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In the model, initial production of an antibody is stimulated by the presence of its
epitope in the viral population at a frequency above a specified threshold. This fre-
quency threshold determines the narrowness of the antibody response. For example,
a high threshold frequency of 0.9 corresponds to a narrow response. Once an anti-
body's initial production is stimulated, the presence of its epitope at any frequency is
sufficient to increase its maturity (
t
in Eq. (1)). If the individual frequencies of epi-
topes for two or more antibodies exceed the stimulation threshold in the same viral
generation, then only one antibody, chosen at random, has its initial production
stimulated. If a V3 sequence carries the epitope for an antibody whose production
has been stimulated, then none of the epitopes from that sequence are available to
stimulate the initial production of any other antibody.
9.4 Simulations
9.4.1 The Simulation Environment
The simulation program was written in FORTRAN 90 and parallelized using the
Message Passing Interface library. Random numbers were generated using the Scal-
able Parallel Random Number Generators Library (SPRNG). Simulation replicates
were run in parallel on an IBM eServer 1350 Linux cluster. Details of the simulation
methods used are given in da Silva (2006b).
9.4.2 Adaptation to Coreceptors
Initial simulations were carried out to demonstrate viral adaptation to chemokine
coreceptors. To study adaptation to CCR5, the viral population was initialized with a
suboptimal R5 V3 sequence and allowed to evolve over several hundred viral gen-
erations in the absence of antibody selection. Figure 2 shows the increase in popula-
tion mean fitness, determined entirely by the functional component of fitness, for
various selection coefficient scaling constants. Fitness increased as the suboptimal
sequence evolved toward the optimal sequence for the phenotype, that is, as the viral
population adapted to the CCR5 chemokine coreceptor.
Figure 3 compares simulated V3 sequences at the end of one simulation replicate
with the suboptimal R5 V3 sequence of the initial population and the optimal R5
sequence. The initial sequence differed from the optimal sequence at three sites, and
the simulated sequences evolved to match the optimal sequence at two of these sites.
At the third, unmatched, site the difference between the initial and optimal sequences
involved amino acids with nearly identical site-specific frequencies, thereby impos-
ing only weak selection for amino acid replacement.
