Section: New Results

Genetic architecture of parasite infection

The problem here is to understand the genetic architecture of a parasitic invasion by investigating the different phenotypes such invasion produces in the host. One such phenotype is called "cytoplasmic incompatibility". Briefly, when a parasite invades a male host, it induces developmental arrest, ultimately, death of the host's offspring unless the fertilised embryo carries the same symbiont inherited from its mother, that is, unless the female is also infected. This has been tentatively explained by a toxin/antitoxin model that involves a toxin deposited by the parasites in the male's sperm that induces the death of the zygote unless neutralised by an antidote produced by the parasites present in the egg. One toxin/antitoxin pair is linked to one gene. Given a set of observed cytoplasmic incompatibilities, the question is how many genes are required to explain it. Formally, and skipping many intermediate modelling steps, this translates into, given a 0/1 matrix M for pairs of male/female (a 0 indicating that either the male is not infected or, if it is, then so is the female meaning that there is no incompatibility, and a 1 indicating that the male is infected while the female is not), what is the minimum number of "rectangles" that enable to cover all the 1s in M? A "rectangle" in this case is a subset of columns and rows such that, if permuted, they can be arranged in the form of a rectangle with only 1s (publication Nor et al., 2010 by the BAMBOO Team and collaborators). One rectangle corresponds to a gene. The model can then be made more complex by considering that genes may have different alleles (different forms), and are expressed in variable quantities. The quantitative version of the problem in particular translates into having to find a minimum number of "triangles" that cover all 1s. All the above problems translate also into different versions of edge covers of a bipartite graph that are for the most part algorithmically original, and always not fully resolved (meaning, there remains open questions, notably regarding complexity). Work on these problems within the Associate Team SIMBIOSI and the results already obtained should lead to a publication in 2012. This work was done in collaboration among others with S. Charlat.