Stochastic modeling and numerical simulation of gene regulatory networks with protein bursting

Lin

2017

Preprint

Burst-like synthesis of protein is a significant source of cell-to-cell variability in protein levels. Negative feedback is a common example of a regulatory mechanism by which such stochasticity can be controlled. Here we consider a specific kind of negative feedback, which makes bursts smaller in the excess of protein. Increasing the strength of the feedback may lead to dramatically different outcomes depending on a key parameter, the noise load, which is defined as the squared coefficient of variation the protein exhibits in the absence of feedback. Combining stochastic simulation with asymptotic analysis, we identify a critical value of noise load: for noise loads smaller than critical, the coefficient of variation remains bounded with increasing feedback strength; contrastingly, if the noise load is larger than critical, the coefficient of variation diverges to infinity in the limit of ever greater feedback strengths. Interestingly, high-cooperativity feedbacks have lower critical noise loads, implying that low-cooperativity feedbacks in burst size can be preferable for noisy proteins. Finally, we discuss our findings in the context of previous results on the impact of negative feedback in burst size and burst frequency on gene-expression noise.

Section: Introductionmentioning

confidence: 99%

High cooperativity in negative feedback can amplify noisy gene expression

Lin

2017

Preprint

“…The parameter δ compares the length of bursting and protein turnover timescale; bursts become instantaneous in the limit of δ → 0. The protein copy-number histograms obtained by stochastic simulation are compared to the transformed probability density functions Simulations of full discrete models (29) and (30), as discrete black markers, are compared to explicit continuous pdfs (15) and (27) where p(x) is the protein pdf in the presence of feedback in burst freqency (15) or burst size (27); the normalisation constant M 0 is equal to the zero-th moment (see (16) and (28)). The discrete model for feedback in burst frequency is in an excellent agreement with the hybrid framework ( Fig 5, top left panel).…”

Section: Resultsmentioning

confidence: 99%

“…The chosen framework belongs to a wider family of piecewise deterministic [22], [23] or hybrid models [24], [25]. Regulation of burst frequency (Fig 1, right top), and partly also burst size (Fig 1, right bottom), have previously been examined using the aforementioned modelling framework [26]- [29]. In the context of burst-size regulation, two alternative versions have been proposed depending on the inclusion or omission of a so-called infinitesimal delay [30], [31].…”

Section: Introductionmentioning

confidence: 99%

Noise induced bimodality in genetic circuits with monostable positive feedback

2018

Preprint

The expression of individual genes can be maintained through positive feedback loop mechanisms. If genes are expressed in bursts, then feedback either affects the frequency with which bursts occur or their size. Here we use a tractable hybrid modelling framework to evaluate how noncooperative positive feedback in burst frequency or burst size impacts the protein-level distribution. We confirm the results of previous studies that noncooperative positive feedback in burst frequency can support bimodal distributions. Intriguingly, bimodal distributions are unavailable in the case of feedback in burst size in the hybrid framework. However, kinetic Monte Carlo simulations of a full discrete model show that bimodality can reappear due to low-copy number effects. The two types of feedbacks lead to dramatically different values of protein mean and noise. We show that small values of leakage imply a small protein mean for feedback in burst frequency but not necessarily for feedback in burst size. We also show that protein noise decreases in response to gene activation if feedback is in burst frequency but there is a transient noise amplification if feedback acts on burst size. Our results suggest that feedback in burst size and feedback in burst frequency may play fundamentally different roles in maintaining and controlling stochastic gene expression.

“…The master equation for the hybrid process as described above takes the form of a partial integro-differential equation [23] ∂p ∂t…”

Section: Constitutive Modelmentioning

confidence: 99%

Controlling noisy expression through auto regulation of burst frequency and protein stability

2019

Preprint

Protein levels can be controlled by regulating protein synthesis or half life. The aim of this paper is to investigate how introducing feedback in burst frequency or protein decay rate affects the stochastic distribution of protein level. Using a tractable hybrid mathematical framework, we show that the two feedback pathways lead to the same mean and noise predictions in the small-noise regime. Away from the small-noise regime, feedback in decay rate outperforms feedback in burst frequency in terms of noise control. The difference is particularly conspicuous in the strong-feedback regime. We also formulate a fine-grained discrete model which reduces to the hybrid model in the large system-size limit. We show how to approximate the discrete protein copy-number distribution and its Fano factor using hybrid theory. We also demonstrate that the hybrid model reduces to an ordinary differential equation in the limit of small noise. Our study thus contains a comparative evaluation of feedback in burst frequency and decay rate, and provides additional results on model reduction and approximation.