Telomere dynamics parameters inferred from mathematical modeling of telomere length distribution

Telomeres, repeated sequences located at the ends of linear chromosomes, are essential for genome integrity. As these regions are subject to dynamics of shortening and lengthening by telomerase, they exhibit length heterogeneity. Telomere length is thus best represented by an entire distribution rather than by a single value. Long-read sequencing technologies now allow us to experimentally access this distribution at high resolution. Our working hypothesis posits that this distribution encodes information that relates to the biochemical mechanisms underlying telomere length dynamics. Here, to numerically infer the biochemical parameters that control telomere shortening and elongation by telomerase, we developed a mathematical model that we fit on long-read-sequencing-derived telomere length distributions of Saccharomyces cerevisiae. We prove that in our model, telomere length can be mathematically represented as an ergodic Markov chain and we provide an explicit expression of the steady-state distribution. We show that the biochemical parameters can be uniquely inferred from the distribution, which we verify on synthetic data with known ground truth parameters. Using experimental telomere length distributions of wild-type and mutants of telomere regulators, we find that our pipeline of parameter inference yields biologically relevant values. We then fit the model to the telomere length distribution of 66 natural yeast strains to reveal the diversity of telomere length regulation parameters. Furthermore, we demonstrate that individual chromosome extremities can sometimes be associated with distinct regulation parameters. Overall, our mathematical model and computational pipeline represent a powerful approach to estimate biochemical parameters affecting telomere length regulation.