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Register a new userInterlinked Dual-Time Feedback Loops can Enhance Robustness to Stochasticity and Persistence of Memory
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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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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.
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.
Cells may control fluctuations in protein levels by means of negative autoregulation, where transcription factors bind DNA sites to repress their own production. Theoretical studies have assumed a single binding site for the repressor, while in most species it is found that multiple binding sites are arranged in clusters. We study a stochastic description of negative autoregulation with multiple binding sites for the repressor. We find that increasing the number of binding sites induces regular bursting of gene products. By tuning the threshold for repression, we show that multiple binding sites can also suppress fluctuations. Our results highlight possible roles for the presence of multiple binding sites of negative autoregulators.
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.
To estimate the time, many organisms, ranging from cyanobacteria to animals, employ a circadian clock which is based on a limit-cycle oscillator that can tick autonomously with a nearly 24h period. Yet, a limit-cycle oscillator is not essential for knowing the time, as exemplified by bacteria that possess an hourglass: a system that when forced by an oscillatory light input exhibits robust oscillations from which the organism can infer the time, but that in the absence of driving relaxes to a stable fixed point. Here, using models of the Kai system of cyanobacteria, we compare a limit- cycle oscillator with two hourglass models, one that without driving relaxes exponentially and one that does so in an oscillatory fashion. In the limit of low input-noise, all three systems are equally informative on time, yet in the regime of high input-noise the limit-cycle oscillator is far superior. The same behavior is found in the Stuart-Landau model, indicating that our result is universal.
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