Poisson Model of a molecular clock for flu variation
For Math for Biologists course (calc, probability, stats)
Nobusawa, Eri, and Katsuhiko Sato. "Comparison of the mutation rates of human influenza A
and B viruses." Journal of virology 80.7 (2006): 3675-3678.
Human influenza A viruses evolve more rapidly than influenza B viruses. To clarify the
cause of this difference, we have evaluated the mutation rate of the nonstructural gene as
revealed by the genetic diversity observed during the growth of individual plaques in
MDCK cells. Six plaques were studied, representing two strains each of type A and B
viruses. A total of 813,663 nucleotides were sequenced, giving rates of 2.0 × 10−6 and 0.6
× 10−6 mutations per site per infectious cycle, which, when extended to 1 year, agree well
with the published annual evolutionary rates.
Genome size: Influenza A is 13,588 nucleotide bases
13588 x probability of a change (2.0 × 10−6) = .027 mutations per genome per reproductive cycle
Too small of a mutation rate to help students develop a conceptual understanding of Poisson.
So start with a 100 base pair genome with a 2% rate of change. In excel have the students run
this for 100 generations. Graph to get the Poisson distribution.
Then students can use this model to think about the small mutation rate of influenza A.
Poisson Distribution simulator: http://www.uni.illinois.edu/~hcrussel/poisson_processes.htm
Assumptions to consider: How quickly does the flu reproduce?
Compare the rates of mutation for humans, horses, birds and pigs.