Many canonical processes in molecular biology rely on the dynamic assembly of higher-order nucleoprotein complexes. In bacteria, the assembly mechanism of ParABS, the nucleoprotein super-complex that actively segregates the bacterial chromosome and many plasmids, remains elusive. We combined super-resolution microscopy, quantitative genome-wide surveys, biochemistry, and mathematical modeling to investigate the assembly of ParB at the centromere-like sequences parS. We found that nearly all ParB molecules are actively confined around parS by a network of synergistic protein-protein and protein-DNA interactions. Interrogation of the empirically determined, high-resolution ParB genomic distribution with modeling suggests that instead of binding only to specific sequences and subsequently spreading, ParB binds stochastically around parS over long distances. We propose a new model for the formation of the ParABS partition complex based on nucleation and caging: ParB forms a dynamic lattice with the DNA around parS. This assembly model and approach to characterizing large-scale, dynamic interactions between macromolecules may be generalizable to many unrelated machineries that self-assemble in superstructures.

Above the upper critical dimension, the breakdown of hyperscaling is associated with dangerous irrelevant variables in the renormalization group formalism at least for systems with periodic boundary conditions. While these have been extensively studied, there have been only a few analyses of finite-size scaling with free boundary conditions. The conventional expectation there is that, in contrast to periodic geometries, finite-size scaling is Gaussian, governed by a correlation length commensurate with the lattice extent. Here, detailed numerical studies of the five-dimensional Ising model indicate that this expectation is unsupported, both at the infinite-volume critical point and at the pseudocritical point where the finite-size susceptibility peaks. Instead the evidence indicates that finite-size scaling at the pseudocritical point is similar to that in the periodic case. An analytic explanation is offered which allows hyperscaling to be extended beyond the upper critical dimension.Comment: 23 pages, 8 figure

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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.