Modeling errors in synthesized tile sets for template manufacturing by DNA self-assembly

This paper presents a detailed analytical framework for errors in DNA self-assembly using synthesized tile sets for template manufacturing. Previous works have shown that due to the smaller cardinality of the employed tile set, a synthesized aggregate has a higher (lower) error rate than a non-synthesized aggregate at high (low) tile concentration; moreover, in the former type of aggregate errors are clustered rather than random. Two novel phenomena referred to as propagation and closing are considered in detail and the analysis of this paper shows that the reported difference in errors between aggregates is caused by these phenomena. A new Markov model is presented and solved; this model confirms that, as reported in the technical literature, a cluster of erroneous tiles is more likely to be generated in a synthesized aggregate with a slower growth speed than the error-free aggregate.