Coagulation-fragmentation for a finite number of particles and application to telomere clustering in the yeast nucleus

TL;DR

This paper introduces a coagulation-fragmentation model for small stochastic systems, deriving explicit formulas and applying it to telomere clustering in yeast nuclei, revealing insights into chromosome organization.

Contribution

It develops a novel coagulation-fragmentation framework with explicit formulas, applied to biological telomere clustering in yeast nuclei.

Findings

Explicit formulas for cluster size and number using hypergeometric functions.

Model accurately predicts telomere organization in yeast nuclei.

Provides a mathematical basis for understanding chromosome clustering dynamics.

Abstract

We develop a coagulation-fragmentation model to study a system composed of a small number of stochastic objects moving in a confined domain, that can aggregate upon binding to form local clusters of arbitrary sizes. A cluster can also dissociate into two subclusters with a uniform probability. To study the statistics of clusters, we combine a Markov chain analysis with a partition number approach. Interestingly, we obtain explicit formulas for the size and the number of clusters in terms of hypergeometric functions. Finally, we apply our analysis to study the statistical physics of telomeres (ends of chromosomes) clustering in the yeast nucleus and show that the diffusion-coagulation-fragmentation process can predict the organization of telomeres.