Fig 1.
Viral dynamics after the initiation of treatment with or without RAL.
(A) Blue and pink lines show the viral load relative to baseline for study participants in the QUAD treatment and RAL-combination therapy, respectively. Black lines represent the median values for each group. In the last phase, between about day 15 and day 30, the viral load in the RAL-combination participants is ~1-log lower (Δ~90% reduction) than the viral load in the quad-therapy group participants. (B) The median viral load profiles for each group present two phases of decay (1a and 2), but in addition the RAL-combination therapy includes an intermediate phase, 1b.
Table 1.
Comparison of the viral load decay rates during treatment with or without RAL.
Rows represent each phase of decay and columns the estimates for each treatment using two methodologies: a heuristic multi-exponential model (two columns on the left) and the SRI model in Fig 2B and Eq (1) (two columns on the right). The estimation of the rate for phase 1b is only applicable in the case of treatment with RAL. All values are in units of day-1. For the SRI model, we also indicate the parameter combination defining the decay rate of each phase.
Fig 2.
(A) The standard model with pre- and post-integration phases of infection. We follow two types of target cells that after infection will be short-lived, , or long-lived,
. Target cells,
, are infected by infectious virus, Vi, at rate
. The infection can be blocked by the activity of RTIs with effectiveness η. These infected cells, I1, are lost at rate δ1, or can undergo provirus integration at rate k and become productively infected cells I2. InSTIs block integration with efficacy ω. Cells with integrated provirus, I2, are lost at rate δ2. Virions are produced by these cells at rate p per cell and are cleared from the circulation at rate c per virion. Protease inhibitors block the production of infectious virus VIi, and lead to production of non-infectious virus VIni, with efficacy ε. The subscripts I and M are used to distinguish virions produced by short-lived and long-lived infected cells, respectively. The dynamics of long-lived cells are similar, but possibly with different rates as indicated. (B) The slow and rapid integration (SRI) model. The SRI model proposes that both short-lived cells with fast integration (I1) and long-lived cells with slow integration (M1) generate productively infected cells that die quickly (I2) (i.e. δ2 = δM2).
Fig 3.
Predicted viral load decay for the quad and RAL-combination treatments using the best fit of the SRI model (Eq (1) when δ2 = δM2) to the data.
The estimated population parameters for each treatment group where used to plot the viral load decline under the effect of RAL+RTI (red) and quad therapy (blue). The dotted blue and red lines show the analytical approximation for the second phase of decay for quad therapy and RAL-combination therapy, respectively (see equation S.14 in S1 Text). The shadowed section highlights phase 1b for RAL-combination therapy. The viral load at the start of phase 2 in patients under RAL-based therapy is reduced with respect to the corresponding level in RAL-free therapy by a factor of . We fixed the values of the following parameters (see text for details): VI(0)/V(0) = 0.98, δM1 = 0.02 day-1, k = 2.6 day-1 and c = 23 day-1 based on previous studies [14,16,39]. In addition, for RAL combination we used η = 0.95, ε = 0 and ω = 0.94, and for the quad therapy η = ε = 0.95 and ω = 0 [14]. The estimated best-fit population parameters are (estimated standard deviation in parenthesis): δ1 = 0.23 (0.04) day-1, k1 = 0.017 (0.01) day-1, δ2 = 0.85 (0.07) day-1 and V(0) = 4.8 (0.07).
Fig 4.
Representative individual fits for the three datasets.
Blue, red and green circles represent HIV RNA measurements for the quad-based-, RAL-combination- and RAL-mono therapy, respectively. Solid black lines represent best fits from the SRI model using the mixed-effects approach. Parameter estimates for each individual are presented in Table E in S1 Text.