Evolutionary Principles in Viral Epitopes - Mathematical Methods and Models in Biomedicine - page 57

epitopes are nine-mers (although 8-mers, 10-mers and even longer epitopes are
also observed). A cleaved nine-mer is presented on an MHC-I molecule only if
its affinity to the MHC molecule is sufficiently high. Normally, MHC-I molecules
present fragments originated from cellular proteins. After viral infection, virus-
originated peptides are presented on these molecules, enabling immune recognition
of the virus [ 6 ]. We have recently developed and improved a set of bioinformatic
tools to estimate all peptides within a virus that can be presented to the immune
system (the CTL epitope repertoire) [ 54 ].
The human leukocyte antigen (HLA) locus, the locus that encodes the MHC
molecules in human, is the most polymorphic locus in the human genome. In the
class I locus HLA-A, B and C have over 2,000 reported alleles, and their number
keeps increasing [ 47 ]. This large polymorphism permits a rapid selection of alleles
that can respond to viral threats. On the other hand, viruses can mutate rapidly. For
example, the human immunodeficiency virus (HIV) mutation rate is approximately
1.e

4 mutations per base pair per division [ 13 ], which is approximately one
mutation per division for the entire viral genome. This high mutation rate, coupled
with a short viral life cycle (24-72 h for most viruses [ 23 ]), allows viruses to modify
their epitope repertoire within a short time. We here provide multiple examples to
show how viruses have evolved to maximize their infectivity in the presence of
threat from the host.

− 3-1.e −

2 Methodology: SIR Score

We have defined the normalized epitope density of a protein or an organism as
the size of immune repertoire (SIR) score [ 24 , 28 , 32 , 35 , 38 , 54 , 55 ]. The number
of predicted CTL epitopes from a sequence was computed by applying a sliding
window of nine amino acids, and computing for each nine-mer and its two flanking
residues whether it is cleaved by the proteasome and whether it binds to the TAP
channel and to a given MHC-I allele (Fig. 1 ). The SIR score was defined as the
ratio between the computed CTL epitope density (fraction of nine-mers that were
predicted to be epitopes) and the epitope density expected within the same number
of random nine-mers. The random nine-mers were taken from a long random
peptide built, using the amino acid distribution calculated over the sequences of
all fully sequences of viruses are available, and taking into account the correlation
between the frequencies of neighbouring amino acids in these viruses [ 55 ]. An
average SIR score of less than 1 represents an under-presentation of epitopes,
whereas an average SIR score of more than 1 represents an over-presentation of
epitopes. For example, assume a hypothetical sequence of 1,008 amino acids (1,000
nine-mers) containing 15 HLA A*0201 predicted epitopes. If the average epitope
density of HLA A*0201 in a large number of random proteins with an amino acid