3D fractal DNA assembly from coding, geometry and protection

We present DNA components whose 3D geometry and cohesive portions are compatible with a fractal 3D assembly. DNA parallelograms have been proposed in Carbone and Seeman [(2002b) Natural Computing 1: 469-480; [(2003) Natural Computing 2: 133-151] as suitable building blocks for a 2D fractal assembly of the Sierpinski carpet. Here we use Mao 3D triangles, which are 3D geometrically trigonal molecules, to construct basic building blocks and we obtain a simplified version of the 2D assembly design. As in the previous 2D construction, we utilize the interplay of coding in the form of cohesive ends, geometrical complementarity and protection of potentially undesirable sites of r eactivity. The schema we propose works for trigonal symmetries and the Mao triangle is one example of a possible DNA trigonal tile.