Mathematical methods for determining cell DNA synthesis rate and age distribution utilizing flow microfluorometry

Abstract

Methods are developed for analyzing and interpreting DNA distributions of cell populations experimentally obtained by flow microfluorometric techniques. The first method derived can be used to compute the mean DNA synthesis rate and a transformation matrix relating a cell age distribution to its corresponding DNA distribution when these two distributions are; known. This transformation matrix is used to compute the cell DNA distribution from a cell age distribution. The second part deals with computing the initial cell age distribution when several measurements of cell DNA distribution are available. This problem is shown to be equivalent to the observability problem for the discrete-time system representing the cell population. The observability condition in system theory and a computing method for determining the initial cell age distribution are discussed. An example using DNA distributions of Chinese hamster cells for the methods is presented.