DNA Splicing Systems with at Most Two Cutting Sites of a Non-Palindromic Restriction Enzyme

The modelling of splicing systems is simulated by the process of cleaving and recombining DNA molecules with the presence of a ligase and restriction enzymes which are biologically called as endodeoxyribonucleases.  The molecules resulting from DNA splicing systems are known as splicing languages. Palindrome is a sequence of strings that reads the same forward and backward.  Research on generalisations of splicing languages in DNA splicing system involving palindromic sequences for restriction enzymes has been done previously. In this research, the splicing languages resulting from DNA splicing systems with one non-palindromic restriction enzyme are determined using the notation from Head splicing system.  The generalisations of splicing languages for DNA splicing systems involving one and two non-overlapping cutting sites of one non-palindromic restriction enzyme are presented in the first and second theorems, respectively, which are proved using direct and induction methods.  The result from the first theorem shows a trivial string which is the initial DNA molecule; while the second theorem determines a splicing language consisting of a set of resulting DNA molecules from the respective DNA splicing system.