Speakers
Description
Telomere length regulation in \textit{Saccharomyces cerevisiae} has been modeled through stochastic rules combining deterministic shortening and
telomerase elongation. We provide a formulation of the single-telomere dynamics as a discrete-time Markov chain depending on parameters controlling shortening, telomerase activation and elongation. On a finite truncated state space, we prove ergodicity and obtain a
unique stationary distribution with an explicit spectral characterization, yielding a deterministic forward map from parameters to observables. This approach replaces costly stochastic simulations by an efficient deterministic computation. Parameter identifiability is addressed through a generating-function identity expressing the stationary distribution in terms of the telomerase activation probability. Parameter estimation is performed by minimizing the
$1$-Wasserstein distance between theoretical and Nanopore empirical
distributions, using the CMA-ES optimization algorithm. A discrete-to-continuous scaling limit leads to an integro-differential equation.
