Mapping Evolutionary Pathways of HIV-1 Drug Resistance. Christopher Lee, UCLA Dept. of Chemistry & Biochemistry

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1 Mapping Evolutionary Pathways of HIV-1 Drug Resistance Christopher Lee, UCLA Dept. of Chemistry & Biochemistry

2 Stalemate: We React to them, They React to Us E.g. a virus attacks us, so we develop a drug, so the virus evolves drug resistance mutations Each step is a reaction to a past attack, based on limited, local information, without considering how the enemy will respond to our actions in the future. What if we had a global picture of HIV s possible evolutionary responses?

3 Rapid Evolution of Drug Resistance in the Global AIDS Epidemic 40 million cases, doubling every 10 years. 60% of patients fail first-line treatment, due to drug resistance; complex multi-drug therapies (HAART) are required. After introduction of a new drug, resistant HIV strains appear within weeks. Worldwide at least new mutations per day.

4 HIV-1 Protease and RT: anti-retroviral drug targets protease RT Protease: responsible for the posttranslational processing of the viral polyproteins to yield the structural proteins and enzymes of the virus Reverse transcriptase (RT): responsible for DNA polymerization

5 Identifying Causes of Drug Resistance It is critical to identify mutations that cause drug resistance, and through enormous efforts worldwide researchers have identified 23 mutation positions in protease and 34 in RT that cause drug resistance. Guides new drug design. Guides drug therapy of each patient: choose a cocktail that will work, avoid useless treatment! Better, more automated ways to do this?

6 Automated Mutation Analysis Previously developed Bayesian method for measuring evidence for mutations (single nucleotide polymorphisms) from chromatogram data, considering peak height, separation, contextsensitive sequencing error rates, uncertainty in alignment, uncertainty in allele frequency, etc. Completely automated. Irizarry et al., Nature Genet. 26, 233 (2000) Hu et al., Pharmacogenomics J., 2, 236 (2002)

7 HIV Has Peformed a Saturating Mutagenesis Experiment for Us 2.3 million high-confidence mutations were detected, from 50,634 AIDS patient samples mutations per kb (compared with ~1 per kb in human). Detected 5.5 out of 9 possible SNP per codon, throughout protease+rt. Each mutation detected an average of 364 times.

8 II. Selection Pressure Mapping: Build an Atlas of HIV Evolution Selection pressure measures whether a given mutation is selected for or against by natural selection. We extended the well-known metric Ka/Ks from whole gene to individual amino acid mutations. Requires a truly massive dataset and good statistics for measuring confidence. Goal: construct a selection pressure map of how HIV is evolving, where the virus is going, to evade our drugs.

9 Use HIV Evolution to Identify Natural Selection for Amino Acid Mutants Negative selection: amino acid changes reduce fitness, and are less frequent than expected. This is the normal situation for a stable gene. Positive selection: amino acid changes improve fitness, and are more frequent than expected. Very uncommon; indicates evolutionary change. Ka / Ks: standard metric for positive selection (Ka / Ks > 1), measured for a gene. Li, W.H. J.Mol.Evol. 36, 96 (1993)

10 Calculating Ka / Ks per Residue v v s t t s v v a t t a s a s a f n f n f n f n N N K K,,,, + + = observed #amino acid changes vs. synonymous mutations at this codon expected #amino acid changes vs. synonymous mutations at this codon ( ) i N i N N i s a a q q i N K K q N N i p LOD a! =! " # $ % & ' =! = (! = ) 1 log 1),, ( log Confidence that Ka/Ks>1 is statistically significant: log-odds score LOD 2 means 99% confidence, LOD 3 means 99.9% confidence.

11 Selection Pressure for Individual Mutations at Each Codon Selection pressure of a specific amino acid substitution (o m) at a specific codon: K a /K s = ( N m N s ) /( n m,t f t + n m,v f v n s,t f t + n s,v f v ) N m #samples with o m mutations at this codon N s #samples with a synonymous mutation at this codon f t transition frequency (a g, t c) in HIV-1 f v transversion frequency (a, g t, c) in HIV-1 n m,t, n m,v #expected transition or transversion o m mutations at this codon n s,t, n s,v #expected transition or transversion synonymous mutations at this codon

12 (b) Selection Pressure for HIV-1 Protease Chen et al., J. Virol. 78, 3722 (2004) Ka/Ks Codon Position Positive selection mapping automatically discovers causes of drug resistance!

13 Selection Pressure Varies Among Different Amino Acid Mutations at One Codon Whole Codon Position Ka/Ks LOD Individual Amino Acid Mutation Mutation K20T K20M K20R K20Q K20N I47V I47R I47T I47M I85V I85L I85S Ka/Ks LOD >300 > K20T, I47V, I85V: known associated with drug resistance

14 Positive Selection of Drug Resistance Associated Codons There are 22 codon positions in protease known to be associated with drug resistance of them are predicted by positive selection. 28 P-value of this match by random chance is

15 Positive Selection of Mutations Associated with Drug Treatment Wu et al. identified 45 protease codons associated with drug treatment, by comparing mutation frequency in treated vs. untreated patients. J. Virology 77, 4836 (2003) of them are predicted by positive selection. 13 P-value of this match is

16 Our Positive Selection Results Match Experimental Phenotypic Fitness Data Loeb et al. constructed ~50% of all possible point mutants of HIV-1 subtype B protease and assayed their biochemical activity. Nature 340, 397 (1989) All mutations tested Positive selected mutations active intermediate inactive P-value of this match is

17 Positive Selection Mapping Identifies Protease Drug Resistance Mutations Correctly identified 19 of 22 known drug resistance mutation positions. Compared with multi-year research process (clinical, biochemical, genetics) that was previously required, this analysis is completely automatic; works directly on output from sequencing machines.

18 III. Build a Reaction Rate Diagram of HIV s Global Evolution A network diagram of the rates of transition between all possible genotypes. Shows the speeds of all possible paths of evolution the viral population will follow, under the pressure of current drug treatments.

19 Selection Pressure is like an Evolutionary Velocity For wildtype, synonymous mutant, and amino acid mutant allele frequencies f o =1, f s =0, f a =0 initially, equal amino acid and synonymous mutation frequency λ, and reproduction rates r o, r a, after one unit of time f o " r o f o 1# 2$ ( ); f s " r o $f o ; f a " r a $f o Assuming λ<<1, Ka/Ks and the normalized f a will be: K a K s = f a f s = r a r o ;"f a = f a f o + f s + f a # $ r a r o So initially the rate of change of the amino acid mutant allele frequency df a /dt is proportional to the selection pressure Ka/Ks.

20 What does Ka/Ks really calculate? WT Ka/Ks calculates selection pressure for mutation X, assuming wildtype (WT) as the starting genotype. So we should write Ka/Ks as being conditioned on WT as the starting point: ( = K a / K s ) X ( Ka / K s ) X WT WT Wildtype protein sequence 30 A single mutant at codon 30 Ka/Ks graph gives rates of flow of HIV population to different mutations.

21 Ka/Ks Ignores Interactions Because different sites interact, the effect of an amino acid mutation at one site can depend on the amino acid at other sites. But Ka/Ks does not consider these interactions; in effect, it assumes that all mutations take place in the wildtype sequence as a completely fixed background.

22 Conditional Ka/Ks Reveals Complete Mutation Network WT We can generalize Ka/Ks to measure the selection pressure for a mutation Y conditioned on the presence of a previous mutation X. We define this as the conditional Ka/Ks: ( K a / Ks) Y X Each edge represents one conditional Ka/Ks value.

23 Conditional Selection Pressure N YaXa : N YsXa : " $ # K a K s % ' & Y Xa = N YaXa /N YsXa n Ya /n Ys #samples with amino acid mutations at Y and X #samples with synonymous mutation at Y and amino acid mutation at X Calculates Ka/Ks at codon Y when an amino acid mutation is present at codon X. Calculate expected neutral ratio, and LOD score for Ka/Ks>1 as before.

24 Conditional Selection Ratio " $ # K a K s % ' & Y X = " $ # " $ # K a K s K a K s % ' & Y Xa % ' & Y Xo Calculate P-value for (Ka/Ks) Y X > 1 via onesided Fisher Exact Test using 2x2 contingency table [(N YaXa, N YsXa ), (N YaXo, N YsXo )]

25 Conditional Selection in Protease Change of Ka/Ks value after conditioning: Specialty (Ka/Ks)_Y Xa (Ka/Ks)_Y Xo 30 Ka/Ks Codon position

26 How can we distinguish Selection Pressure from Linkage Disequilibrium? Statistical correlations between mutations could reflect functional selection, or linkage disequilibrium between mutations. Ordinarily, no easy way to distinguish these two models, because they reflect different assumptions.

27 Co-occurrence of mutations may just reflect their evolutionary history When mutations occur infrequently during evolution, they will initially be strongly linked to pre-existing mutations on that branch (e.g. AR) A R W AR AR S SW SI S S I Two forces weaken linkage: high mutation rate (if the same mutation occurs many times independently during evolution); high recombination rate ( shuffles the deck )

28 How to distinguish linkage from selection? One possible solution would be to reconstruct the phylogenetic tree of all the sample sequences A S R I W AR AR S SW SI S Computationally difficult: 1000s of sequences? Tree methods fail for high levels of recombination or mutation; also fail in presence of selection pressure (convergent evolution)

29 Incompatible Assumptions Phylogeny methods: assume little or no recombination, low levels of mutation, neutral or weak selection Ka/Ks: assume multiple independent mutation events, star topology (no common ancestry except root); high recombination helps. HIV: high mutation, recombination.

30 Phylip Neighbor-joining Tree for Specialty HIV 2002 Data (2500 seqs) Fits star topology

31 Separate Linkage from Selection using Synonymous Mutations Synonymous mutations should not be under amino acid selection, so they should give a direct readout of pure linkage. So, compare pairwise correlations of amino acid mutations (A) and synonymous mutations (S): Compare AA vs. AS, SS

32 Dramatically different levels of linkage (r) for AA vs AS, SS AA AS SS

33 Drug Treatment is the source of AA Correlation Stanford Treated AA Stanford Untreated AA AS SS AS SS

34 Mutation Associations (Protease, AA) 5 A 1 1 A

35 Direct Evidence of Selection Pressure Interactions From the point of view of linkage, there is no difference between a SNP that is synonymous vs. nonsynonymous. The only difference is at the level of amino acid selection pressure. The difference between AA and AS/SS must be selection pressure.

36 Conditional Selection Ratio " $ # K a K s % ' & Y X = " $ # " $ # K a K s K a K s % ' & Y Xa % ' & Y Xo Calculate P-value for (Ka/Ks) Y X > 1 via onesided Fisher Exact Test using 2x2 contingency table [(N YaXa, N YsXa ), (N YaXo, N YsXo )]

37 Strong Evidence for Conditional Selection Pressure Much of the selection pressure in HIV protease is actually conditional! These effects are not symmetric: (Ka/Ks) Y X (Ka/Ks) X Y 228 codon pairs meet our criteria for positive conditional selection pressure: (Ka/Ks) Y Xa > 1 and (Ka/Ks) Y X > 1 LOD>3 and p<10-3 (Fisher Exact Test)

38 Comparison with Correlated Mutation Data Wu et al identified 92 codon pairs that displayed correlated mutations in treated vs. untreated patients. At the same LOD cutoff, conditional Ka/Ks identified 87 of these codon pairs as having a positive selection ratio (p-value = ). NB: these were predicted from sequence data with no drug treatment information at all.

39 Building a Reaction Rate Diagram of HIV s Global Evolution Conditional Ka/Ks network shows rates of transition between all possible genotypes, represented as directed graph of nodes (individual mutations) and edges (production rate of mutation Y given mutation X). Shows the speeds of all possible evolutionary pathways the viral population will follow, under the selection pressure of current drug treatments.

40 Fast Mutation Paths of HIV Protease

41 Different Paths to the Same Genotype can Differ in Speed Chen & Lee, Biology Direct (2006) WT WT / /88 90 and 30 are mutations known to directly cause drug resistance; 10, and 88 are secondary mutations that stabilize the mutant protein. Our analysis distinguishes them: faster path first introduces the drug resistance mutation, then the stabilizing mutation. NB: speed of a multistep path is generally controlled by its slowest step.

42 Danger: Fast Paths to Multi-Drug Resistance Multiple resistance: the combination of three mutations (at codons 82 (V82A/T/S), 84 (I84V), and 90 (L90M)) is resistant to most available protease inhibitors Rapid evolution of this triple mutant is a serious threat to individual treatment and to control of the global AIDS epidemic. Our map shows where the fast paths to this combination are. Don t want to go there!

43 Reveals Accelerated Paths to Multi-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: WT Use the order in which drugs are given (which in turn can select for one mutation over another) to pick a slower path!

44 Kinetic Traps that Slow Evolution Kinetic Trap: Many accelerated paths to mutations at 41, but no fast paths to drug resistant mutations from there

45 A Database for Positive Selection Mapping of HIV Pan et al. Nucleic Acids Res. 35: D371-D375 (2007)

46 How Meaningful Are These Results? One obvious question is how much of these results is noise (sampling error, bias, etc.) as opposed to signal (real drug-resistance and viral fitness effects). To answer this, we have sought to apply this method to completely independent datasets, to test whether our results are reproducible.

47 Multiple Independent Datasets Specialty: 50,634 samples representing a mix of treated and untreated patient samples from the U.S. Treated: 1,797 samples collected by Stanford University from patients with specific drug treatments Untreated: 2,628 samples collected by Stanford University specifically from untreated patients Africa: 399 African HIV-1 subtype C samples downloaded from Los Alamos HIV Sequence Database

48 Totally independent datasets give reproducible results

49 Reproducible Results Of 24 positively selected positions in the Treated dataset, 23 were also positively selected in the Specialty dataset (p= ). This reproducibility even extended to the much smaller untreated datasets. Of nine positively selected positions in the African dataset, seven were also positively selected in the Untreated dataset (p= ). NB: different subtypes! Simulated dataset: no positive selection detected

50 Reproducible Ka/Ks Values Ka/Ks analysis: Specialty vs. Treated Treated Primary drug resistance Accessory drug resistance Function unknown Specialty Chen & Lee, Biology Direct 1: 14 (2006)

51 Specialty vs. Treated Datasets The Ka/Ks values are remarkably consistent, considering that the input data were collected from different sets of patients, with different drug treatment regimens, during different time periods, by different investigators; the Specialty dataset has no drug treatment information, and indeed contains a large mixture of patients who received no drug treatment at all; the Treated dataset contains only about 1/30 th the number of samples.

52 Challenge: Conditional Ka/Ks Reproducibility Whereas unconditional Ka/Ks uses the whole dataset to calculate amino acid selection pressure, conditional (Ka/Ks) Y Xa restricts the analysis to the small subset of samples with an amino acid mutation at codon X (e.g. 100x less). Can this analysis work for a dataset as small as the Treated data (1797 samples)?

53 Reproducible Conditional Ka/Ks Results Specialty Treated Untreated WT WT WT / / /90 These data suggest that the results are not sampling artifacts, and represent real patterns of drug-associated selection pressure within the HIV population in the wild!

54 Reproducible Results Conditional Ka/Ks: Specialty vs. Treated Primary drug resistance Accessory drug resistance 25 Function unknown Treated Specialty For codons with sufficient counts (N Xa >400), the results match the Specialty results surprisingly well. Chen & Lee, Biology Direct 1: 14 (2006)

55 Experiment: Which Mutation Happened First in Patients? (Shafer, Stanford) Take multiple samples at different time points during each patient s treatment. Identified pairs of mutations that cooccur, then re-examined previous samples to see which mutation occurred first.

56 Different Paths to the Same Genotype Can Differ in Speed WT D N 57 30N/88D Slow step is the first step of each path: 30N path is about six-fold faster..

57 88D / 30N Comparison with Longitudinal Studies WT D N 57 30N/88D v(pathx) : v(pathy) = 1.05: 0.16 = 6.6 PathX 30N->30N88D 13 patients PathY 88D->30N88D 2 patients Longitudinal Data n(pathx): n(pathy) =13: 2

58 Different Paths to the Same Genotype Can Differ in Speed WT M S >300 73S/90M 90M mutations known to directly cause drug resistance but reduce protein stability; 73S mutations stabilize the mutant protein. Our analysis distinguishes them: faster path first introduces the drug resistance mutation, then the stabilizing mutation.

59 90M / 73S Comparison with Longitudinal Studies WT M S >300 73S/90M v(pathx) : v(pathy) = 0.37: 21 Longitudinal Data PathX 30N->30N88D 3 patients PathY 88D->30N88D 31 patients n(pathx): n(pathy) =3: 31

60 Shafer Longitudinal Results For 23 mutation pairs with a preferred path predicted by our conditional Ka/Ks data (p=0.01), 20 match the preferred kinetic pathway observed in Shafer s longitudinal patient studies. Statistically significant match, p=0.0002