Modeling poliovirus replication dynamics from live time-lapse single-cell imaging data

Figure 1. Sigmoidal functions fit to experimental data and distributions of fitted parameters when the sigmoidal functions are fit to a population of infection events generated by Liu et al.16 without drug treatment. (A) Example of sigmoidal function fit to experimentally data of GFP intensity measured in arbitrary units (a.u.). A sigmodal curve (black line) is fitted to intensity observations from a single infection event (purple dots), allowing for the estimation of the midpoint (blue) and the maximum intensity value (orange). (B) Example of double-sigmoidal function fit to a single infection event where lysis is observed. A double sigmodal curve (black line) is fitted to intensity observations from a single infection event (purple dots), allowing for the estimation of the midpoint (blue), the maximum intensity value (orange), and the time point of lysis (green). (C) Distribution of slopes calculated at the midpoint. The slope is related to the viral replication rate. (D) Distribution of the maximum intensity. (E) Distribution of the amount of time until the half of the maximum intensity is reached. (F) Distribution of the length of infection time.

Figure 2. Illustration of PV replication cycle and parameter estimation procedure. (A) The replication cycle of PV as represented in the model of Schulte et al.23. This figure is adapted from that work. Numbered steps correspond to individually modeled reactions given in Table 1. (B) Computational procedure to compare the output of the mechanistic model of a single PV infection to the experimental data obtained from populations of single-cell infections.

Figure 3. Time until first occurrence of events as estimated from our model of PV infection when the model is fit to the experimental data shown in Fig. 1C–F. (A) Hours until protein is first produced. (B) Hours until the first production of positive sense RNA. (C) Hours until the first production of negative sense RNA.

Figure 4. Estimates of mechanistic parameter posterior distributions in our model of PV infection from fitting the model to experimental data generated without drug treatment (Fig. 1C–F). Parameters are estimated by fitting the model described by the equations in Table 1 and illustrated in Fig. 2A. The parameters shown correspond to those labeled in each reaction. (A) Translation, which occurs in step 3 of the model. (B) Compartmentalization, a part of step 4. (C) Circularization, step 5. (D, E) Replication of positive and negative sense RNA, step 6. (F) Packaging, step 7. (G) The maximum number of compartments possible, considered in step 6. (H) The maximum number of replication cycles permitted by cellular resources, a limiting factor in step 4. (I) Consumption of the protein product 3A, step 4. (J) The probability for a newly synthesized genome to stay in the replication complex, step 8.

Figure 5. Principal component analysis of parameter distributions estimated from fitting our mechanistic model of PV infection to experimental data (Fig. 1C–F). (A) The amount of variance explained by the first 6 principal components. The white labeling provides the cumulative amount of variance explained by including all components up to and including the labeled one. (B–G) Relative contribution of features for each of the first six principal component axes.

Figure 6. Comparison of posterior parameter distributions between the no drug treatment and drug treatments. Asterisks indicate distributions that differ significantly from the no drug treatment after Bonferroni correction for multiple testing. Non significant (ns) corresponds to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p > 0.05$$\end{document}p>0.05, a single asterisk corresponds to p \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\le$$\end{document}≤ 0.05, two asterisks correspond to p \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\le$$\end{document}≤ 0.01, three correspond to p \documentclass[12pt]{minimal} \usepackage{amsmath}…