Nonspecific transcription factor binding can reduce noise in the expression of downstream proteins

Abstract

Transcription factors (TFs) interact with a multitude of binding sites on DNA and partner proteins inside cells. We investigate how nonspecific binding/unbinding to such decoy binding sites affects the magnitude and time-scale of random fluctuations in TF copy numbers arising from stochastic gene expression. A stochastic model of TF gene expression, together with decoy site interactions is formulated. Distributions for the total (bound and unbound) and free (unbound) TF levels are derived by analytically solving the chemical master equation under physiologically relevant assumptions. Our results show that increasing the number of decoy binding sides considerably reduces stochasticity in free TF copy numbers. The TF autocorrelation function reveals that decoy sites can either enhance or shorten the time-scale of TF fluctuations depending on model parameters. To understand how noise in TF abundances propagates downstream, a TF target gene is included in the model. Intriguingly, we find that noise in the expression of the target gene decreases with increasing decoy sites for linear TF-target protein dose-responses, even in regimes where decoy sites enhance TF autocorrelation times. Moreover, counterintuitive noise transmissions arise for nonlinear dose-responses. In summary, our study highlights the critical role of molecular sequestration by decoy binding sites in regulating the stochastic dynamics of TFs and target proteins at the single-cell level.

Model reduction for a class of singularly perturbed stochastic differential equations: Fast variable approximation

“…In this section, we quantify the error between the moments of the fast variable of the original system given by (24) and (25) and moments of the reduced fast system given by (17) - (18). To this end, we have the following Lemma, which is an extension to the results in the commutative diagram in Figure 1.…”

“…It has been show that the amount of non-regulatory binding sites -also referred to as decoy sites -can alter the speed and the shape of the response of protein X [15], [16], [17]. Stochastic effects of this system have also been studied in [18], using the chemical Master equation. In this section, we model the dynamics of the system using the chemical Langevin equation and obtain a reduced model, taking into account the time-scale separation in the system.…”

A matter of time — How transient transcription factor interactions create dynamic gene regulatory networks

“…Highly Occupied Target (HOT) regions - regions of DNA that contain a high proportion of non-canonical TF binding [42] - may function like HSP90 by reducing the noise caused by translational bursts in TF production. By sequestering TFs away from gene targets, off-target binding to 'decoy' sites may buffer fluctuations in TF concentration, thereby maintaining a mean number of active TFs within the cell over time [43, 44]. …”

Enhancement of gene expression noise due to nonspecific transcription factor binding

“…When bound TFs are protected from degradation β = 0, the mean free TF count x f = x f ,0 = k x B x /γ f becomes independent of decoy numbers. 45,52 In contrast, with bound TF degradation β > 0 , the mean free TF count monotonically decreases with increasing decoy numbers, with the decrease being faster for stronger binding affinity (or lower dissociation constant). This point is exemplified in Fig.…”

“…Prior theoretical work of on this topic has highlighted the role of decoys as noise buffers, in the sense that, the presence of decoys attenuates random fluctuations in number of freely (unbound) available copies of the TF. [45][46][47][48][49][50][51][52][53][54][55] However, these results are based on the assumption that sequestration of TF at a decoy site protects the TF from degradation. Relaxing this assumption to consider an arbitrary decay rate of the bound TF, we uncover a novel role of decoys as both noise amplifiers and buffers.…”