The last decade has seen a spectacular development of genomic physics both in bacteria and eukaryotes. This is due in large part to the development of experimental techniques, which allow to probe (i) the motion of nucleic acids (chromosomal DNA and RNA) in vivo by means of microscopy techniques and (ii) the interactions of these nucleic acids with other actors of the cell (like proteins and molecular motors) by means of high-throughput sequencing techniques. I will focus on three different processes : (i) the modeling of translation with a ballistic model describing the motion of ribosomes on messenger RNA, (ii) the physical mechanism of liquid-liquid phase separation, which is found to be universally spread in the cells to increase, locally and transiently, the concentration of a molecular actor (proteins, RNA etc.). We illustrate this process with the example of the bacterial DNA segregation where liquid-liquid phase separation is used to increase the local concentration in order to catalyze ATP hydrolysis. Finally (iii) I give a general framework on how polymer physics can help to infer the organization of DNA in vivo from microscopy and high-throughput sequencing experiments and apply it to the modeling of bacterial DNA in Escherichia coli and to the epigenetic regulation via polycomb domains in Drosophila.

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The ParABS system is composed of three components: a centromeric sequence, parS, and two proteins, the ParA (ATPase) and the ParB DNA binding proteins. Hundreds of ParB proteins assemble dynamically to form nucleoprotein parS-anchored complexes (ParBS) that serve as substrates for ParA molecules to catalyze positioning and segregation events. We address the theoretical modeling of ParBS with a Lattice Gas models and compare it to experiments [1]. We give evidences that (i) ParBS is formed via a Liquid-Liquid Phase Separation in the metastable region of the phase diagram and (ii) this nucleation is catalyzed with the parS sequence [1].[1] Guilhas, Walter,... & Nollmann (2020). ATP-driven separation of liquid phase condensates in bacteria. Mol. Cell, 79, 293-303.

ParAB S , the most widespread bacterial DNA segregation system, is composed of a centromeric sequence, parS , and two proteins, the ParA ATPase and the ParB DNA binding proteins. Hundreds of ParB proteins assemble dynamically to form nucleoprotein parS -anchored complexes that serve as substrates for ParA molecules to catalyze positioning and segregation events. The exact nature of this ParB S complex has remained elusive, what we address here by revisiting the Stochastic Binding model (SBM) introduced to explain the non-specific binding profile of ParB in the vicinity of parS . In the SBM, DNA loops stochastically bring loci inside a sharp cluster of ParB. However, previous SBM versions did not include the negative supercoiling of bacterial DNA, leading to use unphysically small DNA persistences to explain the ParB binding profiles. In addition, recent super-resolution microscopy experiments have revealed a ParB cluster that is significantly smaller than previous estimations and suggest that it results from a liquid-liquid like phase separation. Here, by simulating the folding of long (≥ 30 kb) supercoiled DNA molecules calibrated with realistic DNA parameters and by considering different possibilities for the physics of the ParB cluster assembly, we show that the SBM can quantitatively explain the ChIP-seq ParB binding profiles without any fitting parameter, aside from the supercoiling density of DNA, which, remarkably, is in accord with independent measurements. We also predict that ParB assembly results from a non-equilibrium, stationary balance between an influx of produced proteins and an outflux of excess proteins, i.e., ParB clusters behave like liquid-like protein condensates with unconventional “leaky” boundaries.

Translation is one of the main steps in the synthesis of proteins. It consists of ribosomes that translate sequences of nucleotides encoded on mRNA into polypeptide sequences of amino acids. Ribosomes bound to mRNA move unidirectionally, while unbound ribosomes diffuse in the cytoplasm. It has been hypothesized that finite diffusion of ribosomes plays an important role in ribosome recycling and that mRNA circularization enhances the efficiency of translation. In order to estimate the effect of cytoplasmic diffusion on the rate of translation, we consider a Totally Asymmetric Simple Exclusion Process (TASEP) coupled to a finite diffusive reservoir, which we call the Ribosome Transport model with Diffusion (RTD). In this model, we derive an analytical expression for the rate of protein synthesis as a function of the diffusion constant of ribosomes, which is corroborated with results from continuous-time Monte Carlo simulations. Using a wide range of biological relevant parameters, we conclude that diffusion in biological cells is fast enough so that it does not play a role in controlling the rate of translation initiation.