Richard Neher

Biozentrum & SIB, University of Basel

slides at neherlab.org/201910_multistrain.html

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

- 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)

- Speed of adaptation is logarithmic in population size
- Environment (fitness landscape), not mutation supply, determines adaptation
- Different models have universal emerging properties

- can we predict fitness?
- pick the closest relative of the future?

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

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

- 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
- $H_{a\beta} = v_a + p_\beta + \sum_{i\in (a,b)} d_i$
- 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

- MDS: $(d+1)$ parameters per virus
- Tree model: $2$ parameters per virus
- Sparse solution

→ identify branches or substitutions that cause titer drop

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

Mutation | effect |

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 |

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

- 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

- 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