Local parallel biomolecular computation

Abstract

Biomolecular ComputationBMC is computation at the molecular scale, using biotechnology engineering techniques. Most proposed methods for BMC used distributed molecular parallelism DP; where operations are executed in parallel on large numbers of distinct molecules. BMC done exclusively by DP requires that the computation execute sequentially within any given molecule though done in parallel for multiple molecules. In contrast, local parallelism LP allows operations to be executed in parallel on each given molecule.Winfree, et al W96, WYS96 proposed an innovative method for LP-BMC, that of computation by unmediated self-assembly of 2D arrays of DNA molecules, applying known domino tiling techniques see Buchi B62 , Berger B66 , and R71, LP81 in combination with recombinant DNA nano-fabrication techniques of Seeman et al SZC94 . The likelihood for successful unmediated self-assembly of computations has not been determined we discuss a simple model of assembly where there may be blockages in self-assembly, but more sophisticated models may have a higher likelihood of success.We develop improved techniques to more fully exploit the potential power of LP-BMC. To increase the likelihood of success of assembly, w e propose instead a re ned step-wise assembly method, which provides control of the assembly in distinct steps. It does not require large volumes or convergence time, even in the worst case assembly model that we assume for our own assembly algorithms. We also introduce the assembly frame, a rigid nano-structure which binds the input DNA strands in place on its boundaries and constrains the shape of the assembly. Our main results are LP-BMC algorithms for some fundamental problems that form the basis of many parallel computations. For these problems we decrease the assembly size to linear in the input size and and signi cantly decrease the number of time steps. We give LP-BMC algorithms with linear assembly size and logarithmic time, for the parallel pre x computation problems, which include integer addition, subtraction, multiplication by a constant number, nite state automata simulation, and ngerprinting hashing a string. We also give LP-BMC methods for perfect shu e and pair-wise exchange using a linear size assembly and constant time. This provides logarithmic time LP-BMC algorithms for the large class of normal parallel algorithms S71, U84, L92 on shu e-exchange networks, e.g. DFT, bitonic merge, xed permutation of data, as well as evaluation of a bounded degree Boolean circuit in time bounded by a logarithmic times the circuit depth. Our LP-BMC methods require much smaller volumes than previous DP-BMC algorithms R95,R98b, OR97 for these problems. All our LP-BMC assembly techniques can be combined with DP-BMC parallelism to simultaneously solve multiple problems with distinct inputs e.g. do parallel arithmetic on multiple inputs, or determine satisfying inputs of a circuit, so they are an enhancement of the power of DP-BMC.

Design and implementation of computational systems based on programmed mutagenesis

“…Several systems for constructing Turing machines have been suggested [4], [17], [21], [14]. The first two, by Beaver [4] and by Smith and Schweitzer [17], suffer from the same problems as the combinatorial search systems above.…”

“…This, again, both slows the computation down and introduces the potential for error. Winfree [21] and Reif [14] propose to implement universal computation via self-assembly of DNA. These techniques are based on the work by Seeman [16] exploring potential for constructing two-and three-dimensional structures out of a number of partially complimentary DNA molecules.…”

“…Preliminary results indicate that assembling even the simplest structures requires prolonged periods of time (16 hours or more for a 2-component system), with less then 50% efficiency of component incorporation [20]. There also exist so far unresolved concerns regarding the possibility that locally assembled substructures may interfere with the formation of global structures [14], [20].…”

Staged Self-assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues

“…There are a handful of existing works in the field of DNA self-assembly that have proposed very basic multiple stage assembly procedures. John Reif (1999) Table 1 Summary of the glue, tile, bin, and stage complexities, the temperature s, the scale factor, the connectivity, and the planarity of our staged assemblies and the relevant previous work Glues Tiles Bins Stages s Scale Conn. Planar n 9 n square Previous work (Adleman et al 2001;Rothemund and Winfree 2000) Hð log n log log n Þ 1 1 2 1 Full Yes…”

Compact Error-Resilient Computational DNA Tiling Assemblies

“…The self-assembly of DNA tiles can be used both as a powerful computational mechanism [8,13,21,24,27] and as a bottom-up nanofabrication technique [18]. Periodic 2D DNA lattices have been successfully constructed with a variety of DNA tiles, for example, double-crossover (DX) DNA tiles [26], rhombus tiles [12], triplecrossover (TX) tiles [7], "4x4" tiles [30], triangle tiles [9], and hexagonal tiles [3].…”