A Non-equilibrium model of the ParBS bacterial system

ParABS systems are a tripartite mechanism that ensure chromosome and low- copy-number plasmid separation in most bacterial species. This thesis focuses on the interaction of two of these elements: centromere DNA sequence ParS and the DNA-binding protein ParB. A new analytical coarse-grained model for the diffusion of ParB dimers on DNA is proposed. A first diffusive model was introduced in recent article but it ignores both the structural transitions of the dimer and the change of nucleotide it is bound to (either CDP or CTP). This model distinguishes between the open and closed states of the protein, therefore taking also in account the transition between these two conformations. Adding this feature in the model is crucial for a more faithful description of the ParBS interaction. Indeed experiments show that the ParS sequence catalyzes the closing transition of ParB, creating clusters of them around itself. The density distribution of ParB over DNA is therefore very peaked near the centromere. The main goal of this thesis is to recreate such distribution through a biophysical model. From a thermodynamical point of view the equilibrium distribution is completely flat. The system is therefore considered to be in a Non Equilibrium Steady State (NESS). The only way this NESS can maintain itself is through the hydrolysis of CTP. In this thesis a continuous limit of the previously (numerically solved) discrete lattice model has been performed in order to obtain an approximate but analytical solution. The latter has been compared with the equilibrium one, gaining information on how much energy this system dissipates.