Resistant (first column), total (second column) and susceptible (third column) enterobacteria predicted for various fecal concentrations of ciprofloxacin <i>C_ss</i>: 0 µg/g (black), 0.9 µg/g (grey), 1.8 µg/g (violet), 2.9 µg/g (blue), 8.7 µg/g (green), 87 µg/g (red), for different treatment durations: A) 1 day, B) 3 days, C) 5 days; D) 10 days.

<p>Resistant (first column), total (second column) and susceptible (third column) enterobacteria predicted for various fecal concentrations of ciprofloxacin <i>C_ss</i>: 0 µg/g (black), 0.9 µg/g (grey), 1.8 µg/g (violet), 2.9 µg/g (blue), 8.7 µg/g (green), 87 µg/g (red), for different treatment durations: A) 1 day, B) 3 days, C) 5 days; D) 10 days.</p

Population parameter estimates and relative standard errors (RSE, in %) of the bacterial kinetic model.

<p>Population parameter estimates and relative standard errors (RSE, in %) of the bacterial kinetic model.</p

Experimental data from individual piglets (grey lines) and observed medians (black dots) versus medians predicted by the model (red lines) for fecal ciprofloxacin concentrations (first column), resistant (second column), total (third column) and susceptible enterobacteria (fourth column) in three treatment groups: A) placebo, B) ciprofloxacin 1.5 mg/kg/day, C) ciprofloxacin 15 mg/kg/day.

<p>The red dotted lines represent the 10% and 90% quantiles of the estimated individual curves.</p

Phases of viral decline affected by the effectiveness of therapy in blocking intracellular viral production and assembly/secretion.

<p>When therapy significantly blocks both intracellular viral production () and assembly/secretion (), the viral load decline has three phases (blue solid), with slopes , , and , respectively. The duration of the first phase () is about 0.25 days and the duration of the second phase () is about 0.88 days using the parameter values below. When , the first-phase viral decline with the slope is not visible (red dashed). When , the second-phase viral decline is not visible (black dash-dotted). Parameter values , , , , , , , , and are from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002959#pcbi-1002959-t002" target="_blank">Table 2</a>. Because was chosen to be 0, when comparing the predicted duration of the first phase in this figure with clinical data one may want to add the length of the pharmacological delay to .</p

Parameter values with standard errors in parenthesis estimated by fitting the standard biphasic model to viral load data.

1<p>Corresponding to a half-life <i>t</i>_1/2 = 0.067 days.</p>2<p>Corresponding to a half-life <i>t</i>_1/2 = 1.65 days.</p

The approximate and the numerical solutions of the multiscale model.

<p><b>A.</b> The short-term approximation (blue solid) is compared with the solution of the multiscale PDE model (black dashed). <b>B.</b> Difference between the long-term approximation and the solution of the multiscale PDE model. Parameter values, chosen from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002959#pcbi-1002959-t002" target="_blank">Table 2</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002959#pcbi.1002959-Rong3" target="_blank">[30]</a>, are , , , , , , , , , , , , and .</p

Comparison of viral load data with model predictions for each patient.

<p>The prediction from the standard biphasic model is shown by the red dashed line and the prediction from the long-term approximation of the full multiscale model is shown by the black solid line. In most cases the two predicted viral load decay curves overlap and cannot be distinguished. The parameter values used to generate the theoretical curves are the best fit values given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002959#pcbi-1002959-t001" target="_blank">Table 1</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002959#pcbi-1002959-t002" target="_blank">2</a>, respectively. Viral rebounds occur due to drug resistance and the decay data (circles) was only fit until resistance was detected or rebound was observed. The limit of viral load detection is indicated by the black dashed line.</p

Parameter values with standard errors in parenthesis estimated by fitting the long-term approximation to viral load data and assuming , , and other fixed parameters as given in Table 2 caption.

1<p>This value is not significantly smaller than 0.</p

Parameter values with standard errors in parenthesis estimated by fitting the long-term approximation to viral load data and assuming , , , and .

1<p>This value is not significantly smaller than 0.</p

Quantifying the Diversification of Hepatitis C Virus (HCV) during Primary Infection: Estimates of the In Vivo Mutation Rate

<div><p>Hepatitis C virus (HCV) is present in the host with multiple variants generated by its error prone RNA-dependent RNA polymerase. Little is known about the initial viral diversification and the viral life cycle processes that influence diversity. We studied the diversification of HCV during acute infection in 17 plasma donors, with frequent sampling early in infection. To analyze these data, we developed a new stochastic model of the HCV life cycle. We found that the accumulation of mutations is surprisingly slow: at 30 days, the viral population on average is still 46% identical to its transmitted viral genome. Fitting the model to the sequence data, we estimate the median <em>in vivo</em> viral mutation rate is 2.5×10⁻⁵ mutations per nucleotide per genome replication (range 1.6–6.2×10⁻⁵), about 5-fold lower than previous estimates. To confirm these results we analyzed the frequency of stop codons (N = 10) among all possible non-sense mutation targets (M = 898,335), and found a mutation rate of 2.8–3.2×10⁻⁵, consistent with the estimate from the dynamical model. The slow accumulation of mutations is consistent with slow turnover of infected cells and replication complexes within infected cells. This slow turnover is also inferred from the viral load kinetics. Our estimated mutation rate, which is similar to that of other RNA viruses (e.g., HIV and influenza), is also compatible with the accumulation of substitutions seen in HCV at the population level. Our model identifies the relevant processes (long-lived cells and slow turnover of replication complexes) and parameters involved in determining the rate of HCV diversification.</p> </div