Fisher waves: An individual-based stochastic model.

The propagation of a beneficial mutation in a spatially extended population is usually studied using the phenomenological stochastic Fisher-Kolmogorov-Petrovsky-Piscounov (SFKPP) equation. We derive here an individual-based, stochastic model founded on the spatial Moran process where fluctuations are treated exactly. The mean-field approximation of this model leads to an equation that is different from the phenomenological FKPP equation. At small selection pressure, the front behavior can be mapped into a Brownian motion with drift, the properties of which can be derived from the microscopic parameters of the Moran model. Finally, we generalize the model to take into account dispersal kernels beyond migration to nearest neighbors. We show how the effective population size (which controls the noise amplitude) and the diffusion coefficient can both be computed from the dispersal kernel.

Cyanobacterial clock, a stable phase oscillator with negligible intercellular coupling.

Accuracy in cellular function has to be achieved despite random fluctuations (noise) in the concentrations of different molecular constituents inside and outside the cell. The circadian oscillator in cyanobacteria is an example of resilience to noise. This resilience could be either the consequence of intercellular communication or the intrinsic property of the built-in biochemical network. Here we investigate the intercellular coupling hypothesis. A short theoretical depiction of interacting noisy phase oscillators, confirmed by numerical simulations, allows us to discriminate the effect of coupling from noise. Experimentally, by studying the phase of concurrent populations of different initial phases, we evaluate a very small upper limit of the intercellular coupling strength. In addition, in situ entrainment experiments confirm our ability to detect a coupling of the circadian oscillator to an external force and to describe explicitly the dynamic change of the mean phase. We demonstrate, therefore, that the cyanobacterial clock stability is a built-in property as the intercellular coupling effect is negligible.

Species abundance distribution and population dynamics in a two-community model of neutral ecology.

Explicit formulas for the steady-state distribution of species in two interconnected communities of arbitrary sizes are derived in the framework of Hubbell's neutral model of biodiversity. Migrations of seeds from both communities as well as mutations in both of them are taken into account. These results generalize those previously obtained for the "island-continent" model and they allow an analysis of the influence of the ratio of the sizes of the two communities on the dominance/diversity equilibrium. Exact expressions for species abundance distributions are deduced from a master equation for the joint probability distribution of species in the two communities. Moreover, an approximate self-consistent solution is derived. It corresponds to a generalization of previous results and it proves to be accurate over a broad range of parameters. The dynamical correlations between the abundances of a species in both communities are also discussed.

Periodic adhesive fingers between contacting cells.

We study in detail the properties of fingers, a particular type of cell-cell adhesive structures appearing in adherens junctions. These periodic patterns break the symmetry of cell-cell contacts. We show that finger formation is driven by cadherin interactions and actin growth. A theoretical model is introduced in which the growth of fingers is limited by membrane tension. The steady shape and formation kinetics of fingers are experimentally measured and compared with the theoretical predictions.

Membrane and acto-myosin tension promote clustering of adhesion proteins.

Physicists have studied the aggregation of adhesive proteins, giving a central role to the elastic properties of membranes, whereas cell biologists have put the emphasis on the cytoskeleton. However, there is a dramatic lack of experimental studies probing both contributions on cellular systems. Here, we tested both mechanisms on living cells. We compared, for the same cell line, the growth of cadherin-GFP patterns on recombinant cadherin-coated surfaces, with the growth of vinculin-GFP patterns on extracellular matrix protein-coated surfaces by using evanescent wave microscopy. In our setup, cadherins are not linked to actin, whereas vinculins are. This property allows us to compare formation of clusters with proteins linked or not to the cytoskeleton and thus study the role of membrane versus cytoskeleton in protein aggregation. Strikingly, the motifs we obtained on both surfaces share common features: they are both elongated and located at the cell edges. We showed that a local force application can impose this symmetry breaking in both cases. However, the origin of the force is different as demonstrated by drug treatment (butanedione monoxime) and hypotonic swelling. Cadherins aggregate when membrane tension is increased, whereas vinculins (cytoplasmic proteins of focal contacts) aggregate when acto-myosin stress fibers are pulling. We propose a mechanism by which membrane tension is localized at cell edges, imposing flattening of membrane and enabling aggregation of cadherins by diffusion. In contrast, cytoplasmic proteins of focal contacts aggregate by opening cryptic sites in focal contacts under acto-myosin contractility.

Analytical solution of a neutral model of biodiversity.

The unified neutral model of biodiversity proposed by S. Hubbell is solved analytically: The distributions of species abundance in the metacommunity and in a local community are calculated exactly as a function of speciation and migration rates and of the size of the community. In the limit of large population sizes the densities of species of given relative abundance are found to be given by universal functions depending only on two parameters.

Clustering in neutral ecology.

The "neutral ecology" model assumes that all organisms in the same trophic level have the same death, duplication, migration and mutation rates and are subjected to a zero sum rule. We show by exact analytical methods that under the assumption of this model, organisms tend to aggregate and form clusters. At dimensions less than or equal to 2, cluster size grows in average and one specie will dominate the whole ecosystem if enough time is allocated. At dimension d=3 (or higher), an equilibrium is reached and cluster sizes are distributed as a power law.

Expansion of insecticidal host range of Bacillus thuringiensis by in vivo genetic recombination.

We describe a novel approach for the insertion of an insecticidal toxin gene into a resident plasmid in Bacillus thuringiensis (Bt). A gene encoding a coleopteran-specific toxin was cloned within a fragment of IS232 and inserted into a plasmid thermosensitive for replication in Bt. The plasmid was used to transform a Bt strain toxic to lepidoptera, and the transformants were then selected at non-permissive temperature for clones in which the vector had integrated into a copy of IS232 present on a resident plasmid. A second recombination event was selected such that the vector was eliminated and the newly introduced toxin gene was conserved. The resulting strain contained only DNA of Bt origin, and displayed insecticidal activity against both lepidoptera and coleoptera.