Dimensional rearrangement of rod-shaped bacteria following nutritional shift-up. I. Theory

Abstract

Theoretical expressions are derived for two models that describe average length and radius of a population of rod-shaped bacteria as a function of time following their transfer to a medium that supports a higher growth rate. The first attributes cell elongation to circular zones produced at a particular time during the cell cycle and which act thereafter at rates proportional to the growth rate; the second is formally identical but considers surface growth rather than length extension. Two possibilities are considered, that the zonal growth rate adjusts immediately to the transition, and that it does so gradually. The results are also displayed graphically, covering a broad range of each of the various parameters involved; values are chosen to permit a direct comparison between the models. Average cell length is seen to undergo a large overshoot and to approach its steady-state value from above, while cell radius remains almost constant or even decreases somewhat before increasing monotonically towards its asymptotic level; both require a considerable period of time to reach steady state. The transient behavior predicted by the two models is found to be quite different even when the steady-state dimensions are identical; the differences between immediate and gradual response of the zonal growth rate are even greater. It is shown that using a dimensionless measure of cell geometry, the aspect ratio, can facilitate selection of the appropriate model.