Chromosome and plasmid segregation in bacteria are mostly driven by ParABS systems. These DNA partitioning machineries rely on large nucleoprotein complexes assembled on centromere sites (parS). However, the mechanism of how a few parS‐bound ParB proteins nucleate the formation of highly concentrated ParB clusters remains unclear despite several proposed physico‐mathematical models. We discriminated between these different models by varying some key parameters in vivo using the F plasmid partition system. We found that “Nucleation & caging” is the only coherent model recapitulating in vivo data. We also showed that the stochastic self‐assembly of partition complexes (i) is a robust mechanism, (ii) does not directly involve ParA ATPase, (iii) results in a dynamic structure of discrete size independent of ParB concentration, and (iv) is not perturbed by active transcription but is by protein complexes. We refined the “Nucleation & caging” model and successfully applied it to the chromosomally encoded Par system of Vibrio cholerae, indicating that this stochastic self‐assembly mechanism is widely conserved from plasmids to chromosomes.
The spectrum of the Quantum Discrete Nonlinear Schrödinger equation on a periodic 1D lattice shows some interesting detailed band structure which may be interpreted as the quantum signature of a two-breather interaction in the classical case. We show that this fine structure can be interpreted using degenerate perturbation theory.
Efficient bacterial chromosome segregation typically requires the coordinated action of a threecomponent, fueled by adenosine triphosphate machinery called the partition complex. We present a phenomenological model accounting for the dynamic activity of this system that is also relevant for the physics of catalytic particles in active environments. The model is obtained by coupling simple linear reaction-diffusion equations with a proteophoresis, or "volumetric" chemophoresis, force field that arises from protein-protein interactions and provides a physically viable mechanism for complex translocation. This minimal description captures most known experimental observations: dynamic oscillations of complex components, complex separation and subsequent symmetrical positioning. The predictions of our model are in phenomenological agreement with and provide substantial insight into recent experiments. From a non-linear physics view point, this system explores the active separation of matter at micrometric scales with a dynamical instability between static positioning and travelling wave regimes triggered by the dynamical spontaneous breaking of rotational symmetry.Controlled motion and positioning of colloids and macromolecular complexes in a fluid, as well as catalytic particles in active environments, are fundamental processes in physics, chemistry and biology with important implications for technological applications [1,2]. In this paper, we focus on an active biological system for which precise experimental results are available. Our work is fully inspired by studies of one of the most widespread and ancient mechanisms of liquid phase macromolecular segregation and positioning known in nature: bacterial DNA segregation systems. Despite the fundamental importance of these systems in the bacterial world and intensive experimental studies extending over 30-years [3-5], no global picture encompasses fully the experimental observations. Partition systems encode only three elements that are necessary and sufficient for active partitioning: two proteins ParA and ParB, and a specific sequence parS encoded on DNA. The pool of ParB proteins is recruited as a cluster of spherical shape centered around the sequence parS, forming the ParBS partition complex [4]. These ParBS cargos interact with ParA bound onto chromosomal DNA (ParA-slow) [6,7], triggering unbinding of ParA by inducing conformational changes through stimulation of adenosine triphosphate (ATP) hydrolysis and/or direct ParB-ParA contact [8], and thereby allowing ParA diffusion in the cytoplasm (ParA-fast) [5]. This process entails the oscillation of ParA from pole to pole and the separation of the ParBS partition complex into two complexes with distinct sub-cellular trajectories and long-term localization. Overall, these interactions result in an equidistant, stable positioning of the duplicated DNA molecules along the cell axis.The specific modeling of ParABS systems falls into two categories: either "filament" (pushing/pulling the cargos, similar to eukaryotic...
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