Analysis of antigen receptor diversity estimation based on microarray technology.

Recently, a promising technique to measure lymphocyte diversity in vivo was developed by a group at the Mayo Clinic, USA. However this technique lacks a statistical analysis of the error associated with the estimates of diversity. Together with this group, we have been developing a mathematical/statistical description of the processes involved in the determination of diversity. So far, we have not been able to fully describe how diversity influences the hybridization behaviour, which is essential to fully understand the errors associated with the estimates. I would like to discuss with you our current models and probe the cunning minds of the EAO members in search for mathematical solutions to this riddle.

Discrete time piecewise models of genetic regulatory networks: single cell and population dynamics.

We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise and contracting mappings whose variables represent gene expression levels. When compared to other models of regulatory networks, these models have an additional parameter which is identified as quantifying interaction delays. In spite of their simplicity, their dynamics presents a rich variety of behaviours. This phenomenology is not limited to piecewise models but extends to smooth nonlinear discrete time models of regulatory networks. After a short review of the general properties of the dynamics of such type of models we shall concentrate on a specific biological question: the allelic exclusion in the recombination mechanism of the Tbeta chains during the maturation of the T cells of the immune system. This example shows the relevance of considering a model of the histories of single cells followed by the analysis of the dynamics of populations of such cells.