Table 1.
Descriptions of model variables and parameters.
Figure 1.
A multi-variant viral dynamic model to quantify response to telaprevir treatment.
Panel a, Superset of HCV genotype 1a variants uncovered in subjects dosed with telaprevir. Each node represents a variant of which the amino acid mutation is printed. Only variants detected in ≥5 subjects are shown. Variants were within 2 nucleotide changes from wild-type HCV. Panel b, Schematic of the model. Panels c and d, correspondence between data and best-fit model for Subject 1. Diamonds, data; solid line, best-fit model; dashed lines, predicted variant contribution to the overall plasma HCV RNA; circles, HCV RNA levels of variants.
Table 2.
Estimates of variants replication rate relative to wild-type HCV (f) and corresponding predictions of their pre-dosing prevalence.
Figure 2.
Correspondence between in vitro replicative fitness and in vivo fitness computed using two alternative methods.
Panel a, in vivo fitness computed using modeling proposed here. Panel b, in vivo fitness computed using the Relative Fitness method. The in vitro fitness was measured in replicon cells and has been reported in [16], [17]. When compared to fitness estimates in vitro, in vivo fitness estimates from modeling correspond better than the estimates from the Relative Fitness method. Relative Fitness was computed as the ratio of rate of change of viral loads (in log-scale) between a variant and wild-type (see methods).
Table 3.
Fitness estimates using relative fitness and production rate ratio (f) in Subject 2.
Figure 3.
Perturbation analysis of Subject 1, had resistant variants not pre-existed prior to dosing.
The simulation was initialized with resistant variants not pre-existed at 0.4 d before dosing; the duration of 0.4 d was chosen as the minimum duration for the plasma HCV RNA of variants to reach steady-state by time = 0. Legends: diamonds, data; lines, models with no variants present at 0.4 day before dosing. Had variants not pre-existed prior to dosing, HCV RNA rebound is expected to occur at later time.
Figure 4.
Comparison between data and best-fit models for alternative cases of replication space T dynamics applied to Subject 1.
Panel a, comparison for plasma HCV RNA. Panel b, comparison for variant prevalence composition. Legends: black lines, overall HCV RNA load; grey lines, fraction of available replication space T/Tmax; colored lines, contribution of variants to HCV RNA load; solid lines, T followed Equation 1 and s was optimally estimated at 0.03 h−1; dashed lines, T followed Equation 1 and s was fixed at 1 h−1; dotted lines, T followed Equation 8 and γ was fixed at 0.05 h−1 — a value comparable to s = 1 h−1 in Equation 1. Alternative representations of similar rate of increase in replication space T provide qualitatively similar fits to data.
Figure 5.
The roles of replication space (T) kinetics to model estimates.
Two cases of T dynamics were examined: first, T synthesis rate s was estimated (range: [0.01–1] h−1) simultaneously with other parameters; second, s was fixed to 1 h−1. Panel a, Maximum likelihood objective function values for both cases. Majority of values are within the objective function differences expected from likelihood ratio for one additional parameter estimated. Panel b, Boxplot of synthesis s values. Panel c, Boxplot of log10 of reproductive ratio. Estimates of reproductive ratio is lower when s is higher (when s was fixed to its upper bound of 1 h−1). Panel d, Fitness fi for both cases. Similar values suggests robustness to assumed synthesis rate s in both cases. Panels e–f, Boxplot of fitness f values of two representative variants T54A and A156T for both cases.
Figure 6.
Estimation results for different values of mutation rates m.
Panel a, maximum likelihood objective values for mutation rates m of 1.2×10−5/cycle, 1.2×10−4/cycle, 1.2×10−3/cycle, and 1.2×10−2/cycle. The objective functions are the lowest with m = 1.2×10−4/cycle, suggesting models fit data best with this m value. Panel b, estimated fitness of selected variants at different m values. Similar ranking of fitness estimates were obtained with these different values of mutation rates. Similar fitness estimates suggests robustness to the assumed mutation rate m. Fitness estimates for m = 1.2×10−2/cycle were not reported because of poor model fits.
Figure 7.
Comparison of cases with (δdrug≠0) and without (δdrug = 0) telaprevir-enhanced infected-cell clearance rate constants.
In δdrug≠0, δdrug was estimated from data while δnodrug was fixed at the average value for Peg-IFN/RBV treatment (5.2×10−3 h−1); in δdrug = 0 case, δnodrug was estimated from data while δdrug was fixed at zero. Panel a, objective values for both cases. The values with δdrug = 0 were higher than those with nonzero δdrug, suggesting better correspondence of data and model fit with δdrug≠0. The number of parameters estimated in both cases is the same. Panels b and c, correspondence between plasma HCV RNA (b) and variant prevalence (c) data and best-fit models for Subject 1. Legends: solid lines, best-fit models with δdrug = 0 case; dotted lines, best-fit models with δdrug≠0 case; dashed lines, variant HCV RNA predicted by best-fit models with δdrug = 0 case. Without δdrug, the best-fit model must trade-off the fitting error on during-dosing second phase decline to match prolonged variants persistence at post-dosing.
Figure 8.
Objective values for alternative equations representing enhanced infected-cell clearance rates δ (Equations 5, 6, and 7).
Each of the models have the same number of parameters estimated for each subject. Models with δi that depend on blockage ε (Equations 5 and 6) have similar quality of fits. However, the model without dependency to ε (Equation 7) has inferior quality of fits.