Proliferative response of mouse spermatogonial stem cells after irradiation: a quantitative model analysis of experimental data.

The testes of CDF1 mice were irradiated with single doses of X-rays ranging from 2-16 Gy. The number of haploid cells in the testis at different times after irradiation (42-350 days) was determined by one-parameter flow cytometry both for irradiated animals and for age-matched controls. Based on literature data on the kinetics of the spermatogenesis in mice, a mathematical model of the (hierarchical) germ tissue was developed. Using this model, the processes of radiation-induced cell loss and subsequent recovery were simulated and free parameters of the model were estimated by fitting the model prediction to the experimental data. One of the aims of the study was to investigate the kinetic behaviour of spermatogonial stem cells and the corresponding control mechanisms. In order to fit the data, the model has to include the following features: (i) A preferential self-repopulation of spermatogonial stem cells following tissue injury. The model-estimated probability of a self-renewing division rises from 50% (the steady-state value) to 95% if the stem-cell population is reduced to 10% of its normal size. (ii) A relatively low, almost constant turnover rate of the stem-cell compartment. It is suggested by the analysis that less than 10% of the spermatogonial stem cells present in the testis divide per day, regardless of the degree of cellular depletion. (iii) A mechanism responsible for incomplete recovery. The observed incomplete recovery of spermatogenesis after single doses exceeding 10 Gy can be described quantitatively assuming that the stem cells are organized into discrete proliferative structures, the number of cells per structure being about 60.