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.
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Article 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.
Version 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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