Computational modelling of interruptional activities between transposable elements using grammars and the linear ordering problem

Abstract

Transposable elements (TEs) are DNA sequences that can either move or copy themselves to new positions within a genome. They constitute approximately 45 % of the human genome. Knowing the evolution of TEs is helpful in understanding the activities of these elements and their impacts on genomes. In this paper, we devise a formal model providing notations/definitions that are compatible with biological nomenclature, while still providing a suitable formal foundation for computational analysis. We define sequential interruptions between TEs that occur in a genomic sequence to estimate how often TEs interrupt other TEs, useful in predicting their ages. We also describe the problem in terms of a matrix problem—the linear ordering problem. We then define the recursive interruption context-free grammar to capture the recursive nature in which TEs nest themselves into other TEs, and associate probabilities to convert the context-free grammar into a stochastic context-free grammar, as well as discuss how to use the CYK algorithm to find a most likely parse tree predicting TE nesting. We also discuss improvements on the theoretical model and adjust the parse trees to capture both sequential and recursive interruptional activities between TEs and obtain more standard evolutionary trees.