Hill kinetics as a noise filter: the role of transcription factor autoregulation in gene cascades

Sequestration of gene products by decoys enhances precision in the timing of intracellular events

Expressed gene products often interact ubiquitously with binding sites at nucleic acids and macromolecular complexes, known as decoys. The binding of transcription factors (TFs) to decoys can be crucial in controlling the stochastic dynamics of gene expression. Here, we explore the impact of decoys on the timing of intracellular events, as captured by the time taken for the levels of a given TF to reach a critical threshold level, known as the first passage time (FPT). Although nonlinearity introduced by binding makes exact mathematical analysis challenging, employing suitable approximations and reformulating FPT in terms of an alternative variable, we analytically assess the impact of decoys. The stability of the decoy-bound TFs against degradation impacts FPT statistics crucially. Decoys reduce noise in FPT, and stable decoy-bound TFs offer greater timing precision with less expression cost than their unstable counterparts. Interestingly, when both bound and free TFs decay at the same rate, decoy binding does not directly alter FPT noise. We verify these results by performing exact stochastic simulations. These results have important implications for the precise temporal scheduling of events involved in the functioning of biomolecular clocks, development processes, cell-cycle control, and cell-size homeostasis.

Noise-induced transitions in gene circuits: A perturbative approach for slow noise

We consider a generic class of gene circuits affected by nonlinear extrinsic noise. To address this nonlinearity we introduce a general perturbative methodology based on assuming timescale separation between noise and gene dynamics, with fluctuations exhibiting a large but finite correlation time. We apply this methodology to the case of the toggle switch, and by considering biologically relevant log-normal fluctuations, we find that the system exhibits noise-induced transitions. The system becomes bimodal in regions of the parameter space where it would be deterministically monostable. We show that by including higher order corrections our methodology allows one to obtain correct predictions for the occurrence of transitions even for not so large correlation time of the fluctuations, thereby overcoming limitations of previous theoretical approaches. Interestingly we find that at intermediate noise intensities the noise-induced transition in the toggle switch affects one of the genes involved, but not the other one.

Temporal signaling, population control, and information processing through chromatin-mediated gene regulation

Chromatin regulation is a key pathway cells use to regulate gene expression in response to temporal stimuli, and is becoming widely used as a platform for synthetic biology applications. Here, we build a mathematical framework for analyzing the response of genetic circuits containing chromatin regulators to temporal signals in mammalian cell populations. Chromatin regulators can silence genes in an all-or-none fashion at the single-cell level, with individual cells stochastically transitioning between active, reversibly silent, and irreversibly silent gene states at constant rates over time. We integrate this mode of regulation with classical gene regulatory motifs, such as autoregulatory and incoherent feedforward loops, to determine the types of responses achievable with duration-dependent signaling. We demonstrate that repressive regulators without long-term epigenetic memory can filter out high frequency noise, and as part of an autoregulatory loop can precisely tune the fraction of cells in a population that expresses a gene of interest. Additionally, we find that repressive regulators with epigenetic memory can sum up and encode the total duration of their recruitment in the fraction of cells irreversibly silenced and, when included in a feed forward loop, enable perfect adaptation. Last, we use an information theoretic approach to show that all-or-none stochastic silencing can be used by populations to transmit information reliably and with high fidelity even in very simple genetic circuits. Altogether, we show that chromatin-mediated gene control enables a repertoire of complex cell population responses to temporal signals and can transmit higher information levels than previously measured in gene regulation.

Silent transcription intervals and translational bursting lead to diverse phenotypic switching

For complex process of gene expression, we use theoretical analysis and stochastic simulations to study the phenotypic diversity induced by silent transcription intervals and translational bursting.

Inherent regulatory asymmetry emanating from network architecture in a prevalent autoregulatory motif

Predicting gene expression from DNA sequence remains a major goal in the field of gene regulation. A challenge to this goal is the connectivity of the network, whose role in altering gene expression remains unclear. Here, we study a common autoregulatory network motif, the negative single-input module, to explore the regulatory properties inherited from the motif. Using stochastic simulations and a synthetic biology approach in E. coli, we find that the TF gene and its target genes have inherent asymmetry in regulation, even when their promoters are identical; the TF gene being more repressed than its targets. The magnitude of asymmetry depends on network features such as network size and TF-binding affinities. Intriguingly, asymmetry disappears when the growth rate is too fast or too slow and is most significant for typical growth conditions. These results highlight the importance of accounting for network architecture in quantitative models of gene expression.

Enhancement of gene expression noise from transcription factor binding to genomic decoy sites

The genome contains several high-affinity non-functional binding sites for transcription factors (TFs) creating a hidden and unexplored layer of gene regulation. We investigate the role of such “decoy sites” in controlling noise (random fluctuations) in the level of a TF that is synthesized in stochastic bursts. Prior studies have assumed that decoy-bound TFs are protected from degradation, and in this case decoys function to buffer noise. Relaxing this assumption to consider arbitrary degradation rates for both bound/unbound TF states, we find rich noise behaviors. For low-affinity decoys, noise in the level of unbound TF always monotonically decreases to the Poisson limit with increasing decoy numbers. In contrast, for high-affinity decoys, noise levels first increase with increasing decoy numbers, before decreasing back to the Poisson limit. Interestingly, while protection of bound TFs from degradation slows the time-scale of fluctuations in the unbound TF levels, the decay of bound TFs leads to faster fluctuations and smaller noise propagation to downstream target proteins. In summary, our analysis reveals stochastic dynamics emerging from nonspecific binding of TFs and highlights the dual role of decoys as attenuators or amplifiers of gene expression noise depending on their binding affinity and stability of the bound TF.