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Epochal evolution shapes the phylodynamics of interpandemic influenza (H3N2). Katia Koelle Sarah Cobey Bryan Grenfell Mercedes Pascual. ?. SI87. VI75. ?. BK79. EN72. TX77. HK68. DIMACS, 9-10 October 2006. Pathogen diversity and cross-immunity. s.

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Epochal evolution shapes the phylodynamics of interpandemic influenza (H3N2)

Katia Koelle Sarah Cobey Bryan Grenfell Mercedes Pascual









DIMACS, 9-10 October 2006

Pathogen diversity and cross-immunity


e.g. Gog & Grenfell, PNAS (2002)

Modeling Cross-Immunity

  • Strains with high sequence similarity must have high cross-immunity

  • Strains with low sequence similarity must have low cross-immunity

Explaining limited diversity of hemagglutinin

Strain-specific cross-immunity

Actual HA1




Explosive diversity

Ferguson, Galvani, Bush, Nature (2003)


Years since infection

Explaining limited diversity

Strain-specific cross-immunity + generalized immunity

Limited diversity

Ferguson, Galvani, Bush, Nature (2003)

Modeling cross-immunity between flu strains

  • Can sequence evolution be used as a proxy for antigenic evolution when modeling influenza’s hemagglutinin?

  • (i.e. does genotype approximate phenotype?)

  • Propose alternative to this genotype-phenotype map for influenza’s hemagglutinin evolution

  • Consider the effect of this new mapping on the phylogenetics and dynamics (i.e. phylodynamics) of influenza H3N2

s= >90%

s= >90%

s= 60-80%

Unrooted ML trees of sequences in the HK68 and EN72 clusters

Influenza clusters

Cluster designations as in Smith et al. 2004

Topology of influenza clusters

  • Strains with high sequence similarity can have low cross-immunity

  • Strains with low sequence similarity can have almost complete cross-immunity

Genotype cannot serve as a proxy for antigenic phenotype

Sequence (genotype)

Sequence (genotype)





Tertiary HA structure


Tertiary HA structure











More genotypes than phenotypes

Genotype-phenotype mapping for RNA 2o structures

Fontana & Schuster, JTB (1998)

Neutral networks

Fontana & Schuster, JTB (1998)

Average structure distance to target

Evolutionary dynamics on neutral networks

Fontana &


JTB (1998)

  • “A neutral mutation does not change the phenotype but it does change the potential for change… What appears to be a sudden and abrupt change at the phenotypic level has been the result of neutral genetic drift.” -Fontana

Neutral network mapping for proteins

Lau and Dill

  • Single sequence changes can result in large changes in protein conformation.

  • Changing a sequence by a large number of mutations may have no appreciable effect on protein conformation.


cross-immunity models


Neutral network topology

Implications for modeling cross-immunity

Bornberg-Bauer & Chan, PNAS (1999)


Modeling influenza’s hemagglutinin

15 a.a.

(45 nucs.)

5 epitopes

Changing the shape of an epitope

  • Adaptation of Kauffman’s NK model that generates neutral networks in genotype space (Newman and Engelhardt)


  • Framework assumes epistatic or context-dependent interaction between amino acids located in the same epitope

15 a.a.

5 epitopes

Neutrality and sequence evolution:subbasins, portals, and epochal evolution









Adapted (for flu  ) from Crutchfield, 2002



Coupling to an epidemiological model



Adapted for clusters, from Gog & Grenfell, PNAS (2002)

Dynamic Consequences of Neutral Network Model


  • Cluster transitions

  • Peaks in incidence during

  • cluster transition years

  • Refractory year

Comparison with observed influenza dynamics

Greene et al. (2006)

Phylogenetic Consequences

Simulated tree

Observed HA tree

(from Smith et al.


  • Explosion of diversity within clusters

  • Cluster transitions cause selective sweeps

  • No need for generalized immunity to limit HA diversity

Expected pattern in genetic diversity arising from epochal evolution

Supporting empirical evidence

Notions of neutrality

Influential sites model

Only changes at very few sites can precipitate a cluster jump, and their ability to do so does not depend on the genetic background in which they occur.

Genetic diversification within clusters does not facilitate adaptive change, and can be safely ignored.

Context-dependent model

Changes at most sites can precipitate a cluster jump if those changes occur in the right genetic background.

Cluster innovations are guided by the process of neutral diffusion, via changing the genetic background of sequences.

See also Wagner, 2005 for a discussion on types of neutrality in non-flu systems

Importance of genetic background, i.e.



Influential sites

Pairwise nucleotide

differences in HA1

Observed pattern in genetic diversity

Boom-and-bust of genetic diversity empirically supported

Observations of tree balance

Diversification within clusters cannot be rejected

under the null, neutral model of random speciation.


  • An alternative, empirically-supported model of influenza’s hemagglutinin evolution can account for both H3N2’s dynamic and the phylogenetic patterns of its HA1.

  • Incorporating appropriate genotype-phenotype maps for the effect of mutations at the phenotypic level may be important for understanding pathogen evolution.


David Alonso, Stefano Allesina,

Luis Chaves, Diego Moreno, Aaron King

Center for the Study of Complex Systems

NSF graduate student fellowship (S.C.)

McDonnell Foundation (Centennial Fellowship to M.P.)

Jamie Lloyd-Smith, Igor Volkov, Mary Poss

CIDD postdoctoral fellowship (K.K.)

Derek Smith, Ron Fouchier, Sharon Greene, Cecile Viboud, Maciej Boni

Patterns of influenza phylodynamics (H3N2)

1. Annual outbreaks

Greene et al. (2006)

Antigenic change

3. Genetic change

2. Genetic drift

Fitch et al. (1997)

Smith et al. (2004)

Patterns of genetic diversity

Antigenic clusters

Characteristics of Influenza Evolution

Sequential replacement of clusters

Cluster #


Smith et al., Science (2004)

Punctuated antigenic change

Gradual genetic change

Characteristics of Influenza Evolution

Genetic distance from 1968 strain

Antigenic distance from 1968 strain

Smith et al., Science (2004)

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