Fig 1.
Different scenarios of competition for a pool of TFs among promoters and other binding sites.
(A) A single promoter copy in isolation without the presence of any other TF binding sites. (B) Multiple copies of identical promoters competing with each other for the TFs. (C) Promoters compete with other competitor sites for the TFs. Competitor sites can correspond to ‘decoy sites’ or promoters driving expression of other gene species. Therefore, although the competitor sites bind to the TFs, they do not regulate the production of mRNA molecules from the target promoters.
Fig 2.
A kinetic model of transcription, incorporating the TFs’ binding and unbinding to multiple competing promoters.
(A) The rate of binding of a TF to a promoter is kon and the rate of unbinding of the TF from the promoter is koff. (B) List of possible stochastic transitions leading to either formation or dissociation of ‘TF-promoter’ complexes, and their respective statistical weights. The weights represent the probability that each transition will occur during a time interval, Δt. TF copy number, promoter copy number, and the instantaneous number of complexes are denoted by NTF, NP and n respectively. (C) While an activator is bound to a promoter, it promotes the binding of RNAP molecules to the promoter, which subsequently leads to the production of an mRNA molecule at a rate r. Each mRNA molecule then decays at a rate γ. Here, m denotes mRNA copy number. The basal transcription rate, when the activator is not bound to the promoter, is assumed to be zero (see S1 Text for a more general model for activators with a nonzero basal rate). (D) List of stochastic transitions leading to changes in mRNA copy number by the action of activators and their respective weights. (E) When a repressor is bound to a promoter, it hinders RNAP binding to the promoter, subsequently blocking mRNA production. However when a promoter is not bound to any repressor molecule, it produces mRNA molecules at a rate r, which again subsequently decay at a rate γ. (F) List of stochastic transitions leading to changes in mRNA copy number by the action of repressors, with respective weights.
Table 1.
Kinetic rates that are used in simulations.
Fig 3.
Our model of TF sharing predicts the behavior of the first two moments of steady-state mRNA distribution across an isogenic population.
(A) Fold change of the mRNA distribution (defined by 〈m〉/(NPr/γ)) as a function of activator number. (B) Variance of mRNA distribution (var(m)) versus activator number. Note that the variance peaks when the activator number equals the promoter number. (C) Fano factor (defined by var(m)/〈m〉) also exhibit a peak as a function of activator number, when the activator number equals the promoter number. (D) Fold change of expression as a function of repressor number. (E) Variance of mRNA distribution versus repressor number. Just like activators, the variance peaks when repressor number equals the promoter number. (F) Fano factor versus repressor number, showing peaks when the repressor number becomes comparable, but slightly higher than the promoter number. In all the plots, symbols represent data from numerical simulations, which are connected by smooth dashed lines to guide the eyes. The parameter values are as specified in Table 1.
Fig 4.
Prediction of mRNA variance as a function of mean, when the promoters share TFs with other competitor sites.
(A) Schematic of a single target promoter sharing TFs with multiple competitor sites. (B) The variance of mRNA molecules per promoter (var(m)/NP) versus the mean per promoter (〈m〉/NP), when the TFs act as activators. (C) The mRNA variance per promoter versus mean per promoter when the TFs act as repressors. In both the subfigures B and C, different numerical data points are obtained for various numbers of competitor sites by varying the TF copy number. Note that all the data for a single target promoter collapse onto a master curve (black curve). Data for a single target promoter is shown by closed symbols, and the data for two target promoters are shown by open symbols. The parameters related to the promoters (kon, koff, r, γ) are taken from the Table 1, while the number of competitor sites are systematically varied and listed in the figures. The master curves are predictions from Eq 3.
Fig 5.
Introduction of competitor sites can lead to multi-modal mRNA distribution.
(A-B) The steady-state number distributions of mRNA molecules produced by two identical promoters are shown in absence of any competitor sites, with varying number of activators (A) and repressors (B). The kinetic rates are taken from Table 1. Insets: The mRNA distributions with a faster TF binding rate (kon = 0.027s-1) than the mRNA degradation rate (γ = 0.011s−1). Other parameters are as specified in Table 1. (C-D) The steady-state mRNA distributions for two identical promoters are shown in presence of competitor sites, when the TFs either act as activators (C) or repressors (D). For these plots, we choose a faster TF binding rate than mRNA degradation rate (as in the insets of A, B) such that the distributions are unimodal in absence of any competitor sites. The number of competitor sites is increased systematically keeping a fixed number of TFs (NTF = 3). For simplicity we assume that the TF binding and unbinding rates to the promoters are the same as to the competitor sites.