Evolutionary Principles in Viral Epitopes - Mathematical Methods and Models in Biomedicine - page 59

3R su s

3.1 Human Versus Viral Epitope Density

In order to check if the MHC allele distribution has evolved to maximize the
presentation of viral epitopes, we measured the epitope density of human and viral
proteins and compared them in the same allele [ 5 ].
Systematically, viral proteins express more epitopes than their human counterpart
over the vast majority of alleles (Fig. 2 empty bars) ( p

7). The most natural
mechanism for such a selection is that HLA alleles, binding residues that are over-
represented in viral sequences are preferred. In order to test this hypothesis, we
produced two random sequences with different amino acid distributions. We trained
two distinct Markov models on all human and all viral proteins, respectively, and
produced very long random sequences (1.e6 amino acids) based on these models.
We then compared the epitope densities of these two random sequences in each
HLA allele (Fig. 2 ). The ratio between the epitope density of the random sequence
based on viral amino acids and the random sequence based on human amino acid
is even larger than the ratio between the real viral and human protein epitope
densities (Fig. 2 )( p

< 1 . e −

02 T test on the ratio between epitopes from the viral and
human Markov models, compared with the ratio between computed epitopes from
the viral and human real protein sequences). The difference between the Markov
models shows that the human MHC system is evolving to recognize the viral
amino acid distribution. The smaller difference between human and viral epitope

< 0 .

0.5

Real Epitotopes
Markov Model Epitopes

0.4

0.3

0.2

0.1

0

-0.1

-0.2

0 5 10 15 20 25 30

Allele Number

Fig. 2 Comparison of epitope density in human and viral proteins. The white bars represent the
ratio between the relative change between the viral and human epitope densities [i.e., (viral epitope
density/human epitope density) 1]. All positive values represent a higher viral epitope density.

The black bars represent the same comparison performed on a random sequence based on human
and viral amino acid distributions

−