Application of local rules and cellular automata in representing protein translation and enhancing protein folding approximation

Abstract

It is self-evident that the coarse-grained view of transcription and protein translation is a result of certain computations. Although there is no single definition of the term “computation,” protein translation can be implemented over mathematical models of computers. Protein folding, however, is a combinatorial problem; it is still unknown whether a fast, accurate, and optimal folding algorithm exists. The discovery of near-optimal folds depends on approximation algorithms and heuristic searches. The hydrophobic–hydrophilic (HP) model is a simplified representation of some of the realities of protein structure. Despite the simplified representation, the folding problem in the HP model was proven to be NP-complete. We use simple and local rules to model translation and folding of proteins. Local rules imply that at a certain level of abstraction an entity can move from a state to another based on its state and information collected from its neighborhood. Also, the rules are simple in a sense that they do not require complicated computation. We use one-dimensional cellular automata to describe translation of mRNA into protein. Cellular automata are discrete models of computation that use local interactions to produce a global behavior of some sort. We will also discuss how local rules can improve approximation algorithms of protein folding and give an example of a CA that accept a certain family of strings to achieve half H–H contacts.