Distribution of bacterial single cell parameters and their estimation from turbidity detection times

The stochastic growth of homogeneous bacterial populations in the wells of a microtiter plate was studied as a function of the random initial cell number and their random individual lag times. These significantly affected the population growth in the well, while the maximum specific growth rate of the population was constant (or its variance was negligible) for each well. We showed the advantages of the mathematical assumption that a transformation of the single cell lag time, called the single cell physiological state (or, more accurately, that of the sub-population generated by the single cell) follow the Beta distribution. Simulations demonstrated what patterns would such assumption generate for the distribution of the detection times observed in the wells. An estimation procedure was developed, based on the beta-assumption, that resulted in an explicit expression for the expected value of the single cell physiological state as a function of measured "time to detection" values using turbidity experiments. The method was illustrated using laboratory data with Escherichia coli, Salmonella enterica subsp. enterica strains. The results gave a basis to quantify the difference between the studied organisms in terms of their single-cell kinetics.