Positions corresponding to lower energy would be more frequently occupied

A variety of mechanisms have been proposed to explain the patterns from diffusion to capture, to membrane curvature and to nucleoid occlusion. Here, we provide for the first time experimental and theoretical evidence that TTC is reduced in the periplasm and that aggregation of small molecules, such as the reduced formazan, at the cell poles is a spontaneous process. If granule formation and positioning in the periplasm is at equilibrium, we would expect the distribution of granules to be consistent with the free energy of a granule at a given position. We therefore looked at the total energy, i.e. the interaction energy between particles, for different numbers of formazan particles and granule positions in the periplasm. Simulations of the model revealed that small spherical granules have a much lower energy at the pole compared to midcell. We found that the average number of molecules in a granule at the pole is larger than that at midcell for equal concentration of molecules in periplasm. We attribute this to a smaller off-rate at the pole that particles dissociate from the granule due to spatial constrains compared to midcell. For larger granules that achieved disk-like shapes, the energy difference between the pole and midcell became less significant. Given the small difference in energy between large midcell and pole granules, if the system could come to equilibrium, the spatial distribution of granules would be more uniform than experimentally observed, where granules localize at the poles in,70% of cells. Since the observed localization frequency is different from what would be expected from equilibrium arguments, we explored the effect on localization due to the rate of addition of molecules. Regardless of addition rate, a seed was likely to form anywhere within the periplasmic space. If molecules were added at a rate faster than that required for them to diffuse to the lower energy position at the pole, the seeds could be trapped in the local energy minimum at midcell. If molecules were added slowly enough so that the small aggregates had enough time to migrate to the pole, then they formed a large aggregate there and reached a quasi-steady state. The experimentally observed ratio of polegranule containing cells was obtained when the addition rate was slower than the typical time of a seed to diffuse from midcell to the pole. The simulation also revealed that the peak of large aggregates was slightly off pole, due to the increased entropy associated with that location, in good agreement with the experimental data. We also explored how granule formation depends on the width of the periplasmic space and the strength of molecular interaction. In both very wide and very narrow periplasms, the distribution of granules was far more uniform. These results make intuitive sense as in wider periplasms, the LDK378 1032900-25-6 geometrical constraint on granule growth and distribution was reduced; while in narrower periplasms, seeds growing in essentially 2D directions must reach a much larger size to overcome the energy barrier.