title: Kinetics of aggregation with a finite number of particles and application to viral capsid assembly.
abstract: The formation of a viral capsid can be seen as a time-dependent process generated by the arrival of aggregates of various sizes at a nucleation site. Based on a model where aggregates arrive at a Poissonian rate to form a capsid particle, we develop kinetics assembly equations, that account for a finite size cluster and thus for rejection of too large aggregate. The model is derived under the assumption that the aggregate distribution has reached an exponential steady state. To account for the stochastic nature of the aggregates arrival, we also derive a stochastic equation to compute the mean time for a cluster to be formed. We find that this time has a minimum for a unique aggregate distribution. We obtain asymptotic expression for this time that we compare with numerically simulations. Finally, we find the mean size of the largest aggregate forming a viral capsid.
authors.affiliation: Group of Computational Biology and Applied Mathematics, Ecole Normale Supérieure, Institute for Biology, IBENS, 46 rue d'Ulm, 75005 , Paris, France.
authors.forename: Nathanael
authors.initials: N
authors.lastname: Hoze
authors.forename: David
authors.initials: D
authors.lastname: Holcman
mesh_terms: D002213:Capsid / Q000502:physiology*; D003198:Computer Simulation; D007700:Kinetics; D055641:Mathematical Concepts; D008954:Models, Biological; D016012:Poisson Distribution; D066329:Protein Aggregates / Q000502:physiology; D013269:Stochastic Processes; D019065:Virus Assembly / Q000502:physiology*
chemical_list: D066329:Protein Aggregates
references.citation: Adv Chem Phys. 2014;155:1-68
references.pmid: 25663722
references.citation: J Chem Phys. 2012 Dec 28;137(24):244107
references.pmid: 23277928
references.citation: J Virol. 2000 Jun;74(11):5142-50
references.pmid: 10799589
references.citation: Proc Natl Acad Sci U S A. 2004 Nov 2;101(44):15556-60
references.pmid: 15486087
references.citation: Phys Biol. 2010 Dec 09;7(4):045005
references.pmid: 21149973
references.citation: J Chem Phys. 2012 Feb 28;136(8):084110
references.pmid: 22380035
references.citation: Phys Rev Lett. 1989 May 22;62(21):2563-2566
references.pmid: 10040020
references.citation: J Virol. 2000 Jul;74(13):5845-55
references.pmid: 10846064
references.citation: PLoS Pathog. 2009 Nov;5(11):e1000652
references.pmid: 19893629
references.citation: Biotechnol Bioeng. 2010 Oct 15;107(3):550-60
references.pmid: 20521301
references.citation: Nano Lett. 2012 Sep 12;12(9):4705-10
references.pmid: 22906128
references.citation: Biophys J. 2002 Aug;83(2):1217-30
references.pmid: 12124301
references.citation: Annu Rev Phys Chem. 2009;60:367-83
references.pmid: 19046126
references.citation: Philos Trans A Math Phys Eng Sci. 2006 Dec 15;364(1849):3357-73
references.pmid: 17090464