Tracking and predicting influenza virus diversity


Richard Neher
Biozentrum & SIB, University of Basel


slides at neherlab.org/201910_multistrain.html

Human seasonal influenza viruses

slide by Trevor Bedford

Positive tests for influenza in the USA by week

Data by the US CDC


  • Influenza viruses evolve to avoid human immunity
  • Vaccines need frequent updates

Influenza B viruses have split into two lineages

Le Yan, RN, Shraiman, bioRxiv, 2018

GISRS -- Influenza virus surveillance

  • comprehensive coverage of the world
  • timely sharing of data through GISAID -- often within 2-3 weeks of sampling
  • hundreds of sequences per week (in peak months)
→ requires continuous analysis and easy dissemination
→ interpretable and intuitive visualization

nextflu.org

joint project with Trevor Bedford & his lab

Beyond tracking: can we predict?

Fitness variation in rapidly adapting populations

  • Speed of adaptation is logarithmic in population size
  • Environment (fitness landscape), not mutation supply, determines adaptation
  • Different models have universal emerging properties
RN, Annual Reviews, 2013; Desai & Fisher; Brunet & Derride; Kessler & Levine

Neutral/Kingman coalescent

strong selection

Bolthausen-Sznitman Coalescent

RN, Hallatschek, PNAS, 2013; see also Brunet and Derrida, PRE, 2007; Desai, Walczak, Fisher, Genetics, 2013

Burst in the tree ↔ high fitness

Predicting evolution

Given the branching pattern:

  • can we predict fitness?
  • pick the closest relative of the future?
RN, Russell, Shraiman, eLife, 2014

Fitness inference from trees

$$P(\mathbf{x}|T) = \frac{1}{Z(T)} p_0(x_0) \prod_{i=0}^{n_{int}} g(x_{i_1}, t_{i_1}| x_i, t_i)g(x_{i_2}, t_{i_2}| x_i, t_i)$$
RN, Russell, Shraiman, eLife, 2014

Prediction of the dominating H3N2 influenza strain

  • no influenza specific input
  • how can the model be improved? (see model by Luksza & Laessig)
  • what other context might this apply?
RN, Russell, Shraiman, eLife, 2014

Hemagglutination Inhibition assays

Slide by Trevor Bedford

HI data sets

  • Long list of distances between sera and viruses
  • Tables are sparse, only close by pairs
  • Structure of space is not immediately clear
  • MDS in 2 or 3 dimensions
Smith et al, Science 2002
Slide by Trevor Bedford

Integrating antigenic and molecular evolution

  • $H_{a\beta} = v_a + p_\beta + \sum_{i\in (a,b)} d_i$
  • each branch contributes $d_i$ to antigenic distance
  • sparse solution for $d_i$ through $l_1$ regularization
  • related model where $d_i$ are associated with substitutions
RN et al, PNAS, 2016

Integrating antigenic and molecular evolution

  • MDS: $(d+1)$ parameters per virus
  • Tree model: $2$ parameters per virus
  • Sparse solution
    → identify branches or substitutions that cause titer drop
RN et al, PNAS, 2016

Rate of antigenic evolution

  • Cumulative antigenic evolution since the root: $\sum_i d_i$
  • A/H3N2 evolves faster antigenically
  • A/H3N2 has a more rapid population turn-over

How many sites are involved?


Mutationeffect
K158N/N189K 3.64
K158R 2.31
K189N 2.18
S157L 1.29
V186G 1.25
S193F 1.2
K140I 1.1
F159Y 1.08
K144D 1.08
K145N 0.91
S159Y 0.89
I25V 0.88
Q1L 0.85
K145S 0.85
K144N 0.85
N145S 0.85
N8D 0.73
T212S 0.69
N188D 0.65

Predicting successful influenza clades

Acknowledgments

  • Trevor Bedford
  • Pavel Sagulenko
  • James Hadfield
  • Emma Hodcroft
  • Tom Sibley
  • and others

Influenza and Theory acknowledgments

  • Boris Shraiman
  • Colin Russell
  • Trevor Bedford
  • Oskar Hallatschek

  • All the NICs and WHO CCs that provide influenza sequence data
  • The WHO CCs in London and Atlanta for providing titer data
  • The GISAID initiative for influenza sequence data sharing

Are antigenic distances tree-like?

There are many ways to escape immunity -- why doesn't influenza speciate?

Le Yan, RN, Shraiman, bioRxiv, 2018

There are many ways to escape immunity -- why doesn't influenza speciate?

Le Yan, RN, Shraiman, bioRxiv, 2018

Combining SIR-models and rapid molecular adaptation

  • Infections with strain $a$: $\frac{d I_a}{dt} = \beta S_a I_a - (\nu+\gamma)I_a$
  • Susceptibility to strain $a$: $S_a =e^{-\sum_b K_{ab} R_b }$
  • Recovered from stain $a$: $\frac{d R_a}{dt} = \nu I_a - \gamma R_a$
  • Cross-immunity: $K_{ab} = e^{-\frac{|a-b|}{d}}$
  • Mutations from $a\to b$ reduce cross-immunity and increase susceptibility
  • Antigenic evolution is essential to establish seasonal patterns
Le Yan, RN, Shraiman, bioRxiv, 2018

Transition from pandemic to seasonal patterns

Le Yan, RN, Shraiman, bioRxiv, 2018

Speciation into antigenically distinct lineages

Le Yan, RN, Shraiman, bioRxiv, 2018