### Human seasonal influenza viruses

slide by Trevor Bedford
- Influenza virus evolves to avoid human immunity
- Vaccines need frequent updates

## Beyond tracking: can we predict?

### Clonal interference and traveling waves

RN, Annual Reviews, 2013; Desai & Fisher; Brunet & Derrida; Kessler & Levine
### Theoretical framework for virus evolution -- population genetics

##### evolutionary processes ↔ trees ↔ genetic diversity

#### Typical tree

#### Bolthausen-Sznitman Coalescent

RN, Hallatschek, PNAS, 2013; see also Brunet and Derrida, PRE, 2007; Desai, Walczak, Fisher, Genetics, 2013
### Bursts in a tree ↔ high fitness genotypes

### 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
### 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
### 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
### HI distances on the phylogenetic tree

## NextStrain architecture

#### Using treetime to rapidly compute timetrees

### 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 full genomes coverage in 10 patients
- full data set at hiv.tuebingen.mpg.de

Zanini et al, eLife, 2015
## Inference of fitness costs

- mutation away from preferred state with rate $\mu$
- selection against non-preferred state with strength $s$
- variant frequency dynamics: $\frac{d x}{dt} = \mu -s x $
- equilibrium frequency: $\bar{x} = \mu/s $
- fitness cost: $s = \mu/\bar{x}$

### Fitness landscape of HIV-1

Zanini et al, Virus Evolution, 2017
### Selection on RNA structures and regulatory sites

Zanini et al, Virus Evolution, 2017
### T-cell turnover is fast in untreated infection

- latent HIV → barcode of a T-cell lineage
- all latent integrated virus derives from late infection
- untreated: T-cell lineages are short lived
- on therapy: T-cell clones live decades

Brodin et al, eLife, 2016
## Summary

- RNA virus evolution can be observed directly
- 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

### Influenza and Theory acknowledgments

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

### nextstrain.org

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

### Acknowledgments

- Fabio Zanini
- Jan Albert
- Johanna Brodin
- Christa Lanz
- GĂ¶ran Bratt
- Lina Thebo
- Vadim Puller