sex, viruses, and the statistical physics of...

Sex, viruses, and the statistical physics of evolution

Thursday, September 24, 2009

Richard Neher KITP Chalk Talk, August ‘09

Cartoon of Evolution

2

Genotypes

Selection

Mutation & Recombination

Sex & Recombination Selection

...ATACG...

...ATGCG...

Mutation

AT

C G



Tree of Life - billions of years

3

4 billion years

sour

ce: t

ree

of li

fe, t

olw

eb.o

rg



Phylogenetic tree of Fruitflies - millions of years

4

~40 Millions of years image from: insects.eugenes.org/species/



Evolution of Influenza A - few years

5

characterized by an unusually high number of amino acidchanges, reflecting the large evolutionary distance betweensections II and IV (19 amino acid changes) and sections VI andVIII (15 amino acid changes) (Table 1). In marked contrast, nosections of the HA phylogeny are merged, resulting in a tree inwhich evolutionary change is more evenly distributed across alleight trunk branches. Across the viral genome as a whole, thegreatest number of amino acid changes occurs along the maintrunk lineages of the HA tree (n = 63), followed by the NA tree(n = 55), strongly supporting the long-term action of immuneselection (antigenic drift) on these glycoproteins.The smallest number of amino acid changes occurs along

branch #4, which connects isolates from the 1950’s (section IV)with those from the 1970’s (section V). Thus, little A/H1N1

evolution is evident over the twenty-year period of the virus’sglobal disappearance [30], supporting earlier suggestions that thissubtype was most likely accidentally reintroduced into humancirculation from a laboratory environment [3,31]. Notably, ouranalysis indicates that the influenza viruses that re-emerged in the1970’s were more closely related in all gene segments to a group ofviruses sampled from the late 1940’s, in particular to isolate A/Roma/1949, supporting earlier serological and partial sequenceanalyses [16,30,32]

Multiple reassortment events within A/H1N1In general, most of the ten clades A–J fall within the same

topological section in each of the segment phylogenies. Forexample, on all eight phylogenies, clade A is positioned within

A/Canterbury/01/2001A/Canterbury/106/2004

A/Memphis/5/2003A/New York/8/2006

A/Otago/5/2005A/New York/223/2003

A/New York/291/2002A/Wellington/1/2001

A/Memphis/1/2001A/New York/239/2001

A/New Caledonia/20/1999A/New South Wales/24/1999

A/TW/4845/99A/New York/233/2000

A/Hong Kong/470/97A/TW/3355/97

A/Nanchang/13/1996A/Charlottesville/31/95A/Memphis/6/1996

A/New York/653/1996A/TW/130/96

A/New York/694/1995A/Hong Kong/427/98

A/New York/146/2000A/South Australia/44/2000

A/Texas/36/91A/Chile/1/83

A/Memphis/39/1983A/Christs Hospital/157/1982

A/Memphis/1/1984A/Tonga/14/1984A/New Zealand/7/1983

A/India/6263/1980A/Memphis/7/1980

A/Memphis/12/1986A/Memphis/3/1987

A/New York/2924-1/1986A/Taiwan/01/1986A/Texas/2922-3/1986

A/Singapore/6/1986A/Baylor/11515/82

A/Baylor/4052/1981A/Brazil/11/1978

A/Hong Kong/117/77A/Lackland/3/1978A/Memphis/10/1978A/USSR/90/1977

A/Arizona/14/1978A/Tientsin/78/1977

A/Roma/1949A/Albany/4835/1948A/Albany/4836/1950

A/Albany/12/1951A/Denver/57

A/Fort Worth/50A/Malaysia/54

A/FORT MONMOUTH/1/47A/Cam/46

A/Hickox/1940A/Weiss/43

A/AA/Huston/1945A/AA/Marton/1943

A/Iowa/1943A/Bel/42

A/Alaska/1935A/PR/8/34

A/Henry/1936A/Phila/1935A/Melbourne/35

A/WSN/1933A/Brevig Mission/1/1918

AB

CD

100 99

96

100

100

100100

E

F

G

100 100100

100

100

100 H

I

94 J

III

IIIIV

VI

VIIIIX

#1

#2

#3

#7

#8

#4

3 aa

2 aa

3 aa

1 aa

5 aa

1 aa

V

96

3 aa

#5

PB2

100

96

100

10082

98

100

100

100

100

99

100

Figure 1. Phylogenetic relationships of the PB2 gene of A/H1N1 influenza viruses (n=71) sampled globally from 1918–2006,estimated using a maximal likelihood (ML) method. All branch lengths are drawn to a scale of nucleotide substitutions per site. The tree isrooted using the oldest sequence, A/Brevig Mission/1/1918, and temporally ordered with the oldest isolates falling at the bottom left of thephylogeny and the newest isolates at the top right. Main phylogenetic sections that are separated by long trunk branches are numbered I–IX andcolored as follows: section I is red, section II is orange, section III is yellow, section IV is light green, section V is dark green, section VI is light blue,section VII is absent due to the position of clade G within section VI (would otherwise be blue), section VIII is purple, and section IX is gray. The trunkbranches separating these sections are labeled #1–#8 and highlighted in dark blue, with the bootstrap value supporting this branch highlighted inyellow and the number of amino acid changes that occur along each branch appearing above in red font. Ten main clades are labeled A–J, withsupporting bootstrap values in light blue, and are colored as follows: clade A is dark red, clade B is orange, clade C is yellow, clade D is olive green,clade E is light blue, clade F is turquoise, clade G is fuchsia, clade H is gray, clade I is pink, and clade J is white. Clades that have undergonereassortment are outlined in red (in this case Clade D).doi:10.1371/journal.ppat.1000012.g001

Evolution of H1N1 Influenza A Virus

PLoS Pathogens | www.plospathogens.org 3 2008 | Volume 4 | Issue 2 | e1000012

Influenza Aglobal epidemic

1918 2005

Nelson et al., 2008Evolution as cause of epidemics



Human immunodeficiency virus (HIV)

6

HIV budding from an immune cell

100nm

Rapid evolution is a hallmark of HIV infections



HIV

7



HIV

7

Virus escapes the immune system by continuous evolution



Evolution in a single patient (blood samples every 6 month)

8

Lemey et al., 2006, Shankarappa et al. 1999

AIDS Reviews 2006;8

126

Since HIV populations evolve at a rate that is several orders of magnitude faster than that of their human hosts, HIV sequences sampled longitudinally will usu-ally accumulate a significant amount of evolutionary change. Longitudinally sampled or “heterochronous”11 sequences can be obtained in one of two ways: either from a single patient over the course of infection, or from different patients over the duration of an epidemic (Fig. 1). Interestingly, phylogenies reconstructed from such sequences have distinctive features that reveal the differences in the dynamics of HIV evolution at the in-ter-host and intra-host levels12.

Within each host, the viral population is targeted by both cellular and humoral immune responses, resulting in relatively strong diversifying selection that is most noticeable in the variable regions of the envelope (env) gene. It has been demonstrated that the rate of amino acid substitution in env correlates with the rate of phe-notypic escape from neutralizing antibodies13. This im-

plies that neutralizing antibody responses cause the relative fitness of different strains within an infection to vary, thus constituting a major force that drives rapid lineage turnover. As a result, intra-host phylogenies of heterochronous env sequences exhibit an asymmetri-cal or “ladder-like” shape, with limited diversity at any one time (Fig. 1)12.

In contrast, HIV evolution at the inter-host level shows little evidence that HIV transmission is driven by a similar selective process14,15. Inter-host phylogenies of HIV sampled through time are not ladder-like and show the persistence of multiple lineages through time (Fig. 1)12. The shape of inter-host phylogenies is pri-marily determined by (selectively) neutral demographic processes12,15.

In summary, HIV lineages within a host vary in their ability to survive and infect new cells, whereas different HIV lineages among hosts show little genetic variation in their ability to infect new individuals. Some lineages

Figure 1. A: HIV-1 within-host phylogeny with branch lengths in time units: partial env gene longitudinally sampled from a single patient over 155 months (subtype B, 129 sequences, 516 bp; patient 9)34,53. B: HIV-1 population phylogeny with branch lengths in time units: full length env gene sampled during the U.S. HIV epidemic from 1981-1995 (subtype B, 39 sequences, 2396 bp)35. C: Root-to-tip divergence as a function of sampling time for the within-host phylogeny. The R2 value is indicated above the regression line. D: Root-to-tip divergence as a function of sampling time for the population phylogeny: divergence estimates for the full length and C2V5 env gene are shown with black squares and open diamonds respectively.

Time (months since seroconversion) Time (year)

Time (year)

Roo

t-to

-tip

div

erge

nce

(nuc

leot

ide

subs

titut

ions

/site

)

R2 = 0.67

R2 = 0.27

Roo

t-to

-tip

div

erge

nce

(nuc

leot

ide

subs

titut

ions

/site

)

R2 = 0.89

0 1 2 3 4 5 6 7 8-1-2 9 10 12 1311

20 40 60 800 100 140 160120

1985 1990 199519801975197019651960

1990 1992 19941988198619841982

Time (years since seroconversion)

0.200.180.160.140.120.100.080.060.04

0.14

0.12

0.10

0.08

0.06

0.04

0.02

0

A B

C D

~ 8% divergence in 10 years ==

many millions of years in Drosophila



Evolution of HIV

9

Resistance to drugs (protease inhibitors):Drug sensitive: PQITLWQRPLVTIKIGGQLKEALLDTGADDTVLEEMNLPGRWKPKMIGGIGGFIKVRQYDQILIEICGHKAIGTVLVGPTPVNIIGRNLLTQIGCTLNFDrug resistant: PQITLWQRPLVTIKVGGQLTEALLDTGADDTILEDMTLPGRWKPKIVGGIGGFIKVRQYDQVPIEICGHKVISTVLIGPTPCNIIGRNLMTQIGLTLNF

The virus has to change: Escape the immune system and drug resistance



Evolution of HIV

9



High mutation rate: μ=3x10-5/generation and site



Evolution of HIV

9




Large population:N=1010 viruses



Evolution of HIV

9



human immune cell

“Viral sex”


Large population:N=1010 viruses



Recombination in viruses - Influenza

10

• 11 genes on 8 segments

• 16 H (hemagglutinin) subtypes

• 9 N (neuraminidase) subtypes

• H1N1, H2N2, H3N2, H5N1 are common

100n

m



Recombination in viruses - Influenza

10

• 11 genes on 8 segments

• 16 H (hemagglutinin) subtypes

• 9 N (neuraminidase) subtypes

• H1N1, H2N2, H3N2, H5N1 are common

100n

m

• Pandemics often follow reassortments, e.g. pandemics 1957 (H2N2) and 1968 (H3N2)

• Reassortment is frequent in waterfowl and swine, where many subtypes circulate.



Spreading of beneficial mutations

11

Mutant individuals reproduce faster(Drug resistant strain)

Time

Popu

latio

n

Fixation probability: ~s Sweep time: ~ ln(Ns) / s



Evolution in asexual and sexual organisms

12

E V O L U T I O N IN S E X U A L AND ASEXUAL POPUL.AT1ONS 441

LARGE POPULATION

SMALL POPULATION

FIGURE 1. Evolution i n sexua l and a s e x u a l populat ions. T h e ha tched and shaded a r e a s show the increased number of mutant individuals following the oc- currence of a favorable mutation. T h e a b s c i s s a I s time. Modified from Muller

(1932).

s i s small , and therefore that p changes very slowly s o tha t i t i s appro-

priate to replace addition by integration. T h i s l e a d s to

In the absence of recombination, p follows the logis t ic curve

Small PopulationSequential innovations:rate ~ N

Time




12


LARGE POPULATION

SMALL POPULATION


(1932).






LARGE POPULATION

SMALL POPULATION


(1932).




Many concurrent mutations:rate ~ log N

Most good mutations are wasted!

Large Population

Time

Time




12


LARGE POPULATION

SMALL POPULATION


(1932).






LARGE POPULATION

SMALL POPULATION


(1932).




Time

Conventional wisdom:rate ~ N

RA Fisher (1930), H Muller (1932), M Kimura and J Crow (1965)


LARGE POPULATION

SMALL POPULATION


(1932).




Many concurrent mutations:rate ~ log N

Most good mutations are wasted!

Large Population

Time

Time



Quantifying the benefits of recombination [for the virus]

13

Example: drug resistance of HIV Drug sensitive: PQITLWQRPLVTIKIGGQLKEALLDTGADDTVLEEMNLPGRWKPKMIGGIGGFIKVRQYDQILIEICGHKAIGTVLVGPTPVNIIGRNLLTQIGCTLNFDrug resistant: PQITLWQRPLVTIKVGGQLTEALLDTGADDTILEDMTLPGRWKPKIVGGIGGFIKVRQYDQVPIEICGHKVISTVLIGPTPCNIIGRNLMTQIGLTLNF

Hypothetical distribution of drug resistance mutations

0 1 2 3 4 5 Resistance mutations




13


Hypothetical distribution of drug resistance mutations • Drug resistance increases due to

selection on existing mutations





13



• Novel mutations keep the wave going

novel mutation

• Drug resistance increases due to selection on existing mutations





13



• Novel mutations keep the wave going

novel mutation

recombination

• Drug resistance increases due to selection on existing mutations

• Via recombination mutations can keep up with the wave and “make it”




Surfing of beneficial mutations

14

!2 0 2 40

0.2

0.4

-4



Evolutionary benefits of recombination

15

Conventional wisdom: rate of evolution ~ N

holds only for very frequent recombination

To slow down evolution, one has to target recombination rather than the population size!!

Realistic recombination: rate of evolution ~ r2 log N



The more recombination, the better?

Is there a cost to recombination?



Genetic interactions

17

So far: Fitness = # beneficial mutations

BUT:

An organism is more than the sum of its parts



The cost of recombination

18

A “recombined” soccer team is worse than the “parents”.



The cost of recombination

18

A “recombined” soccer team is worse than the “parents”.

Relay racing teams don’t have that problem!



Genetic interaction and recombination

19

Different reassortments of Influenza A:

Recombination explores -- selection amplifies the best



Genetic interaction and recombination

19

no recombination moderate recombination frequent recombination

Different reassortments of Influenza A:

Recombination explores -- selection amplifies the best



Allele vs genotype selection

20

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

Quasi Linkage Equilibrium (QLE)Allele selection

Genotype selectionClonal Competition (CC)

Mating freq./selection

Rel.

epis

tasi

s

Recombination rate/selection

Stre

ngth

of I

nter

actio

n



The success of selection

21

0 0.1 0.2 0.3 0.40.2

0.3

0.4

recombination

F final

rc

Selection on the properties of the parts.

“All Stars team”

Selection on the combinations“the best clubs”



Connecting theory and observations

22

Large data bases of HIV sequences and drug resistance allow us to study:

• The recombination rate in HIV

• Selection strength of HIV evolution without drugs

• Drug resistance mutations: team players or independent?

• Does recombination vary from patient to patient?

• Does it vary at different stages of the disease?

• With modern sequencing technology we can soon monitor viral populations at unprecedented resolution.




22








Do such observations, together with theoretical insight, explain the differences between drugs and patients?




22








Do such observations, together with theoretical insight, explain the differences between drugs and patients?

What can we learn about the evolutionary process in general?



Sequencing Costs per Base

23

1990 1995 2000 2005 201010

!5

10!4

10!3

10!2

10!1

100

101

year

Co

st p

er

base [

$]

Data

Exponential decay: ! = 2.5 years



Experiment & Theory

24

Darwin’s Theory

Observations:PaleontologyDiversity of species



Experiment & Theory

24

Experiments in the Lab• Bacteria or viruses• Sequencing and Phenotyping

Darwin’s Theory

Observations:PaleontologyDiversity of species

Quantitative TheoryDynamics



Collaborators

25

Boris Shraiman, KITP

Daniel Fisher, Stanford

Thomas Leitner, LANL


sex, viruses, and the statistical physics of...

Documents