Origins of Binary Gene Expression in Post-transcriptional Regulation by MicroRNAs

MicroRNA-mediated regulation of gene expression is characterised by some distinctive features that set it apart from unregulated and transcription factor-regulated gene expression. Recently, a mathematical model has been proposed to describe the dynamics of post-transcriptional regulation by microRNAs. The model explains the observations made in single cell experiments quite well. In this paper, we introduce some additional features into the model and consider two specific cases. In the first case, a non-cooperative positive feedback loop is included in the transcriptional regulation of the target gene expression. In the second case, a stochastic version of the original model is considered in which there are random transitions between the inactive and active expression states of the gene. In the first case we show that bistability is possible in a parameter regime, due to the presence of a non-linear protein decay term in the gene expression dynamics. In the second case, we derive the conditions for obtaining stochastic binary gene expression. We find that this type of gene expression is more favourable in the case of regulation by microRNAs as compared to the case of unregulated gene expression. The theoretical predictions relating to binary gene expression are experimentally testable.Comment: 10 Pages, 5 Figure

Emergent Bistability : Effects of Additive and Multiplicative Noise

Positive feedback and cooperativity in the regulation of gene expression are generally considered to be necessary for obtaining bistable expression states. Recently, a novel mechanism of bistability termed emergent bistability has been proposed which involves only positive feedback and no cooperativity in the regulation. An additional positive feedback loop is effectively generated due to the inhibition of cellular growth by the synthesized proteins. The mechanism, demonstrated for a synthetic circuit, may be prevalent in natural systems also as some recent experimental results appear to suggest. In this paper, we study the effects of additive and multiplicative noise on the dynamics governing emergent bistability. The calculational scheme employed is based on the Langevin and Fokker-Planck formalisms. The steady state probability distributions of protein levels and the mean first passage times are computed for different noise strengths and system parameters. In the region of bistability, the bimodal probability distribution is shown to be a linear combination of a lognormal and a Gaussian distribution. The variances of the individual distributions and the relative weights of the distributions are further calculated for varying noise strengths and system parameters. The experimental relevance of the model results is also pointed out.Comment: 16 pages, 11 figures, version accepted for publication in Eur. Phys. J.

Noise-induced Regime Shifts: A Quantitative Characterization

Diverse complex dynamical systems are known to exhibit abrupt regime shifts at bifurcation points of the saddle-node type. The dynamics of most of these systems, however, have a stochastic component resulting in noise driven regime shifts even if the system is away from the bifurcation points. In this paper, we propose a new quantitative measure, namely, the propensity transition point as an indicator of stochastic regime shifts. The concepts and the methodology are illustrated for the one-variable May model, a well-known model in ecology and the genetic toggle, a two-variable model of a simple genetic circuit. The general applicability and usefulness of the method for the analysis of regime shifts is further demonstrated in the case of the mycobacterial switch to persistence for which experimental data are available.Comment: 10 Pages, 9 figures, revtex4-1, published versio

Phenotypic Heterogeneity in Mycobacterial Stringent Response

A common survival strategy of microorganisms subjected to stress involves the generation of phenotypic heterogeneity in the isogenic microbial population enabling a subset of the population to survive under stress. In a recent study, a mycobacterial population of M. smegmatis was shown to develop phenotypic heterogeneity under nutrient depletion. The observed heterogeneity is in the form of a bimodal distribution of the expression levels of the Green Fluorescent Protein (GFP) as reporter with the gfp fused to the promoter of the rel gene. The stringent response pathway is initiated in the subpopulation with high rel activity.In the present study, we characterize quantitatively the single cell promoter activity of the three key genes, namely, mprA, sigE and rel, in the stringent response pathway with gfp as the reporter. The origin of bimodality in the GFP distribution lies in two stable expression states, i.e., bistability. We develop a theoretical model to study the dynamics of the stringent response pathway. The model incorporates a recently proposed mechanism of bistability based on positive feedback and cell growth retardation due to protein synthesis. Based on flow cytometry data, we establish that the distribution of GFP levels in the mycobacterial population at any point of time is a linear superposition of two invariant distributions, one Gaussian and the other lognormal, with only the coefficients in the linear combination depending on time. This allows us to use a binning algorithm and determine the time variation of the mean protein level, the fraction of cells in a subpopulation and also the coefficient of variation, a measure of gene expression noise.The results of the theoretical model along with a comprehensive analysis of the flow cytometry data provide definitive evidence for the coexistence of two subpopulations with overlapping protein distributions.Comment: 24 pages,8 figures, supplementary information and 5 supplementary figure

Emergent Correlations in Gene Expression Dynamics as Footprints of Resource Competition

Genetic circuits need a cellular environment to operate in, which naturally couples the circuit function with the overall functionality of gene regulatory network. To execute their functions all gene circuits draw resources in the form of RNA polymerases, ribosomes, and tRNAs. Recent experiments pointed out that the role of resource competition on synthetic circuit outputs could be immense. However, the effect of complexity of the circuit architecture on resource sharing dynamics is yet unexplored. In this paper, we employ mathematical modelling and in-silico experiments to identify the sources of resource trade-off and to quantify its impact on the function of a genetic circuit, keeping our focus on regulation of immediate downstream proteins. We take the example of the fluorescent reporters, which are often used as protein read-outs. We show that estimating gene expression dynamics from readings of downstream protein data might be unreliable when the resource is limited and ribosome affinities are asymmetric. We focus on the impact of mRNA copy number and RBS strength on the nonlinear isocline that emerges with two regimes, prominently separated by a tipping point, and study how correlation and competition dominate each other depending on various circuit parameters. Focusing further on genetic toggle circuit, we have identified major effects of resource competition in this model motif, and quantified the observations. The observations are testable in wet-lab experiments, as all the parameters chosen are experimentally relevant.Comment: 15 pages, 7 figure

Quantitative Modelling of Diffusion-driven Pattern Formation in microRNA-regulated Gene Expression

MicroRNAs are extensively known for post-transcriptional gene regulation and pattern formation in the embryonic developmental stage. We explore the origin of these spatio-temporal patterns mathematically, considering three different motifs here. For three scenarios, (1) simple microRNA-based mRNA regulation with a graded response in output, (2) microRNA-based mRNA regulation resulting in bistability in the dynamics, and (3) a coordinated response of microRNA (miRNA), simultaneously regulating the mRNAs of two different pools, detailed dynamical analysis, as well as the reaction-diffusion scenario have been considered and analyzed in the steady state and for the transient dynamics further. We have observed persistent-temporal patterns, as a result of the dynamics of the motifs, that explain spatial gradients and relevant patterns formed by related proteins in development and phenotypic heterogenetic aspects in biological systems. Competitive effects of miRNA regulation have also been found to be capable to cause spatio-temporal patterns, persistent enough to direct developmental decisions. Under coordinated regulation, miRNAs are found to generate spatio-temporal patterning even from complete homogeneity in concentration of target protein, which may have impactful insights in choice of cell-fates.Comment: 31 page