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1.0
0.8
0.6
X4
X4R5
R5
0.4
0.2
0.0
0
10
20
30
40
50
60
Generation
Fig. 4.
Changes in viral population mean fitness over viral generations in the absence of anti-
body selection for populations initialized with optimal (R5) or near-optimal (X4 and X4R5)
V3 sequences. Lines are means of 20 replicate simulations. Simulations were run with a selec-
tion coefficient scaling factor of 0.25. Other parameter values are as described in Fig. 2.
and the initial affinity (
N
0
) to 10
-3
allows a 1000-fold increase. The value for the
remaining free parameter, the intrinsic rate of increase of affinity (
r
), was set to 0.25,
which gives viral population turnovers at intervals of about 3 months. The threshold
epitope frequency in the viral population at which antibody initial production is
stimulated was set to 0.1, 0.5, and 0.9 in separate simulations.
9.4.3.1 Effect of the Stimulation Threshold
Figure 5 shows changes in the components of fitness over time starting with a viral
population of optimal R5 V3 sequences and with antibody selection. With antibody
selection, the neutralization component of fitness cycled as antibody affinity in-
creased and then new, neutralization-resistant viral variants progressively replaced
older, sensitive variants. Increasing the antibody production stimulation threshold
increased the period of the neutralization fitness cycles, but in every case the virus
escaped humoral control. Note that with each increase in the neutralization compo-
nent of fitness, which corresponds to viral escape from the circulating antibody, the
functional component of fitness decreased. This shows a clear trade-off between
fitness components: adaptation to antibody surveillance necessarily reduced adapta-
tion to the chemokine coreceptor. The final value of the functional component of
fitness in each simulation was about 0.6 (compared with an initial value of 1.0).
