What drives antigenic drift in a single influenza

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

Antigenic drift n n 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

HA 1 987 nt Russell Kightley Media rkm. com. au

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

HA 1 polymorphism – within-year max pwd (7%) mean pairwise distance out of 329 amino acids (4%) 14 24

HA 1 polymorphism – local datasets n Coiras et al, Arch. Vir. (2001) n Schweiger et al, Med. Microbiol. Immunol. (2002) n Pyhälä et al, J. Med. Virol. (2004)

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

Neutral Epidemic Model Exiting a population class via mutation

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

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

Non-neutral model n n 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 )

Keeping track of hosts q 0 q 30 completely immune ( to I 0 ) completely naive j+k is distance between immunizing and challenging (infecting) strain

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

Equations

Equations total immunity in population cross-immunity between strains m amino acids apart

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

Population genetics Fisher’s Fundamental Theorem 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.

Under neutrality

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

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

I(t)

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

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

Partial correlations immunity : immune-escape/mutation :

Partial correlations immunity : immune-escape/mutation :

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

When sampling from parameter space … 1. if goal is to map out a parameter space, choice of distribution does not matter 2. be careful summarizing relationships between parameters, because choice of distribution may be quite significant 3. non-monotonicity make PCCs meaningless (e. g. PCC=0 does not imply independence) 4. PCCs assume linear relationships between parameters (PRCCs do not) 5. Remember that you are calculating statistics on deterministic quantities

Host immunity drives antigenic drift

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

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 GM 28016, NSF, and Stanford University )