Undesired usage and the robust self-assembly of heterogeneous structures

Inspired by multiprotein complexes in biology and recent successes in synthetic DNA tile and colloidal self-assembly, we study the spontaneous assembly of structures made of many kinds of components. The major challenge with achieving high assembly yield is eliminating incomplete or incorrectly bound structures. Here, we find that such undesired structures rapidly degrade yield with increasing structural size and complexity in diverse models of assembly, if component concentrations reflect the composition (that is, stoichiometry) of the desired structure. But this yield catastrophe can be mitigated by using highly non-stoichiometric concentrations. Our results support a general principle of 'undesired usage'-concentrations of components should be chosen to account for how they are 'used' by undesired structures and not just by the desired structure. This principle could improve synthetic assembly methods, but also raises new questions about expression levels of proteins that form biological complexes such as the ribosome.