Stochastic interacting systems in biophysics : immunology and development
Jonathan Desponds (LPT)

This work presents two problems of biology requiring data analysis and
models from statistical mechanics : population dynamics in immunology and
gene regulation in embryo development. In immunology I study the problem
of somatic evolution in the adaptive immune system : selection of and
competition among cells that form a close-to-Darwinian system within one
individual. First, I consider different potential hypotheses for selective
dynamics : division and death signals through antigen binding or cytokines,
dynamical parameters for division, death and fluctuations of the
environment. I explore their impact on clone sizes. Experimentally, these
clone sizes show heavy tail distributions for different species and
different pools of cells. Two families of models emerge : models where
noise is consistent at the level of the clone and models where it varies
from cell to cell. I show how clone size distributions help discriminate
between these models and relate the shape of the distribution and the
exponent of the power law to biological parameters. Second, I explore the
specifics of the complex stochastic network of clones and antigens : its
dimensionality, connectivity and dynamics. I study the effect of selection
at different time scales and the speed of evolution of the clones.
The second part of this dissertation concerns embryo development. In the
fly embryo, it is crucial that nuclei can evaluate their position within
the organism accurately to determine cell fate and build a healthy
organism. This positional information is obtained, transferred, and
maintained through diffusion of proteins and activation of genetic
networks. More specifically, the patterning of the antero-posterior axis
in drosophila requires the hunchback gene, activated by the Bicoid
protein. I analyze data from fluorescent live imaging in the early cell
cycles of the embryo. I build a tailor-made model to analyze
autocorrelation functions of fluorescence time traces overcoming all
biological and experimental challenges (noise, calibration, short traces,
transgene construct) to extract the parameters of hunchback activation. I
examine several po- tential types of dynamics for gene switiching
(Poisson, Markovian or non-Markovian) and predict their impact on
positional information and the accuracy of bicoid gradient readout.