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generations, as described above (Section 9.4.2). For populations initialized with an
optimal X4 V3 sequence, the final value of the functional component of fitness was
about 0.5. Therefore, after escaping humoral control, X4 virus remained less well
adapted to its coreceptor than R5 virus was to its coreceptor (0.6). However, this
difference is considerably smaller than the difference between the maximum values
of the functional fitness components of the two phenotypes (1.0 and 0.6 for R5 and
X4, respectively).
9.5 Conclusions and Future Directions
The main obstacle to simulating selection at the molecular genetic level is a lack of
knowledge of the fitness effects of individual nucleotide and amino acid changes.
For HIV-1 V3, this obstacle is easily surmounted because, in the context of selection
by coreceptors, mean site-specific amino acid frequencies are measures of amino
acid site-specific marginal relative fitnesses (da Silva 2006a). Using this approach to
model selection by coreceptors on V3 produced plausible evolutionary dynamics.
Selection by neutralizing antibodies may be simulated for defined epitopes by as-
suming a plausible model of affinity maturation. Affinity maturation was modeled as
a logistic increase in affinity. This aspect of the model could be made more realistic
by incorporating knowledge of the actual dynamics of affinity maturation for specific
antibodies. Inclusion of changes to antibody titer may also add to the realism. This
could be accomplished by assuming logistic growth of antibody numbers, scaled
from zero to one, and using the product of the antibody titer and affinity maturation
as a measure of neutralization capacity. A more difficult problem in simulating the
neutralizing antibody response to HIV-1 may be the definition of conformational
epitopes. The current model uses linear V3 epitopes of monoclonal antibodies known
to neutralize primary isolates. However, it is apparent that the most potent neutraliza-
tion
in vivo
is by antibodies with conformational V3 epitopes (Gorny et al. 2002).
Unfortunately, these epitopes have yet to be described.
With the current model, a maximum of four consecutive antibody responses to
newly emerged (or initialized) viral variants were each followed by viral escape
before the final escape from humoral control. A cyclical pattern of antibody
response and viral escape and final loss of humoral control is also observed in
patients (Wei et al. 2003; Richman et al. 2003). In the model, this occurred regard-
less of the stimulation threshold for initial antibody production, the strength of
coreceptor selection, or the coreceptor utilization phenotype of the virus. The other
consistent result is a decrease in V3 function associated with escape from neutrali-
zation. This decrease in function corresponds to a decrease in viral infectivity.
Such a pattern has not been reported from either
in vivo
or
ex vivo
studies of HIV.
However, this predicted trade-off between fitness components might help explain
the relatively low viral population size during the nonsymptomatic, chronic phase
of infection (Coffin 1999). As was expected, the decrease in V3 function was
greater with stronger coreceptor selection. Of more interest, however, is that after
escape from humoral control, the fitness difference between R5 and X4 virus was
diminished from about 60% to about 20%. This predicted reduction in the difference
