Fig 1.
The mechanistic problem underlying bimodal fate-selection programs: Promoter toggling is theoretically sufficient to generate bimodality, but only in a narrow parameter regime.
(A) A simplified fate-selection decision in HIV. Upon infection of a CD4+ T lymphocyte, HIV either enters into an active state of replication (red), producing viral progeny and destroying the host cell, or enters into a quiescent state of silenced gene expression termed proviral latency (blue). This fate bifurcation between active replication and latency is not controlled by the cell state [27] but rather by an HIV gene-regulatory program that can generate bimodal gene-expression distributions from its long terminal repeat (LTR) promoter. (B) The LTR is accurately described by a 2-state promoter model (e.g., random telegraph models) in which the LTR switches between an inactive (represented by Prom-Gene that is crossed out, top) to an active (represented by Prom-Gene) state of expression at rate kON. In the active state, mRNAs are produced, before the promoter flips back to the inactive state at rate kOFF. Promoter toggling between these active and inactive states can produce bimodal distributions in gene-expression products, but only within a restricted regime of phase space. Each parameter set was checked to see if it generated unimodal latency (blue), unimodal active replication (red), or bimodality (orange), as described in the Materials and methods section. For the modality analysis, each mode was required to contain at least 0.1% of the population; otherwise, the parameter set was determined to produce a unimodal population.
Fig 2.
Long terminal repeat (LTR) promoter toggling is sufficient to generate bimodality and control HIV fate.
(A) Schematic of the open-loop HIV circuit. Doxycycline addition induces transcription from the Tet-ON promoter. Shield-1 addition controls the stability of the transactivator of transcription (Tat) fused to Dendra-FKBP fusion protein. Tat induces transcription from the HIV LTR. (B) The (Iso) term represents an independent isoclonal population; consequently, each cell within a clone has the same integration site for the LTR. Nine Iso populations were exposed to 48 different doxycycline and Shield-1 conditions (S2 and S3 Figs and S1–S23 Data), and bimodality was tested for by the Hartigan Dip Test [39] (the threshold for determining bimodality was p < 0.3, agreeing with an independent test, S3 Fig and S24 Data). Gray squares indicate populations that were determined to be unimodal, and black squares represent bimodal populations. (C) Open-loop stochastic model of Tat transactivation of the LTR by 1 of 3 mechanisms. Left column, increasing burst frequency by promoting transitions into the LTRON state (left, increasing kON, blue); middle column, increasing burst size by increasing transcriptional efficiency (middle, increasing α, red); and right column, increasing burst size through addition of a third promoter state (effectively inhibiting kOFF, green arrow). Note that for the model in which Tat effectively modulates kOFF (right), there is an additional production of mCh from the LTRON state (arrow not shown) at rate α so that changes in burst sizes can be generated without altering transcriptional efficiency. Model equations and details are presented in S1–S3 Tables. Plotted histograms are steady-state results of 1,000 simulations (at 1,000 hours) showing that slowing promoter toggling by inhibiting transitions into the active state is sufficient to generate bimodal distributions (i.e., right column, middle panel). Insets: Zoom of α modulation so the scale of the x-axis matches the kON (left column) and kOFF (right column) modulation graphs (S1 Data).
Fig 3.
Positive-feedback strength controls whether the expression distribution is unimodal or bimodal in HIV.
(A) Schematic of the LTR-mCherry-IRES-Tat-FKBP closed-loop, positive-feedback circuit. The transactivator of transcription (Tat) stability is tuned through the addition of Shield-1 to alter Tat feedback strength (i.e., loop transmission) (S9 Fig). (B) Flow cytometry histograms showing bimodal distribution for 9 isoclonal cell lines exposed to various concentrations of Shield-1. A fraction of isoclones can naturally generate bimodal distributions with low feedback strength (e.g., red [0 nM Shield-1]), but with intermediate positive-feedback strength, bimodal distributions are more prevalent (e.g., green [100 nM Shield-1] or blue [500 nM Shield-1]). The “ON”/ “OFF” threshold was set based on the background level of expression from a naïve Jurkat cell line. (C) Measurement of bimodality for each Shield-1 condition for each isoclonal population in (B) as quantified by the Hartigan Dip Test. The results agree with another metric for measuring bimodality (S7 Fig and S30 Data). Gray squares are determined to be unimodal, and black squares are bimodal. (D) A closed-loop stochastic model (in contrast to the open-loop model in Fig 2C) of long terminal repeat (LTR) promoter toggling that incorporates Tat positive feedback through 1 of 3 alternate mechanisms (Fig 2C). Note that for Tat modulation of kOFF (right), both the LTRON state and the Tat-LTRON state produce mCh and Tat at the same rate, α, as described for Fig 2C. The steady-state results for 1,000 simulation runs (modeled for 1,000 hours) show that Tat inhibition of promoter turnoff is sufficient to generate bimodalities (right column, middle panel), whereas alternate Tat positive-feedback mechanisms are unable to generate bimodality in the requisite parameter regimes (S26 Data).
Fig 4.
HIV positive feedback appears optimized to robustly generate bimodal distributions.
(A) Varying the positive-feedback strength changes the toggling kinetics to yield a larger regime for bimodality within the physiological parameter range. The results for the parameter scans are shown for “No Feedback” (left) and increasing feedback strengths. Whether a population was unimodal latent (blue), unimodal active replication (red), or bimodal (orange) was determined for each set of parameters as described in the Materials and methods section. For the modality analysis, each mode was required to contain at least 0.1% of the population. (B) The percent of toggling kinetics that yield bimodal distributions for varying feedback strengths. The asterisks above the bars represent the feedback strengths shown in (A) (S35 Data).
Fig 5.
Nonlatching positive feedback substantially dampens the Poissonian noise-mean inverse relationship, allowing stochastic extinction despite increasing mean-expression levels.
(A) In the classical Poisson or super-Poissonian transcriptional burst models [50], the expression mean scales with variance (σ2 ∝ μ) such that the noise magnitude (CV2 = σ2 / μ2) decreases proportionally to the inverse of the mean. Nonlatching positive feedback breaks the Poissonian relationship such that σ2 ∝ μN with 1 < N < 2 [44]. In the extreme case where N = 2, CV2 becomes independent of the mean. (B) Monte-Carlo (Gillespie) simulations for three different population mean values in absence (left) and presence (right) of positive feedback showing that stochastic extinction can be decoupled from the mean (when N = 2). (C) Analysis of the data in Fig 3 shows that the Tat circuit displays partial decoupling of noise and mean (N ≈ 1.5).