Bio-array images processing and genetic networks modelling

The new tools available for gene expression studies are essentially the bio-array methods using a large variety of physical detectors (isotopes, fluorescent markers, ultrasounds...). Here we present first rapidly an image-processing method independent of the detector type, dealing with the noise and with the peaks overlapping, the peaks revealing the detector activity (isotopic in the presented example), correlated with the gene expression. After this primary step of bio-array image processing, we can extract information about causal influence (activation or inhibition) a gene can exert on other genes, leading to clusters of genes co-expression in which we extract an interaction matrix M and an associated interaction graph G explaining the genetic regulatory dynamics correlated to the studied tissue function. We give two examples of such interaction matrices and graphs (the flowering genetic regulatory network of Arabidopsis thaliana and the lytic/lysogenic operon of the phage Mu) and after some theoretical rigorous results recently obtained concerning the asymptotic states generated by the genetic networks having a given interaction matrix and reciprocally concerning the minimal (in the sense of having a minimal number of non-zero coefficients) matrices having given stationary stable states.     

Hardware (DNA) circuits

A scheme is presented whereby a new genetic control circuit can be introduced into an organism, permitting the experimenter to turn the expression of a given gene (or set of genes) on or off at will. The proposed scheme involves a positive feedback loop--here, a positive regulator, the CII protein of phage lambda, with its structural gene engineered so as to require CII for its expression. This feedback loop creates the possibility of two stable steady states, with gene cII ON or OFF. Genes added downstream of cII and lacking a promoter will follow the same expression as cII. Two additional circuits allow the experimenter to switch at will between the ON and OFF states.     

A simple framework to describe the regulation of gene expression in prokaryotes

Based on the bimolecular mass action law and the derived mass conservation laws, we propose a mathematical framework in order to describe the regulation of gene expression in prokaryotes. It is shown that the derived models have all the qualitative properties of the activation and inhibition regulatory mechanisms observed in experiments. The basic construction considers genes as templates for protein production, where regulation processes result from activators or repressors connecting to DNA binding sites. All the parameters in the models have a straightforward biological meaning. After describing the general properties of the basic mechanisms of positive and negative gene regulation, we apply this framework to the self-regulation of the trp operon and to the genetic switch involved in the regulation of the lac operon. One of the consequences of this approach is the existence of conserved quantities depending on the initial conditions that tune bifurcations of fixed points. This leads naturally to a simple explanation of threshold effects as observed in some experiments.     

Demographic and genetic structures of white sea bream populations (Diplodus sargus, Linnaeus, 1758) inside and outside a Mediterranean marine reserve

We studied the white sea bream (Diplodus sargus), a protandrous hermaphroditic fish, in two protected and unprotected areas in southwestern France. We observed a significant difference in the demographic structure between the two areas. Females were present in two different age distributions inside and outside the marine reserve with younger females outside. This suggests plasticity in the age of sexual inversion in the case of an exploited population. Genetic differentiation was weak and apparent at only one locus of 26 surveyed (FST = 0.007, p = 0.04). Our data suggest that gene flow between the two areas is important, or the separation between the two sites is recent. Our data on the white sea bream show that fishes inside and outside the marine reserve are very similar genetically, which means that the 'reserve effect' is truly a demographic one, not the result of genetic differences.     

Mathematical approaches to differentiation and gene regulation

We consider some mathematical issues raised by the modelling of gene networks. The expression of genes is governed by a complex set of regulations, which is often described symbolically by interaction graphs. These are finite oriented graphs where vertices are the genes involved in the biological system of interest and arrows describe their interactions: a positive (resp. negative) arrow from a gene to another represents an activation (resp. inhibition) of the expression of the latter gene by some product of the former. Once such an interaction graph has been established, there remains the difficult task to decide which dynamical properties of the gene network can be inferred from it, in the absence of precise quantitative data about their regulation. There mathematical tools, among others, can be of some help. In this paper we discuss a rule proposed by Thomas according to which the possibility for the network to have several stationary states implies the existence of a positive circuit in the corresponding interaction graph. We prove that, when properly formulated in rigorous terms, this rule becomes a theorem valid for several different types of formal models of gene networks. This result is already known for models of differential [C. Soulé, Graphic requirements for multistationarity, ComPlexUs 1 (2003) 123-133] or Boolean [E. Rémy, P. Ruet, D. Thieffry, Graphic requirements for multistability and attractive cycles in a boolean dynamical framework, 2005, Preprint] type. We show here that a stronger version of it holds in the differential setup when the decay of protein concentrations is taken into account. This allows us to verify also the validity of Thomas' rule in the context of piecewise-linear models. We then discuss open problems.