Surface-limited growth: a model for the synchronization of a growing bacterial culture through periodic starvation

This article analyses the Surface-Limited Growth Model put forward to explain the very tight synchrony, over more than ten division cycles, obtained experimentally by subjecting a growing bacterial culture to alternating periods of starvation and dilution, using inorganic phosphate as the limiting substrate. The Model states that when an essential nutrient is in limited supply, the rate of growth of an individual cell will be proportional to its surface area (and the current concentration of the limiting substance) rather than to its volume. This decrease in dimensionality from volume to surface is expected to favor the smaller cells and so result ultimately in a narrower size distribution. The Surface-Limited Growth Model deals with cell growth under unusual nutritional conditions, and its predictions depend on how the cell replication cycle is assumed to behave under these same circumstances. Two alternatives are considered: the volume at which cells divide is the same during the starvation phase as during steady-state exponential growth, and the cells adjust immediately to the changing growth rate. In the latter case, we have tested both C + D constant with time and C + D variable (where C + D is the time between initiation of chromosome replication and the corresponding cell division), the incremental value at any instant being computed separately for each individual cell from its current effective growth rate. The simulation results are of two sorts depending on the auxiliary assumptions used. Either the dilution-starvation cycles have no effect whatsoever on the cell volume distribution, or the width of the distribution decreases gradually with time, approaching zero slowly and asymptotically, but the mean cell volume decreases as well--directly contradicting experimental observations. We conclude that the Surface-Limited Growth Model is incapable of explaining the synchronization of cells by periodic starvation of a growing bacterial culture.