The spatio-temporal dynamics of interacting genetic incompatibilities. Part I: the case of stacked underdominant clines.

We explore the interaction between two genetic incompatibilities (underdominant loci in diploid organisms) in a population occupying a one-dimensional space. We derive a system of partial differential equations describing the dynamics of allele frequencies and linkage disequilibrium between the two loci, and use a quasi-linkage equilibrium approximation in order to reduce the number of variables. We investigate the solutions of this system and demonstrate the existence of a solution in which the two clines in allele frequency remain stacked together. In the case of asymmetric incompatibilities (i.e. when one homozygote is favored over the other at each locus), these stacked clines propagate in the form of a traveling wave. We obtain an approximation for the speed of this wave which, in particular, is decreased by recombination between the two loci but is always larger than the speed of "one cline alone".

Stopping a reaction-diffusion front.

We revisit the problem of pinning a reaction-diffusion front by a defect, in particular by a reaction-free region. Using collective variables for the front and numerical simulations, we compare the behaviors of a bistable and monostable front. A bistable front can be pinned as confirmed by a pinning criterion, the analysis of the time independent problem, and simulations. Conversely, a monostable front can never be pinned, it gives rise to a secondary pulse past the defect and we calculate the time this pulse takes to appear. These radically different behaviors of bistable and monostable fronts raise issues for modelers in particular areas of biology, as for example, the study of tumor growth in the presence of different tissues.

Regulation of alginate catabolism involves a GntR family repressor in the marine flavobacterium Zobellia galactanivorans DsijT.

Marine flavobacteria possess dedicated Polysaccharide Utilization Loci (PULs) enabling efficient degradation of a variety of algal polysaccharides. The expression of these PULs is tightly controlled by the presence of the substrate, yet details on the regulatory mechanisms are still lacking. The marine flavobacterium Zobellia galactanivorans DsijT digests many algal polysaccharides, including alginate from brown algae. Its complex Alginate Utilization System (AUS) comprises a PUL and several other loci. Here, we showed that the expression of the AUS is strongly and rapidly (<30 min) induced upon addition of alginate, leading to biphasic substrate utilization. Polymeric alginate is first degraded into smaller oligosaccharides that accumulate in the extracellular medium before being assimilated. We found that AusR, a GntR family protein encoded within the PUL, regulates alginate catabolism by repressing the transcription of most AUS genes. Based on our genetic, genomic, transcriptomic and biochemical results, we propose the first model of regulation for a PUL in marine bacteria. AusR binds to promoters of AUS genes via single, double or triple copies of operator. Upon addition of alginate, secreted enzymes expressed at a basal level catalyze the initial breakdown of the polymer. Metabolic intermediates produced during degradation act as effectors of AusR and inhibit the formation of AusR/DNA complexes, thus lifting transcriptional repression.

Toward Multiscale Modeling of Molecular and Biochemical Events Occurring at Fertilization Time in Sea Urchins.

We review here previous theoretical and experimental works, which aim to model major events that occur at the time of fertilization in the sea urchin. We discuss works that perform experiments and develop hypotheses that link different scales of biological systems such as the intracellular Ca2+ concentration oscillations and the swimming behavior of sperm, the Ca2+ wave propagation and the fertilization membrane elevation of the egg, and the mRNA translational activation and the completion of the first mitotic division of the early embryo. The aim of this review is on one hand, to highlight the value of systems biology for understanding the mechanisms associated with fertilization and early embryonic development in sea urchins. On the other hand, this review attempts to illustrate, for mathematicians and bioinformaticians, the potential that represent these molecular and cellular events for modeling clear physiological processes.

A phenomenological model of cell-cell adhesion mediated by cadherins.

We present a phenomenological model intended to describe at the protein population level the formation of cell-cell junctions by the local recruitment of homophilic cadherin adhesion receptors. This modeling may have a much wider implication in biological processes since many adhesion receptors, channel proteins and other membrane-born proteins associate in clusters or oligomers at the cell surface. Mathematically, it consists in a degenerate reaction-diffusion system of two partial differential equations modeling the time-space evolution of two cadherin populations over a surface: the first one represents the diffusing cadherins and the second one concerns the fixed ones. After discussing the stability of the solutions of the model, we perform numerical simulations and show relevant analogies with experimental results. In particular, we show patterns or aggregates formation for a certain set of parameters. Moreover, perturbing the stationary solution, both density populations converge in large times to some saturation level. Finally, an exponential rate of convergence is numerically obtained and is shown to be in agreement, for a suitable set of parameters, with the one obtained in some in vitro experiments.

Reaction-diffusion front crossing a local defect.

The interaction of a Zeldovich-Frank-Kamenetsky reaction-diffusion front with a localized defect is studied numerically and analytically. For the analysis, we start from conservation laws and develop simple, collective variable, ordinary differential equations for the front position and width. Their solutions are in good agreement with the solutions of the full problem. Finally, using this reduced model, we explain the pinning of the front on a large defect and obtain a quantitative criterion.