systematic data fitting comparing 30 mechanistic models to arrive at a set of equations that most parsimoniously explains the available data. In multiple stages of modeling, we recapitulated (1) peripheral CD4^{+} and CD8^{+} T cell subset reconstitution dynamics following transplant and (2) T cell subset dynamics and SHIV viral rebound following ATI. Before ATI, all animals had suppressed plasma viral loads below the limit of detection, allowing analysis of T cell reconstitution dynamics independent of virusmediated pressure. At each step, we applied model selection theory to select the simplest set of mechanisms capable of explaining the observed data (Burnham et al., 2002). Our model predicts that postrebound viral control might be possible during autologous geneedited HSPC transplantation if therapy achieves (1) a sufficient fraction of geneprotected, autologous HSPCs (2) a high dose of transplant product relative to a residual endogenous population of stem cells that persists following conditioning, and (3) enhancement of SHIVspecific immune responses following transplantation. Further, our model predicts, that under these conditions, spontaneous viral control after ATI is likely if ΔCCR5 T cells (tracked by CD4^{+}CCR5^{} T cells) are allowed to reconstitute prior to ATI. These results are consistent with the cure achieved by the Berlin and London Patients who received a transplant with 100% HIVresistant cells after intense conditioning (Allers et al., 2011; Hütter et al., 2009). In the autologous setting where 100% CCR5 editing may not be feasible, adjunctive measures that augment virusspecific immunity, such as therapeutic vaccination, infusion of HIVspecific chimeric antigen receptor (CAR) T cells or use of neutralizing antibodies, may synergize with HSPC transplantation to achieve posttreatment control (Haworth et al., 2017; Zhen et al., 2017).
Although the model predicts a potential benefit for more potent conditioning that favors engraftment of SHIVresistant cells, a more aggressive conditioning regimen may also deplete SHIVspecific immune responses and lead to less favorable toxicity profiles. On the other hand, in the absence of conditioning, the number of endogenous HSPCs will remain too high. Thus, postrebound control following ΔCCR5 transplant requires not only highly potent myeloablative conditioning, it also requires a higher percentage of geneedited cells to counteract the loss of SHIVspecific immunity. Furthermore, due to the high levels of endogenous HSPCs and lack of an engraftment ‘niche’, the longterm persistence of transplanted, CCR5edited HSPC would be exceedingly low. Alternatively, nongenotoxic conditioning regimens that target only HSPC for transplantation may prevent the loss of SHIVspecific immune cells (Palchaudhuri et al., 2016; Czechowicz et al., 2019; Srikanthan et al., 2020).
We previously demonstrated the link between disruption of the immune response during transplant and increased magnitude of viral rebound during treatment interruption (Peterson et al., 2017; Reeves et al., 2017). Here, we confirm that the increase of viral load median and nadir at ATI compare to the preART stage is correlated with the reduction of the SHIVspecific immune response during transplant, but also predict that a reduction of viral load burden at ATI compared to preART in animals receiving CCR5edited cells in the transplant is correlated to a recovery of the SHIVspecific immunity.
Our results are somewhat limited by a small sample size of 22 animals, only 12 of which underwent ΔCCR5 transplant. For that reason, several model parameters were assumed to be the same among all animals (i.e. without random effects). However, the number of observations for each animal was large enough to discriminate among several different plausible model candidates. Due to the small sample size, we also performed projections by varying the parameters related to transplantation (i.e. dose, fraction of protected cells, and residual endogenous HSPCs) and using only the estimated individual parameters rather than sampling from estimated population distributions. Reassuringly, our results align with prior mechanistic studies of cellular reconstitution after stem cell transplantation (Jameson, 2002; Douek et al., 2000; Guillaume et al., 1998; Krenger et al., 2011; Roux et al., 2000). Our analysis also suggests that the majority of reconstituting CD4^{+}CCR5^{} T cells do not proliferate and have slow rates consistent with estimates of thymic export from previous studies (Douek et al., 2000; Krenger et al., 2011; Roux et al., 2000).
Recent studies from our group and others make clear that although a preparative conditioning regimen (e.g. TBI) is essential to maximize engraftment of transplanted HSPCs, it does not clear 100% of host lymphocytes, especially those in tissues (Peterson et al., 2017; Peterson et al., 2018; Donahue et al., 2015; Radtke et al., 2017). The best fitting model predicts that incomplete elimination of lymphocytes by TBI prevents CD4^{+}CCR5^{} cells from predominating posttransplant. We found that the rapid expansion of CD4^{+}CCR5^{+} and CD8^{+} T cells during the first few weeks after HSPC transplantation is most likely due to lymphopeniainduced proliferation of residual endogenous cells after TBI rather than thymic reconstitution. CD4^{+}CCR5^{} T cells arising from thymic export of both transplanted and remaining cells are overwhelmed by more rapidly populating CD4^{+}CCR5^{+} T cells within weeks of transplantation. Going forward, we will need to identify anatomic sites (namely viral reservoir tissues such as spleen and lymph nodes) and associated mechanisms that allow activated CD4^{+}CCR5^{+} to survive conditioning.
A final important observation from our model is that CD4^{+} T cell kinetics conducive to viral control may not be reached until 20–60 weeks after transplant. Therefore, our model suggests that ATI should be delayed until CD4^{+}CCR5^{} T cells reconstitute (as a proxy for ΔCCR5 CD4^{+} T cell reconstitution) to their natural steady state. Furthermore, optimized timing of ATI would ideally be based on reconstitution of all CD4^{+} and CD8^{+} T cell subsets ensuring approximately steady state levels before discontinuing ART.
In conclusion, our mathematical model recapitulates, to an unprecedented degree of accuracy and detail, the complex interplay between reconstituting SHIVsusceptible CD4^{+} T cells, SHIVresistant CD4^{+} T cells, infected cells, virusspecific immune cells, and replicating virus following autologous, CCR5edited HSPC transplantation. Our results illustrate the capabilities of mathematical models to glean insight from preclinical animal models and highlight that modeling will be required to optimize strategies for HIV cure.
Materials and methods
Study design
Request a detailed protocolWe employed a multistage approach using ordinary differential equation models of cellular and viral dynamics to analyze data from SHIVinfected pigtailed macaques that underwent autologous HSPC transplantation during ART and to find conditions for postrebound control when geneedited cells were included in the transplant product. First, we modeled T cell dynamics and reconstitution following transplant and before ATI, assuming that low viral loads during suppressive ART do not affect cell dynamics (Figure 1B). In the second stage, we added viral load data during primary infection and after ATI and fit models to the T cell and viral dynamics simultaneously from data pre and postATI (Figure 1C). We then used the most parsimonious model, as determined by AIC, to perform simulated experiments for different transplant conditions, focusing on variables including fraction of protected cells, dose, depletion of HSPCs after conditioning, and time of ATI after transplant to find thresholds for viral control postATI.
Experimental data
Request a detailed protocolTwentytwo juvenile pigtail macaques were intravenously challenged with 9500 TCID50 SHIV1157ipd3N4 (SHIVC) (Peterson et al., 2017; Peterson et al., 2018). After 6 months, the macaques received combination antiretroviral therapy (ART): tenofovir (PMPA), emtricitabine (FTC), and raltegravir (RAL). After ~30 weeks on ART, 17 animals received total body irradiation (TBI) followed by transplantation of autologous HSPCs. In 12/17 animals the transplant product included CCR5 geneedited HSPCs (ΔCCR5 group); HSPC products in 5/17 animals were not edited (WT group). After an additional 25 weeks following transplant, when viral load was well suppressed, animals underwent ATI (Peterson et al., 2017). A control group of five animals did not receive TBI or HSPC transplantation and underwent ATI after ~50 weeks of treatment. One and six of the animals in the WT and ΔCCR5 groups, respectively, were necropsied before ATI. One of the animals in the control group was necropsied before ATI (Figure 1A). Plasma viral loads and absolute peripheral Tcell counts from CD4^{+}CCR5^{}, CD4^{+}CCR5^{+} and total CD8^{+} and subsets (naive, central memory [T_{CM}], and effector memory [T_{EM}]) were measured for the control and WT group as described previously (Peterson et al., 2017). We analyzed peripheral T cell counts and plasma viral load from infection until 43 weeks posttransplant (~25 weeks preATI and ~20 weeks postATI).
Mathematical modeling of T cell reconstitution dynamics
Request a detailed protocolWe modeled the kinetics of CD4^{+} and CD8^{+} T cell subsets in blood including residual endogenous, transplanted cells that home to the BM, and progenitor cells in the BM/thymus both from transplant and residual endogenous. We included CD8^{+} T cells in the model because CD8^{+} and CD4^{+} T cells may arise from new naïve cells from the thymus and compete with each other for resources that impact clonal expansion and cell survival (Jameson, 2002; Mehr and Perelson, 1997; Margolick and Donnenberg, 1997). We assumed that expansion of CD4^{+} and CD8^{+} T cells in the blood derives from: (1) export of naïve cells differentiated from a progenitor compartment in the BM/Thymus (Guillaume et al., 1998; Spits, 2002) ([either from transplanted (Douek et al., 2000; Douek et al., 1998)] or residual endogenous CD34^{+} HSPCs) and further differentiation to an activated effector state (Voehringer et al., 2008; Bender et al., 1999; Kieper and Jameson, 1999; Sallusto et al., 2004; Le Saout et al., 2008; Sprent and Surh, 2011; Buchholz et al., 2013; Farber et al., 2014; Kaech et al., 2002), or (2) lymphopeniainduced division of mature, residual endogenous cells that persist through myeloablative TBI (Jameson, 2002; Schluns et al., 2002; Schluns et al., 2000; Goldrath et al., 2004; Voehringer et al., 2008) as factors that drive T cell proliferation are more accessible (i.e. selfMHC molecules on antigenpresenting cells [Bender et al., 1999; Kieper and Jameson, 1999; Tanchot, 1997] and γchain cytokines such as IL7 and IL15 [Schluns et al., 2002; Schluns et al., 2000; Goldrath et al., 2004; Tan et al., 2001]). However, as they grow, cells compete for access to these resources, limiting clonal expansion (Jameson, 2002) such that logistic growth models are appropriate (Mehr and Perelson, 1997).
In our mathematical model, transplanted HSPCs T home to the bone marrow at a rate k_{e}. We assumed a singlecell compartment for T cell progenitors in the bone marrow (BM)/thymus represented by variable P. We assumed that P renew logistically with maximum rate r_{p}, differentiate into naïve CD4^{+} and CD8^{+} T cells at rates λ_{f} and λ_{e}, respectively, or are cleared at rate d_{p} (Stiehl and MarciniakCzochra, 2011; Stiehl et al., 2014; Stiehl and MarciniakCzochra, 2017). We assumed two CD4^{+} T cell compartments: SHIVnonsusceptible, i.e. CD4^{+} T cells that do not express CCR5 (CD4^{+}CCR5^{} T cells) N, and a SHIVsusceptible compartment, S (CD4^{+}CCR5^{+} T cells). Only the N compartment includes CD4^{+} naïve cells migrating from the thymus (Bleul et al., 1997; Zaitseva et al., 1998; Berkowitz et al., 1998) at an input rate λ_{f}P cells per day (Douek et al., 2000; McCune, 1997). N cells grow with maximum rate r_{n}, upregulate CCR5 (27) at rate λ_{n}, and are cleared from the periphery at rate d_{n}. The S compartment does not have a thymic input but can grow with maximum division rate r_{s}, downregulate CCR5 (27) at a rate λ_{s}, and are cleared at rate d_{s}. We model CD8^{+} T cell reconstitution assuming a compartment for naïve and central memory cells, M, and a compartment for the effector memory subset, E. We assumed that M cells have thymic input of λ_{e}P cells per day, grow logistically with maximum division rate r_{m}, differentiate to effector memory at rate λ_{m}, and are cleared at rate d_{m}. The E compartment grows with maximum division rate r_{e} and is cleared at rate d_{e}. We added variables T_{p}, P_{p}, N_{p1} and N_{p2}, representing CCR5 genemodified transplanted HSPCs, T cell progenitor cells in BM/thymus, and blood CD4^{+}CCR5^{} T cells with CD4^{+}CCR5^{} and CD4^{+}CCR5^{+} kinetics, respectively. These compartments have the same structure as T, P, N and S, but with two differences. First, the value of T_{p} at transplantation is a fraction f_{p} of the total number of infused cells. Second, the N_{p1} cell compartment do not upregulate CCR5 when transitioning to N_{p2}. We model the competition of CD4^{+} and CD8^{+} T cells for resources that allow cell division using a logistic equation that depends on the difference between the total number of competing cells, i.e. A = N_{p1}+N_{p2}+N+S+M+E, and a carrying capacity K (Jameson, 2002). Under these assumptions we constructed the following model form:
where ${\hat{r}}_{p}={r}_{p}\left({\lambda}_{f}+{\lambda}_{e}+{d}_{p}\right)$, ${\hat{r}}_{n}={r}_{n}\left({\lambda}_{n}+{d}_{n}\right)$, ${\hat{r}}_{s}={r}_{s}\left({\lambda}_{s}+{d}_{s}\right)$, ${\hat{r}}_{m}={r}_{m}\left({\lambda}_{m}+{d}_{m}\right)$, $\hat{r}}_{e}={r}_{e}{d}_{e$, as well as $K}_{w}=K\frac{{\hat{r}}_{w}}{{r}_{w}$ for each model variable $w\in \left\{p,n,s,m,e\right\}$. We did this reparameterization to have compound parameters that were identifiable.
When simulating the model, we assumed ${t}_{0}$ as the time of transplantation. For the transplant groups the system is in a transient stage due to conditioning (TBI) at ${t}_{0}$, therefore initial values cannot be obtained from steady state equations. Transplantation is modeled as $T\left({t}_{0}\right)=\left(1{f}_{p}\right)D$ and ${T}_{p}\left({t}_{0}\right)={f}_{p}D$. For the control group we used ${t}_{0}$ at a similar time relative to the transplant groups. Since the control group did not have any transplantation or TBI, we assumed $T\left({t}_{0}\right)={T}_{p}\left({t}_{0}\right)={P}_{p}\left({t}_{0}\right)={N}_{p}\left({t}_{0}\right)=0$. Other initial values were calculated assuming steady state: $P\left({t}_{0}\right)=\frac{{q}_{2}{q}_{3}{q}_{4}{K}_{p}}{\left({q}_{1}+1\right){q}_{3}{q}_{4}+q2\left({q}_{4}+1\right)}$, $N\left({t}_{0}\right)=\frac{{q}_{1}{q}_{3}{q}_{4}{K}_{p}}{\left({q}_{1}+1\right){q}_{3}{q}_{4}+q2\left({q}_{4}+1\right)}$, $S\left({t}_{0}\right)=\frac{{q}_{3}{q}_{4}{K}_{p}}{\left({q}_{1}+1\right){q}_{3}{q}_{4}+q2\left({q}_{4}+1\right)}$, $M\left({t}_{0}\right)=\frac{{q}_{2}{q}_{4}{K}_{p}}{\left({q}_{1}+1\right){q}_{3}{q}_{4}+q2\left({q}_{4}+1\right)}$ and $E\left({t}_{0}\right)=\frac{{q}_{2}{K}_{p}}{\left({q}_{1}+1\right){q}_{3}{q}_{4}+q2\left({q}_{4}+1\right)}$. Here ${q}_{1}=\frac{{\hat{r}}_{s}\text{}}{{\lambda}_{n}}\left(\frac{{K}_{p}}{{K}_{s}}1\right)$, ${q}_{2}=\frac{{\hat{r}}_{n}\text{}}{{\lambda}_{f}}\left({q}_{1}\left(\frac{{K}_{p}}{{K}_{n}}1\right){\lambda}_{s}\right)$, ${q}_{3}=\frac{{\hat{r}}_{m}\text{}}{{\lambda}_{e}}\left(\frac{{K}_{p}}{{K}_{m}}1\right)$ and ${q}_{4}=\frac{{\hat{r}}_{e}\text{}}{{\lambda}_{m}}\left(\frac{{K}_{p}}{{K}_{e}}1\right)$. A parsimonious, curated version of this model was selected from a series of models with varying mechanistic and statistical complexity (Figure 3—source data 2).
Mathematical modeling of SHIV infection and T cell response dynamics
Request a detailed protocolWe next adapted the curated T cell reconstitution model by combining several adaptations of the canonical model of viral dynamics (Reeves et al., 2017; Perelson, 2002; Perelson et al., 1997; Hill et al., 2018; Borducchi et al., 2016; De Boer, 2007; Wodarz and Nowak, 1999; Pandit and de Boer, 2016). Here, virus V infects only CD4^{+}CCR5^{+} T cells (Ho et al., 2009) S at rate β. We modeled ART by reducing the infection rate to zero. A fraction τ of the infected cells produce virus, I_{p}, and the other fraction become unproductively infected, I_{u} (Reeves et al., 2017; Doitsh et al., 2010; Matrajt et al., 2014). I_{P} cells arise only from activation of a persistent set of latently infected cells at rate $\xi \overline{L}$. We modeled ATI by assuming infection β is greater than zero after some delay following ATI. We approximate this delay as the sum of the time of ART to washout (~3 days) and the time of successful activation (${t}_{sa}$) of a steady set of latently infected cells. For simplicity, we assumed that $\xi \overline{L}=\frac{1}{{t}_{sa}}$ and assumed that ${t}_{sa}$ has lognormal distribution among the animal population with high variance (Conway et al., 2019; Hill et al., 2014; Prague et al., 2019). All infected cells die at rate δ_{I} (Reeves et al., 2017). I_{P} cells produce virus at a rate π per cell, that is cleared at rate γ. CD8^{+} M cells proliferate in the presence of infection with maximum rate ω_{8}. A fraction f of these cells become SHIVspecific CD8^{+} effector T cells, E_{h}, that are removed at a rate d_{h} (De Boer, 2007; Wodarz and Nowak, 1999; Wodarz et al., 2000). These effector cells may reduce virus production (π) or increase infected cell clearance (δ_{I}) by 1/ (1+θE_{h}) or by (1+κE_{h}), respectively (Elemans et al., 2011; Klatt et al., 2010; Wong et al., 2010; Borducchi et al., 2016; Cardozo et al., 2018). We assumed that nonsusceptible CD4^{+} T cells may upregulate CCR5 and replenish the susceptible pool during infection (Okoye et al., 2007; Okoye et al., 2012; Okoye and Picker, 2013) with rate ω_{4}. For cell growth the total number of competing cells is given by A =N_{p1}+N_{p2}+N+S+I_{p}+I_{u}+M+E+E_{h}. The model in Equation 2 is modified to include:
When simulating this model, we assume ${t}_{0}=0$ as the moment of SHIV challenge, and ${t}_{x}$ as the moment of transplantation after challenge. We modeled conditioning by: (1) adding a term ${k}_{T}C$ in all blood cell compartments $C\in \left\{N,S,{I}_{p},{I}_{u},M,E,{E}_{h}\right\}$ and (2) the term ${k}_{H}P$ for the HSPC compartment $P$. ${k}_{T}$ and ${k}_{H}$ are different than zero only during the 2 days before transplant (${t}_{x}2\le t{t}_{x}$). Transplantation is modeled as an input only when $t={t}_{x}$ to cell compartments $T$ and ${T}_{p}$ with amounts $\left(1{f}_{p}\right)D$ and ${f}_{p}D$, respectively. A parsimonious version of this model was selected from a series of models with varying mechanistic and statistical complexity (Figure 3—source data 2).
Nonlinear mixedeffects modeling
Request a detailed protocolTo fit our models (Equations 2, 3) to the transplant data, we used a nonlinear mixedeffects modeling approach (Lavielle, 2014). Within this approach, we modeled a state variable vector $v$ with observations at time $i$ for each animal $j$ as $lo{g}_{10}{v}_{ij}={f}_{v}\left({t}_{ij},{\mathrm{\Psi}}_{j}\right)+{\u03f5}_{v}$. Here, ${f}_{v}$ describes the solution of the nonlinear models in Equations 2 or 3 for the state variable vector $v$ at observation time ${t}_{ij}$ with animalspecific parameter set $\mathrm{\Psi}}_{j$. The distribution of measurement noise is assumed as ${\u03f5}_{v}\sim \mathcal{\mathcal{N}}\left(0,{\sigma}_{v}^{2}\right)$.
In the mixedeffects model, it is assumed that for an animal $j$ each single parameter $\psi}_{j}\in {\mathrm{\Psi}}_{j$ is drawn from a probability distribution across the population. This distribution includes the fixed effects $\overline{\psi}$ representing the median value over the population, and the random effects ${\eta}_{j}$ representing its variability in the population, assumed to be normally distributed with standard deviation ${\sigma}_{\psi}$, that is ${\eta}_{j}\sim \mathcal{\mathcal{N}}\left(0,{\sigma}_{\psi}^{2}\right)$. We assumed that the random effects of the parameters ${\eta}_{j}$ might not be independent. In that case, the vector of random effects ${\eta}_{j}$ follows a multinormal distribution: $\eta \sim \mathcal{\mathcal{N}}\left(0,\mathrm{\Omega}\right)$, being $\mathrm{\Omega}$ the variancecovariance matrix based on the values ${\sigma}_{\psi}$ and correlations between the individual parameters in $\eta $.
We fit each model to all data points from all animals simultaneously using a maximum likelihood approach. We assumed that individual observations of each state variable ${v}_{ij}$ for each animal $j$ at each time point ${t}_{ij}$ are independent. For each model, we obtained the Maximum Likelihood Estimation (MLE) of the standard deviation of the measurement error for the observations ${\sigma}_{v}$, and each parameter fixed effects $\overline{\psi}$ and standard deviation of the random effects ${\sigma}_{\psi}$ (or elements in matrix $\mathrm{\Omega}$ when applicable) using the Stochastic Approximation of the Expectation Maximization (SAEM) algorithm embedded in the Monolix software (http://www.lixoft.eu).
Fitting T cell reconstitution before ATI
Request a detailed protocolWe first fit the observed blood T cell kinetics after HSPC transplantation and before analytical treatment interruption (ATI) using the model in Equation 2. During this procedure, we defined the vector ${v}^{\left(1\right)}$ to model the log_{10} of the observed blood CD4^{+}CCR5^{}, CD4^{+}CCR5^{+}, total CD8^{+}, CD8^{+} T_{N} + T_{CM}, and CD8^{+} T_{EM} cell counts which are represented in Equation 2 by the variables $\left\{N+{N}_{p1}+{N}_{p2},S,C,M,E\right\}$, respectively with $C=M+E$ and solution ${f}^{\left(1\right)}$.
We defined the statistical form of each parameter in $\mathrm{\Psi}}^{\left(1\right)$ in the following form: parameters ${\widehat{r}}_{p}^{j},\text{}{\widehat{r}}_{m}^{j},{\widehat{r}}_{e}^{j},{\lambda}_{f}^{j},{\lambda}_{e}^{j},{\lambda}_{n}^{j},{\lambda}_{s}^{j},{\lambda}_{m}^{j}$ were modeled as ${\psi}_{j}=\overline{\psi}{e}^{{n}_{j}}$; parameter ${K}_{p}^{j}$ was modeled as ${\psi}_{j}={10}^{\overline{\psi}+{n}_{j}}$; ${K}_{n}^{j},{K}_{s}^{j},{K}_{m}^{j},{K}_{e}^{j}$ were modeled as ${\psi}_{j}={10}^{{K}_{p}^{j}\overline{\psi}{e}^{{n}_{j}}}$; and initial values in the transplant group: ${N}^{j}\left({t}_{0}\right),{S}^{j}\left({t}_{0}\right),{M}^{j}\left({t}_{0}\right)$ and ${E}^{j}\left({t}_{0}\right)$ had the model ${\psi}_{j}={10}^{\overline{\psi}+{n}_{j}}.$ We explored the possibility that ${r}_{n}=0$, in that case we assumed ${\hat{d}}_{n}^{j}={\lambda}_{n}^{j}\left(1+\overline{\psi}{e}^{{n}_{j}}\right)$. We fixed the HSPC homing rate k_{e} = 1/day (Lapidot et al., 2005; Chute, 2006), and ${f}_{p}$ and $D$ as described in Figure 3—source data 1. Since at ${t}_{0}$ the system is in a transient stage due to conditioning (TBI), we estimated blood cell concentrations at ${t}_{0}$, but fixed the number of HSPCs that remained in the BM/thymus $P\left({t}_{0}\right)$ to $6\times {10}^{6}$ based on the estimated minimum number of infused HSPCs needed for engraftment in the same animal model (Radtke et al., 2017).
We fit instances of models with varying statistical and mechanistic complexity in Equation 2 to blood T cell counts during transplant and before ATI (Figure 1B) assuming that one or multiple mechanisms are absent, or that certain mechanisms have equal kinetics (Figure 3—source data 2 includes all 24 competing models with the different statistical assumptions).
Fitting T cell and viral load dynamics before and after ATI
Request a detailed protocolNext, we fit the model in Equations 23 to the pre and postATI blood T cell counts and plasma viral loads (Figure 1B). Here, we defined ${v}^{\left(2\right)}$ for variables $\left\{N+{N}_{p1}+{N}_{p2},R,{C}_{4},{C}_{8},M,E,V\right\}$ with $V$ indicating the observed plasma viral load,$N+{N}_{p1}+{N}_{p2}$ indicating the observed blood CD4^{+}CCR5^{} T cell concentration, $R=S+{I}_{p}+{I}_{u}$ the observed blood CD4^{+}CCR5^{+} T cell concentration, ${C}_{8}$ the total CD8^{+} T cell concentration, ${C}_{4}=R+N+{N}_{p1}+{N}_{p2}$ the total CD4^{+} T cell concentration and the others statevariables as specified for ${v}^{\left(1\right)}$. We included ${C}_{4}$ because we had total CD4^{+} T cell counts, but CD4^{+} T subset counts during the primary infection stage were not available in many of the animals. For this model, we defined the parameter set $\mathrm{\Psi}}^{\left(2\right)$ by adding to the parameters in the previous section the parameters relative to virus dynamics (i.e. $\mathrm{\Psi}}^{\left(2\right)}=\left\{{\mathrm{\Psi}}^{\left(1\right)},{\kappa}^{j},{\theta}^{j},{\beta}^{j},{\pi}^{j},{\omega}_{4}^{j},{\omega}_{8}^{j},{I}_{50}^{j},{d}_{h}^{j},{t}_{sa}^{j}\right\$ but fixing the values in $\mathrm{\Psi}}^{\left(1\right)$ to the MLE values using Figure 3—source data 3). For parameters ${\kappa}^{j},{\theta}^{j},\text{}{\beta}^{j},{\pi}^{j},\text{}{\omega}_{4}^{j},\text{}{\omega}_{8}^{j},\text{}{I}_{50}^{j}\text{}$, we used a model with form ${\psi}_{j}={10}^{\overline{\psi}+{n}_{j}}$, and for ${d}_{h}^{j}$ and ${t}_{sa}^{j}$ we used ${\psi}_{j}=\overline{\psi}{e}^{{n}_{j}}$. We included the possibility that immunity might be different at ATI compared to preART by assuming the forms ${\psi}_{}^{j,ATI}={10}^{\overline{\psi}+{n}_{j}+{\varsigma}_{\psi ,\text{ATI}}}$ for ${\omega}_{8}^{j}$ and ${I}_{50}^{j}$, and ${\psi}_{}^{j,ATI}=\overline{\psi}{e}^{{n}_{j}+{\varsigma}_{\psi ,\text{ATI}}}$ for ${d}_{h}^{j}$ during ATI. We evaluated single or combination of mechanistic hypotheses along with different statistical assumptions as listed in Figure 5—source data 1 using AIC. $V\left(0\right)$ was fixed to a small value below the limit of detection, and ${I}_{p}\left(0\right)$ and ${I}_{u}\left(0\right)$ were calculated as $\tau cV\left(0\right)/\pi $ and $\left(1\tau \right)cV\left(0\right)/\pi $, respectively. We fixed the following parameters: $\gamma =23$/day (Ramratnam et al., 1999), ${\delta}_{I}=1$/day (Markowitz et al., 2003; Cardozo et al., 2017), $\tau =0.05$ (Doitsh et al., 2010), and $f=$ 0.9 (Borducchi et al., 2016). The value of ${k}_{h}$ was constrained to obtain a value of the HSPCs after conditioning $P\left({t}_{x}\right)={P}_{r}=6\times {10}^{6}$ (Radtke et al., 2017). We fixed values of ${t}_{x}$, ${f}_{p}$ and $D$ as described in Figure 3—source data 1.
We fit several instances of the model in Equation 3 to pre and postATI blood T cell counts and plasma viral loads (Figure 1B) using the best model obtained for Equation 2 (Figure 5—source data 1 includes all four competing models and respective statistical assumptions). At the time of SHIV infection, values for the cell compartments were calculated from steady state equations with the same form as for the group without transplantation (‘control’) in the previous section.
Model selection
Request a detailed protocolTo determine the best and most parsimonious model among the instances, we computed the loglikelihood (log L) and the Akaike Information Criteria (AIC=2log L+2 m, where m is the number of parameters estimated) (Burnham et al., 2002). We assumed a model has similar support from the data if the difference between its AIC and the best model (lowest) AIC is less than two (Burnham et al., 2002).
Effective reproductive ratio when ${r}_{n}=0$ and $\kappa =0$
Request a detailed protocolWe calculated an approximate effective reproductive ratio ${R}_{eff}$ for our model (Equations 2, 3) by computing the average number of offspring produced by one productively infected cell ${I}_{p}$ at ATI assuming all cell compartments have reached steady state after transplantation during ART. This number is the product of the average lifespan of one ${I}_{p}$, the virus production rate by this latently infected cell, the lifespan of produced virions from this cell, the rate at which each virion infects the pool of susceptible cells at steady state, the fraction of these infections that become productive and the reduction of virus production, cell infection, and cell death by SHIVspecific immune cells at ATI. Using this approach, we obtain that ${R}_{eff}=\frac{\tau \beta \overline{S}\pi}{\gamma {\delta}_{I}\left(1+\theta {\overline{E}}_{h}\right)}$, with $\overline{S}\approx \frac{{\lambda}_{f}\overline{P}}{\frac{{\hat{d}}_{n}{\hat{r}}_{s}}{{\lambda}_{n}}\left(\frac{{K}_{p}}{{K}_{s}}1\right){\lambda}_{s}}$ and $\overline{E}}_{h}\approx \frac{f{\omega}_{8}{\lambda}_{e}{K}_{p}}{a{d}_{h}{\delta}_{I}{t}_{sa}{\hat{r}}_{m}\left(\frac{{K}_{p}}{{K}_{m}}1\right)$ the steady state values of variables $S$ (SHIVsusceptible cells) and ${E}_{h}$ (SHIVspecific effector cells) during ART, with $a=\frac{{\lambda}_{e}}{{\hat{r}}_{m}\left(\frac{{K}_{p}}{{K}_{m}}1\right)}+\frac{{\lambda}_{f}{\lambda}_{n}}{{\hat{d}}_{n}{\hat{r}}_{s}\left(\frac{{K}_{p}}{{K}_{s}}1\right){\lambda}_{s}{\lambda}_{n}}+\frac{{\lambda}_{f}{\hat{r}}_{s}\left(\frac{{K}_{p}}{{K}_{s}}1\right)}{{\hat{d}}_{n}{\hat{r}}_{s}\left(\frac{{K}_{p}}{{K}_{s}}1\right){\lambda}_{s}{\lambda}_{n}}$$+\frac{{\lambda}_{e}{\lambda}_{m}}{{\hat{r}}_{m}\left(\frac{{K}_{p}}{{K}_{m}}1\right){\hat{r}}_{e}\left(\frac{{K}_{p}}{{K}_{e}}1\right)}+\frac{f{\omega}_{8}{\lambda}_{e}}{{d}_{h}{\delta}_{I}{t}_{sa}{\hat{r}}_{m}\left(\frac{{K}_{p}}{{K}_{m}}1\right)}$. By assuming that the total amount of infused cells (dose $D$ and fraction of CCR5editing ${f}_{p}$) home to the BM/Thymus rapidly, and that the amount of remaining HSPCs after TBI and immediately before transplant is $P\left({t}_{x}\right)={P}_{r}$, the approximate steady state for $P$ is $\overline{P}\approx \frac{{K}_{p}}{a}\cdot \frac{\left(1{f}_{p}\right)D+{P}_{r}}{D+{P}_{r}}=\frac{{K}_{p}}{a}\left(1\frac{{f}_{p}D}{D+{P}_{r}}\right)$. Together this gives the following expression for the effective reproductive ratio:
Here, ${R}_{T}$ then represents the effective reproductive ratio during transplant in the absence of geneediting when cells have reached steady state.
Data availability
All data generated or analysed during this study are included in the manuscript and supporting files. Source data files have been provided for Figures 2 to 7. Details of the source data for each figure are in the Transparent Reporting form.
References

Cd4+ T cell division in irradiated mice requires peptides distinct from those responsible for thymic selectionJournal of Experimental Medicine 190:367–374.https://doi.org/10.1084/jem.190.3.367

CXCR4 and CCR5 expression delineates targets for HIV1 disruption of T cell differentiationJournal of Immunology 161:3702–3710.

BookModel Selection and Multimodel Inference:New York: SpringerVerlag.https://doi.org/10.1016/j.ecolmodel.2003.11.004

The dynamics of simian immunodeficiency virus after depletion of CD8+ cellsImmunological Reviews 285:26–37.https://doi.org/10.1111/imr.12691

Stem cell homingCurrent Opinion in Hematology 13:399–406.https://doi.org/10.1097/01.moh.0000245698.62511.3d

Predictions of time to HIV viral rebound following ART suspension that incorporate personal biomarkersPLOS Computational Biology 15:e1007229.https://doi.org/10.1371/journal.pcbi.1007229

T cell dynamics in HIV1 infectionAnnual Review of Immunology 21:265–304.https://doi.org/10.1146/annurev.immunol.21.120601.141053

Why don't CD8+ T cells reduce the lifespan of SIVinfected cells in vivo?PLOS Computational Biology 7:e1002200.https://doi.org/10.1371/journal.pcbi.1002200

Human memory T cells: generation, compartmentalization and homeostasisNature Reviews Immunology 14:24–35.https://doi.org/10.1038/nri3567

Longterm reduction in peripheral blood HIV type 1 reservoirs following reducedintensity conditioning allogeneic stem cell transplantationJournal of Infectious Diseases 207:1694–1702.https://doi.org/10.1093/infdis/jit086

Insight into treatment of HIV infection from viral dynamics modelsImmunological Reviews 285:9–25.https://doi.org/10.1111/imr.12698

LongTerm control of HIV by CCR5 Delta32/Delta32 StemCell transplantationNew England Journal of Medicine 360:692–698.https://doi.org/10.1056/NEJMoa0802905

Maintaining the norm: tcell homeostasisNature Reviews Immunology 2:547–556.https://doi.org/10.1038/nri853

Effector and memory Tcell differentiation: implications for vaccine developmentNature Reviews Immunology 2:251–262.https://doi.org/10.1038/nri778

BookMixed Effects Models for the Population Approach: Models, Tasks, Methods and ToolsBoca Raton: Chapman and Hall/CRC.

Tcell homeostasis in HIV1 infectionSeminars in Immunology 9:381–388.https://doi.org/10.1006/smim.1997.0096

Thymic function in HIV1 diseaseSeminars in Immunology 9:397–404.https://doi.org/10.1006/smim.1997.0098

Blind Tcell homeostasis and the CD4/CD8 ratio in the Thymus and peripheral bloodJournal of Acquired Immune Deficiency Syndromes and Human Retrovirology 14:387–398.https://doi.org/10.1097/0004256019970415000001

Progressive CD4+ central–memory T cell decline results in CD4+ effector–memory insufficiency and overt disease in chronic SIV infectionJournal of Experimental Medicine 204:2171–2185.https://doi.org/10.1084/jem.20070567

Naive T cells are dispensable for memory CD4+ T cell homeostasis in progressive simian immunodeficiency virus infectionJournal of Experimental Medicine 209:641–651.https://doi.org/10.1084/jem.20112071

P. L. J., CD4+ t‐cell depletion in HIV infection: mechanisms of immunological failureImmunological Reviews 254:54–64.https://doi.org/10.1111/imr.12066

HIV1 CCR5 gene therapy will fail unless it is combined with a suicide geneScientific Reports 5:srep18088.https://doi.org/10.1038/srep18088

Modelling viral and immune system dynamicsNature Reviews Immunology 2:28–36.https://doi.org/10.1038/nri700

A distinct hematopoietic stem cell population for rapid multilineage engraftment in nonhuman primatesScience Translational Medicine 9:eaan1145.https://doi.org/10.1126/scitranslmed.aan1145

Mechanisms that contribute to a profound reduction of the HIV1 reservoir after allogeneic stem cell transplantAnnals of Internal Medicine 169:674–683.https://doi.org/10.7326/M180759

Central memory and effector memory T cell subsets: function, generation, and maintenanceAnnual Review of Immunology 22:745–763.https://doi.org/10.1146/annurev.immunol.22.012703.104702

Interleukin7 mediates the homeostasis of naïve and memory CD8 T cells in vivoNature Immunology 1:426–432.https://doi.org/10.1038/80868

Cutting edge: requirement for IL15 in the generation of primary and memory antigenspecific CD8 T cellsThe Journal of Immunology 168:4827–4831.https://doi.org/10.4049/jimmunol.168.10.4827

Development of alphabeta T cells in the human ThymusNature Reviews Immunology 2:760–772.https://doi.org/10.1038/nri913

Effective Multilineage engraftment in a mouse model of fanconi Anemia using Nongenotoxic AntibodyBased conditioningMolecular Therapy  Methods & Clinical Development 17:455–464.https://doi.org/10.1016/j.omtm.2020.02.001

Clonal selection and therapy resistance in acute leukaemias: mathematical modelling explains different proliferation patterns at diagnosis and relapseJournal of the Royal Society Interface 11:20140079.https://doi.org/10.1098/rsif.2014.0079

Characterization of stem cells using mathematical models of multistage cell lineagesMathematical and Computer Modelling 53:1505–1517.https://doi.org/10.1016/j.mcm.2010.03.057

Stem cell selfrenewal in regeneration and Cancer: insights from mathematical modelingCurrent Opinion in Systems Biology 5:112–120.https://doi.org/10.1016/j.coisb.2017.09.006

Gene editing of CCR5 in autologous CD4 T cells of persons infected with HIVNew England Journal of Medicine 370:901–910.https://doi.org/10.1056/NEJMoa1300662

A new theory of cytotoxic T–lymphocyte memory: implications for HIV treatmentPhilosophical Transactions of the Royal Society of London. Series B: Biological Sciences 355:329–343.https://doi.org/10.1098/rstb.2000.0570

CXCR4 and CCR5 on human thymocytes: biological function and role in HIV1 infectionJournal of Immunology 161:3103–3113.
Decision letter

Miles P DavenportReviewing Editor; University of New South Wales, Australia

Aleksandra M WalczakSenior Editor; École Normale Supérieure, France
In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.
Acceptance summary:
The search for an HIV 'cure' includes a number of approaches. These include eradication of the latent virus, as well as strategies to prevent viral replication. The known clinical examples of HIV 'cure' have occurred in patients that have received bone marrow transplants where the new donor marrow lacked the CCR5 gene that encodes an HIV coreceptor molecule. Thus, understanding how reduced CCR5 expression affects viral replication is an important question. In this study, the authors investigate viral control in SHIV infected macaques following autologous CCR5 geneedited transplantation. To this end, they combine experimental data on SHIVinfected macaques with mathematical models describing viral and immune cell dynamics using a stepwise approach. This as a very innovative interdisciplinary study that provides important insights to inform potential future treatment regimens against HIV.
Decision letter after peer review:
Thank you for submitting your article "Thresholds for postrebound SHIV control after CCR5 geneedited autologous hematopoietic cell transplantation" for consideration by eLife. Your article has been reviewed by Aleksandra Walczak as the Senior Editor, a Reviewing Editor, and two reviewers. The reviewers have opted to remain anonymous.
The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.
As the editors have judged that your manuscript is of interest, but as described below that additional work is required before it is published, we would like to draw your attention to changes in our revision policy that we have made in response to COVID19 (https://elifesciences.org/articles/57162). First, because many researchers have temporarily lost access to the labs, we will give authors as much time as they need to submit revised manuscripts. We are also offering, if you choose, to post the manuscript to bioRxiv (if it is not already there) along with this decision letter and a formal designation that the manuscript is "in revision at eLife". Please let us know if you would like to pursue this option. (If your work is more suitable for medRxiv, you will need to post the preprint yourself, as the mechanisms for us to do so are still in development.)
Summary:
In this study, the authors investigate the requirements for viral control in SHIV infected macaques under CCR5 geneedited HSPC transplantation treatment. To this end, they combine experimental data on SHIVinfected macaques with mathematical models describing viral and immune cell dynamics using a stepwise approach. The Materials and methods and Results are presented in a thorough way. The article utilizes a robust data set and also uses detailed mathematical models and extensive analyses to capture the relevant dynamics.
Essential revisions:
1) The authors perform model selection based on the AIC values to determine the appropriate mathematical model describing the observed dynamics. However, the reliability of the obtained AIC values also depends on the identifiability of the estimated model parameters. Can you say anything about the extent to which you are overfitting in these models? The number of parameters is quite large and you see some quite substantial correlations (Supplementary file 3).
2) Conditioning and CCR5deleted autologous HSCT depletes existing infected cells and preexisting immunity to SHIV and ultimately increases the proportion of infectionresistant cells after reconstitution. It's therefore not obvious that extensive conditioning is necessarily the best strategy, and you have shown this in Peterson et al., 2017 and Reeves et al., 2017. Could this be worth highlighting early on? It may help to increase the impact of the insights you derive from the modeling.
3) When modeling reconstitution in deltaCCR5 individuals – you assume that the CCR5 cells all behave like CCR5 cells in WT transplants. This doesn't seem like a valid assumption; a proportion of CCR5/ cells will become activated (as they do in WT transplants) and so the CCR5/ cell kinetics should be a mixture of the CCR5 and CCR5+ kinetics. The same parameters could be used in the two groups. How sensitive are your conclusions to this issue?
4) Subsection “A reduction in SHIVspecific immunity leads to higher viral rebound set points and CD4^{+}CCR5+ T cell depletion following ATI in transplanted animals” and Figure 5E – this section needs more interpretation/discussion. It's surprising that the only difference in parameters between the control and treatment groups was the time to virus rebound; so presumably differences across groups derive from the steady state sizes of the different populations? Are latently infected cells depleted in the transplant groups? And it's puzzling that delayed rebound in transplant groups is taken to imply more depleted immunity. Shouldn't it imply less depletion? Also – elevated virus load after ATI only occurs in the WT transplant group, not both. Please clarify and expand this section.
5) Subsection “PostATI viral control requires a large HSPC dose containing a high fraction of CCR5edited cells”: Are strategies 1 and 2 not in conflict? Or does more potent conditioning somehow not necessarily imply a greater reduction in antiSHIV immunity?
In summary, the reviewers acknowledged the analysis of an important topic by a unique dataset. However, they identified some major aspects that addressed the parameter identifiability within the model estimates as well as identifying the role of conditioning and dynamics of CCR5 cells. Therefore, we would like to ask you to analyze/comment on parameter identifiability for individual model estimates and validate the robustness of parameter estimates and, hence, model selection. This will be subject to rereview to determine if these issues have been satisfactorily addressed.
[Editors' note: further revisions were suggested prior to acceptance, as described below.]
Thank you for resubmitting your work entitled "Thresholds for postrebound SHIV control after CCR5 geneedited autologous hematopoietic cell transplantation" for further consideration by eLife. Your revised article has been evaluated by Aleksandra Walczak (Senior Editor) and a Reviewing Editor.
The manuscript has been improved but the reviewers have identified some remaining issues that need to be addressed before acceptance, as outlined below:
1) Figure 2—figure supplement 1, Panel B: The statistical comparison total vs. TN+TCM does not make sense. As I assume that Total=T_{N}+T_{CM}+T_{EM}, "Total" does not contain additional information when there is already a comparison T_{N}+T_{CM} vs. T_{EM}.
2) The manuscript contains a lot of typos and needs proofreading.
3) The Berlin and London patients are still not described.
4) The authors should provide all data and code used to perform the analyses.
https://doi.org/10.7554/eLife.57646.sa1Author response
Essential revisions:
1) The authors perform model selection based on the AIC values to determine the appropriate mathematical model describing the observed dynamics. However, the reliability of the obtained AIC values also depends on the identifiability of the estimated model parameters. Can you say anything about the extent to which you are overfitting in these models? The number of parameters is quite large and you see some quite substantial correlations (Supplementary file 3).
We carefully took into account the following factors to reduce overfitting of the model and unidentifiability of the parameters as much as possible:
1) We divided the fits in two steps: (1) T cell reconstitution following TBI during virus suppression while on ART and (2) T cell and virus dynamics for the whole study period. The first step modeling fits to the isolated kinetics of T cells: expansion, overshoot and steady state. This method allows identification of parameters related to T cell reconstitution that do not correlate with parameters of virus dynamics. In the second step we fit to the same T cell subsets and to viral load data from acute infection and during ART interruption, fixing the parameters unrelated to virus infection and response from the first step. By using the two steps, parameters of the T cell dynamics related and unrelated to the virus dynamics are separately estimated.
2) The data during step (1) was frequently sampled for multiple T cell subsets allowing parameter identification related to each subset that were unrelated to virus dynamics (which is normally difficult when fitting models to viral loads only).
3) We transformed the model for step (1) as presented in the Materials and methods section after Equation 2 to ensure structural identifiability. Specifically, we combined several parameters, such as proliferation (r_{i}), transition/differentiation and death rates (d_{i}) into compound parameters and estimated the compound parameters. Whereas the individual rates were not identifiable, compound rates (capturing correlated behaviors) were.
4) The reparameterization shows that some different differentiation parameters (λ_{i}) cannot be equal to zero, but others can be. For those that could take on a value of zero, we performed model selection to obtain a better fit and avoid overfitting.
5) We did careful model selection with reasonable models for step (1) (Figure 3—source data 2) using AIC to reject the most complex models and thus avoid overfitting (given the large amount of data compared to the number of parameters, AICc did not result in different outcomes). For each model we were careful in evaluating which parameters might not be practically identifiable and which ones correlated using the software Monolix:
a) For practical identifiability we used the relative standard error (standard error/population parameter value). Since the standard error is based on the diagonal of the inverse of the Fisher information matrix, it describes how much information each parameter gives to calculate the likelihood, and therefore gives information on how identifiable a parameter can be relative to the available data. We made sure the best model had small % relative standard error (%RSE<=40) for most of the estimated parameters (Figure 3—source data 3). For some parameters, the standard deviation of the random effects were estimated to be close to zero but with very high %RSE values. We therefore assume those parameters have no random effects (standard deviation equal to zero), i.e. all animals have the same estimated individual value for that parameter.
b) For correlations among parameters Monolix also uses the inverse of the Fisher Information Matrix to give information about those correlations. For those with high correlation we fit the model again but explicitly including the statistical relationship between the parameters in the variancecovariance matrix Ω of the mixedeffects model (corr≠0 in Figure 3—source data 2 and Figure 5—source data 1 means that the correlations were explicitly part of Ω in the mixedeffect model—therefore they were estimated parameters also included in the AIC). We made sure that for the best model the estimated correlation was identifiable (i.e. low %RSE in Figure 3—source data 3 and Figure 5—source data 2). This means that when drawing individual parameter values from the distribution in the mixedeffect model, the estimated correlation was also taken into account.
6) Because of the possibility of lack of convergence by the SAEM fitting algorithm in Monolix, we repeated the fitting procedure for each model 10 times having randomly selected initial guesses for the parameters. From the 10 attempts we selected the case with the highest likelihood.
7) When fitting the model for step (2) we fixed all the estimated parameters in step one, including those with correlations. For practical identifiability and correlations of the parameters related with virus dynamics and response to the virus we followed the same procedure as in item 5 (all summarized in the “statistical assumptions” in Figure 5—source data 1. See also the %RSE for best model estimates in Figure 5—source data 2 – most of them with %RSE <=40%).
8) For both steps, we fixed some parameters based on estimation from previous studies.
We recognized the possibility of model overfitting and unidentifiability of parameters, but we believe that the careful steps we took reduced those two problems significantly.
2) Conditioning and CCR5deleted autologous HSCT depletes existing infected cells and preexisting immunity to SHIV and ultimately increases the proportion of infectionresistant cells after reconstitution. It's therefore not obvious that extensive conditioning is necessarily the best strategy, and you have shown this in Peterson et al., 2017 and Reeves et al., 2017. Could this be worth highlighting early on? It may help to increase the impact of the insights you derive from the modeling.
We have included a sentence in the Introduction explaining that extensive conditioning is a necessary condition (despite the loss of preexisting immunity) to reduce the number of endogenous HSCs so that transplanted CCR5deleted HSCs can outcompete with them.
We also added a sentence in the Discussion saying that in the absence of conditioning the number of endogenous HSPCs will remain too high. In this case, the amount that would have to be taken from the animals for exvivo CCR5 deletion and transplantation for SHIV remission would be unrealistic, and their engraftment potential would be low.
3) When modeling reconstitution in deltaCCR5 individuals – you assume that the CCR5 cells all behave like CCR5 cells in WT transplants. This doesn't seem like a valid assumption; a proportion of CCR5/ cells will become activated (as they do in WT transplants) and so the CCR5/ cell kinetics should be a mixture of the CCR5 and CCR5+ kinetics. The same parameters could be used in the two groups. How sensitive are your conclusions to this issue?
We agree with the reviewers that the CCR5/ cell kinetics could be a mixture of the CCR5 and CCR5+ kinetics. We added models that include this feature (12 new mechanistic models for T cell reconstitution part, and 4 new mechanistic ones for the section including viral dynamics) and found that the results/conclusions of the paper are not sensitive to this change:
1) We modified Equation 2 and Figure 3A to account for the possibility that CD4^{+}CCR5disrupted cells can have kinetics of CCR5 and CCR5+ cells, N_{p1} and N_{p2} compartments in the model, respectively.
a) We therefore added 12 more models including N_{p2} (models 1324 in Figure 3—source data 2) with the same statistical assumptions for the models without N_{p2}.
b) We fit the new 12 models to the T cell reconstitution data and found that the best model with compartment N_{p2} has almost the same AIC (Figure 3—source data 2 models 11 and 23) and parameter estimates (Figure 3—source data 3) that the best model without N_{p2}.
c) From this part we deduced that:
i) T cell reconstitution data could not be used to distinguish if CD4^{+}CCR5disrupted cells have a mixture of the CCR5 and CCR5+ kinetics.
ii) But regardless, the model with mixture of the CCR5 and CCR5+ kinetics didn’t differ at all from a model without that mixture.
2) When fitting viral load, we also tried to fit the model using the compartment N_{p2} (Models 58 in Supplementary file 5)
a) From this step we found that the model with mixture of the CCR5 and CCR5+ for disrupted cells had a significantly lower AIC (Figure 5—source data 1).
b) However model fits and comparisons between parameters and viral load steady state did not change (Figure 5, Figure 5—figure supplement 1, Figure 5—figure supplement 2, Figure 5—figure supplement 3, Figure 5—source data 2 and Figure 5—source data 3).
c) When using the best model with corresponding parameter estimates the model projections using different fp, Dose and Pr did not change either (Figure 6AB). Minimum fp and Dose:Pr were very close to values obtained before: 76%94%, and D:Pr>5, respectively (Figure 6C). Also, the relation of immune response (R_{T}) and minimum f_{p} was the same (Figure 6D).
d) Finally, when using the model for projections of viral control for different times of ATI, we obtain the same decrease pattern of time to control.
We edited the text to include these analyses.
4) Subsection “A reduction in SHIVspecific immunity leads to higher viral rebound set points and CD4^{+}CCR5+ T cell depletion following ATI in transplanted animals” and Figure 5E – this section needs more interpretation/discussion. It's surprising that the only difference in parameters between the control and treatment groups was the time to virus rebound; so presumably differences across groups derive from the steady state sizes of the different populations? Are latently infected cells depleted in the transplant groups? And it's puzzling that delayed rebound in transplant groups is taken to imply more depleted immunity. Shouldn't it imply less depletion? Also – elevated virus load after ATI only occurs in the WT transplant group, not both. Please clarify and expand this section.
Since the best model we obtained allowed distinct SHIVspecific CD8s parameter values for the ATI and preART stages, we reanalyzed the data and model results using a different approach to address what drives different kinetics between the control and transplant groups.
1) We looked first at how viral load burden differed during ATI compared to preART using three summary statistics: median, nadir and final viral loads from viral peak onwards for each stage (ATI vs preART). Figure 4BD now presents that result.
2) We compared each of these summary statistics per group and found that in the three summary statistics viral burden during ATI is maintained or slightly decreased for the control group, increased for the WTtransplant group (no CCR5edition), and is increased for the CCR5edited group but not nearly to the degree seen in the WT group.
3) Then, we compared how the model predicts that SHIVspecific immunity changed during ATI with respect to preART using the parameters directly related to SHIVspecific CD8^{+} T cells (since we can only measure this with the model and not in the data). We found that SHIVimmunity change at ATI compared to preART was correlated to the change in viral burden between ATI and preART (median and nadir viral load during ATI:preART). These results are now presented in Figure 5CD. SHIVimmunity during ATI slightly increased for the control group (ratio over 1), decreased for the WTtransplant group, and was recovered for the CCR5edited group
We have clarified and expanded these analyzes in the viral and T cell dynamics modeling result section.
Regarding if latently infected cells are depleted in the transplant groups, Peterson et al., 2017 and Reeves et al., 2017 support that conclusion. However, answering this question from a mathematical modeling perspective was beyond the scope of this study. For that reason, we did not explicitly have a model for the SHIVlatently infected cell compartment, or how they could have been depleted during conditioning (as we did for all other cell compartments). We only added a constant parameter $\xi \overline{L}$ to account for their reactivation. In the model, time to rebound was only related to latent cell reactivation $({t}_{\mathrm{\text{sa}}}=\frac{1}{\xi \overline{L}})$, but viral load kinetics after peak was related to SHIVimmunity as described above. It is possible that delayed rebound is a response to some depletion of latent cells during conditioning, and therefore, less reactivated latent cells. In that sense there is a connection of delayed rebound and depletion of SHIVimmunity during conditioning. However, exploring this relationship was beyond the scope of this study. Therefore, we have taken out the figure presenting how time to rebound was different among groups and its discussion from the manuscript to avoid confusion to the message we are presenting. Also, this result has already been presented in Peterson et al., 2018.
5) Subsection “PostATI viral control requires a large HSPC dose containing a high fraction of CCR5edited cells”: Are strategies 1 and 2 not in conflict? Or does more potent conditioning somehow not necessarily imply a greater reduction in antiSHIV immunity?
We believe they are not in conflict in the sense that we don’t mean in strategy 1 to reduce conditioning, but to find ways to augment antiSHIV immunity despite conditioning. Several examples could include antiSHIV CAR T cells and/or immunotherapies based on broadly neutralizing antibodies to specifically target the persistent viral reservoir but not virusspecific immune cells, and/or conditioning strategies that are targeted more specifically to HSPCs, without impacting differentiated immune subsets. In that sense we have changed the wording of strategy 1 as “augment antiSHIV immunity despite conditioning”.
In summary, the reviewers acknowledged the analysis of an important topic by a unique dataset. However, they identified some major aspects that addressed the parameter identifiability within the model estimates as well as identifying the role of conditioning and dynamics of CCR5 cells. Therefore, we would like to ask you to analyze/comment on parameter identifiability for individual model estimates and validate the robustness of parameter estimates and, hence, model selection. This will be subject to rereview to determine if these issues have been satisfactorily addressed.
We appreciate the reviewer’s comments and acknowledgements and believe we have addressed to the best of our abilities the major aspects regarding parameter identifiability/model selection, role of conditioning and dynamics of CCR5 cells.
[Editors' note: further revisions were suggested prior to acceptance, as described below.]
The manuscript has been improved but the reviewers have identified some remaining issues that need to be addressed before acceptance, as outlined below:
1) Figure 2—figure supplement 1, Panel B: The statistical comparison total vs. TN+TCM does not make sense. As I assume that Total=T_{N}+T_{CM}+T_{EM}, "Total" does not contain additional information when there is already a comparison T_{N}+T_{CM} vs. T_{EM}.
We have changed Figure 2—figure supplement 1, Panel B: taking out the statistical comparison for total vs. TN+TCM
2) The manuscript contains a lot of typos and needs proofreading.
We have proofread the manuscript and took care of the typos we found.
3) The Berlin and London patients are still not described.
We have included a description of the Berlin and London patients in the Introduction.
4) The authors should provide all data and code used to perform the analyses.
Besides of the code already submitted we have provided the code for analyses in Figure 2, Figure 3, Figure 4, Figure 5 and Figure 6.
https://doi.org/10.7554/eLife.57646.sa2Article and author information
Author details
Funding
National Institute of Allergy and Infectious Diseases (UM1 AI126623)
 E Fabian CardozoOjeda
 Christopher W Peterson
 HansPeter Kiem
 Joshua T Schiffer
National Institute of Allergy and Infectious Diseases (R01 AI150500)
 E Fabian CardozoOjeda
 Joshua T Schiffer
National Center for Advancing Translational Sciences (KL2 TR002317)
 Elizabeth R Duke
Center for AIDS Research (New Investigator Award P30 AI027757)
 Daniel B Reeves
Washington Research Foundation (Postdoctoral Fellowship)
 Daniel B Reeves
National Institutes of Health (P51 OD010425)
 HansPeter Kiem
The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.
Acknowledgements
This study was supported by grants from the National Institutes of Health, National Institute of Allergy and Infectious Diseases (UM1 AI126623, R01 AI150500). ERD is supported by the National Center for Advancing Translational Sciences of the National Institutes of Health under Award Number KL2 TR002317. DBR is supported by a Washington Research Foundation postdoctoral fellowship, and a CFAR NIA P30 AI027757. NHP studies were supported by NIH P51 OD010425. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health or the Washington Research Foundation.
Ethics
Animal experimentation: The data used in this work were collected in strict accordance with the recommendations in the Guide for the Care and Use of Laboratory Animals of the National Institutes of Health. The study protocol was approved by the Institutional Animal Care and Use Committees (IACUC) protocols (#323503) of the Fred Hutchinson Cancer Research Center and the University of Washington.
Senior Editor
 Aleksandra M Walczak, École Normale Supérieure, France
Reviewing Editor
 Miles P Davenport, University of New South Wales, Australia
Publication history
 Received: April 7, 2020
 Accepted: December 27, 2020
 Version of Record published: January 12, 2021 (version 1)
Copyright
© 2021, CardozoOjeda et al.
This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.
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