In Vitro Implementation of k-shortest Paths Computation with Graduated PCR

Abstract

In this paper, an in vitro implementation of DNA computing for solving k-shortest paths problem of a weighted graph is reported. The encoding is designed in such a way that every path is encoded by oligonucleotides and the length of the path is directly proportional to the length of oligonucleotides. For initial pool generation, parallel overlap assembly is employed for efficient generation of all candidate answers. After the initial solution is subjected to amplification by polymerase chain reaction (PCR), k-shortest paths could be visualized by polyacrylamide gel electrophoresis (PAGE) and the selection can be done. The visualization of the output, in fact, relies on the appearance of DNA bands on a gel image. Further, it is shown that a method called graduated PCR is a good subsequent bio-molecular reaction for obtaining molecular information hidden in the output DNA. Graduated PCR is also crucial to prove the correctness of the in vitro computation. The experimental results show the effectiveness of the proposed DNA-based computation and prove that the k-shortest paths problem has been successfully solved on a DNA computer.