Using lateral capillary forces to compute by self-assembly

Investigations of DNA computing have highlighted a fundamental connection between self-assembly (SA) and computation: in principle, any computation can be performed by a suitable self-assembling system. In practice, exploration of this connection is limited by our ability to control the geometry and specificity of binding interactions. Recently, a system has been developed that uses surface tension to assemble plastic tiles according to shape complementarity and likeness of wetting [Bowden, N., Terfort, A., Carbeck, J. & Whitesides, G. M. (1997) Science 276, 233–235]. Here the capacity of this system to compute by SA is explored. Tiles were prepared to test the system's ability to generate three structures of increasing complexity: a periodic checkerboard tiling, an aperiodic Penrose tiling, and a computational tiling that simulates a one-dimensional cellular automaton. Matching rules for these tilings were enforced by coating tiles with patterns of hydrophobic and hydrophilic patches or wetting codes. Energetic, kinetic, and mechanistic details of SA explain differences between experimental structures and mathematically ideal ones. In particular, the growth mechanism observed appears incompatible with computations that make use of a chosen input.