Information Technology Reference
In-Depth Information
appears that the infection of each cell type has different and specific consequences.
For instance, if HIV-1 does not infect dendritic cells, the only effect is a reduction of
the cytotoxic activity in recognizing new strains of the virus.
On the contrary, extending the infection to macrophages has a more striking
implication since it weakens the innate response during the first phase. Moreover, it
partially reduces the number of active antigen-presenting cells (B cells are also pre-
senting). In such a way the efficiency in stimulating the growth of helper cells and
triggering both cytotoxic activity and humoral response is impaired.
We assume that the infection of a cell is a stochastic event. There is a fixed prob-
ability that an HIV-1 infects a target cell. Once inside the target cell, the virus re-
mains silent until, with a certain probability
p
w
, it starts to transcribe its RNA ge-
nome in the host DNA. In such a way, we account for variants of the virus with a
low value of
p
w
, which may be interpreted either as strains having a poor adaptation
(those having good chances to become extinct) or as strains that are activated very
late. Newly assembled virions in productively infected cells accumulate inside the
cell at a rate given by another parameter,
p
r
. With the same rate
p
r
, a part of these
virions bud from cell membranes. Hence, if
p
r
is high, the accumulation of virions
inside the cells causes cell rupture and consequent release of viral content into extra-
cellular space. Finally, HIV-1 mutates in productively infected cells with a mutation
rate given by a third parameter,
p
m
.
The activation (
p
w
), replication (
p
r
), and mutation rate (
p
m
) are a triplet of numbers
between 0 and 1. The virus is represented by two binary strings (each l bitlong), one
corresponds to the epitope (i.e., the B-cell-receptor's binding site) and the other to the
peptide (i.e., the MHC class I and II binding site). It is possible to specify an arbitrary
number of epitopes and peptides. A string of
l
bits can assume 2
l
possible values. How-
ever, since the virus is represented by one epitope and one peptide, each viral strain is
identified by 2
l
bits. This means that for
l
equal to 12 the potential number of different
virus strains becomes equal to 16,777,216 (2
24
). Note that if
p
m
is equal to 1×10
-2
per
bit, the probability of having, at least, one mutation in a 24-bit string is 1-(1-
p
m
)
24
~
0.22, in accordance with other studies (Perelson and Nelson 1999).
Recently, we started to associate a “meaning” to parts of the bit strings in order to
specify the functional properties of the simulated virus (Castiglione, Poccia,
D'Offizi, and Bernaschi 2004). We map the genotype to the phenotype by means of
a simple formula that computes the values
p
w
,
p
r
, and
p
m
from different, non-
overlapping, zones of the binary string that describes the epitope of the virus. Since
the bit-mutation is completely random, it may flip any of the bits representing the
peptide or the epitope. In either case there is a nontrivial outcome:
(1)
if the peptide
is modified, the affinity with the (class I or II) MHC molecules changes. This corre-
sponds to the appearance of variants of the virus that might not undergo the cytotoxic
activity of CD8 cells. (2) if the epitope is modified, then one of the three values of
the triplet (
p
w
,
p
r
,
p
m
) is modified.
By looking at the results of the simulations, one can observe the population dynam-
ics of the lymphocyte cells classified according to their specificity and state (i.e., dupli-
cating, anergic, and so on), the plasma viremia and proviral HIV, the concentration of
anti-HIV antibodies produced, and the magnitude of cytotoxic response. An example
