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

Nathanael Hoze and David Holcman ()
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Nathanael Hoze: Universitätstrasse 16, Institut für Integrative Biologie, ETH
David Holcman: Applied Mathematics and Computational Biology, Institute for Biology École Normale Supérieure

A chapter in Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology, 2017, pp 205-239 from Springer

Abstract: Abstract 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.

Keywords: Viral Capsid Assembly; Telomere Clustering; Coagulation-fragmentation Processes (CFP); Longer Chromosome Arms; Telomere Organization (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-62627-7_10

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DOI: 10.1007/978-3-319-62627-7_10

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