The baby-machine system, which produces newborn Escherichia coli cells from cultures immobilized on a membrane, was developed many years ago in an attempt to attain optimal synchrony with minimal disturbance of steady-state growth. In the present article, we describe in some detail a model designed to analyse such cells with a view to characterizing the nature and quality of the synchrony in a quantitative manner; it can also serve to evaluate the methodology itself, its potential and its limitations.
The model consists of "ve elements, giving rise to "ve adjustable parameters (and a proportionality constant): a major, essentially synchronous group of cells with ages distributed normally about zero; a minor, random component from a steady-state population on the membrane that had undergone only very little age selection during the elution process; a "xed background count, to account for the signals recorded by the electronic particle counter produced by debris and electronic noise; a time-shift, to allow for di!erences between collection time and sampling time; and the coe$cient of variation of the interdivision-time distribution, taken to be a Pearson type III.
The model is "tted by nonlinear least-squares to data from cells grown in glucose minimal medium. The standard errors of the parameters are quite small, making their estimates all highly signi"cant; the quality of the "t is striking.
We also provide a simple yet rigorous procedure for correcting cell counts obtained in an electronic particle counter for the e!ect of coincidence. An example using real data produces an excellent "t.