  Designing components that can robustly self-assemble into structures with
biological complexity is a grand challenge for material science. Proofreading
and error correction is required to improve assembly yield beyond equilibrium
limits, using energy to avoid kinetic traps in the energy landscape. Here we
introduce an explicit two staged proofreading scheme for patchy particle
colloidal assemblies that substantially improves assembly yield and robustness.
The first stage implements local rules whereby particles increase their binding
strengths when they detect a local environment corresponding to a desired
target. The second stage corrects remaining errors, adding a reverse pathway
inspired by kinetic proofreading. The scheme shows significant yield
improvements, eliminating kinetic traps, giving a much broader temperature
range with high yield. Additionally, the scheme is robust against quenched
disorder in the components. Our findings illuminate a pathway for advancing
programmable design of synthetic living materials, potentially fostering the
synthesis of novel biological materials and functional behaviors.
