  We use a nonequilibrium variational principle to optimize the steady-state,
shear-induced interconversion of self-assembled nanoclusters of DNA-coated
colloids. Employing this principle within a stochastic optimization algorithm
allows us to discover design strategies for functional materials. We find that
far-from-equilibrium shear flow can significantly enhance the flux between
specific colloidal states by decoupling trade-offs between stability and
reactivity required by systems in equilibrium. For isolated nanoclusters, we
find nonequilibrium strategies for amplifying transition rates by coupling a
given reaction coordinate to the background shear flow. We also find that shear
flow can be made to selectively break detailed balance and maximize probability
currents by coupling orientational degrees of freedom to conformational
transitions. For a microphase consisting of many nanoclusters, we study the
flux of colloids hopping between clusters. We find that a shear flow can
amplify the flux without a proportional compromise on the microphase structure.
This approach provides a general means of uncovering design principles for
nanoscale, autonomous, functional materials driven far from equilibrium.
