What drives antigenic drift in a single influenza season?

1. What drives antigenic drift in a single influenza season? Maciej F. BoniStanford UniversityDepartment of Biological Sciences DIMACS Workshop on Evolutionary Considerations in Vaccine Use Rutgers University, June 29, 2005

2. Antigenic drift • Defined as the accumulation of point mutations in influenza surface proteins (haemagglutinin and neuraminidase) • Antigenic drift enables influenza to escape host immunity and re-infect populations with previously acquired immunity

3. HA1 987nt Russell Kightley Media rkm.com.au

4. Strains have accumulated mutations. But how many? epidemic strain NOV APR Flu epidemics and antigenic drift weekly illnesses/10,000 inhabitants (NL) 20 1996 1997 1998 de Jong et al (2000)

5. HA1 polymorphism – within-year max pwd (7%) 24 mean pairwise distance out of 329 amino acids (4%) 14

6. HA1 polymorphism – local datasets • Coiras et al, Arch. Vir. (2001) • Schweiger et al, Med. Microbiol. Immunol. (2002) • Pyhälä et al, J. Med. Virol. (2004)

7. Number of infections with epidemic-originating strain Number of infections with a strain k mutations away Neutral Epidemic Model

8. Exiting a population class via mutation Neutral Epidemic Model

9. Strain frequencies are Poisson-distributed Frequency of strain k: Mean number of mutations per virus moves forward in time according to a molecular clock

10. you may have conferred immunity from a previous season to one of these strains. Modeling antigenic drift and immunity the epidemic-originating strain -2 -1 0 1 2 3 4

11. Modeling antigenic drift and immunity the epidemic-originating strain -2 -1 0 1 2 3 4 Distance between immunizing strain and challenging strain determines level of cross-immunity. We model this as an infectivity reduction and say it wanes exponentially with distance:

12. Non-neutral model • Amino-acid replacements in influenza surface proteins confer a fitness benefit via increased transmissibility • Hosts have some immunity structure from vaccination or previous infections ( need both )

13. j+kis distance between immunizing and challenging (infecting) strain Keeping track of hosts

14. infectivity reduction by previous infection with a strain j amino acids away force of infection of strain k total force of infection Keeping track of variables

15. Equations

16. total immunity in population cross-immunity between strains mamino acids apart Equations

17. mean fitness of strain population: W Equations fitness of strain k

18. Fisher’s Fundamental Theorem Population genetics Define mean antigenic drift in virus population as: This is the Price Equation, thus, the basic influenza population dynamics can be viewed in a standard population genetic framework.

19. Under neutrality

20. Takes 7 aa-changes to escape 50% immunity I(t)

21. Define the excess antigenic drift as: How do you know when the epidemic ends?

22. I(t)

23. Little immune escape per mutation, thus little fitness variation for natural selection to act on. Very few mutations required to escape immunity, so little drift occurs slow immune escape medium immune escape fast immune escape

24. In general, how do the parameters affect the model results?

25. Partial correlations immunity : immune-escape/mutation :

26. Partial correlations immunity : immune-escape/mutation :

27. Partial correlations immunity : immune-escape/mutation : controllable by vaccination

28. When sampling from parameter space … • if goal is to map out a parameter space, choice of distribution does not matter • be careful summarizing relationships between parameters, because choice of distribution may be quite significant • non-monotonicity may make PCCs meaningless (e.g. PCC=0 does not imply independence) • PCCs assume linear relationships between parameters (PRCCs do not) • Remember that you are calculating statistics on deterministic quantities

29. Host immunity drives antigenic drift

30. Public health implications • Vaccination strategies: under-vaccination or imperfect vaccination may cause much excess antigenic drift. • Pandemic implications: need to consider the effects of vaccination during the 2nd year after a pandemic, and their effects on the 3rd year after a pandemic.

31. Thanks Marcus W. Feldman Stanford University, Department of Biological Sciences Julia R. Gog Cambridge University, Department of Zoology Viggo Andreasen University of Roskilde, Department of Mathematics and Physics Freddy B. Christiansen University of Aarhus, Department of Biology ( and for funding to NIH grant GM28016, NSF, and Stanford University )