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9.3.1.1 The Functional Component of Fitness
The functional component of fitness was estimated from V3 amino acid mean site-
specific relative frequencies. Site-specific frequencies were calculated for the viral
population infecting a single patient and were then averaged across patients. These
mean site-specific frequencies are linearly related to the site-specific marginal fitness
effects of the amino acids, measured as relative virion infectivity, and are equivalent
to the relative marginal fitnesses of the amino acids when scaled from 0 to 1 (da
Silva 2006a). The marginal relative fitness of a particular V3 loop is simply the
product of the 35 site-specific marginal relative fitnesses of its 35 amino acid sites.
V3 amino acid site-specific frequencies were calculated from sequences associ-
ated with a patient and a chemokine coreceptor-usage phenotype in the HIV Se-
quence Database. Only sequences from subtype B, the most studied and sequenced
HIV-1 subtype, were used. Mean site-specific frequencies vary among chemokine
coreceptor-usage phenotypes (Fig. 1), as would be expected if these frequencies are
measures of site-specific marginal fitnesses with respect to the interaction between
V3 and a chemokine coreceptor. Therefore, the fitness of a particular V3 loop was
calculated from the site-specific relative fitnesses of each phenotype and the loop
was assigned the phenotype that gave the highest fitness.
To explore the effect of the strength of selection by a coreceptor on viral adapta-
tion, amino acid site-specific selection coefficients were multiplied by a scaling
constant ranging from 0 to 1. Selection coefficients were calculated by subtracting
the relative fitness of the amino acid under consideration from that of the most fre-
quent amino acid at the same site, which is assigned a relative fitness of 1. A higher
scaling constant corresponds to stronger selection.
This method of estimating fitness assumes no fitness interactions (epistasis) among
amino acids at different sites. However, the amino acids of the V3 loop are known to
co-vary between pairs of sites (Korber, Farber, Wolpert, and Lapedes 1993), indicating
epistatic interactions between sites. To take this into account, the fitness of a sequence
in which only one member of a pair of associated amino acids was present was reduced.
Fitness was reduced by a factor equal to the ratio of the expected mean frequency of a
covarying pair of amino acids (the product of their individual mean frequencies) to the
observed mean frequency of the pair (which is higher).
9.3.1.2 The Neutralization Component of Fitness
To calculate the neutralization component of fitness requires a model of the neutralizing
antibody response to HIV-1 that describes how the probability of neutralization of a
virion changes over time. In the absence of any directly applicable model, I have
made the reasonable assumptions that antibody affinity maturation increases logistially
(Rundell, DeCarlo, Hogenesch, and Doerschuk 1998) and that neutralization is
