Title
Evolution dynamics of repeated genome elements. |
Version
française |

**Location**

INRIA, Project
CAFÉ

BP 93, 06902 France

Jointly with the team
Genetics and Dynamics of
Populations
of the CEFE-CNRS in Montpellier.

**Information**

**Description**

Genomes are mostly made of elements belonging to the category of repeated ADN sequences. In order to understand the evolution of microsatellite DNA sequences (tandemly-repeated sequences) the CEFE team is studying their distributions generated by models that include several different mutation forces. Those models are Markov chains where each state represents a microsatellite length. Transitions between the states are given by various mutation processes. An important problem is that those models do not have known analytical solutions, which hinders our comprehension of microsatellite evolution. The steady-state equations of those models are linear recurrences whose coefficients arise from the mutation probabilities. This internship is about searching for analytical solutions of those recurrences.

The main goal of this internship is to apply the closed-form solution procedures developped in the CAFÉ project to the steady-state equations of the Markov chains that model microsatellite evolution. Given the many parameters involved in those equations, existence of a generic closed-form solution is unlikely, so one has to determine, by applying the algorithms step by step, the (eventual) values of the parameters for which such solutions exist. To perform those calculations, it will be necessary to implement in a computer algebra system a newly developped algorithm (or at least its main components) for solving linear recurrences with hypergeometric (i.e. binomial coefficients or linear exponentials). The intern will be able to visit the CEFE team in Montpellier to discuss the biological aspects of this project.

**Références**

Abramov et al.,
*On Liouvillian solutions of linear ordinary difference equations
with hypergeometric coefficients*, in preparation.

Ellegren H (2004), Nature Reviews Genetics **5**:435--445.

Munoz F. et al., *Models of dinucleotide microsatellite evolution
in the yeast, work and human genomes*, in preparation.

**Tools**

Unix workstation, computer algebra system.

**Duration**

3-4 months.