Matrix splicing system

Abstract

The string splicing system was introduced by Tom Head, which stands as an abstract model for the DNA recombination under the influence of restriction enzymes and ligase enzymes. However, it is observed that strings are not very capable of modelling the complex chemical process. Hence, in this article, matrix splicing system is introduced with a new splicing operation among the matrices. It is shown with an illustration that the DNA recombination process can be simulated by the matrix splicing system, which justifies the suitability of the matrices for modelling the complex processes of the molecules. The properties of the components of the system such as cutting rules and the splicing rules are discussed. Besides some properties of the system, it is shown that this system stands as a theoretical model for splicing strings in parallel. The abstraction of the ligase enzymes is explained which is missing in all the splicing models that have come out so far. The ability of the system in generating new patterns is also outlined.

Keywords:

• DNA splicing
• cutting rule
• splicing rule
• cut-matrices
• recombinants

2000 AMS Subject Classification :

• 15A15
• 68Q05

Notes

|V| is the cardinality of the set V.

Sometimes, we use ‘k ^th component of a cutting rule’ instead of ‘w in the k ^th position of the cutting rule’.

If a component occurs k times, k>1, we assign a number called ‘Repetition’ for w, which is k−1. If a component occurs only once in a cutting rule C, then its Repetition is taken as zero.

If an element of B _M is a component of a cutting rule, then the cutting will be in any of the four borders of the matrix.

Degree of a vertex is the number of edges incident on that vertex.

if are the vertices of a graph, the degree sequence of the graph is the sequence ).

[x]is the greatest integer function.

Set of matrices.

‘The splicing product of M ₁ and M ₂ ’ means the matrix got as a result of splicing M ₁ and M ₂.

R is said to be symmetric, iff for every pair (a, b)∈R, (b, a) is also in R.

Ligase and the ligase enzyme are one and the same.