Mathematical modelling of splicing systems on DNA molecules

Abstract

Splicing system was originally developed by Tom Head in 1987 as the generative capacity of systems of restriction enzymes acting on DNA molecules. Splicing system can be modelled mathematically. The language which results from a splicing system is called a splicing language. This language can further be analyzed using concepts in formal language theory, which is a branch of theoretical computer science and applied discrete mathematics. A splicing language contains the initial strings of DNA molecules and is closed under the application of splicing rules. Among the different types of splicing languages is the strictly locally testable language. In this thesis, some examples of not strictly locally testable language are given and some theorems concerning different combination of restriction enzymes in a strictly locally testable language are stated with the proofs. This thesis also discusses simple splicing system, which includes several new theorems regarding the concepts of factors, constants and prime constants of a language, and also some facts on solid codes. Some examples on maximal firm subwords and the automaton that recognize a splicing system are also included and discussed. Lastly, the wet-lab experiment that has been done to verify the mathematical model and to show the difference between the adult and limit language are presented. This experiment has successfully tested the hypothesis that a particular splicing system will converge to a fixed set of strings.