Fig 1.
Schematic of the HIV-1 latency circuit.
The events associated with HIV-1 transcription and translation that govern the latency of an HIV-1 infected cell are depicted as a set of reactions (see Eqs (1)–(18) in Methods). The entities involved in the reactions are described in Results and the rate constants of the reactions are in Table 1.
Table 1.
Model parameters and their typical values.
Fig 2.
Basal reactivation of latently infected cells.
Time-evolution of protein copy numbers in latently infected cells obtained by stochastic simulations of the HIV-1 latency circuit (Methods) in the absence of intervention. Trajectories (lines) of each of the 2000 cells in one realization are shown. Those crossing the activation threshold of 500 copies (dashed line) are in purple and the rest in grey. The parameters employed for the simulations except kNFκB and kBasal are in Table 1. The values of the latter parameters and the resulting percentage activation, fon, are: (A) kNFκB = 9 × 10−5 molecules s-1 and kBasal = 6.14 × 10−3 s-1 yielding fon = 0.0395; (B) kNFκB = 10−4 molecules s-1 and kBasal = 6.14 × 10−3 s-1 yielding fon = 0.0475; (C) kNFκB = 9 × 10−5 molecules s-1 and kBasal = 7 × 10−3 s-1 yielding fon = 0.053; and (D) kNFκB = 10−4 molecules s-1 and kBasal = 7 × 10−3 s-1 yielding fon = 0.0656.
Fig 3.
Influence of PKC agonists on latent cell reactivation.
(A) The fraction of cells reactivated, fon, as a function of the fold-increase, ϕPKCa, in the rate of NF-κB synthesis, predicted using our stochastic simulations (Methods). Representative realizations showing the time-evolution of protein copy numbers in activated (purple) and latent (grey) cells with (B) ϕPKCa = 1.76 yielding fon = 0.1 and (C) ϕPKCa = 3.87 yielding fon = 0.38. The remaining parameters are in Table 1. (D) Dose-response curve for bryostatin-1 obtained by mapping ϕPKCa to the dosage [D] (symbols) that yield the measured fon [33] (Inset). The best-fit of the Hill equation (Eq (22)) (solid line) and the 95% confidence interval (dashed lines) are also shown. The best-fit parameter estimates are ϕ0 = 5.3 ± 0.3 and ϕM = 6 ± 2 nM (R2 = 0.98).
Fig 4.
Influence of HDACi’s on latent cell reactivation.
(A) The fraction of cells reactivated, fon, as a function of the fold-increase, ϕHDACi, in the rate of HIV-1 transcription, predicted using our stochastic simulations (Methods). Representative realizations showing the time-evolution of protein copy numbers in activated (purple) and latent (grey) cells with (B) ϕHDACi = 1.24 yielding fon = 0.066 and (C) ϕHDACi = 1.36 yielding fon = 0.0825. The remaining parameters are in Table 1. Dose-response curves for (D) VPA, (E) NaBut, and (F) TSA, obtained by mapping ϕHDACi to the dosage [D] (symbols) that yield the measured fon [33] (Insets). The best-fits of the Hill equation (Eq (22)) (solid line) and the 95% confidence interval (dashed lines) are also shown. The best-fit parameter estimates are (D) ϕ0 = 0.57 ± 0.08, ϕM = 1.4 ± 0.5 mM (R2 = 0.98); (E) ϕ0 = 1.35 ± 0.08, ϕM = 1.1 ± 0.2 mM (R2 = 0.99); and (F) ϕ0 = 2.3 ± 0.4, ϕM = 300 ± 100 nM (R2 = 0.99).
Fig 5.
Co-stimulation with PKC agonists and HDACi’s.
The fraction of cells reactivated, fon, following simultaneous exposure to 1 nM (blue) or 10 nM (red) bryostatin-1 and (A) VPA, (B) NaBut, and (C) TSA, observed experimentally [33] (symbols) and predicted by our simulations (lines). The values of ϕPKCa and ϕHDACi corresponding to the individual drug concentrations employed were obtained from the dose-response curves in Figs 3 and 4, respectively. Simulations based on confidence limits on these parameter values yielded 95% confidence limits on our predictions (shaded regions). All the other parameters are in Table 1.
Fig 6.
Synergy between PKC agonists and HDACi’s.
(A) The fraction of cells reactivated, fon predicted by our simulations for different values of ϕPKCa and ϕHDACi, the fold-increase in the rate of NF-κB synthesis and HIV-1 transcription due to a PKC agonist and an HDACi, respectively. The lines are contours of constant fon. (B) The corresponding synergy between the drugs, β, predicted using Eqs (19)–(21). The maximum synergy is indicated.
Fig 7.
Drug concentrations yielding maximum synergy.
Synergy as a function of the concentrations of bryostatin-1 and (A) VPA, (B) NaBut, and (C) TSA, obtained by mapping ϕPKCa and ϕHDACi in Fig 6B to drug concentrations using the dose-response curves in Figs 3 and 4. The maximum synergy attainable is indicated.
Fig 8.
The synergy-efficacy trade-off.
(A) The contours of constant fon (Fig 6A) superimposed on the synergy heatmap (Fig 6B). (B) The maximum synergy as a function of fon demonstrating the synergy-efficacy trade-off (symbols). The line is a quadratic fit to guide the eye. (C) The values of ϕPKCa and ϕHDACi that maximize β as functions of fon and (D) the associated drug concentrations estimated using the dose-response curves (Figs 3 and 4).