The effects of intrinsic noise on the behaviour of bistable cell regulatory systems under quasi-steady state conditions

We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady state approximation based on the semi-classical approximation of the partial differential equation for the generating function associated with the Chemical Master Equation. Such approximation proceeds by optimising an action functional whose associated set of Euler-Lagrange (Hamilton) equations provide the most likely fluctuation path. We show that, under appropriate conditions granting time scale separation, the Hamiltonian can be re-scaled so that the set of Hamilton equations splits up into slow and fast variables, whereby the quasi-steady state approximation can be applied. We analyse two particular examples of systems whose mean-field limit has been shown to exhibit bi-stability: an enzyme-catalysed system of two mutually-inhibitory proteins and a gene regulatory circuit with self-activation. Our theory establishes that the number of molecules of the conserved species are order parameters whose variation regulates bistable behaviour in the associated systems beyond the predictions of the mean-field theory. This prediction is fully confirmed by direct numerical simulations using the stochastic simulation algorithm. This result allows us to propose strategies whereby, by varying the number of molecules of the three conserved chemical species, cell properties associated to bistable behaviour (phenotype, cell-cycle status, etc.) can be controlled.Comment: 33 pages, 9 figures, accepted for publication in the Journal of Chemical Physic

Protein synthesis driven by dynamical stochastic transcription

In this manuscript we propose a mathematical framework to couple transcription and translation in which mRNA production is described by a set of master equations while the dynamics of protein density is governed by a random differential equation. The coupling between the two processes is given by a stochastic perturbation whose statistics satisfies the master equations. In this approach, from the knowledge of the analytical time dependent distribution of mRNA number, we are able to calculate the dynamics of the probability density of the protein population.Comment: 20 pages, 3 figure

Stochastic modelling and analysis of metabolic heterogeneity in single cells

A wide range of cellular processes are inherently stochastic. While stochasticity of gene transcription and translation or cellular growth profiles is well-understood, little is known about the stochastic properties of metabolism. Recent experimental findings strongly suggest that metabolism may indeed be subject to stochastic phenomena, which has questioned the traditional deterministic view of metabolism and casts crucial doubt on the general validity of this modelling paradigm. In this thesis, we examine stochastic aspects of metabolic reactions in detail. We focus on stochastic versions of classic deterministic models for metabolic reactions coupled with well-established stochastic models for gene expression. We incorporate experimental measurements of kinetic parameters in the study, which results in a specific multiscale structure of the presented class of models. In the course of this thesis, we present numerous models with increasing complexity, focussing on three key contributions. Firstly, we present the derivation of an analytical tool to approximate stationary metabolite distributions in closed-form by exploiting the multiple scales. As a result, we propose a strikingly-accurate analytical tool for exploring the parameter space. Secondly, we reveal which parameters have strong impacts on the stationary metabolite distributions and identify conditions for increased coefficients of variation and highly-complex bimodal and multimodal patterns. Finally, we propose a general strategy to obtain closed-form approximations in more complex models, such as multi-step pathways and regulatory processes commonly found in metabolism, such as allostery or end-product inhibition. The results in this thesis lay the groundwork for future studies of metabolic heterogeneity and offer numerous biological hypotheses that could soon be tested in light of recent progress in single-cell measurements of cellular metabolites.Open Acces

Stochastic Gene Expression in a Lentiviral Positive Feedback Loop: HIV-1 Tat Fluctuations Drive Phenotypic Diversity

Stochastic gene expression has been implicated in a variety of cellular processes, including cell differentiation and disease. In this issue of Cell, Weinberger et al. (2005) take an integrated computational-experimental approach to study the Tat transactivation feedback loop in HIV-1 and show that fluctuations in a key regulator, Tat, can result in a phenotypic bifurcation. This phenomenon is observed in an isogenic population where individual cells display two distinct expression states corresponding to latent and productive infection by HIV-1. These findings demonstrate the importance of stochastic gene expression in molecular "decision-making."Comment: Supplemental data available as q-bio.MN/060800

Effect of transcription factor resource sharing on gene expression noise

Gene expression is intrinsically a stochastic (noisy) process with important implications for cellular functions. Deciphering the underlying mechanisms of gene expression noise remains one of the key challenges of regulatory biology. Theoretical models of transcription often incorporate the kinetics of how transcription factors (TFs) interact with a single promoter to impact gene expression noise. However, inside single cells multiple identical gene copies as well as additional binding sites can compete for a limiting pool of TFs. Here we develop a simple kinetic model of transcription, which explicitly incorporates this interplay between TF copy number and its binding sites. We show that TF sharing enhances noise in mRNA distribution across an isogenic population of cells. Moreover, when a single gene copy shares it\u27s TFs with multiple competitor sites, the mRNA variance as a function of the mean remains unaltered by their presence. Hence, all the data for variance as a function of mean expression collapse onto a single master curve independent of the strength and number of competitor sites. However, this result does not hold true when the competition stems from multiple copies of the same gene. Therefore, although previous studies showed that the mean expression follows a universal master curve, our findings suggest that different scenarios of competition bear distinct signatures at the level of variance. Intriguingly, the introduction of competitor sites can transform a unimodal mRNA distribution into a multimodal distribution. These results demonstrate the impact of limited availability of TF resource on the regulation of noise in gene expression

Characterization of the heat-shock circuit in Campylobacter jejuni

This thesis consists of two different works developed on two distinct research themes, both of them included in the broader issue of bacterial virulence. The first part concerns the molecular characterization of the heat-shock regulatory circuit in the food-borne pathogen Campylobacter jejuni. The heat-shock response, being cellular damage protection mechanism, is involved in the establishment of successful infections in different bacteria. Moreover, in C. jejuni, this regulatory circuit emerged as a crucial pathway for the shift between commensalism and pathogenicity in different hosts, tanks to the peculiarity to modulate host-pathogen interactions. This evidence makes the heat-shock circuit characterization indispensable to elucidate the molecular basis of C. jejuni pathogenicity and virulence. In the human pathogen C. jejuni, the response to thermic stress is controlled by a regulatory circuit, which acts at the transcriptional level and involves the repressors HspR and HrcA. To characterize the molecular mechanism underpinning HspR and HrcA regulatory function, we investigated in detail the HspR and HrcA interactions with target promoter regions. The characterization allowed the identification of their binding sites, and highlight a complex architecture resulting from protein-DNA interactions. The second section is inherent to urease activity in the presence of gold-based compounds. The urease enzyme is a virulence factor for different pathogenic bacteria, of which Helicobacter pylori, Mycobacterium tuberculosis, Cryptococcus neoformans, Yersinia pestis, and Proteus mirabilis. This peculiarity makes the urease an interesting target for potential new specific-drugs against ureolytic pathogens. In this work, we analysed the inhibition ability of different gold-based compounds on urease, investigating the potentiality of these compounds as future antimicrobials in ureolytic bacteria