DNA solution of a graph coloring problem

An unenumerative DNA computing model for vertex coloring problem

The solution space exponential explosion caused by the enumeration of the candidate solutions maybe is the biggest obstacle in DNA computing. In the paper, a new unenumerative DNA computing model for graph vertex coloring problem is presented based on two techniques: 1) ordering the vertex sequence for a given graph in such a way that any two consecutive labeled vertices i and i+1 should be adjacent in the graph as much as possible; 2) reducing the number of encodings representing colors according to the construture of the given graph. A graph with 12 vertices without triangles is solved and its initial solution space includes only 283 DNA strands, which is 0.0532 of 3(12) (the worst complexity).

Computer-aided organic synthesis

It is tempting for those in the field of organic synthesis to liken the process of retrosynthesis to a game of chess. That the world chess champion was recently defeated by a computer leads us to think that perhaps new and powerful computing methods could be applied to synthetic problems. Here the analogy between synthesis and chess is outlined. Achievements in the 35-year history of computer-aided synthetic design are described, followed by some more recent developments.

Rational design of DNA sequences for nanotechnology, microarrays and molecular computers using Eulerian graphs

Nucleic acids are molecules of choice for both established and emerging nanoscale technologies. These technologies benefit from large functional densities of 'DNA processing elements' that can be readily manufactured. To achieve the desired functionality, polynucleotide sequences are currently designed by a process that involves tedious and laborious filtering of potential candidates against a series of requirements and parameters. Here, we present a complete novel methodology for the rapid rational design of large sets of DNA sequences. This method allows for the direct implementation of very complex and detailed requirements for the generated sequences, thus avoiding 'brute force' filtering. At the same time, these sequences have narrow distributions of melting temperatures. The molecular part of the design process can be done without computer assistance, using an efficient 'human engineering' approach by drawing a single blueprint graph that represents all generated sequences. Moreover, the method eliminates the necessity for extensive thermodynamic calculations. Melting temperature can be calculated only once (or not at all). In addition, the isostability of the sequences is independent of the selection of a particular set of thermodynamic parameters. Applications are presented for DNA sequence designs for microarrays, universal microarray zip sequences and electron transfer experiments.