Biology subjects

Grima, R.

Publications and source records attributed to Grima, R..

41 records · Page 3Linked to original sources

bioRxiv2020

Effects of cell cycle variability on lineage and population measurements of mRNA abundance

Many models of gene expression do not explicitly incorporate a cell cycle description. Here we derive a theory describing how mRNA fluctuations for constitutive and bursty gene expression are influenced by stochasticity in the duration of the cell cycle and the timing of DNA replication. Analytical expressions for the moments show that omitting cell cycle duration introduces an error in the predicted mean number of mRNAs that is a monotonically decreasing function of η, which is proportional to the ratio of the mean cell cycle duration and the mRNA lifetime. By contrast, the error in the variance of the mRNA distribution is highest for intermediate values of η consistent with genome-wide measurements in many organisms. Using eukaryotic cell data, we estimate the errors in the mean and variance to be at most 3% and 25%, respectively. Furthermore, we derive an accurate negative binomial mixture approximation to the mRNA distribution. This indicates that stochasticity in the cell cycle can introduce fluctuations in mRNA numbers that are similar to the effect of bursty transcription. Finally, we show that for real experimental data, disregarding cell cycle stochasticity can introduce errors in the inference of transcription rates larger than 10%.Competing Interest StatementThe authors have declared no competing interest.View Full Text

systems biology↗

bioRxiv2020

Dynamical phase diagram of an auto-regulating gene in fast switching conditions

While the steady-state behavior of stochastic gene expression with auto-regulation has been extensively studied, its time-dependent behavior has received much less attention. Here, under the assumption of fast promoter switching, we derive and solve a reduced chemical master equation for an auto-regulatory gene circuit with translational bursting and cooperative protein-gene interactions. The analytical expression for the time-dependent probability distribution of protein numbers enables a fast exploration of large swaths of parameter space. For a unimodal initial distribution, we identify three distinct types of stochastic dynamics: (i) the protein distribution remains unimodal at all times; (ii) the protein distribution becomes bimodal at intermediate times and then reverts back to being unimodal at long times (transient bimodality) and (iii) the protein distribution switches to being bimodal at long times. For each of these, the deterministic model predicts either monostable or bistable behaviour and hence there exist six dynamical phases in total. We investigate the relationship of the six phases to the transcription rates, the protein binding and unbinding rates, the mean protein burst size, the degree of cooperativity, the relaxation time to the steady state, the protein mean and the type of feedback loop (positive or negative). We show that transient bimodality is a noise-induced phenomenon that occurs when protein expression is sufficiently bursty and we use theory to estimate the observation time window when it is manifest.

systems biology↗

bioRxiv2019

Multi-scale bursting in stochastic gene expression

Transcriptional bursting is a major source of noise in gene expression. The telegraph model of gene expression, whereby transcription switches between "on" and "off" states, is the dominant model for bursting. Recently it was shown that the telegraph model cannot explain a number of experimental observations from perturbation data. Here we study an alternative model that is consistent with the data and which explicitly describes RNA polymerase recruitment and polymerase pause release, two steps necessary for mRNA production. We derive the exact steady-state distribution of mRNA numbers and an approximate steady-state distribution of protein numbers which are given by generalized hypergeometric functions. The theory is used to calculate the relative sensitivity of the coefficient of variation of mRNA fluctuations for thousands of genes in mouse fibroblasts. This indicates that the size of fluctuations is mostly sensitive to the rate of burst initiation and the mRNA degradation rate. Furthermore we show that (i) the time-dependent distribution of mRNA numbers is accurately approximated by a modified telegraph model with a Michaelis-Menten like dependence of the effective transcription rate on RNA polymerase abundance. (ii) the model predicts that if the polymerase recruitment rate is comparable or less than the pause release rate, then upon gene replication the mean number of RNA per cell remains approximately constant. This gene dosage compensation property has been experimentally observed and cannot be explained by the telegraph model with constant rates. Statement of SignificanceThe random nature of gene expression is well established experimentally. Mathematical modelling provides a means of understanding the factors leading to the observed stochasticity. There is evidence that the classical two-state model of stochastic mRNA dynamics (the telegraph model) cannot describe perturbation experiments and a new model that includes polymerase dynamics has been proposed. In this paper, we present the first detailed study of this model, deriving an exact solution for the mRNA distribution in steady-state conditions, an approximate time-dependent solution and showing the model can explain gene dosage compensation. As well, we use the theory together with transcriptomic data, to deduce which parameters when perturbed lead to a maximal change in the size of mRNA fluctuations.

systems biology↗

bioRxiv2019

Revisiting the reduction of stochastic models of genetic feedback loops with fast promoter switching

Propensity functions of the Hill-type are commonly used to model transcriptional regulation in stochastic models of gene expression. This leads to an effective reduced master equation for the mRNA and protein dynamics only. Based on deterministic considerations, it is often stated or tacitly assumed that such models are valid in the limit of rapid promoter switching. Here, starting from the chemical master equation describing promoter-protein interactions, mRNA transcription, protein translation and decay, we prove that in the limit of fast promoter switching, the distribution of protein numbers is different than that given by standard stochastic models with Hill-type propensities. We show the differences are pronounced whenever the protein-DNA binding rate is much larger than the unbinding rate, a special case of fast promoter switching. Furthermore we show using both theory and simulations that use of the standard stochastic models leads to drastically incorrect predictions for the switching properties of positive feedback loops and that these differences decrease with increasing mean protein burst size. Our results confirm that commonly used stochastic models of gene regulatory networks are only accurate in a subset of the parameter space consistent with rapid promoter switching.\n\nStatement of SignificanceA large number of models of gene regulatory networks in the literature assume that since promoter switching is fast then transcriptional regulation can be effectively modeled using Hill functions. While this approach can be rigorously justified for deterministic models, it is presently unclear if it is also the case for stochastic models. In this article we prove that this is not the case, i.e. stochastic models of gene regulatory systems, namely those with feedback loops, describing transcriptional regulation using Hill functions are only valid in a subset of parameter conditions consistent with fast promoter switching. We identify parameter regimes where these models are correct and where their predictions cannot be trusted.

systems biology↗

bioRxiv2018

A stochastic model of corneal epithelium maintenance and recovery following perturbation

Various biological studies suggest that the corneal epithelium is maintained by active stem cells located in the limbus, the so-called Limbal Epithelial Stem Cell (LESC) hypothesis. While numerous mathematical models have been developed to describe corneal epithelium wound healing, only a few have explored the process of corneal epithelium homeostasis. In this paper we present a purposefully simple stochastic mathematical model based on a chemical master equation approach, with the aim of clarifying the main factors involved in the maintenance process. Model analysis provides a set of constraints on the numbers of stem cells, division rates, and the number of division cycles required to maintain a healthy corneal epithelium. In addition, our stochastic analysis reveals noise reduction as the epithelium approaches its homeostatic state, indicating robustness to noise. Finally, recovery is analysed in the context of perturbation scenarios.

biophysics↗