New Approaches to in silico Design of Epitope-Based Vaccines

68 CHAPTER 6. EPITOPE ASSEMBLY
Ginodi et al. [119], for example, is based on a linear scoring function S with
n−1
S(P ) = S1(fN) + S2(p1) + S3(pi) + S4(pn) + S5(fC) (6.1)
i=2
where P = p1 . . . pn is a peptide fragment with N-terminally flanking residue fN and
C-terminally flanking residue fC. The function’s linearity allows for a simple rearrangement,
S ′ , such that considering epitope tuples is sufficient to determine the summed cleavage
scores for a set of peptides in a string-of-beads construct. For nonameric peptides
P 1 , P 2 , . . . , P k arranged in a polypeptide P 1 − P 2 − . . . − P k it is
with
and
k
S(P i k+1
) =
i=1
i=1
S ′ (P i−1 − P i ) (6.2)
S ′ (P i−1 − P i ) = Ssuf(P i−1 ) + Spre(P i ) (6.3)
Spre(P ) = S1(fN) + S2(p1) +
Ssuf(P ) =
5
S3(pi) (6.4)
i=2
8
S3(pi) + S4(p9) + S5(fC) (6.5)
i=6
where P 0 and P k+1 correspond to the dummy epitope ε = ɛ1ɛ2 . . . ɛ9 and Si(ɛj) = 0 for
i = 1, . . . , 5 and j = 1, . . . , 9. Incorporation of the cleaved fragment predictor proposed
by Ginodi et al. can thus be achieved by assigning the negative of the score S ′ to the
respective edges. A drawback of employing S ′ instead of S is that it does not provide us
with cleavage probabilities for the individual vaccine epitopes: Epitope orders that would
render a vaccine epitope unlikely to be cleaved cannot be detected during construction
of the graph. Hence, specific exclusion of such orders is not possible. Penalization of
epitope orders yielding good cleavage scores for unintended junctional peptides, however,
is possible to a certain extent. This can be achieved by incorporating (a fraction of) the
cleavage scores of junctional peptides into the corresponding edge weight.
6.4 Experimental Results
6.4.1 Efficiency
The complexity of the TSP and thus of the epitope ordering problem raises the question of
whether an optimal epitope order can be found in reasonable time for real world problems.
We employ the ILP solver CPLEX [53] as well as a highly effective implementation of the
LKH (LKH, version 2.0.5) [114] to solve the epitope ordering problem for different-sized
epitope sets.