Abstract
The intracellular environment is densely populated and extremely organized. Several transport processes take place within this environment: the walking and translocation of molecular motors on microfilaments, as well as on DNA and messenger RNA (mRNA). In this thesis we study the translocation of ribosomes on mRNA ,which permits the translation of the genetic code into proteins and which from a physical point of view is an example of a one dimensional directed transport process. It is a non-linear, stochastic and non-equilibrium thermodynamic phenomenon that belongs to non-equilibrium statistical physics.Gene translation is the major steps involved in gene expression, which is regulated by several mechanisms that are still poorly understood. By providing a physical study of translation kinetics, we hope to contribute to a better understanding of the regulation of protein production during this step. Such an understanding should also impact medical research on diseases related to gene expression deregulation such as cancer and neurodegenerative diseases.A first chapter is devoted to the biological context of translation and to a brief description of ribosome profiling experiments, a deep sequencing method performed by our biologist colleagues. It has allowed, over the last ten years, considerable progress in translation research, but the complexity of the studied system requires a more advanced physico-mathematical modeling approach.The second chapter describes the paradigmatic model of one-dimensional directed transport, the Totally Asymmetric Simple Exclusion Process (TASEP) lattice gas model, and its variants, closer to the actual ribosomal translocation process, are studied. We show that an extended particle generates non-negligible exclusion effects in the low density phase. In particular, exclusion at the translation start (initiation) has the largest effect on the average density along the lattice when the ratio of the initiation rate to the hopping rate of the particle is less than or equal to 0.1, while when this ratio is higher, such an edge effect at the lattice exit also becomes non-negligible.In the third chapter, we model the set of mRNAs, sequenced in the ribosome profiling experiment (or Ribo-Seq), by a ballistic model where ribosomes are point particles moving deterministically on filaments having, what is rarely considered, a finite lifetime. We show that, for parameters with typical biological values, the finite lifetime effect is negligible when considering the whole set of mRNAs (polysomes), but becomes important when considering populations of mRNAs sorted by their number of ribosomes, the k-somes. We precisely characterize this effect by a parametric analysis of the model and define three regimes of degradation depending on to the translation initiation rate, the degradation rate of mRNAs , and the time for the ribosomes to cross the mRNA.In the last chapter, we demonstrate, for the first time to our knowledge, this finite lifetime effect on the Ribo-Seq profiles of monosomes, disomes, trisomes and tetrasomes (k-somes for k=1,2,3 and 4). We then compare our model with several thousands of Ribo-Seq profiles obtained by our collaborators (biologists from the IGF and bioinformaticians from the LIRMM). We observe that our model describes qualitatively the k-some profiles, but that a mechanism generates a non-negligible discrepancy between the densities of the model and the experimental profiles when the number k of ribosomes increases. From our study in Chapter 2, we believe that this discrepancy could be due to the interaction between ribosomes, which is not taken into account within the ballistic model. Finally, in this chapter we propose a method for inferring the kinetic parameters of translation, the initiation rate and the ribosome hopping rate using the monosome and the polysome densities.