Quantitative theory of entropic forces acting on constrained nucleotide sequences applied to viruses.

We outline a theory to quantify the interplay of entropic and selective forces on nucleotide organization and apply it to the genomes of single-stranded RNA viruses. We quantify these forces as intensive variables that can easily be compared between sequences, outline a computationally efficient transfer-matrix method for their calculation, and apply this method to influenza and HIV viruses. We find viruses altering their dinucleotide motif use under selective forces, with these forces on CpG dinucleotides growing stronger in influenza the longer it replicates in humans. For a subset of genes in the human genome, many involved in antiviral innate immunity, the forces acting on CpG dinucleotides are even greater than the forces observed in viruses, suggesting that both effects are in response to similar selective forces involving the innate immune system. We further find that the dynamics of entropic forces balancing selective forces can be used to predict how long it will take a virus to adapt to a new host, and that it would take H1N1 several centuries to adapt to humans from birds, typically contributing many of its synonymous substitutions to the forcible removal of CpG dinucleotides. By examining the probability landscape of dinucleotide motifs, we predict where motifs are likely to appear using only a single-force parameter and uncover the localization of UpU motifs in HIV. Essentially, we extend the natural language and concepts of statistical physics, such as entropy and conjugated forces, to understanding viral sequences and, more generally, constrained genome evolution.