Coagulation-Fragmentation with a Finite Number of Particles: Models, Stochastic Analysis, and Applications to Telomere Clustering and Viral Capsid Assembly

Coagulation-fragmentation processes with a finite number of particles is a recent class of mathematical questions that serves modeling some cell biology dynamics. The analysis of the models offers new challenging questions in probability and analysis: the model is the clustering of particles after binding, the formation of local subclusters of arbitrary sizes and the dissociation into subclusters. We review here modeling and analytical approaches to compute the size and number of clusters with a finite size. Applications are clustering of chromosome ends (telomeres) in yeast nucleus and the formation of viral capsid assembly from molecular components. The methods to compute the probability distribution functions of clusters and to estimate the statistical properties of clustering are based on combinatorics and hybrid Gillespie-spatial simulations. Finally, we review models of capsid formation, the mean-field approximation, and jump processes used to compute first passage times to a finite size cluster. These models become even more relevant for extracting parameters from live cell imaging data.