Virus evolution and population genetics

Richard Neher
Biozentrum, University of Basel

slides at neherlab.org/201904_computational_biology.html

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)
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

Some viruses evolve a million times faster than animals

Animal haemoglobin

HIV protein

Development of sequencing technologies

We can now sequence...

thousands of bacterial isolates
thousands of single cells
populations of viruses, bacteria or flies
diverse ecosystems

HIV-1 evolution within one individual

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

Immune escape in early HIV infection

Population genetics & evolutionary dynamics

evolutionary processes ↔ trees ↔ genetic diversity

Selective sweeps

Viruses carrying a beneficial mutation have more offspring: on average $1+s$ instead of $1$
$s$ is called selection coefficient
Fraction $x$ of viruses carrying the mutation changes as $x(t+1) = \frac{(1+s)x(t)}{(1+s)x(t) + (1-x(t))}$
In continuous time → logistic differential equation: $\frac{dx}{dt} = sx(1-x) \Rightarrow x(t) = \frac{e^{s(t-t_0)}}{1+ e^{s(t-t_0)}}$

Mutation rates and diversity and neutral sites

Zanini et al, Virus Evolution, 2017

Balance between mutation and deleterious mutations

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: $s = \mu/\bar{x}$

Time-scaled phylogenies

Tree building optimization with temporal constraints

Time stamps single out a root
Root can be found by optimizing root-to-tip regression
BEAST: Markov-Chain Monte Carlo tree sampler
If topology is correct, temporal constraints can be accounted for in linear time
Multiple tools: treedate, LSD, treetime

Time-scaled phylogenies

Attach sequences and dates

Propagate temporal constraints via convolutions

Integrate up-stream and down-stream constraints

Time-scaled phylogenies

Calibration points can be longitudinal samples, ancient DNA or fossils
Rates can vary between proteins and organisms from 0.01/year to $<10^{-8}$ /y
Some site change often, some rarely → saturation
The apparent rate changes over time
Divergence times are often under estimated.

Virus evolution and population genetics

Viruses

Evolution of HIV

HIV infection

Some viruses evolve a million times faster than animals

Animal haemoglobin

HIV protein

Development of sequencing technologies

We can now sequence...

HIV-1 evolution within one individual

Immune escape in early HIV infection

Immune escape in early HIV infection

Population genetics & evolutionary dynamics

evolutionary processes ↔ trees ↔ genetic diversity

Selective sweeps

Mutation rates and diversity and neutral sites

Balance between mutation and deleterious mutations

Time-scaled phylogenies

Tree building optimization with temporal constraints

Time-scaled phylogenies

Attach sequences and dates

Propagate temporal constraints via convolutions

Integrate up-stream and down-stream constraints

Time-scaled phylogenies

treetime.ch

Exercise sheet

Alignment

Dates and other metadata