Algorithmic DNA Self-assembly

Abstract

Self-assembly is the ubiquitous process by which objects autonomously assemble into complexes. This phenomenon is common in nature and yet is poorly understood from mathematical and programming perspectives. It is believed that self-assembly technology will ultimately permit the precise fabrication of complex nanostructures. Of particular interest is DNA self-assembly. Double and triple crossover DNA molecules have been designed that can act as four-sided building blocks for DNA self-assembly. Experimental work has been done to show the effectiveness of using these building blocks to assemble DNA crystals and perform DNA computation. With these building blocks (called tiles) in mind, researchers have considered the power of the tile self-assembly model.

The tile assembly model extends the theory of Wang tilings of the plane by adding a natural mechanism for growth. Informally, the model consists of a set of four sided Wang tiles whose sides are each associated with a type of glue. The bonding strength between any two glues is determined by a glue function. A special tile in the tile set is denoted as the seed tile. Assembly takes place by starting with the seed tile and attaching copies of tiles from the tile set one by one to the growing seed whenever the total strength of attraction from the glue function meets or exceeds a fixed parameter called the temperature.

Algorithmic DNA self-assembly is both a form of nanotechnology and a model of DNA computing. As a computational model, algorithmic DNA self-assembly encodes the input of a computational problem into DNA patterns and then manipulates these patterns to produce new DNA patterns that encode the desired output of the computational problem. As a nanotechnology, algorithmic DNA self-assembly aims to design tiles with carefully chosen glue types on their four sides. Two tiles are said to be of different types if their sides have different glue types. Useful tile types are nontrivial to design but relatively easy to duplicate in large quantity. A key design challenge for algorithmic DNA self-assembly is to use only a small number of different tile types to assemble a target nanostructure.

This talk will survey recent results in algorithmic DNA self-assembly and discuss future research directions.