title: Increasing Redundancy Exponentially Reduces Error Rates during Algorithmic Self-Assembly.
abstract: While biology demonstrates that molecules can reliably transfer information and compute, design principles for implementing complex molecular computations in vitro are still being developed. In electronic computers, large-scale computation is made possible by redundancy, which allows errors to be detected and corrected. Increasing the amount of redundancy can exponentially reduce errors. Here, we use algorithmic self-assembly, a generalization of crystal growth in which the self-assembly process executes a program for growing an object, to examine experimentally whether redundancy can analogously reduce the rate at which errors occur during molecular self-assembly. We designed DNA double-crossover molecules to algorithmically self-assemble ribbon crystals that repeatedly copy a short bitstring, and we measured the error rate when each bit is encoded by 1 molecule, or redundantly encoded by 2, 3, or 4 molecules. Under our experimental conditions, each additional level of redundancy decreases the bitwise error rate by a factor of roughly 3, with the 4-redundant encoding yielding an error rate less than 0.1%. While theory and simulation predict that larger improvements in error rates are possible, our results already suggest that by using sufficient redundancy it may be possible to algorithmically self-assemble micrometer-sized objects with programmable, nanometer-scale features.
authors.affiliation: †Computation and Neural Systems, California Institute of Technology, Pasadena, California 91125, United States.
authors.forename: Rebecca
authors.initials: R
authors.lastname: Schulman
authors.affiliation: ‡Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.
authors.forename: Christina
authors.initials: C
authors.lastname: Wright
authors.affiliation: §Computer Science, Computation and Neural Systems, and Bioengineering, California Institute of Technology, Pasadena, California 91125, United States.
authors.forename: Erik
authors.initials: E
authors.lastname: Winfree
mesh_terms: D000465:Algorithms; D003460:Crystallization; D004247:DNA / Q000737:chemistry*
chemical_list: D004247:DNA
keywords: DNA nanotechnology; algorithmic self-assembly; crystal growth; error correction