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The kinetics of the self-assembly of nanocomponents into a virus,nanocapsule, or other composite structure is analyzed via a multiscaleapproach. The objective is to achieve predictability and to preserve keyatomic-scale features that underlie the formation and stability of thecomposite structures. We start with an all-atom description, the Liouvilleequation, and the order parameters characterizing nanoscale features of thesystem. An equation of Smoluchowski type for the stochastic dynamics of theorder parameters is derived from the Liouville equation via a multiscaleperturbation technique. The self-assembly of composite structures fromnanocomponents with internal atomic structure is analyzed and growth rates arederived. Applications include the assembly of a viral capsid from capsomers, aribosome from its major subunits, and composite materials from fibers andnanoparticles. Our approach overcomes errors in other coarse-graining methodswhich neglect the influence of the nanoscale configuration on the atomisticfluctuations. We account for the effect of order parameters on the statisticsof the atomistic fluctuations which contribute to the entropic and averageforces driving order parameter evolution. This approach enables an efficientalgorithm for computer simulation of self-assembly, whereas other methodsseverely limit the timestep due to the separation of diffusional and complexingcharacteristic times. Given that our approach does not require recalibrationwith each new application, it provides a way to estimate assembly rates andthereby facilitate the discovery of self-assembly pathways and kinetic dead-endstructures.

Self-Assembly of Nanocomponents into Composite Structures: Derivation and Simulation of Langevin Equations