Error catastrophe for viruses infecting cells: analysis of the phase transition in terms of error classes

Abstract

RNA viruses offer a very exciting arena in which to study evolution in ‘real time’ owing to both their high replication rate—many generations per day are possible—and their high mutation rate, leading to a large phenotypic variety. They can be regarded as a swarm of genetically related mutants around a dominant or master genetic sequence. This system is called a ‘viral quasi-species’. Thus, a common framework to describe RNA viral dynamics is by means of the quasi-species equation (QSE). The QSE is in fact a system of a very large number of nonlinear coupled equations. Here, we consider a simpler formulation in terms of ‘error classes’, which groups all the sequences differing from the master sequence by the same number of genomic differences into one population class. From this, based on the analogies with Bose condensation, we use thermodynamic inspired observables to analyse and characterize the ‘phase transition’ through the so-called ‘RNA virus error catastrophe’.