Second-order functions are the simplest correlations between flow cytometric light scatter and bacterial diameter.

Second-order mathematical relationships between bacterial cell diameter determined by electric particle analyser and flow cytometric forward light scatter in axenic cultures are obtained and discussed. Since it is technically impossible today to obtain both measurements for each individual cell, standard regression techniques cannot be applied. To overcome this limitation, we assume that these two parameters are related by a monotone increasing function that enables their mathematical relationships to be studied. Our conclusion is that forward light scatter data cannot be linearly transformed into bacterial size values by an accurate and universal function. However, second-order relationships seem to be the simplest satisfactory relationships between cell diameter and forward light scatter in eubacteria.