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A Formal Language Model of DNA Polymerase Enzymatic Activity

Enaganti S. K., Kari L., Kopecki S.

Fundamenta Informaticae

2015

Vol. 138, nr 1/2

179--192

We propose and investigate a formal language operation inspired by the naturally occurring phenomenon of DNA primer extension by a DNA-template-directed DNA Polymerase enzyme. Given two DNA strings u and v, where the shorter string v (called primer) is Watson-Crick complementary and can thus bind to a substring of the longer string u (called template) the result of the primer extension is a DNA string that is complementary to a suffix of the template which starts at the binding position of the primer. The operation of DNA primer extension can be abstracted as a binary operation on two formal languages: a template language L1 and a primer language L2. We call this language operation L1-directed extension of L2 and study the closure properties of various language classes, including the classes in the Chomsky hierarchy, under directed extension. Furthermore, we answer the question under what conditions can a given language of target strings be generated from a given template language when the primer language is unknown. We use the canonic inverse of directed extension in order to obtain the optimal solution (the minimal primer language) to this question.

On the Regularity of Iterated Hairpin Completion of a Single Word

Kari L., Seki S., Kopecki S.

Fundamenta Informaticae

2011

Vol. 110, nr 1-4

201-215

Hairpin completion is an abstract operation modeling a DNA bio-operation which receives as input a DNA strand w = xaya, and outputs w' = xayax, where x denotes the Watson- Crick complement of x. In this paper, we focus on the problem of finding conditions under which the iterated hairpin completion of a given word is regular. According to the numbers of words a and a that initiate hairpin completion and how they are scattered, we classify the set of all words w. For some basic classes of words w containing small numbers of occurrences of a and a, we prove that the iterated hairpin completion of w is regular. For other classes with higher numbers of occurrences of a and a, we prove a necessary and sufficient condition for the iterated hairpin completion of a word in these classes to be regular.