The Modelling of DNA Splicing Systems with Two Non-Palindromic Restriction Enzymes

DNA splicing system is mathematically modelled by the process of recombinant DNA which focuses on the possible reaction of sets of restriction enzymes and a ligase. The restriction enzymes are known as endodeoxyribonucleases that allow DNA molecules to be cut and reassociated. The cutting point of a restriction enzyme is determined by its cleavage pattern in the formation of a triple: left context, crossing and right context. The molecules resulting from DNA splicing systems are depicted as splicing languages. A palindrome is a sequence of strings that reads the same forward and backward. Researches on splicing languages in DNA splicing system involving palindromic sequences of restriction enzymes have been done previously. In this research, the splicing languages generated from DNA splicing systems with two non-palindromic restriction enzymes are generalised using Head's splicing model. The generalisations of splicing languages for DNA splicing systems involving two non-palindromic restriction enzymes with same and different crossings are given as theorems, which are proved by induction and direct methods respectively. By using these theorems, the splicing languages from the DNA splicing systems are determined and demonstrated through some examples.