Catching old influenza virus with a new Markov model

We have developed a novel Markov model which models the genetic distance between viruses based on the Hemagglutinin (HA) gene, a major surface antigen of the avian influenza virus. Using this model we estimate the probability of finding highly similar virus sequences separated by long time gaps. Our biological assumption is based on neutral evolutionary theory, which has been applied previously to study this virus [Gojobori, Moriyama, and Kimura. PNAS Vol 87. 1990]. Our working hypothesis is that after a long enough time gap and with the high mutation rate usually found in RNA viruses, many site mutations should accumulate, leading to distinct modern variants. We obtained 3439 HA protein sequences isolated through years 1918 to 2006 from around the globe, aligned them to a consensus sequence using the NCBI alignment tool, and used a Hamming distance metric on the aligned sequences. We tested our hypothesis by combining a standard Poisson process with a Markov model. The Poisson process models the occurrences of mutations in a given time interval, and the Markov model estimates the probabilities of changes to the genetic distances due to mutations. By coalescing all sequences at a given genetic distance to a single state, we obtain a tractable Markov chain with a number of states equal to the length of the base peptide sequence. The model predicts that the probability of finding highly similar virus after several decades is extremely small. The existence of recent viruses which are very similar to older viruses suggests that potentially there exists some reservoir which preserves viruses over long periods.