  The kinetics of the self-assembly of nanocomponents into a virus,
nanocapsule, or other composite structure is analyzed via a multiscale
approach. The objective is to achieve predictability and to preserve key
atomic-scale features that underlie the formation and stability of the
composite structures. We start with an all-atom description, the Liouville
equation, and the order parameters characterizing nanoscale features of the
system. An equation of Smoluchowski type for the stochastic dynamics of the
order parameters is derived from the Liouville equation via a multiscale
perturbation technique. The self-assembly of composite structures from
nanocomponents with internal atomic structure is analyzed and growth rates are
derived. Applications include the assembly of a viral capsid from capsomers, a
ribosome from its major subunits, and composite materials from fibers and
nanoparticles. Our approach overcomes errors in other coarse-graining methods
which neglect the influence of the nanoscale configuration on the atomistic
fluctuations. We account for the effect of order parameters on the statistics
of the atomistic fluctuations which contribute to the entropic and average
forces driving order parameter evolution. This approach enables an efficient
algorithm for computer simulation of self-assembly, whereas other methods
severely limit the timestep due to the separation of diffusional and complexing
characteristic times. Given that our approach does not require recalibration
with each new application, it provides a way to estimate assembly rates and
thereby facilitate the discovery of self-assembly pathways and kinetic dead-end
structures.
