  Transient bonds between fast linkers and slower particles are widespread in
physical and biological systems. In spite of their diverse structure and
function, a commonality is that the linkers diffuse on timescales much faster
compared to the overall motion of the particles they bind to. This limits
numerical and theoretical approaches that need to resolve these diverse
timescales with high accuracy. Many models, therefore, resort to effective, yet
ad-hoc, dynamics, where linker motion is only accounted for when bound. This
paper provides a mathematical justification for such coarse-grained dynamics
that preserves detailed balance at equilibrium. Our derivation is based on
multiscale averaging techniques and is broadly applicable. We verify our
results with simulations on a minimal model of fast linker binding to a slow
particle. We show how our framework can be applied to various systems,
including those with multiple linkers, stiffening linkers upon binding, or slip
bonds with force-dependent unbinding. Importantly, the preservation of detailed
balance only sets the ratio of the binding to the unbinding rates, but it does
not constrain the detailed expression of binding kinetics. We conclude by
discussing how various choices of binding kinetics may affect macroscopic
dynamics.
