International Journal of Computational Intelligence Research. ISSN 0973-1873 Vol.1, No.2 (2005), pp. 127-137 © Research India Publications http://www.ijcir.info In Vitro Implementation of k-shortest Paths Computation with Graduated PCR Zuwairie Ibrahim 1,2 , Yusei Tsuboi 2 , Osamu Ono 3 and Marzuki Khalid 1 1 Department of Mechatronic and Robotics, Faculty of Electrical Engineering, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor Darul Takzim, Malaysia zuwairie@fke.utm.my, marzuki@utmkl.utm.my 2 Institute of Applied DNA Computing, Meiji University, 1-1- Higashimita, Tama-ku, Kawasaki-shi, Kanagawa-ken, 214-8571 Japan zuwairie@isc.meiji.ac.jp, tsuboi@isc.meiji.ac.jp, ono@isc.meiji.ac.jp 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. Keywords: DNA computing, k-shortest paths, graduated PCR, hybridization-ligation, parallel overlap assembly. I. Introduction Gordon E. Moore [1] has observed an exponential growth in the number of transistors per integrated circuit against time. This is the definition of Moore’s Law, meaning that more and more transistors can be crammed into a single chip until the silicon itself reaches its finite atomic scale limitation. Since the traditional silicon based computer is restricted by its fundamental physical limitation, researchers have been searching for alternative medium for computation and Deoxyribonucleic Acid (DNA) would turn out to be the answer. A molecular computing paradigm based on DNA molecules has appeared in 1994 when Leonard M. Adleman [2]-[3] launched a novel in vitro approach to solve the so-called Hamiltonian path problem (HPP) with seven vertices by DNA molecules. The goal of HPP is to determine whether a path exists that will commerce at the start city, finish at the end city, and pass through each city of the remaining cities exactly once. While in conventional silicon-based computer, information is stored as binary numbers in silicon-based memory, he encoded the information of the vertices by a randomly DNA sequences. The computation is performed in bio-molecular reactions fashion involving hybridization, denaturation, ligation, and polymerase chain reaction. The output of the computation, also in the form of DNA molecules can be read and printed by electrophoretical fluorescent method. DNA molecules are composed of single or double DNA fragments or often called oligonucleotides or strands. Nucleotides form the basis of DNA. A single-stranded fragment has a phospho-sugar backbone and four kinds of bases denoted by the symbols A, T, G, and C for the bases adenine, thymine, guanine, and cytosine respectively. These four nucleic acids, which can occur in any order, combine in Watson-Crick complementary pairs to form a double strand helix of DNA. Due to the hybridization reaction, A is complementary with T and C is complementary with G. As an example, any sequence oligonucleotides, such as 5’-ACCTG-3’ has a complementary sequence, 3’-TGGAC-5’. Digits 5’ and 3’ denote orientation of DNA oligonucleotides. Until now, it is well-known that some properties of DNA could be used as indicators for solving weighted graph problems. As such, in 1998, a length-based DNA computing for traveling salesman problem (TSP) has been proposed by Narayanan and Zorbalas [4]. A constant increase of DNA strands has been encoded according to the actual length of the distance. A drawback of this method is that, there is a