Paul W. K. Rothemund

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Molecular self-assembly gives rise to a great diversity of complex forms, from crystals and DNA helices to microtubules and holoenzymes. We study a formal model of pseudo-crystalline self-assembly, called the Tile Assembly Model, in which a tile may be added to the growing object when the total interaction strength with its neighbors exceeds a parameter 7-.(More)
Algorithms and information, fundamental to technological and biological organization, are also an essential aspect of many elementary physical phenomena, such as molecular self-assembly. Here we report the molecular realization, using two-dimensional self-assembly of DNA tiles, of a cellular automaton whose update rule computes the binary function XOR and(More)
We introduce a new model of molecular computation that we call the sticker model. Like many previous proposals it makes use of DNA strands as the physical substrate in which information is represented and of separation by hybridization as a central mechanism. However, unlike previous models, the stickers model has a random access memory that requires no(More)
Self-assembly is the ubiquitous process by which simple objects autonomously assemble into intricate complexes. It has been suggested that intricate self-assembly processes will ultimately be used in circuit fabrication, nano-robotics, DNA computation, and amorphous computing. In this paper, we study two combinatorial optimization problems related to(More)
Self-assembly creates natural mineral, chemical, and biological structures of great complexity. Often, the same starting materials have the potential to form an infinite variety of distinct structures; information in a seed molecule can determine which form is grown as well as where and when. These phenomena can be exploited to program the growth of complex(More)
Copying and counting are useful primitive operations for computation and construction. We have made DNA crystals that copy and crystals that count as they grow. For counting, 16 oligonucleotides assemble into four DNA Wang tiles that subsequently crystallize on a polymeric nucleating scaffold strand, arranging themselves in a binary counting pattern that(More)
From ligand-receptor binding to DNA hybridization, molecular recognition plays a central role in biology. Over the past several decades, chemists have successfully reproduced the exquisite specificity of biomolecular interactions. However, engineering multiple specific interactions in synthetic systems remains difficult. DNA retains its position as the best(More)