Fig 1.
Alternatives to the Pinkevych et al. interpretation of rebound dynamics.
Time-to-rebound data can be explained equally well by frequent reactivation in a realistically heterogeneous cohort (Fig 1B–D) as by rare reactivation in a homogeneous population (Fig 1A). Top row: Observed rebound times in “Cohort 3” [8] and best fits from models described in text. Bottom row: Representative rebound trajectories from 10 participants randomly simulated with the best-fit parameters for each model. (A) The best-fit model derived by Pinkevych et al. All participants are identical, with k = 1/(5.1 days). We fixed r = 0.4/day and fit V0 = 4 c/ml. (B) Allowing interperson variation in growth rate, r. We assumed the population distribution of r was log10-normal with log10-mean μr = –0.4 (10μr = 0.4/day) [1,8,10–12] and fit the log10-standard deviation σr = 0.2 (consistent with [1,12]). We fixed k = 4 cells/day and fit V0 = 0.15 c/ml. (C) Allowing interperson variation in the activation rate, k. We assumed the population distribution of k was log10-normal with μk = 0.6 (10μk = 4 cells/day) [1,12] and fit the log10-standard deviation σk = 0.55 (less than estimated in [1,12], similar to [13]). We fixed r = 0.4/day and fit V0 = 0.15 c/ml. (D) Allowing interperson variation in both activation rate and growth rate. We assumed the population distribution of k and r were log10-normal. Taking μr and σr to be –0.4 (10μr = 0.4/day) and 0.1 and μk = 0.6 (10μk = 4 cells/day), we fit σk = 0.45. We additionally fit V0 = 0.15 c/ml. For all simulations, the definition of viral rebound was set to 50 c/ml and the drug washout time to zero. In general, only two model parameters are identifiable from the cohort data and so the choice of which were fixed and which were fit was arbitrary. Higher V0 values paired with lower r values could fit equally well, as could either paired with higher drug washout times. Note that in simulating the Pinkevych et al. model, we allow for the possibility that multiple reactivating cells contribute to viral rebound, as otherwise the model cannot be used to describe higher activation rates.
Fig 2.
Alternatives to the Pinkevych et al. interpretation of founder virus ratios.
Viral genotyping during early rebound in six participants in cohort 4 [9,14] identified multiple unique viral strains contributing to rebound and characterized their relative frequencies. Ratios were defined as the number of sequences from one strain divided by the number of sequences from the next most prevalent strain. The cumulative distribution function (CDF) for the frequency of each ratio, with all participant data combined, is shown (solid black line). Pinkevych et al. used maximum likelihood estimation to determine the activation rate k that best explains this distribution, assuming all strains start at the same level and grow at the same rate once reactivated. The CDF for the ratios using their estimated activation rate (k = 1/(3.6 days)) is shown (dashed blue line). Alternatively, we assume that strains activate at the same time (high activation rate) but that the growth rates of individual strains are normally distributed with unknown mean and variance. Using maximum likelihood estimation, we infer that an interstrain standard deviation in growth rate of 0.09/day can explain the observed clone ratios (dotted red line). This estimate increases to 0.19 under alternate assumptions about the sampling procedure (see S1 Text).