Fig 1.
Schematic of the mathematical model.
(A) Model of the ex vivo assay. The events in the ex vivo cultures (left) leading to the dynamics (right) and the reported suppressive capacity (S) as the difference in the antigen load in the cultures with and without CD8 T-cells. The model enables prediction of S and hence analysis of its longitudinal measurements along with in vivo measurements such as viremia (bottom), when integrated in a model of in vivo dynamics. (B) Model of in vivo dynamics. The events driving in vivo infection contained in our model, including the CD8 T-cell suppressive capacity reflected in the effector response (yellow arrow), linking the ex vivo and in vivo datasets (Methods).
Fig 2.
Model fits longitudinal in vivo virological and ex vivo suppressive capacity data.
Model predictions (lines) from simultaneous fitting of the best-fit model (Methods) to all the three datasets (symbols), namely, viremia (left panels), SIV DNA (middle panels) and suppressive capacity (right panels). Macaques highlighted in red were progressors while those in black were controllers. The dashed line in the left panels indicates 400 copies mL-1. Open symbols are below the limit of detection. The predictions for the remaining 12 macaques are presented in S10 Fig. The resulting population parameter estimates are in Table 1 and individual parameter estimates are in S10 Table.
Table 1.
Population parameter estimates for the best-fit model.
Estimates of the parameters from fitting the best-fit model (model #1, S1 Table) to the macaque data (Fig 2). Percent standard errors are in parentheses. dI, θE, and dE were fixed based on previous studies (Methods). Random effects for log10 β’ and log10 T(0) were removed as they were estimated to be below 0.1 (Methods).
Fig 3.
Natural controllers elicit stronger CD8 T-cell responses than progressors.
Best-fit model predictions (Fig 2) showed a higher (A) recruitment/killing rate and (B) antigen-induced proliferation rate of CD8 T-cells in controllers (gray) compared to non-controllers (red). Each symbol represents a macaque and the bar is the median. (C) Predictions using the best-fit parameters showed higher suppressive capacity in controllers than non-controllers. * indicates p = 0.04 at the last time point using a Mann-Whitney U test.
Fig 4.
Early cumulative suppressive capacity is a marker of natural control.
Dynamics of (A) viremia and (B) suppressive capacity predicted for virtual patients using our best-fit model. Trajectories for fifty controllers and fifty progressors are shown. Black dashed line indicates 400 copies mL-1. Correlation between set-point viral load and cumulative suppressive capacity S28 (see text) for (C) 100000 simulated individuals and (D) the 16 macaques studied. The black curve in (C) is a LOESS regression curve to visualize the inverse correlation. (E) The fraction of virtual individuals achieving control (gray bars) or experiencing progressive disease (red bars) as a function of S28. Each bar has of width 0.1 units of S28. The black curve is a fit of the estimated fractions to a first-order Hill function (Methods). The blue line represents the minimum S28 for >95% controllers, with control defined as set-point viral load <400 copies mL-1. Spearman’s ρ was calculated for assessing the correlations.