Modelling nucleocytoplasmic transport with application to the intracellular dynamics of p53
Supervisors: Jean Clairambault and Roberto Natalini
Eukaryotic cells have a complex and highly compartmentalized structure. Their distinguishing feature is the presence of a nucleus, where genetic information are stored and protected. The nucleus controls cell activities by gene expression regulation.
In order to make the nucleus fulfill its tasks, molecules and macromolecules, as proteins or RNA, need to cross the nuclear membrane to enter or exit the nucleus. Nucleocytoplasmic transport is an essential machinery and has a central role in cellular functioning.
The aim of this PhD thesis is to write a model of active nucleocytoplasmic transport that would take into account the spatial distribution of molecules and structures within the cell. We will write a two compartment convection-reaction-diffusion model that will describe the kinetic interactions between proteins: equations for cargo, importins and Ran will be written in the cytoplasm and in the nucleus. We would like to point out the primary role of motor proteins in the transport mechanism and describe it explicitly in the cytoplasm. The crossing of the nuclear envelope will be modelled through a Kedem-Katchalsky condition at the nuclear boundary.
Another object of this thesis is to apply our findings on a specific protein: p53. The protein p53 is known as "The guardian of the genome" because of its crucial roles in the life of a cell. It can arrest the cell cycle, activate transcription of gene responsible for DNA repair and cause apoptosis. It is known that p53 becomes inefficient in 50% of cancers cells. Furthermore it is known that transport mechanisms are injured in cancer cells. We will design a molecular-based mathematical model of the dynamics of p53 to clarify its functioning in the case of damaged cells.
Nucleocytoplasmic transport will be modelled through a system of Partial Differential Equations. One of the objects of this thesis will be to prove the existence and uniqueness of global solutions, to study their qualitative behavior and to look for particular solutions, as pattern formation and traveling waves. Numerical simulations will be used to compare our results with experimental data. The code we have was written and implemented by Roberto Natalini's group. Numerical analysis ad-hoc methods have been studied for this kind of problems by the same group.