Virus evolution and the predictability of next year's flu


Richard Neher
Biozentrum, University of Basel

Viruses

tobacco mosaic virus (Thomas Splettstoesser, wikipedia)

bacteria phage (adenosine, wikipedia)

influenza virus wikipedia

human immunodeficiency virus wikipedia
  • rely on host to replicate
  • little more than genome + capsid
  • genomes typically 5-200k bases (+exceptions)
  • many infectious diseases are caused by viruses
  • very important function in microbial eco-systems
  • most abundant organisms on earth $\sim 10^{31}$

Evolution of HIV


  • Chimp → human transmission around 1900 gave rise to HIV-1 group M
  • ~100 million infected people since
  • subtypes differ at 10-20% of their genome
  • HIV-1 evolves ~0.1% per year
image: Sharp and Hahn, CSH Persp. Med.

HIV infection

  • $10^8$ cells are infected every day
  • the virus repeatedly escapes immune recognition
  • integrates into T-cells as latent provirus
image: wikipedia

HIV-1 evolution within one individual



silouhette: clipartfest.com, Zanini at al, 2015. Collaboration with Jan Albert and his group


Population sequencing to track all mutations above 1%

  • diverge at 0.1-1% per year
  • almost whole genome coverage in 10 patients
  • full data set at hiv.tuebingen.mpg.de
Zanini et al, eLife, 2015; antibody data from Richman et al, 2003

Theoretical framework for virus evolution -- population genetics

evolutionary processes ↔ trees ↔ genetic diversity

Neutral models and beyond

Neutral models

  • all individuals are identical → same offspring distribution
  • Kingman coalesence and diffusion theory are dual descriptions
  • everything is easy to calculate
  • perturbations like background selection can be included

But: neutral models not suitable for RNA viruses!

Clonal interference and traveling waves

RN, Annual Reviews, 2013; Desai & Fisher; Brunet & Derride; Kessler & Levine

Neutral/Kingman coalescent

strong selection

Bolthausen-Sznitman Coalescent

RN, Hallatscheck, PNAS, 2013; see also Brunet and Derrida, PRE, 2007

Traveling waves and the Bolthausen-Snitman coalescent

  • Branching process approximation: $P(n_i, t|x_i)$
  • Does a sample (blue dots) have a common ancestor $\tau$ generations ago?
    $\quad Q_b = \langle \sum_i \left(\frac{n_i}{\sum_j n_j}\right)^b\rangle \approx \frac{\tau-T_c}{T_c(b-1)} $
  • All other merger rates are also consistent with the Bolthausen-Sznitman coalescent:
    $\quad\lambda_{b,k} = \frac{(k-2)!(b-k)!}{T_c (b-1)!}$
RN, Hallatscheck, PNAS, 2013; see also Brunet and Derrida, PRE, 2007

U-shaped polarized site frequency spectra



RN, Hallatscheck, PNAS, 2013
Zanini et al, eLife, 2015

Bursts in a tree ↔ high fitness genotypes

Can we read fitness of a tree?

Human seasonal influenza viruses

slide by Trevor Bedford


  • Influenza virus evolves to avoid human immunity
  • Vaccines need frequent updates

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

Validate on simulation data

  • simulate evolution
  • sample sequences
  • reconstruct trees
  • infer fitness
  • predict ancestor of future
  • compare to truth
RN, Russell, Shraiman, eLife, 2014

Validation on simulated data

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

nextstrain.org

Summary

  • RNA virus evolution can be observed directly
  • Extensive reversion to preferred amino acid sequence
  • Rapidly adapting population require new population genetic models
  • Those model can be used to infer fit clades
  • Future influenza population can be anticipated
  • Automated real-time analysis can help fight the spread of disease

HIV acknowledgments

  • Fabio Zanini
  • Jan Albert
  • Johanna Brodin
  • Christa Lanz
  • Göran Bratt
  • Lina Thebo
  • Vadim Puller

Influenza and Theory acknowledgments

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

nextstrain.org

  • Trevor Bedford
  • Colin Megill
  • Pavel Sagulenko
  • Wei Ding
  • Sidney Bell
  • James Hadfield