Increase Telomerase

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Do the telomeric repeats increase in number down the generations?

Telomeres are increased in length after every cell cycle, by the activity of the enzyme telomerase. Every cell in the body of an eukaryote should therefore contain a greater number of telomeric repeats than what was originally the found in the chromosome of the first cell formed after fertilization.

In gonads, the mother cells, from which the eggs and sperms form, should also contain an increased number of telomeric repeats, which would be passed on to the gametes, and thereby, to the next generation. Theoretically, every new generation should have higher number of telomeric repeats than the parental generation.

Is this assumption true, or is there a mechanism which prevents this from happening and maintains an average telomeric repeat number in a particular organism? If you have any knowledge in this respect, could you kindly explain the matter and provide some references, if possible?

They always increase by a subnumerial factor of 3, which is the exponent of the subset of critical mass.