Experimental Implementation of Hybrid Concentration-Controlled Direct-Proportional Length-Based DNA Computing for Numerical Optimization of the Shortest Path Problem

DNA computing often makes use of hybridization, whether for vastly generating the initial candidate answers or amplification via polymerase chain reaction (PCR). The main idea behind DNA computing approaches for solving weighted graph problems is that if the degree of hybridization can be controlled, then it is able to generate more double-stranded DNAs (dsDNAs), which represents the solu- tion to the problem during initial pool generation. Previously, concentration and melting temperature of DNA have been exploited for controlling DNA hybridization during an in vitro computation. In this pa- per, we present an improved direct-proportional length-based DNA computing (DPLB-DNAC), which combines two characteristics: length and concentration for encoding and at the same time, effectively control the degree of hybridization of DNA. The encoding by length is realized whereby the cost of each path is encoded by the length of the DNA strands in a proportional way. On the other hand, the control of concentration is done by varying the amount of input DNA strands, based on the input graph. The proposed approach shows improvements in terms of materials usage and scalability. The experimental results demonstrate the feasibility of the proposed approach for solving weighted graph problems, such as the shortest path problem.