No abstract

DNA compaction in a bacterial cell is in part carried out by entropic (depletion) forces induced by "free" proteins or crowding particles in the cytoplasm. Indeed, recent in vitro experiments highlight these effects by showing that they alone can condense the E. coli chromosome to its in vivo size. Using molecular dynamics simulations and a theoretical approach, we study how a flexible chain molecule can be compacted by crowding particles with variable sizes in a (cell-like) cylindrical space. Our results show that with smaller crowding agents the compaction occurs at a lower volume fraction but at a larger concentration such that doubling their size is equivalent to increasing their concentration fourfold. Similarly, the effect of polydispersity can be correctly mimicked by adjusting the size of crowders in a homogeneous system. Under different conditions, however, crowding particles can induce chain adsorption onto the cylinder wall, stretching the chain, which would otherwise remain condensed.

A chain molecule can be entropically collapsed in a crowded medium in a free or confined space. Here, we present a unified view of how molecular crowding collapses a flexible polymer in three distinct spaces: free, cylindrical, and (two-dimensional) slit-like. Despite their seeming disparities, a few general features characterize all these cases, even though the φ c -dependence of chain compaction differs between the two cases: a > a c and a < a c , where φ c is the volume fraction of crowders, a the monomer size, and a c the crowder size. For a > a c (applicable to a coarse-grained model of bacterial chromosomes), chain size depends on the ratio aφ c /a c , and "full" compaction occurs universally at aφ c /a c ≈ 1; for a c > a (relevant for protein folding), it is controlled by φ c alone and crowding has a modest effect on chain size in a cellular environment (φ c ≈ 0.3). Also for a typical parameter range of biological relevance, molecular crowding can be viewed as effectively reducing the solvent quality, independently of confinement.

Despite much renewed interest in cylindrically confined polymers with linear or nonlinear topology, often considered as model chromosomes, their scaling predictions, especially on chain elasticity and relaxation, have not been reconciled with numerical data. Of particular interest is their "effective spring constant"given in the scaling form of k eff $ N Àa D Àg , where N is the number of monomers and D the diameter of the cylindrical space. If the blob-scaling approach produces a ¼ 1 and g ¼ 2 À 1/n ¼ 1/3 with n ¼ 3/5 the Flory exponent, a series of numerical studies indicate a z 0.75 and unexpectedly large g z 0.9. Using computer simulations, we show that there exists a crossover from the formerly called unexpected to blob-scaling regime at a certain value of D z 10 (in units of monomer sizes) for sufficiently large N (>N cr ). Our results suggest that N cr z 1000, if the farthermost distance is used as the chain size: a quantity relevant in single-chain manipulations or for ring polymers (e.g., bacterial chromosomes). Accordingly, chain relaxation dynamics is expected to show a similar crossover. Our results imply that the applicability of the blob scaling approach depends on how confined chains are characterized.

In a crowded cellular interior, dissolved biomolecules or crowders exert excluded volume effects on other biomolecules, which in turn control various processes including protein aggregation and chromosome organization. As a result of these effects, a long chain molecule can be phaseseparated into a condensed state, redistributing the surrounding crowders. Using computer simulations and a theoretical approach, we study the interrelationship between molecular crowding and chain organization. In a parameter space of biological relevance, the distributions of monomers and crowders follow a simple relationship: the sum of their volume fractions rescaled by their size remains constant. Beyond a physical picture of molecular crowding it offers, this finding explains a few key features of what has been known about chromosome organization in an E. coli cell.