Mapping evolutionary pathways ofMapping evolutionary pathways ofHIV-1 drug resistance usingHIV-1 drug resistance using

conditional selection pressureconditional selection pressure

Christopher Lee, UCLA

HIV-1 Protease and RT:anti-retroviral drug targets

• Protease: responsible for the post-translational processing of the viralpolyproteins to yield the structural proteinsand enzymes of the virus

• Reverse transcriptase (RT): responsiblefor DNA polymerization

protease RT

Selection Pressure Mapping: Build anAtlas of HIV Evolution

• Selection pressure measures whether an amino acidmutation is selected for (Ka/Ks>1) or against(Ka/Ks<1) by evolution, vs. synonymous mutations.

• Dataset: sequencing of 50,000 HIV clinical samplesby Specialty Labs. Inc. 30-fold higher density ofpolymorphism information than human sequences.

• Goal: construct a selection pressure map of how HIVis evolving, where the virus is “going”, to evade ourdrugs.

Calculating Ka / Ks per Residue

vvstts

vvatta

s

a

s

a

fnfn

fnfn

N

N

K

K

,,

,,

+

+=

observed #amino acid changes vs.synonymous mutations at this codon

expected #amino acid changes vs.synonymous mutations at this codon

( ) iNiN

Nis

aa qq

i

N

K

KqNNipLOD

a

!

=

!""#

$%%&

'!==(!= ) 1log)1,,|(log 1010

Confidence that Ka/Ks>1 is statistically significant: log-odds score

LOD 2 means 99% confidence, LOD 3 means 99.9% confidence.

Maximum Likelihood estimation of Ka/Ks using PAML takes intoaccount inferred phylogeny, ft/fv ratio, mutation rates, etc.

(b) Selection Pressure for HIV-1 Protease

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1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97

Codon Position

Ka/K

s

Positive selection mapping automatically discovers causes of drug resistance!

HIV Protease Positive SelectionChen, Perlina & Lee, J. Virol. (2004)

Positive Selection Mapping IdentifiesDrug Resistance Mutations

• Correctly identified 19 of 22 knowndrug resistance mutation positions.

• Compared with multi-year researchprocess (clinical, biochemical,genetics) that was previouslyrequired, this analysis is completelyautomatic; works directly on outputfrom sequencing machines.

Build a Reaction Rate Diagram of HIV’sGlobal Evolution

• A network diagram of the rates oftransition between all possiblegenotypes. Ka/Ks is proportional torate of increase of a mutation.

• Shows the speeds of all possiblepaths of evolution the viralpopulation will follow, under thepressure of current drug treatments.

Selection Pressure is like anEvolutionary Velocity

For wildtype, synonymous mutant, and amino acid mutant allelefrequencies fo=1, fs=0, fa=0 initially, equal amino acid and synonymousmutation frequency λ, and reproduction rates ro, ra, after one unit of time

!

fo " ro fo 1# 2$( ); fs " ro$fo; fa " ra$fo

Assuming λ<<1, Ka/Ks and the normalized ∆fa will be:

!

Ka

Ks

=fa

fs=ra

ro; "fa =

fa

fo + f s + fa# $

ra

ro= $

Ka

Ks

So initially the rate of change of the amino acid mutant allele frequencydfa/dt is proportional to the selection pressure Ka/Ks.

What does Ka/Ks really calculate?

WT Wildtype protein sequence

30 A single mutant at codon 30

Ka/Ks calculates selectionpressure for mutation X,assuming wildtype (WT) asthe starting genotype. So weshould write Ka/Ks as beingconditioned on WT as thestarting point:

WT

1082

90

45

3016.3

0.5

0.36.3

3.5

Ka/Ks graph gives rates offlow of HIV population todifferent mutations.

WTXsaXsaKKKK |)/()/( =

Ka/Ks Ignores Interactions

• Because different sites interact, theeffect of an amino acid mutation atone site can depend on the aminoacid at other sites.

• But Ka/Ks does not consider theseinteractions; in effect, it assumesthat all mutations take place in thewildtype sequence as a completelyfixed background.

84

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7148

WT

1082

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30

XYsa KK |)/(

Conditional Ka/Ks Reveals CompleteMutation Network

We can generalize Ka/Ks tomeasure the selection pressurefor a mutation Y conditioned onthe presence of a previousmutation X. We define this asthe conditional Ka/Ks:

Each edge represents one conditional Ka/Ks value.

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0.30.2

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Fast Mutation Paths of HIV Protease

Different Paths to the Same Genotypecan Differ in Speed

WT 11.69

34.50

0.52 5.37

90

10 10/90

90 mutations are known to directly cause drug resistance but lowerstability; 10 is site of compensatory mutations that improve stability.

Our analysis distinguishes them: faster path first introduces the drugresistance mutation, then the stabilizing mutation.

NB: speed of a multistep path is generally controlled by its slowest step.

Chen & Lee, Biol. Dir. (2006)

Conditional Ka/Ks“rate” shown oneach edge.

Pathway to doublemutant: simplestpossible “subgraph”of the conditionalKa/Ks network.

Reproducible Results in IndependentDatasets

WT 11.69

34.50

0.52 5.37

90

10 10/90

Specialty Stanford-Treated Stanford-Untreated

WT 10.81

13.32

0.88 4.66

90

10 10/90

WT 0.23

2.35

0.21 1.97

90

10 10/90

Highly reproducible in independent studies ofdifferent patients. They indicate real patterns ofdrug-associated selection pressure within theHIV population in the wild.

Conditional Ka/Ks: Specialty vs. Treated

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ate

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Primary drug resistance

Accessory drug resistance

Function unknown

Quantitative Reproducibility

For codons withsufficient counts(NXa>400), the resultsmatch the Specialtyresults surprisinglywell.

Chen & Lee, Biol. Dir. (2006)

Experiment: Which Mutation HappenedFirst in Patients? (Shafer, Stanford)

• Take multiple samples at differenttime points during each patient’streatment.

• Identified pairs of mutations that co-occur, then re-examined previoussamples to see which mutationoccurred first.

Slow step is the first step of each path: 30N path is aboutsix-fold faster..

WT0.16

57

1.05 876

88D

30N 30N/88D

Different Paths to the Same Genotype Can Differin Speed

Pan et al. Nucleic Acids Res. 35: D371-D375 (2007)http://www.bioinformatics.ucla.edu/HIV

88D / 30N Comparison withLongitudinal Studies

v(PathX) : v(PathY) = 1.05: 0.16 = 6.6

PathX 30N->30N88D 13 patients PathY 88D->30N88D 2 patients

n(PathX): n(PathY) =13: 2

Longitudinal Data

WT0.16

57

1.05 876

88D

30N 30N/88D

90M mutations known to directly cause drug resistance butreduce protein stability; 73S mutations stabilize the mutantprotein.

Our analysis distinguishes them: faster path first introducesthe drug resistance mutation, then the stabilizing mutation.

WT171

>300

0.37 21

90M

73S 73S/90M

Different Paths to the Same Genotype Can Differin Speed

WT171

>300

0.37 21

90M

73S 73S/90M

90M / 73S Comparison withLongitudinal Studies

v(PathX) : v(PathY) = 0.37: 21

PathX 73S →73S90M 3 patients PathY 90M→73S90M 31 patients

n(PathX): n(PathY) =3: 31

Longitudinal Data

Shafer Longitudinal Results

• For 23 mutation pairs with apreferred path predicted by ourconditional Ka/Ks data (p=0.01),20 match the preferred kineticpathway observed in Shafer’slongitudinal patient studies.

• Statistically significant match,p=0.0002

Danger: Fast Paths to Multi-DrugResistance

• Multiple resistance: the combination ofthree mutations (at codons 82 (V82A/T/S),84 (I84V), and 90 (L90M)) is resistant tomost available protease inhibitors

• Rapid evolution of this triple mutant is aserious threat to individual treatment and tocontrol of the global AIDS epidemic.

• Our map shows where the fast paths to thiscombination are. Don’t want to go there!

WT

842.1249.30 825.16

90 7412.42 9.0416.2871 847.2615.26

90

82

Reveals Accelerated Paths toMulti-Drug Resistance

The path that includes mutation at codons 74 and 71 is 3 times faster than the direct path, and 7 times faster in its first step:

Use the order in which drugs are given (which in turncan select for one mutation over another) to pick aslower path!

Amino Acid Pairs Showing StrongNegative Selection Are Neighbors

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Selection

The Future of SNP Analysis?

• It should be emphasized that theonly input to this analysis was singlenucleotide polymorphism discoveryfrom chromatograms.

• No information about drug treatment,time, etc.

• Yet conditional Ka/Ks yields drug-resistance mutations; kinetics &temporal order; pathways.

A New Level of Strategic Intelligence

• A global picture of how HIV will respond inthe future to our drug treatments.

• Ka/Ks velocities tell us where HIVpopulation is going, detectable even whilemutations still rare.

• Moreover, since these selection pressuresare due to our actions (drugs), they aremanipulable.

• Even slowing DR evolution two-fold couldmake a big difference for control of theepidemic.

HIV Positive Selection Database

http://www.bioinformatics.ucla.edu/HIV

•Atlases of HIV drug resistance evolution from Specialty dataset.

•Analysis tools (snpindex).

AcknowledgementsLamei Chen: Ka/Ks analysisQi Wang: linkage analysisCalvin Pan: new analyses of cond. Ka/KsAlexander Alekseyenko: Nested List

Specialty Laboratories, Inc.Alla Perlina, Beatrisa Boyadzhyan

UCLA Collaborators:Christina Kitchen, Paul Krogstad

http://www.bioinformatics.ucla.edu/HIV