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Copyright Ó 2006 by the Genetics Society of America
DOI: 10.1534/genetics.106.062885
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Site-Specific Amino Acid Frequency, Fitness and the Mutational Landscape
Model of Adaptation in Human Immunodeficiency Virus Type 1
Jack da Silva1
School of Molecular and Biomedical Science, University of Adelaide, Adelaide, SA 5005, Australia
Manuscript received July 6, 2006
Accepted for publication July 17, 2006
ABSTRACT
Analysis of the intensely studied HIV-1 gp120 V3 protein region reveals that the among-population mean
site-specific frequency of an amino acid is a measure of its relative marginal fitness. This surprising result may
arise if populations are displaced from mutation–selection equilibrium by fluctuating selection and if the
probability of fixation of a beneficial amino acid is proportional to its selection coefficient.
K
NOWING the effect on fitness of every amino acid at
every site of a protein would greatly facilitate the
study of adaptive evolution at the molecular level. Such
data would help determine the frequency distribution of
fitness effects of new beneficial mutations, which is key to
understanding the dynamics of adaptation (Orr 2002),
allow protein variation to be more easily interpreted, and
allow the realistic simulation of protein evolution. But,
such data are difficult to obtain empirically and are therefore not available for any protein. However, for human
immunodeficiency virus type 1 (HIV-1) proteins, amino
acid site-specific frequencies calculated across virus populations infecting different patients appear to correlate
with the marginal fitness effects of the amino acids
(Hung et al. 1999; Reza et al. 2003), suggesting a simple
method of estimating the site-specific marginal fitnesses
of amino acids.
HIV-1 third variable region: I investigated this correlation using sequence data from the third variable region (V3) of the HIV-1 exterior envelope glycoprotein
(gp120), located on the surface of the virus particle
(virion). V3 is the main determinant of which one of two
cell-surface chemokine receptors (CCR5 or CXCR4) is
used by a virion as a coreceptor to enter a cell, which
determines the type of cell infected (Speck et al. 1997).
V3 also modulates the use of each coreceptor (de Jong
et al. 1992; Hung et al. 1999) and thereby affects the ratelimiting step in cell entry (Platt et al. 2005). Finally, V3
is also the main target of antibodies that interfere with
cell entry (Zolla-Pazner 2004). Because of its critical
1
Address for correspondence: School of Molecular and Biomedical Science,
Molecular Life Sciences Bldg., Gate 8, Victoria Dr., University of Adelaide,
Adelaide, SA 5005, Australia. E-mail: [email protected]
Genetics 174: 1689–1694 (November 2006)
function and its exposure to neutralizing antibodies, V3
has been the focus of intense study, resulting in the data
necessary to test the correlation.
Site-specific marginal fitness: Data on V3 site-specific
fitness effects of amino acids are available from a study
that employed site-directed mutagenesis to modify the
amino acid at V3 site 25 (Hung et al. 1999). This study
measured the effects of different amino acids at site 25
on the number of cells infected (infectivity) in a standardized assay. Note that infectivity is the appropriate
measure of the effect of V3 on fitness under the assay
conditions; the sole function of V3 appears to be in cell
entry, and this component of fitness is unlikely to trade
off against the remaining components of fitness, such as
the rate of viral genome integration into the host cell
genome, the rate of provirus (integrated viral genome)
replication, and virion budding, which are controlled
by other viral proteins (Coffin 1999). The site-directed
mutagenesis study was conducted using CCR5-utilizing
HIV-1 of subtype B, the phylogenetic clade most common in Europe and North America and the most sequenced and studied.
Site-specific amino acid frequency: I calculated sitespecific frequencies of subtype B V3 amino acids for the
viral population infecting a patient and then averaged
frequencies across patients. Among-population means of
frequencies were used because the site-specific frequency
of an amino acid in any one population is expected to be
dynamic, being dependent on the population’s level of
adaptation, and thus a poor predictor of the amino acid’s
marginal fitness. This procedure was repeated for each of
the three coreceptor usage viral phenotypes: exclusively
CCR5 utilizing (R5) (269 sequences from 58 patients),
exclusively CXCR4 utilizing (X4) (109 sequences from 11
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J. da Silva
Figure 2.—Simple least-squares linear regression of scaled
virion relative infectivity on the scaled among-population
mean relative frequency of the amino acid at site 25 of subtype
B V3 from R5 virus. Data point labels are amino acid oneletter codes. The regression equation is y ¼ 0.15 1 0.84x.
Figure 1.—V3 amino acids in order of decreasing (top to
bottom) site-specific frequency for each coreceptor usage phenotype. Residues in boldface type are unique to a phenotype at
that site. Site 25, which was the target of a site-directed mutagenesis experiment, is indicated. I downloaded V3 amino acid
sequences from the HIV Sequence Database (http://hiv-web.
lanl.gov) on May 2, 2005. Since V3 varies in sequence among
subtypes (clades) of HIV-1 (Kuiken et al. 1999), I restricted
the analysis to subtype B, which is the subtype used in the sitedirected mutagenesis experiment. V3 also varies in sequence
among coreceptor usage phenotypes. Therefore, I used only
sequences from virus with known coreceptor usage, identified
in the database as using CCR5 (R5), CXCR4 (X4), or both coreceptors (R5X4). Finally, since the objective was to calculate
site-specific amino acid frequencies within patients (populations) and then average these values across patients, I considered only sequences associated with an identified patient. I
omitted from the data set sequences identified as contaminants and sequences with unidentified residues or missing either conserved terminal cysteine residue (these residues are
absolutely conserved and form a disulfide bond between
them). Subtype B V3 is most commonly 35 amino acids long.
To avoid uncertainties in sequence alignment (site homology),
I used only sequences 35 amino acids long that aligned unambiguously (without gaps) with the vast majority of other sequences in the data set.
patients), and dual coreceptor utilizing (R5X4) (60 sequences from 16 patients). The rank order of amino acid
frequencies at most sites, including site 25, varies among
coreceptor-usage phenotypes (Figure 1), as would be expected if the sites function in determining or modulating
coreceptor usage.
Site-specific fitness and frequency: I regressed relative infectivity, scaled between 0 and 1, on the amongpopulation mean relative frequency of the amino acid at
site 25, also scaled between 0 and 1. This was done only
for R5 virus because infectivity was measured for R5
virus. The regression shows a highly significant relationship (slope ¼ 0.84; d.f. ¼ 1, 5; P ¼ 6.64 3 107), with
frequency explaining 99% of the variance in infectivity
(r 2 ¼ 0.99) (Figure 2). This surprisingly strong and linear relationship demonstrates that the among-population
mean site-specific frequency of an amino acid is indeed
a very good predictor of the amino acid’s marginal
fitness.
The intercept of the regression line (0.15) is also significantly different from zero (P ¼ 1.18 3 104). Assuming that amino acids are not naturally observed at
V3 site 25 if they render V3 nonfunctional, the 15%
infectivity observed for amino acids with zero frequency
suggests that some other factor accounts for this level of
infectivity and that V3 accounts for only 85% of the
infectivity component of fitness. Since we are interested
only in the portion of fitness attributable to V3, infectivity can be scaled from the intercept to 1, giving a
one-to-one relationship between marginal relative fitness (w) and relative frequency (f ), both scaled between
0 and 1: w ¼ f. The selection coefficient of amino acid j
relative to any reference amino acid i at the same site can
then be calculated by rescaling fitness to wi ¼ 1 and calculating the absolute difference between fitnesses: sj ¼
j1 wjj. If the reference amino acid is the most common
at a site, the selection coefficient is simply sj ¼ 1 fj.
Selection coefficients: V3 site-specific amino acid selection coefficients were calculated relative to the most
common residue at each respective site for the R5 phenotype. These calculations assume no linkage among
sites, which is reasonable given the high rate of effective
recombination (between viral variants) (1.38 3 104 recombination events/adjacent nucleotide site/generation)
(Shriner et al. 2004a) relative to the mutation rate
(2.4 3 105 point mutations/nucleotide site/generation)
(Mansky and Temin 1995). Site-specific selection coefficients range from 0.180 to 0.999, with a mean of
0.923 (median ¼ 0.970; Figure 3), suggesting strong
Note
Figure 3.—Histogram of subtype B R5 V3 site-specific
amino acid selection coefficients relative to the most common
residue at each respective site. N ¼ 71.
selection. Even if a small intrapatient effective population size of Ne ¼ 103 infected cells (Achaz et al. 2004;
Shriner et al. 2004b) is assumed and the minimum selection coefficient is used, then 2Nes ¼ 360 ? 1, indicating
that selection will prevail over genetic drift.
Selection: Strong selection on V3 by coreceptors is
consistent with a lack of genetic drift in this region in
comparison to other similar-sized regions under severe
population bottlenecks in culture (Yuste et al. 2000). It
is also consistent with the convergent evolution, among
patients shortly after infection, of subtype B V3 sequences toward the R5 sequence with the most common
residue at each site (Figure 1) (Zhang et al. 1993). Given
such apparent strong selection by the coreceptor, the
high variability of V3 within and among patients suggests that equally strong forces displace sequences away
from the sequence with the highest fitness relative to the
interaction with CCR5. These forces may be migration,
in the sense of repeat infections, or selection by either
the alternative coreceptor or the immune system. Migration on its own may be excluded, since in the absence
of strong opposing selection it would have no effect (all
populations would consist of the sequence with the
highest fitness). This leaves opposing selection by the
alternative coreceptor, CXCR4, or the immune system.
Numerous studies, using a wide variety of methods of
comparative sequence analysis, have implicated coreceptors or the immune system or both as sources of positive
selection of V3 (e.g., Bonhoeffer et al. 1995; Yamaguchi
and Gojobori 1997; Nielsen and Yang 1998; Gerrish
2001; Williamson 2003; Templeton et al. 2004).
Mutation–selection balance: Mutation–selection balance cannot explain the high frequencies of less favored
amino acids. Given a genetically homogenous virus population at the time of infection (Derdeyn et al. 2004)
and the early evolution of V3 toward the R5 sequence
with the most common residue at each site (Zhang et al.
1993), and assuming no migration between patients,
amino acid polymorphism within a population infecting
a patient is assumed to arise via mutation. At mutation–
selection equilibrium, the most favored amino acid at
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each site is the most frequent, with each alternative
(deleterious) amino acid present at a mean frequency
of p ¼ m/s, where m is the rate of mutation to the
deleterious amino acid and s is its selection coefficient
relative to the most preferred amino acid (Crow and
Kimura 1970). For example, in the case of glutamic acid
(E), the second most common residue at site 25 of R5 V3
sequences (Figure 1), the mutation rate from the most
common residue, aspartic acid (D), ignoring any mutation bias, is predicted to be 1.6 3 105/codon/generation and s ¼ 0.18. This gives p ¼ 8.9 3 105, which is
much lower than the observed mean frequency of 0.35.
Episodic adaptation: The high frequencies of less
favored residues may be explained if V3 is displaced
from mutation–selection balance, either at the time of
infection, after which V3 evolves rapidly toward the R5
sequence with the most common residue at each site, or
during chronic infection when it is subject to strong opposing selection, as argued above. Although the alternative coreceptor, CXCR4, may impose strong selection
during the late stages of disease progression (Templeton
et al. 2004), the immune system is expected to periodically select escape mutants throughout the chronic stage
of infection (da Silva 2003; Wei et al. 2003; Williamson
2003; Templeton et al. 2004; Frost et al. 2005). For
example, antibodies may impose frequency-dependent
selection by targeting epitopes consisting of the most
common residues at sites, but such sites may eventually
become shielded from antibody surveillance by changes
in other protein regions (Wei et al. 2003; Frost et al.
2005). This scenario could result in the episodic adaptation of V3 to CCR5.
The mutational landscape model: Under weak selection and mutation (see Orr 2002), each step in an episode of adaptation can be described by the mutational
landscape model of Gillespie (1984, 1991). In this
model, a beneficial amino acid of fitness rank j spreads
to fixation as the next step in adaptation, when an
amino acid of fitness rank i is the current wild type at the
site, with probability
Pij ¼
Pj
;
P1 1 P2 1 1 Pi1
ð1Þ
where P is the probability of fixation and the subscripts
denote the marginal fitness ranks of the beneficial
amino acids within one mutational step of the wild type,
with 1 indicating the highest fitness and j , i. This
model assumes no recombination and considers mutations at all sites of a sequence. However, the model can
be applied to a single amino-acid site if free recombination is assumed or if it is assumed that the most
preferred amino acid is present at all other sites (i.e.,
that there is no potential for adaptation at other sites).
Since Pj 2sj for a new mutation (Haldane 1927) and
Pj 2Nsjpj for standing variation (Orr and Betancourt
2001), Pij is, in either case, proportional to sj. For example, in the case of new mutations,
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J. da Silva
Figure 4.—The probability that a beneficial amino acid of
fitness rank j will be the next to spread to fixation, given that
an amino acid of fitness rank i is the current wild type (Pij),
plotted against the amino acid’s marginal relative fitness
(wj), both scaled between 0 and 1. Pij was calculated for V3
site 25 residues, using Equation 2 (see text) with selection
coefficients calculated relative to residues K (circles), A
(squares), and Q (triangles). One-letter amino acid codes
are shown. The diagonal line is for y ¼ x.
Pij ¼
sj
:
s1 1 s2 1 1 si1
ð2Þ
Therefore, Pij is linearly related to sj and wj, and, after
scaling both variables between 0 and 1, Pij wj regardless of which amino acid is the current wild type
(Figure 4). This means that regardless of the level of
adaptation of the population, a particular beneficial
amino acid will be the next to spread to fixation with a
probability that is proportional to its marginal fitness.
If Pij is taken to be the proportion of populations fixed
for an amino acid of fitness rank j at a particular site or
the site-specific frequency of this amino acid averaged
across many populations, then this relationship may
explain why among-population mean site-specific frequencies of amino acids and their marginal relative
fitnesses, both scaled between 0 and 1, are equal.
Assumptions of the model: The mutational landscape model of adaptive evolution is based on two fundamental assumptions: that selection prevails over genetic
drift (2Nes ? 1) and that mutation is rare (Nem > 1,
where here m is the number of mutations per nucleotide
site per generation) (Orr 2002). Under these conditions, a single beneficial mutation is expected to spread
to fixation before the next beneficial mutation begins
spreading. Although the model was originally described
as assuming strong selection (Gillespie 1984, 1991),
selection in the model is strong only in relative terms,
compared to 1/Ne; in absolute terms selection is assumed to be weak: 1/Ne > s > 1 (Orr 2002). HIV-1
clearly violates the assumptions of weak selection and
mutation; V3 experiences strong selection, as shown
above, and the point mutation rate for HIV-1 is high.
Strong selection and mutation may mean that more
than one beneficial mutation spread through the population simultaneously. Such clonal interference (Gerrish
and Lenski 1998) among beneficial mutations at different amino acid sites on different genomes would
tend to reduce probabilities of fixation. However, clonal
interference is expected to be weak for HIV-1 because
the effective recombination rate is more than five times
the mutation rate and, therefore, amino acid sites can
be considered unlinked.
The question then is, Is there clonal interference
among beneficial mutations at a single amino-acid site?
The answer depends on the probability that more than
one beneficial mutation segregate at the same site. This,
of course, depends on the beneficial mutation rate,
which depends on the level of adaptation at a given site
(the wild-type amino acid at the site). I calculated the
proportion of nucleotide point mutations that produce
a beneficial amino acid change using the rank order of
fitnesses of amino acids at V3 site 25 (Figure 2). Excluding mutations at multiple codon positions, because
the frequency of these is very low (m2 and m3) compared
to the frequency of mutations at a single codon position
(m), and ignoring any mutation bias, the proportion of
nucleotide point mutations that are beneficial, averaged
among codons for each amino acid, ranges from 0.037
for arginine (R) to 0.389 for glycine (G) and is 0.182
averaged across all amino acids observed at site 25 [except aspartic acid (D), which has the highest fitness].
Then, the rate of beneficial mutations per codon is the
product of the probability of a mutation in the codon
(including synonymous mutations) and the proportion
of these mutations that are beneficial. Allowing for the
highest beneficial mutation rate at site 25, that is, with
glycine as the wild-type amino acid, the rate of beneficial mutations per codon is 3 nucleotide sites/codon 3
2.4 3 105 mutations/nucleotide site/generation 3 0.389
beneficial mutations/mutation ¼ 2.8 3 105 beneficial
mutations/codon/generation. Therefore, with a census
population size of N ¼ 107 infected cells (Chun et al.
1997) there will be a maximum total of 2.8 3 102 beneficial mutations at V3 site 25 each generation within a
population. However, the probability that a new beneficial mutation becomes fixed is proportional to Ne/N
(Kimura 1964), which for HIV-1 is 103/107 ¼ 104.
Therefore, at most 104 3 2.8 3 102 ¼ 2.8 3 102 new
beneficial mutations each generation ultimately become fixed. This is equivalent to one beneficial mutation that ultimately becomes fixed arising every 36
generations or more, on average, for the highest beneficial mutation rate at site 25. For the mean beneficial
mutation rate at site 25 (1.3 3 105), one beneficial
mutation that ultimately becomes fixed arises every 77
generations or more. To determine whether multiple
beneficial mutations will segregate at the same site, we
need to know how long it takes a single new beneficial
mutation to spread to fixation. This can be calculated
numerically from the frequency of a beneficial mutation
Note
after one generation of selection in a haploid organism
(the HIV-1 provirus is haploid): p9 ¼ p(1 1 s)/(ps 1 1),
where p is the frequency in the current generation. With
initial frequency p ¼ 1/N ¼ 107 for a new mutation, the
number of generations taken to reach a frequency of
99% ranges from 6, for mutation G / D (s ¼ 34.9), to
51, for mutation G / R (s ¼ 0.5). Therefore, in the
extreme case of the highest beneficial mutation rate and
lowest selection coefficient, we can expect some clonal
interference (on average, a new beneficial mutation
fixes every 36 generations or more and it takes such a
mutation 51 generations to spread to near fixation).
However, with the average beneficial mutation rate,
clonal interference is not expected regardless of the
magnitude of the selection coefficient (on average, a
new beneficial mutation fixes only every 77 generations
or more).
A recent study with a DNA bacteriophage system
under moderately strong selection (s ¼ 0.11–0.39) and
weak mutation is the only empirical examination of the
mutational landscape model to date (Rokyta et al.
2005). The fitnesses of nine beneficial amino acid replacements that occurred as first steps in episodes of
adaptation were measured, and the frequencies of the
replacements across 20 replicate populations were compared to expectations under the model. Modifying the
model to account for mutation bias and population
bottlenecks resulting from the experimental protocol
improved its fit to the observed distribution of amino
acid replacement frequencies. In the case of HIV-1, population size is constant during chronic infection and
mutation bias may be unimportant since selection is
strong. The empirical support from the Rokyta et al.
study suggests that the model is robust to violations of
the assumption of weak selection. Indeed, the model
requires only that fixation probabilities be proportional
to s (Rokyta et al. 2005).
Most of the arguments above assume that the source
of beneficial variants is new mutations within the population. However, variation may also be introduced by
migration in the form of multiple infections of the same
patient. Nevertheless, long-term studies of subtype B
HIV-1-infected patients have not reported evidence of
repeat infections (e.g., Shankarappa et al. 1999). Repeat
infections may be rare because sexual transmission is
the main route of infection in North America and western Europe (UNAIDS 2004), where subtype B predominates, and the probability of infection per coital act
is ,0.5% (Gray et al. 2001). And, perhaps more importantly, sexual transmission involves a severe bottleneck
of the donor viral population, possibly due to strong
selection by host target cells, resulting in typically only a
single variant transmitting successfully (Derdeyn et al.
2004). Consequently, the impact of migration on genetic variation is expected to be minor compared to that
of mutation and selection. For example, even with the
successful transmission and integration of 102 distinct
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genomes, a migration event would contribute only a
very small fraction of the 2.4 3 106 mutant genomes
generated by mutation each generation (2 days)
(Markowitz et al. 2003) in a population (for an HIV-1
genome size of 104 nucleotides). Therefore, mutation
produces several orders of magnitude more variation in
a population in a single generation than can be contributed by a rare migration event.
Another assumption made in applying the mutational
landscape model to HIV-1 is that the HIV-1 populations
studied here are true replicates. Strictly speaking, this
assumption is violated because populations differ in a
variety of ways, including differences in specific immunity (cytotoxic T-lymphocyte and antibody responses)
among patients. However, the main source of selection
of V3 of interest here is the chemokine receptor CCR5,
which is expressed intact on cells targeted by HIV-1 in
every infected individual. The intact, expressed protein
appears to exhibit little adaptive variation within humans and among higher primates with respect to HIV-1
(Zhang et al. 2003). Therefore, CCR5 represents a homogenous source of selection among patients. Indeed,
HIV-1 adapts to CCR5 shortly after infection, rapidly
evolving the V3 sequence with the most common amino
acid at each site for the CCR5-utilizing phenotype (Figure
1) (Zhang et al. 1993). Therefore, although the subtype
B HIV-1 populations analyzed here are not true replicates, they are as similar with respect to the source of
selection under study as one might expect to find in a
nonexperimental setting.
Conclusion: It will be interesting to see if the correlation between mean frequency and fitness observed
here holds more generally, which should depend on
whether fluctuating selection within populations combined with constant, strong selection across populations
is a common condition. If so, the ability to estimate sitespecific marginal fitnesses of amino acids from their
among-population mean site-specific frequencies should
open new avenues of research into the dynamics of adaptation at the molecular level.
I thank Alexei Drummond, for suggesting the interpretation of the
intercept of the regression line in Figure 2, and two anonymous
reviewers whose comments greatly improved the manuscript. I also
acknowledge the support of the Discipline of Genetics and the School
of Molecular and Biomedical Science of The University of Adelaide.
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Communicating editor: D. Begun