Pré-Publication, Document De Travail Année : 2026

Estimating an initial telomere length distribution from the Laplace transform of its senescence times distribution

Résumé

This work follows from a previous study on the estimation of an initial distribution of telomere length from a senescence times distribution done in [10.1051/m2an/2026022, J. Olayé]. In this previous study, we have presented an estimation method based on the fact that our telomere shortening model can be approximated by a transport equation. This method has encouraging results, but fails to provide a good estimation when the variability of the initial telomere length distribution is too small. We improve here this method by approximating our model with an advection-diffusion equation, which allows us to better take into account the randomness of the shortening values. We show that under this approximation, there exists a simple link between the Laplace transform of the initial telomere length distribution and that of the senescence times distribution. Then, by using a numerical method for inverting Laplace transforms called Gaver-Stehfest algorithm, we exploit this link to construct a new estimator.

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hal-05566881 , version 1 (25-03-2026)

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Jules Olayé. Estimating an initial telomere length distribution from the Laplace transform of its senescence times distribution. 2026. ⟨hal-05566881⟩
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