Modelling programmed frameshifting with frameshift machines

The translation of a messenger RNA into a functional protein is one of the most fundamental molecular processes in a cell. Groups of three ribonucleotides, called codons, uniquely specify amino acids to be used in the construction of a protein. When the translation process skips a number of bases it is possible for the reading frame of the RNA to be shifted. By making use of multiple reading frames, organisms and viruses are able to encode multiple proteins in a single gene. We propose here a formal model of these frameshifting events and investigate its basic mathematical properties and their relevance to biological systems. In addition, multiple time-efficient algorithms are created for use in the study of frameshifting. Some of these algorithms are created to work in general, for any type of frameshifting which could be found in organisms, while others are optimized for known specialized types of frameshifting.