Biology subjects

Bokes, P.

Publications and source records attributed to Bokes, P..

26 records · Page 2Linked to original sources

bioRxiv2019

Mixture distributions in a stochastic gene expression model with delayed feedback

Noise in gene expression can be substantively affected by the presence of production delay. Here we consider a mathematical model with bursty production of protein, a one-step production delay (the passage of which activates the protein), and feedback in the frequency of bursts. We specifically focus on examining the steady-state behaviour of the model in the slow-activation (i.e. large-delay) regime. Using a quasi-steady-state (QSS) approximation, we derive an autonomous ordinary differential equation for the inactive protein that applies in the slow-activation regime. If the differential equation is monostable, the steady-state distribution of the inactive (active) protein is approximated by a single Gaussian (Poisson) mode located at the globally stable steady state of the differential equation. If the differential equation is bistable (due to cooperative positive feedback), the steady-state distribution of the inactive (active) protein is approximated by a mixture of Gaussian (Poisson) modes located at the stable steady states; the weights of the modes are determined from a WKB approximation to the stationary distribution. The asymptotic results are compared to numerical solutions of the chemical master equation.

systems biology↗

bioRxiv2019

Optimal bang--bang feedback for bursty gene expression

Stochasticity in gene expression poses a critical challenge to the precise control of cellular function. In this paper we examine how precisely can a stochastically expressed protein attain a given target expression level. We consider a protein which is produced in bursts and which is able to control its expression via a negative feedback loop; we specifically focus on feedback of a bang-bang type which turns off the production of the protein whenever its concentration exceeds a given threshold. Using a piecewise deterministic mathematical formalism, we derive explicit expressions for the probabilistic distribution of the protein concentration, and for the mean square deviation from the target level. Employing a combination of analytic and numerical optimization, we identify the optimal value of the bang-bang threshold, in terms of minimising the deviation, and examine the dependence of the optimal value on the target level and the sub-threshold burst frequency. The systematic analysis allows us to formulate a number of quantitative and qualitative conclusions about the controllability of burst like gene expression. Finally, we outline directions for future research into the topic.

systems biology↗

bioRxiv2019

Cell volume distributions in exponentially growing populations

Stochastic effects in cell growth and division drive variability in cellular volumes both at the single-cell level and at the level of growing cell populations. Here we consider a simple and tractable model in which cell volumes grow exponentially, cell division is symmetric, and its rate is volume-dependent. Consistently with previous observations, the model is shown to sustain oscillatory behaviour with alternating phases of slow and fast growth. Exact simulation algorithms and large-time asymptotics are developed and cross-validated for the single-cell and whole-population formulations of the model. The two formulations are shown to provide similar results during the phases of slow growth, but differ during the fast-growth phases. Specifically, the single-cell formulation systematically underestimates the proportion of small cells. More generally, our results suggest that measurable characteristics of cells may follow different distributions depending on whether a single-cell lineage or an entire population is considered.

systems biology↗

bioRxiv2019

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

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.

systems biology↗

bioRxiv2018

Noise induced bimodality in genetic circuits with monostable positive feedback

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.

systems biology↗

bioRxiv2018

Maintaining gene expression levels by positive feedback in burst size in the presence of infinitesimal delay

Synthesis of individual molecules in the expression of genes often occurs in bursts of multiple copies. Gene regulatory feedback can affect the frequency with which these bursts occur or their size. Whereas frequency regulation has traditionally received more attention, we focus specifically on the regulation of burst size. It turns out that there are (at least) two alternative formulations of feedback in burst size. In the first, newly produced molecules immediately partake in feedback, even within the same burst. In the second, there is no within-burst regulation due to what we call infinitesimal delay. We describe both alternatives using a minimalistic Markovian drift-jump framework combining discrete and continuous dynamics. We derive detailed analytic results and efficient simulation algorithms for positive noncooperative autoregulation (whether infinitesimally delayed or not). We show that at steady state both alternatives lead to a gamma distribution of protein level. The steady-state distribution becomes available only after a transcritical bifurcation point is passed. Interestingly, the onset of the bifurcation is postponed by the inclusion of infinitesimal delay.

systems biology↗

bioRxiv2018

Buffering gene expression noise by microRNA based feedforward regulation

Cells use various regulatory motifs, including feedforward loops, to control the intrinsic noise that arises in gene expression at low copy numbers. Here we study one such system, which is broadly inspired by the interaction between an mRNA molecule and an antagonistic microRNA molecule encoded by the same gene. The two reaction species are synchronously produced, individually degraded, and the second species (microRNA) exerts an antagonistic pressure on the first species (mRNA). Using linear-noise approximation, we show that the noise in the first species, which we quantify by the Fano factor, is sub-Poissonian, and exhibits a nonmonotonic response both to the species lifetime ratio and to the strength of the antagonistic interaction. Additionally, we use the Chemical Reaction Network Theory to prove that the first species distribution is Poissonian if the first species is much more stable than the second. Finally, we identify a special parametric regime, supporting a broad range of behaviour, in which the distribution can be analytically described in terms of the confluent hypergeometric limit function. We verify our analysis against large-scale kinetic Monte Carlo simulations. Our results indicate that, subject to specific physiological constraints, optimal parameter values can be found within the mRNA-microRNA motif that can benefit the cell by lowering the gene-expression noise.

systems biology↗

bioRxiv2017

High Cooperativity In Negative Feedback Can Amplify Noisy Gene Expression

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.

systems biology↗