[A mathematical model concerning the DNA-karyogram in connection with the cell cycle. I. Communication. The derivation of the DNA frequency distribution from the duration of the single phases of cell cycle (author's transl)]

Abstract

Stimulated by our own experience on flow microfluorometry we establish a mathematical model concerning the connection between the duration of the single phases of cell cycle and frequency distribution of cell nuclei as a function of their DNA content. For the establishment of the equations we need some simplified suppositions. We interprete the distribution curve (DNA karyogram) as 3 superimposing portions: 1. A Gaussian distribution of G1-phase cells at the first or 2c-peak. 2. A Gaussian distribution of G2 + M phase cells at the second or 4c-peak (twofold DNA content). 3. Nuclei from the S-phase with DNA content between the mean values of the two Gaussian curves. Our model has the following pecularities: 1. The establishment of the equation for the curve and therefore the addition of the partial curves is done in a logarithmical (log-normal) system. Here we can assume the same standard deviation both for the first and the second peak. 2. The superimposing of the S-phase acts on the whole curve and not only between the mean values of the Gaussian curves. Here the integral of the Gaussian distribution is employed for the equation. The equations are elaborated for the whole curve with the periods of the single phases as parameter, for the positions of the maxima and the minimum and for the quotient of the arguments of the maxima ("rhythm of reduplication") as a function of the duration of the single phases. Some examples are given and drawn in diagrams. They demonstrate the shape of the DNA karyogram and the rhythm of reduplication as funtions of the duration of the single phases of the cell cycle. The transformation in the linear system distorts the shape of the curve up to the disappearance of the second peak. The results from the model are the base for the interpretation of DNA karyograms, originating for instance from cytophotometry, mainly from flow microfluorometry. With the model we can estimate a change in direction and quantity of the curves altered by different phases of the cell cycle.