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

TL;DR

This paper introduces an improved method for estimating initial telomere length distributions by using an advection-diffusion approximation and Laplace transform inversion, enhancing accuracy over previous models.

Contribution

It develops a novel estimation approach linking Laplace transforms of telomere lengths and senescence times via an advection-diffusion model, employing the Gaver-Stehfest algorithm.

Findings

The new method better accounts for variability in initial telomere lengths.

It establishes a simple link between Laplace transforms of key distributions.

Numerical results demonstrate improved estimation accuracy.

Abstract

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. Olay{\'e}]. 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.