Winner-take-all dynamics in self-assembly

Understanding competitive nucleation between different crystal polymorphs is critical for the selective self-assembly of any particular structure. For crystals made of one or a few components, selectivity is often accomplished through carefully designed annealing protocols. In highly multi-component systems, we argue for a new winner-take-all mechanism that enhances selectivity through depletion. For such systems, nucleation and growth of one structure can deplete monomers in a way that dramatically reduces the nucleation rates of all other structures without significantly affecting its own nucleation rate. We identify regimes of winner-take-all depletion using theory and rare-event sampling methods in multi-component self-assembly with unequal component concentrations. We present experimental evidence for such winner-take-all dynamics in a system of single-stranded DNA molecules able to assemble into three distinct two-dimensional crystal configurations.