A Tile-Based Error Model for Forward Growth of DNA Self-Assembly

This paper deals with the error tolerance of forward growth for DNA self-assembly. A model based on a single tile attachment is proposed. This model captures the features of the so-called corner attachment by considering the binding of the bonds between a tile and the current error-free aggregate. An analysis of this process and its implications on possible errors due to single and double mismatches are pursued. It is shown that an attachment in forward growth may result in mismatches by considering the label set of each tile and ensuring its possible existence with respect to an aggregate. The bounds (lower and upper) on the cardinality of a label set for DNA self-assembly, are proven. The proposed model is used to assess the error tolerance of different tile sets with and without block redundancy (such as proofreading).