Fig 1.
Schematic of the mathematical model of SHIV dynamics with bNAb therapy.
Orange and green arrows indicate processes involved in the growth and control of infection, respectively, while magenta arrows indicate processes initiated or enhanced by bNAbs. Corresponding model equations are described in Methods. Steady state analysis of the model indicates two outcomes of the infection: chronic infection with high viremia that marks progressive disease (red filled square), typically realized in the absence of treatment, and viremic control (blue filled square), a switch to which is orchestrated by early bNAb therapy.
Table 1.
Model parameters fixed from previous studies.
Table 2.
Population parameter estimates (μ, σ) estimated by simultaneously fitting our model (Eqs 13–20) to data of V, A1 and A2 from untreated macaques and responders (Methods).
Standard errors (SE) are shown in brackets.
Fig 2.
Model fits viral dynamics in responder macaques.
Model fits (blue lines) to viral load data [10] (symbols) from the 10 controller macaques, shown in individual panels. Empty symbols mark measurements showing undetectable viremia and filled symbols above detection. The latter were used for fitting and the former censored. Black dotted lines in all panels indicate the viral load detection limit (100 RNA copies/mL). The corresponding bNAb concentration dynamics are in Fig 3. In all panels, phase I (yellow) marks the duration when bNAbs are present in circulation, phase II (green) the viremic resurgence post the clearance of bNAbs, phase III (blue) the ensuing viremic control, and, where relevant, phase IV (pink), in two parts, the disruption of this control using anti-CD8α and anti-CD8β Abs, respectively. For the macaque MVJ, we demonstrate the loss of viral control that occurs when effector depletion levels are increased (magenta dashed line), as is observed with the macaque DFIK. The digitized data used for the fitting is available as a supplementary excel file (S1 Data). In all cases, predictions without bNAb therapy are included for comparison (red lines). Parameter values used are in Table 1 and S1 Table. Macaques DEWP, MVJ, DFFX, DFKX, and DFIK were inoculated intrarectally and DEWL and MAF intravenously with 1000 TCID50 (50% tissue culture infective dose) of SHIVAD8-EO virus. DEMR, DEBA, and DEHW received 100 TCID50 intravenously. The treatments are summarized in S10 Table.
Fig 3.
bNAb pharmacokinetics in responders.
Fits of model predictions (lines) to data from individual macaques (symbols) of bNAb plasma concentrations for the ten responders in Nishimura et al. [10] obtained by simultaneously fitting our model (Eqs 13–20) to V, A1 and A2 across all macaques. Methods for the fitting procedure. The resulting parameter estimates are in S1 Table. The bNAb serum half-lives averaged across all macaques are 9.0 days (range 2.7–15.8 days) for 3BNC117, and 8.2 days (range 2.5–16.3 days) for 10-1074.
Fig 4.
Fits (red lines) to the acute phase viral loads of the ten untreated macaques in Nishimura et al. [10] obtained by simultaneously fitting our model (Eqs 13–20) to V, A1 and A2 across all macaques. Methods for the fitting procedure. The best-fit parameter estimates are in S2 Table.
Table 3.
Summary table comparing the Akaike information criterion (AIC) of the main model with model variants.
Fig 5.
Bifurcation diagrams indicating the two distinct outcomes of progressive disease and viremic control.
Model calculations of the steady state (a) viral load, (b) normalized effector level (E* = EdE/ρ), and (c) normalized level of exhaustion (Q* = Qdq/κ), obtained by varying the viral clearance rate. The stable states of progressive disease and viremic control are shown in red and blue, respectively. Thin black lines represent unstable steady states. In (b), the intermediate unstable state lies close to the state of viremic control. The steady states are separated by other state variables, including the level of exhaustion, evident in (c). Parameter values used are in Tables 1 and 2. Bifurcation diagrams for other parameters are shown in S15 Fig.
Fig 6.
Early bNAb therapy induces a switch to viremic control.
(a,b) Model fits (blue lines) to viral load data [10] (symbols) from the responder macaques DEWP and MVJ, representative of macaques displaying minimal or substantial viral load rebound post therapy, respectively. (The parameter values used are in Table 1 and S1 Table). The corresponding dynamics of (c,d) the effector response and (e,f) the level of effector exhaustion. The phases are color coded as in Fig 2. Red lines in all panels indicate model predictions with the same parameter values but in the absence of bNAb therapy. Our model predicts thus that bNAb therapy switches disease dynamics from reaching the high viremic, disease progressive state to the state of viremic control. Black dotted lines in (a,b) indicate the viral load detection limit (100 RNA copies/mL).
Fig 7.
Model predictions of untreated infection dynamics with higher initial effector pool.
Model predictions of effector, viral, and exhaustion dynamics for untreated infection show control with high (green) and progression with low (red) initial effector numbers (E*(0)). All other parameters are the same as those that yield the best-fit to the macaque DEHW (S1 Table).
Fig 8.
bNAbs succeed whereas ART fails to establish long-term viremic control.
Simulated dynamics of (a) viral load, (b) effector response, (c) effector exhaustion, and (d) the latent reservoir, are shown with ART (reverse transcriptase inhibitors—green solid lines, protease inhibitors—orange dashed lines; Methods) in comparison with the corresponding dynamics without treatment (red lines) and with bNAb treatment (blue lines) using parameters that capture in vivo data for the macaque MVJ (symbols). (Parameter values used are in Table 1 and S1 Table). The duration of ART is shown as a gray region. The black dotted lines in (a) indicates the viral load detection limit (100 RNA copies/mL).