Mathematical modelling of persistent splicing systems in DNA computing

Abstract

Splicing system is a bio-inspired computational model that interprets the cutting and pasting behavior of DNA molecules in the presence of restriction enzymes. Splicing system is defined under the framework of formal language theory. In this research the relation between different types of splicing systems and languages such as uniform, null-context, permanent, persistent and strictly locally testable languages are investigated. Then, the characteristics of persistent and permanent splicing systems are explored in detail. The interesting point about these two systems is that if restriction enzymes are chosen from actual biological sense, then the resulting systems are often persistent and permanent. Their main feature is that the property of crossing of a site is preserved and consequently, the enzymes cleavage process persists. Some sufficient conditions are provided for splicing systems to be persistent and permanent. New concepts of self-closed, crossingpreserved and extended crossing-preserved are introduced. These new concepts are closely connected to the notions of persistent and permanent systems. Moreover, fuzzy splicing system is introduced as an extension of splicing systems. In fact, by considering the threshold languages generated by fuzzy splicing systems, their computational power is increased. In other words, there are some fuzzy splicing systems that generate non-regular languages, while splicing systems with finite components can only generate regular languages. At the end of this research, a laboratory experiment has been conducted to biologically validate the behavior of persistent splicing systems.