  We describe collective-move Monte Carlo algorithms designed to approximate
the overdamped dynamics of self-assembling nanoscale components equipped with
strong, short-ranged and anisotropic interactions. Conventional Monte Carlo
simulations comprise sequential moves of single particles, proposed and
accepted so as to satisfy detailed balance. Under certain circumstances such
simulations provide an approximation of overdamped dynamics, but the accuracy
of this approximation can be poor if e.g. particle-particle interactions vary
strongly with distance or angle. The twin requirements of simulation efficiency
(trial moves of appreciable scale are needed to ensure reasonable sampling) and
dynamical fidelity (true in the limit of vanishingly small trial moves) then
become irreconcilable. As a result, single-particle moves can underrepresent
important collective modes of relaxation, such as self-diffusion of particle
clusters. However, one way of using Monte Carlo simulation to mimic real
collective modes of motion, retaining the ability to make trial moves of
reasonable scale, is to make explicit moves of collections of particles. We
will outline ways of doing so by iteratively linking particles to their
environment. Linking criteria can be static, conditioned upon properties of the
current state of a system, or dynamic, conditioned upon energy changes
resulting from trial virtual moves of particles. We argue that the latter
protocol is better-suited to approximating real dynamics.
