Mathematical model to study the aging of the human follicle according to the telomerase activity.

The aim of this work is to study the aging rate at which human follicles reach the preovulatory state. To this end, both telomere length and telomerase activity effects on granulosa cells (GCs) aging has been studied. GCs are somatic cells which determine the development of the oocyte. A human preantral follicle takes approximately 85 days to achieve the preovulatory size, going through several stages (Gougeon, 1996). The telomere length of GCs of each class of follicles, during folliculogenesis, are modelled using a chemical master equation formalism similar to the one in Wesch et al. (2016). Seven differential ordinary systems of equations, corresponding to seven stages of the follicule maturation, concatenated in time, are considered. The mitotic and death rates are approximated by using the mean number of GCs in each class of follicles and the time they remain on each stage. The influence of different telomerase activity rates and the telomere shortening of the preovulatory follicle is studied. Some cases of infertility are associated with low levels of telomerase activity and short telomeres in GCs. The method aims at understanding how low levels of telomerase activity in preovulatory stages lead to the accumulation of aged GCs. In the case of higher telomerase activities, the mathematical model predicts a more juvenile outcome in preovulatory follicles. Juvenile GCs, could be critical for embryo development if the oocyte were fertilized, since GCs, transformed in corpus luteum, must divide and increase their size (Alila and Hansel, 1984) to sustain early pregnancy (Csapo et al., 1972).

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