Elongation of rod-shaped bacteria

Three models relating cell length to generation time are considered for rod-shaped bacteria growing under steady-state conditions; all three presuppose linear elongation. The first model assumes that the rate of elongation is proportional to the instantaneous number of chromosome replication forks per cell; the others, that it is inversely related to the generation time and doubles a fixed time prior to cell division. One of these (model 2) treats this relationship as continuous, with the doubling occurring during the last division cycle (at chromosome termination), while the other is a discrete model in which the doubling in rate takes place at chromosome initiation. Expressions are derived for mean cell length and length at birth in each case. Comparison with experimental data on E. coli B/r using non-linear least-squares techniques results in an excellent fit for model 2 and unsatisfactory ones for the others, the best estimate for the time at which the rate doubles being 15·3 min prior to cell division and for the minimum length at birth (i.e., as the growth rate of the culture tends to zero), 1·47 μm. The functional relationship between cell radius and generation time implied by model 2 is also presented. This model again produces a good fit to the experimental data and provides, for the first time, a direct estimate of the volume/origin ratio at initiation of chromosome replication 0·35 ± 0·05 μm³ (s.e.). The results obtained here are compared with various qualitative observations reported in the literature and with such numerical data as are available.