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Recently, several studies have investigated the transcription process associated to specific genetic regulatory networks. In this work, we present a stochastic approach for analyzing the dynamics and effect of negative feedback loops (FBL) on the transcriptional noise. First, our analysis allows us to identify a bimodal activity depending of the strength of self-repression coupling D. In the strong coupling region D>>1, the variance of the transcriptional noise is found to be reduced a 28 % more than described earlier. Secondly, the contribution of the noise effect to the abundance of regulating protein becomes manifest when the coefficient of variation is computed. In the strong coupling region, this coefficient is found to be independent of all parameters and in fair agreement with the experimentally observed values. Finally, our analysis reveals that the regulating protein is significantly induced by the intrinsic and external noise in the strong coupling region. In short, it indicates that the existence of inherent noise in FBL makes it possible to produce a basal amount of proteins even though the repression level D is very strong.
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Organisms are equipped with regulatory systems that display a variety of dynamical behaviours ranging from simple stable steady states, to switching and multistability, to oscillations. Earlier work has shown that oscillations in protein concentrations or gene expression levels are related to the presence of at least one negative feedback loop in the regulatory network. Here we study the dynamics of a very general class of negative feedback loops. Our main result is that in these systems the sequence of maxima and minima of the concentrations is uniquely determined by the topology of the loop and the activating/repressing nature of the interaction between pairs of variables. This allows us to devise an algorithm to reconstruct the topology of oscillating negative feedback loops from their time series; this method applies even when some variables are missing from the data set, or if the time series shows transients, like damped oscillations. We illustrate the relevance and the limits of validity of our method with three examples: p53-Mdm2 oscillations, circadian gene expression in cyanobacteria, and cyclic binding of cofactors at the estrogen-sensitive pS2 promoter.
Genes and proteins regulate cellular functions through complex circuits of biochemical reactions. Fluctuations in the components of these regulatory networks result in noise that invariably corrupts the signal, possibly compromising function. Here, we create a practical formalism based on ideas introduced by Wiener and Kolmogorov (WK) for filtering noise in engineered communications systems to quantitatively assess the extent to which noise can be controlled in biological processes involving negative feedback. Application of the theory, which reproduces the previously proven scaling of the lower bound for noise suppression in terms of the number of signaling events, shows that a tetracycline repressor-based negative-regulatory gene circuit behaves as a WK filter. For the class of Hill-like nonlinear regulatory functions, this type of filter provides the optimal reduction in noise. Our theoretical approach can be readily combined with experimental measurements of response functions in a wide variety of genetic circuits, to elucidate the general principles by which biological networks minimize noise.
The molecular network in an organism consists of transcription/translation regulation, protein-protein interactions/modifications and a metabolic network, together forming a system that allows the cell to respond sensibly to the multiple signal molecules that exist in its environment. A key part of this overall system of molecular regulation is therefore the interface between the genetic and the metabolic network. A motif that occurs very often at this interface is a negative feedback loop used to regulate the level of the signal molecules. In this work we use mathematical models to investigate the steady state and dynamical behaviour of different negative feedback loops. We show, in particular, that feedback loops where the signal molecule does not cause the dissociation of the transcription factor from the DNA respond faster than loops where the molecule acts by sequestering transcription factors off the DNA. We use three examples, the bet, mer and lac systems in E. coli, to illustrate the behaviour of such feedback loops.
Gene transcription is a stochastic process mostly occurring in bursts. Regulation of transcription arises from the interaction of transcription factors (TFs) with the promoter of the gene. The TFs, such as activators and repressors can interact with the promoter in a competitive or non-competitive way. Some experimental observations suggest that the mean expression and noise strength can be regulated at the transcription level. A Few theories are developed based on these experimental observations. Here we re-establish that experimental results with the help of our exact analytical calculations for a stochastic model with non-competitive transcriptional regulatory architecture and find out some properties of Noise strength (like sub-Poissonian fano factor) and mean expression as we found in a two state model earlier. Along with those aforesaid properties we also observe some anomalous characteristics in noise strength of mRNA and in variance of protein at lower activator concentrations.
Multiple interlinked positive feedback loops shape the stimulus responses of various biochemical systems, such as the cell cycle or intracellular calcium release. Recent studies with simplified models have identified two advantages of coupling fast and slow feedback loops. Namely, this dual-time structure enables a fast response while enhancing resistances of responses and bistability to stimulus noise. We now find that in addition: 1) the dual-time structure confers resistance to internal noise due to molecule number fluctuations, and 2) model variants with altered coupling, which better represent some specific systems, share all the above advantages. We develop a similar bistable model with a fast autoactivation loop coupled to a slow loop, which minimally represents positive feedback that may be essential for long-term synaptic potentiation (LTP). The advantages of fast response and noise resistance carry over to this model. Empirically, LTP develops resistance to reversal over ~1 h. The model suggests this resistance may result from increased amounts of synaptic kinases involved in positive feedback.
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