IMUVA, Departamento de Matemática Aplicada, Escuela de Ingenierías Industriales, Universidad de Valladolid, Spain.
IVIRMA, Madrid. Av del Talgo, Madrid, 68. 28023, Spain; IdiPaz, Calle de Pedro Rico, Madrid, 6. 28029, Spain.
J Theor Biol. 2019 Feb 7;462:446-454. doi: 10.1016/j.jtbi.2018.11.036. Epub 2018 Nov 29.
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).
这项工作的目的是研究人类卵泡达到排卵前状态的衰老速度。为此，研究了端粒长度和端粒酶活性对颗粒细胞（GCs）衰老的影响。GCs 是决定卵母细胞发育的体细胞。一个人类的原始卵泡大约需要 85 天才能达到排卵前的大小，经历几个阶段（Gougeon，1996）。在卵泡发生过程中，使用类似于 Wesch 等人的化学主方程形式主义（2016）来模拟每个卵泡类别的 GCs 的端粒长度。考虑了七个微分常微分方程组，对应于卵泡成熟的七个阶段，在时间上串联。通过使用每个卵泡类别的平均 GCs 数量和它们停留在每个阶段的时间来近似有丝分裂和死亡率。研究了不同端粒酶活性率和排卵前卵泡端粒缩短的影响。一些不孕病例与 GCs 中端粒酶活性水平低和端粒短有关。该方法旨在了解低水平的端粒酶活性在排卵前阶段如何导致老化的 GCs 积累。在端粒酶活性较高的情况下，数学模型预测排卵前卵泡的结果更年轻。如果卵母细胞受精，年轻的 GCs 可能对胚胎发育至关重要，因为转化为黄体的 GCs 必须分裂并增加其大小（Alila 和 Hansel，1984）以维持早期妊娠（Csapo 等人，1972）。
