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Komarova, Nowak, Hahn, Kwong, and Shaw 2003; Richman, Wrin, Little, and
Petropoulos 2003). However, HIV-1-specific antibodies are not detected until 20 days
after the onset of symptoms (Wei et al. 2003). Assuming that the onset of symptoms
coincides with peak viremia, about 6 weeks after infection, then HIV-1-specific anti-
bodies are not detected until approximately 2 to 3 months after infection. Antibodies
capable of neutralizing HIV-1 are detected approximately 2.5 months after peak vire-
mia, or 4 months after infection (Wei et al. 2003; Richman et al. 2003). This initial
neutralizing response is followed by a turnover of the viral population that results in
resistant virus. A new neutralizing response is then stimulated and followed by viral
turnover. The viral turnover may occur in as little as 2.5 to 3 months (Wei et al. 2003)
and the interval between neutralizing antibody responses varies between 3 and 10
months (Richman et al. 2003).
The mode of neutralization escape by the virus appears to involve amino acid
changes both within and outside epitopes. In addition to amino acid changes in the
central region of V3, other changes associated with resistance involve glycosylation
motifs within or outside V3 (Wei et al. 2003). These motifs are binding sites for
glycans that somehow interfere with antibody binding.
9.3 The Model
The basic data structure of the model represents a cell that may be infected by zero or
more proviruses, each represented by its V3 DNA sequence. A vector of such cells
represents the population of target cells in a patient. The population sizes of target cells
and proviruses are held constant for simplicity and to simulate the quasi-stable state
during the 5 or so years of the asymptomatic, chronic stage of infection in untreated
patients. Simulation flow follows the HIV replication cycle. An infected cell forms
virions by pairing its proviruses at random. The fitness of a virion, which depends on
its V3 amino acid sequences, determines its probability of escaping neutralization and
integrating its genome into that of a new host cell. In reality, a virion has many gp120
molecules on its surface, each with a V3 loop, and these molecules are potentially
translated from any of the proviruses sharing a host cell. In the model, it is assumed
that a virion possesses all of the possible V3 loops translated from the proviruses shar-
ing its host cell and that its fitness is equal to that of the V3 loop with the highest fit-
ness. The calculation of fitness from a V3 amino acid sequence is described below. A
virion infects a randomly chosen cell, which may already be infected, with a probabil-
ity equal to its fitness (scaled from 0 to 1). During the reverse transcription step, cross-
overs between the two copies of the virion's genome and mutation of the final recom-
binant DNA copy occur probabilistically at specified rates.
9.3.1 Fitness
Fitness is determined by the amino acid sequence of a V3 loop and consists of two
components. The functional component of fitness reflects a V3 loop's interaction
with chemokine coreceptors and is the probability of infection. The neutralization
component of fitness reflects a V3 loop's interaction with antibodies and is the prob-
ability of escaping neutralization. Total fitness is the product of these probabilities.
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