The interplay of intrinsic and extrinsic bounded noises in genetic networks

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a genetic network. The influence of intrinsic and extrinsic noises on genetic networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: $(i)$ the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, $(ii)$ a model of enzymatic futile cycle and $(iii)$ a genetic toggle switch. In $(ii)$ and $(iii)$ we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possibile functional role of bounded noises

Effect of promoter architecture on the cell-to-cell variability in gene expression

According to recent experimental evidence, the architecture of a promoter, defined as the number, strength and regulatory role of the operators that control the promoter, plays a major role in determining the level of cell-to-cell variability in gene expression. These quantitative experiments call for a corresponding modeling effort that addresses the question of how changes in promoter architecture affect noise in gene expression in a systematic rather than case-by-case fashion. In this article, we make such a systematic investigation, based on a simple microscopic model of gene regulation that incorporates stochastic effects. In particular, we show how operator strength and operator multiplicity affect this variability. We examine different modes of transcription factor binding to complex promoters (cooperative, independent, simultaneous) and how each of these affects the level of variability in transcription product from cell-to-cell. We propose that direct comparison between in vivo single-cell experiments and theoretical predictions for the moments of the probability distribution of mRNA number per cell can discriminate between different kinetic models of gene regulation.Comment: 35 pages, 6 figures, Submitte

On the spontaneous stochastic dynamics of a single gene: complexity of the molecular interplay at the promoter

International audienceBACKGROUND: Gene promoters can be in various epigenetic states and undergo interactions with many molecules in a highly transient, probabilistic and combinatorial way, resulting in a complex global dynamics as observed experimentally. However, models of stochastic gene expression commonly consider promoter activity as a two-state on/off system. We consider here a model of single-gene stochastic expression that can represent arbitrary prokaryotic or eukaryotic promoters, based on the combinatorial interplay between molecules and epigenetic factors, including energy-dependent remodeling and enzymatic activities. RESULTS: We show that, considering the mere molecular interplay at the promoter, a single-gene can demonstrate an elaborate spontaneous stochastic activity (eg. multi-periodic multi-relaxation dynamics), similar to what is known to occur at the gene-network level. Characterizing this generic model with indicators of dynamic and steady-state properties (including power spectra and distributions), we reveal the potential activity of any promoter and its influence on gene expression. In particular, we can reproduce, based on biologically relevant mechanisms, the strongly periodic patterns of promoter occupancy by transcription factors (TF) and chromatin remodeling as observed experimentally on eukaryotic promoters. Moreover, we link several of its characteristics to properties of the underlying biochemical system. The model can also be used to identify behaviors of interest (eg. stochasticity induced by high TF concentration) on minimal systems and to test their relevance in larger and more realistic systems. We finally show that TF concentrations can regulate many aspects of the stochastic activity with a considerable flexibility and complexity. CONCLUSIONS: This tight promoter-mediated control of stochasticity may constitute a powerful asset for the cell. Remarkably, a strongly periodic activity that demonstrates a complex TF concentration-dependent control is obtained when molecular interactions have typical characteristics observed on eukaryotic promoters (high mobility, functional redundancy, many alternate states/pathways). We also show that this regime results in a direct and indirect energetic cost. Finally, this model can constitute a framework for unifying various experimental approaches. Collectively, our results show that a gene - the basic building block of complex regulatory networks - can itself demonstrate a significantly complex behavior

Developmental noise : explaining the specific heterogeneity of individual organisms

International audienceRecent research in molecular developmental biology has shown that the stochastic character of development (i.e., developmental noise) can produce phenotypic heterogeneity even in the absence of any other source of change (genetic and environmental). More precisely, developmental noise triggers phe- notypic heterogeneity amongst the members of a clonal population (synchronic heterogeneity) and even within an individual organism over time (diachronic heterogeneity), in a stable and homogeneous environment. This paper deals with such stochasticity in order to explore its epistemological relevance and role, both as explanans and as explanandum. First, I investigate whether developmental noise is part of the explanation of the physical characteristics of individual organisms (i.e., the phenotypic outcome of development). Then, I try to assess whether or not heterogeneity due to stochastic events in development can be explained by a selective-evolutionary history. My final aim is to argue for the two following theses. First, from the developmental point of view, I argue that developmental biologists need to take into account developmental noise in order to explain the uniqueness of each individual organism and its own heterogeneity over time, at the phenotypic level at least, that genetic and environmental changes cannot explain alone. Second, from the evolutionary point of view, I critically evaluate explanations of developmental stochasticity in term of adaptation, in particular the idea that noise is a trait that has been selected to increase the capacity of natural populations to evolve (“evolvability”). Then, I identify other ways in which biologists should try to explain developmental noise. I conclude by highlighting the limits of any univocal explanatory approach in biology

Tribological Behaviour of Orthopaedic Ti-13Nb-13Zr and Ti-6Al-4V Alloys

The aim of this study is to compare the tribological behaviour of novel orthopaedic implant alloy Ti-13Nb-13Zr with that of the standard Ti-6Al-4V ELI alloy, available in four different microstructural conditions produced by variations in the heat treatments. The friction and wear tests were performed by using a block-on-disc tribometer in Ringer's solution at ambient temperature with a normal load of 20-60 N and sliding speed of 0.26-1.0 m/s. It was found that variations in microstructures produced significant variations in the wear resistance of Ti-6Al-4V ELI alloy. The wear losses of materials solution treated (ST) above the beta transus temperature are significantly lower compared with those of materials ST in the (alpha + beta) phase field and are almost insensitive to applied load and sliding speed. Wear loss of the (alpha + beta) ST Ti-6Al-4V ELI alloy continuously increased as applied load was increased and was highest at the highest sliding speed. The Ti-6Al-4V ELI alloy in all microstructural conditions possesses a much better wear resistance than cold-rolled Ti-13Nb-13Zr alloy. Friction results and morphology of worn surfaces showed that the observed behaviour is attributed to the predominant wear damage mechanism