Journal of Mathematical Biology

, Volume 70, Issue 7, pp 1685–1705 | Cite as

Kinetics of aggregation with a finite number of particles and application to viral capsid assembly

  • Nathanael Hoze
  • David Holcman


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.


Kinetics Model First passage time Takas equation Cluster formation Asymptotics Viral capsid assembly Aggregation Stochastic assembly Becker–Doering equation 

Mathematics Subject Classification

60 Probability theory and stochastic processes 



N. Hoze is supported by a Labex MemoLife fellowship. D. H. research is supported by an ERC-starting-Grant


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Group of Computational Biology and Applied MathematicsEcole Normale Supérieure, Institute for Biology, IBENSParisFrance

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