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.

The Miles theory of wave amplification by wind is extended to the case of finite depth h and a shear flow with (constant) vorticity {\Omega}. Vorticity is characterised through the non-dimensional parameter {\nu} = {\Omega} U_1 /g, where g the gravitational acceleration, U_1 a characteristic wind velocity and k the wavenumber. The notion of 'wave age' is generalised to account for the effect of vorticity. Several widely used growth rates are derived analytically from the dispersion relation of the wind/water interface, and their dependence on both water depth and vorticity is derived and discussed. Vorticity is seen to shift the maximum wave age, similar to what was previously known to be the effect of water depth. At the same time, a novel effect arises and the growth coefficients, at identical wave age and depth, are shown to experience a net increase or decrease according to the shear gradient in the water flow.

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.