Bacterial chromosome organization II: few special cross-links, cell confinement, and molecular crowders play the pivotal roles

Using a bead-spring model of bacterial DNA polymers of {\em C. crescentus} and {\em E. coli} we show that just $33$ and $38$ effective cross-links at special positions along the chain contour of the DNA can lead to the large-scale organization of the DNA polymer, where confinement effects of the cell walls play a key role in the organization. The positions of the $33$ cross-links along the chain contour are chosen from the contact map data of {\em C. crescentus}. We represent $1000$ base pairs as a coarse-grained monomer in our bead-spring flexible ring polymer model of the DNA. Thus a $4017$ beads on a flexible ring polymer represents the {\em C. crescentus} DNA with $4017$ kilo-base pairs. Choosing suitable parameters from our preceding study, we also incorporate the role of molecular crowders and the ability of the chain to release topological constraints. We validate our prediction of the organization of the {\em C. crescentus} with available experimental contact map data and also give a prediction of the approximate positions of different segments within the cell in 3D. For the {\em E. coli} chromosome with $4.6$ million base pairs, we need around $38$ effective cross-links with cylindrical confinement to organize the chromosome. We also predict the 3D organization of the {\em E. coli} chromosome segments within the cylinder which represents the cell wall.