Fig 1.
The BIR:BTR ratio controls promoter availability and the PPRR:PBR ratio controls transcriptional cycling.
(A) Schematic of three-state transcriptional cycling model, including five species: an unavailable promoter (UP, in blue), an available (but unbound) promoter (AP, in teal), a bound promoter (BP, in yellow), RNA, and protein. A cycle of transcription occurs when the promoter transitions from BP to AP and back to BP. (B-C) Deterministic solution of steady-state mRNA counts when varying BIR and BTR for fixed values of PBR and PPRR (B) or when varying PBR and PPRR for fixed values of BIR and BTR (C). Parameter ranges are varied low to high via arrow directionality and correspond to the following sets: PBR = [0.1 0.5 1 5 10 50 100 500] hr-1, PPRR = [0.1 0.5 1 5 10 50 100] hr-1, BIR = [0.005 0.01 0.05 0.1 0.5 1 5 10 50] hr-1, and BTR = [0.005 0.01 0.05 0.1 0.5 1 5 10 50] hr-1. Heatmap indicates log of average mRNA levels. (D-E) Pie charts representing the fractional probability of UP (blue), AP (teal), and BP (yellow) when varying the BIR:BTR ratio for fixed PBR and PPRR (D) or when varying PBR:PPRR ratio for fixed BIR and BTR (E). (F-G) Fano Factor calculated for the same range of simulations presented in (D) and (E), respectively. Fractional promoter state probabilities and Fano factors were calculated from 1,000 single-cell stochastic simulations under basal conditions out to 10 days for each parameter combination. Square inset in (B) corresponds to the following parameter set: PBR = 10 hr-1, PPRR = 10 hr-1, BIR = [0.01 0.05 0.1 0.5 1] hr-1, and BTR = [0.01 0.05 0.1 0.5 1] hr-1. Square inset in (C) corresponds to the following parameter set: BTR = 0.1 hr-1, BIR = 0.1 hr-1, PPRR = [1 5 10 50 100] hr-1, and PBR = [1 5 10 50 100] hr-1.
Table 1.
Model development and parameter space.
Fig 2.
The initial distribution of promoter states influences the heterogeneity in transcriptional activation modeled as an increase in PPRR.
(A) Three representative pie charts of fractional promoter-state probability of UP (blue), AP (teal) and BP (yellow) for BIR:BTR ratios of 0.1, 1, and 10 with PBR and PPRR held constant at 10 hr-1. Basal conditions were calculated from 1000 single-cell stochastic simulations out to 10 days for each parameter combination. At time = 0, PPRR was increased two-fold (B), and new fractional probabilities were captured at 2 hours. (B) Representative trajectories for BIR:BTR = 10 (pink), BIR:BTR = 1 (green), and BIR:BTR = 0.1 (cerulean). Each line represents one stochastic simulation out to 24 hours. Only 100 simulations are plotted for each condition for ease of visualization. Gray regions on the right represent the probability density of mRNA counts at 24 hours, with kernel smoothing. (C-D) Average mRNA counts (C) and Fano factor (D) for the three BIR:BTR ratios at 0, 1, 2, 4 and 24 hours. Average mRNA values and Fano factor were calculated from 1,000 single-cell stochastic simulation for each parameter combination. Error bars represent 95% bootstrapped confidence intervals. (E) Three representative pie charts of fractional promoter-state probability of UP (blue), AP (teal) and BP (yellow) for PPRR:PBR ratios of 0.1, 1, and 10 with BIR and BTR held constant at 0.1 hr-1. Fractional probabilities were calculated as described in (A). (F) Representative trajectories for PPRR:BBR = 0.1 (yellow), PPRR:PBR = 1 (green), and PPRR:PBR = 10 (orange). Data presented as described in (B). (G-H) Average mRNA counts (G) and Fano factor (H) for the three PPRR:PBR ratios at 0, 1, 2, 4 and 24 hours. Data presented as described in (C-D).
Fig 3.
Positive feedback on PPRR activation does not influence bimodality of the mRNA and protein distributions in the three-state transcriptional cycling model.
(A) Updated three-state promoter system with HIV nucleosome remodeling, RelA recruitment, and Tat-mediated transcript elongation, which is amplified via positive feedback. Positive feedback is modeled as a saturating function with an amplitude, A, and half-max, K. (B) Heatmap of average protein counts at 24 hours with feedback. Protein counts were generated through stochastic simulation for 1,000 cells for each combination of K and A, which were varied over 5 orders of magnitude. The other parameters were fixed as follows: BIR = 0.1 hr-1, BTR = 1 hr-1, PBR = PPRR = 10 hr-1 (C) Kernel fittings of mRNA counts at 24 hours. Each box contains the probability density curve for that parameter combination.
Fig 4.
Transcriptional activation in the presence of PPRR positive feedback predominately alters activation of more permissive initial promoter states.
(A) Three representative fractional promoter-state probability pie charts with the addition of feedback of UP (blue), AP (teal) and BP (yellow) for BIR:BTR ratios of 0.1, 1, and 10 with PBR and PPRR held constant at 10 hr-1. Data presented as described in Fig 2A. (B) Representative simulated trajectories with feedback for BIR:BTR = 10 (pink), BIR:BTR = 1 (green), and BIR:BTR = 0.1 (cerulean) presented as described in (Fig 2B). Gray regions on the right represent the probability density of mRNA counts at 24 hours, with kernel smoothing, with feedback (black) and without feedback (red). (C-D) Fold-change in mRNA counts (C) and Fano factor (D) for the three BIR:BTR ratios at 0, 1, 2, 4 and 24 hours as compared to non-feedback simulations. Data were generated through stochastic simulation for 1,000 cells for each parameter combination. Error bars represent 95% bootstrapped confidence intervals. (E) Three representative pie charts of fractional promoter-state probability with the addition of feedback of UP (blue), AP (teal) and BP (yellow) for PPRR:PBR ratios of 0.1, 1, and 10 with BIR and BTR held constant at 0.1 hr-1. Fractional probabilities were calculated as described in (A). (F) Representative simulated trajectories with feedback for PPRR:PBR = 0.1 (yellow), PPRR:PBR = 1 (green), and PPRR:PBR = 10 (orange). Data presented as described in (B). (G-H) Fold-change mRNA counts (G) and Fano factor (H) for the three PPRR:PBR ratios for timepoints of 0, 1, 2, 4 and 24 hours as compared to non-feedback simulations. Data presented as described in (C-D).
Fig 5.
The three-state transcriptional cycling model reproduces transcriptional activation heterogeneity observed for a range of latent HIV integrations.
(A) Ratio of enrichment of total histone H3 to acetylated H3 (AcH3) in Jurkat T cells at the indicated target promoters quantified by ChIP-qPCR. Data are presented as mean of % input (non-IP control) ± SD of two biological replicates. (B) Experimental GFP-HIV trajectories for the four HIV integrations, plotted with 95% confidence intervals and normalized via experimental setup. (C-E) Scatterplots of three-state promoter simulation with feedback compared to experimental measurements for mRNA Average (C), Fano factor (D), and CV (E). Error bars represent 95% bootstrapped confidence intervals (C) Fractional state probabilities under basal conditions of UP (blue), AP (teal) and BP (yellow) for the four integrations based upon the three-state model. Simulations were run 10,000 times. (F) Representative simulated protein trajectories over 24 hours of the 4 integrations. (G) Violin kernel fitting of protein distributions at basal conditions and at 24 hours of the four integrations. Black bar represents mean. Red dashed line represents a protein threshold of 275 with percentages as the amount above that threshold. Experimental data in this figure reproduced from [4].
Table 2.
Parameters selected for experimental fitting with PPRR activation.
Fig 6.
Implementing transcriptional activation via increases in multiple parameters reproduces transcriptional activation heterogeneity observed for a range of latent HIV integrations with more biological accuracy.
(A) Schematic of multi-point three-pronged activation in the transcriptional cycling model for HIV. (B-D) Scatterplots of three-state promoter simulation with feedback compared to experimental measurements for mRNA Average (B), Fano factor (C), and CV (D). Error bars represent 95% bootstrapped confidence intervals. (E) Fractional state probabilities under basal conditions for the four integrations based upon the three-state model. Simulations were run 1,000 times. (F) Simulated trajectory protein data of 50 representative cells out to 24 hours of the four integrations. (G) Violin kernel fitting of protein distributions at basal conditions and at 24 hours of the four integrations. Black bar represents the mean. Red dashed line represents a protein threshold of 275 with percentages as the amount above that threshold.
Table 3.
Parameters selected for experimental fitting with multi-point activation.
Fig 7.
Multi-step activation can be broken down into discrete activation lines which influence noise and protein counts by 24 hours.
(A-B) Average protein counts (A) and Fano factor (B) for the four activation options at 24 hours. Protein counts were generated through stochastic simulation for 1,000 cells for each parameter combination. Error bars represent 95% bootstrapped confidence intervals. (C) Simulated trajectory protein data of 50 representative cells out to 24 hours of the four activation lines with the four integrations. (D) Violin kernel fitting of protein distributions at basal conditions and at 24 hours of the four activation lines with the four integrations. Black bar represents the mean.
Table 4.
Ratio Parameter Descriptions.