Loop-Extruder-Mediated Rigidity Can Globally Order Bacterial Chromosomes

Many bacterial chromosomes show large-scale linear order, so that a locus's genomic position correlates with its position along the cell. In the model organism , for instance, the left and right arms of the circular chromosome lie in different cell halves. However, no mechanisms that anchor loci to the cell poles have been identified, and it remains unknown how this so-called “left--right” organization arises. Here we construct a biophysical model that explains how global chromosome order could be established via an active loop extrusion mechanism. Our model assumes that the motor protein complex MukBEF extrudes loops on most of the chromosome but is excluded from the terminal region by the protein MatP, giving rise to a partially looped ring polymer structure. Using three-dimensional simulations of loop extrusion on a chromosome, we find that our model can display stable left--right chromosomal order in a parameter regime consistent with prior experiments. We explain this behavior by considering the effect of loop extrusion on the bending rigidity of the chromosome, and derive necessary conditions for left--right order to emerge. Finally, we develop a phase diagram for the system, where order emerges when the loop size is large enough and the looped region is compacted enough. Our work provides a theoretical and mechanistic explanation for how loop-extruders can establish linear chromosome order in and how this order leads to accurate gene positioning within the cell, without locus anchoring.