Temperature gradient-based DNA computing for graph problems with weighted edges

We propose an encoding method of numerical data in DNA using temperature gradient. We introduce melting temperature (Tm) for this purpose. Melting temperature is a unique characteristic to manipulate the hybridization and denaturation processes that used in the key steps in DNA computing such as the solution generation step and the amplification step. DNA strands of lower melting temperature tend to denature with ease and also be easily amplified by slightly modified polymerase chain reaction, called denaturation temperature gradient polymerase chain reaction. Using these properties, we implement a local search molecular algorithm using temperature gradient, which is contrasted to conventional exhaustive search molecular algorithms. The proposed methods are verified by solving an instance of the travelling salesman problem. We could effectively amplify the correct solution and the use of temperature gradient made the detection of solutions easier.