Abstract
Cellular organisms appear organized. Bacteria use membraneless compartments to confine chemical reactions in space and time. There is a general paradigm of intracellular space self-organization that distinguishes between self-assembly, molecular structures assembled by passive phase transition mechanisms, and dissipative structures, generated for example by reaction-diffusion processes. If self-assemblies correspond to the evolution towards thermodynamic equilibrium, dissipative structures are manifestations of an out-of-equilibrium energy cost. We illustrate this paradigm by studying the segregation of bacterial genome, in this case the F-plasmid segregation of Escherichia coli, based on the ParABS partition system. Segregation is a crucial step in the bacterial cell cycle since it ensures the transmission of genetic information in daughter bacteria before division.The ParABS system consists of a parS centromeric sequence; a ParB protein which is able to bind to DNA, specifically on the parS sequence and not specifically elsewhere; and a ParA ATPase protein than can bind to DNA. Interactions between ParB proteins on DNA and specific adsorption on the parS sequence lead to the formation of a three-dimensional focus called the ParBS complex located around the parS sequence. Interactions between ParA and ParB proteins lead to the positioning of this complex at the center of the cell cytoplasm. After replication, two ParBS complexes exist and are segregated by the action of ParA proteins at positions 1/4 and 3/4 of the intracellular space.We first seek to explain the formation of ParBS complexes by a passive phase separation mechanism between high- and low-density states of ParB proteins in space. We construct two statistical physics models using tools borrowed from the physics of phase transitions. Our second approach rigorously defines all the elements of the biological system consisting of the interacting DNA-polymer and ParB proteins and allows us to formulate a first-order phase transition existence criterion that is verified by the DNA. We can draw the phase diagrams of this transition. These two models allow us to argue that the physiological thermodynamic regime of this biological system is a regime of metastable coexistence in ParB proteins on DNA. The parS sequence plays the role of a defect or nucleation seed. We use a third approach to explain the relationship between the three-dimensional and DNA distributions of ParB proteins around the parS sequence.We try to explain the fluorescence recovery curves from photobleaching experiments on ParBS complexes. We construct an in silico photobleaching method, i.e. we reproduce these recovery curves from a phenomenological equation solved numerically. We then develop a system of equations that describe the evolution of proteins on DNA from the previous statistical physical approach to produce an in silico photobleaching taking into account that ParBS complexes are the result of phase separation. We show that a pure passive system does not allow photobleaching experiments because of the Ostwald maturation undergone by the complexes. We correct this approach by including ParA proteins and their biochemical cycle in our simulations. We show that the interactions between ParA and ParB proteins and the hydrolysis of ATP allows the survival of several ParBS complexes thanks to an inversion mechanism of Ostwald's ripening. This fundamental approach explains the positioning of ParBS complexes during segregation.