Graph-theoretical formulation of the generalized epitope-based vaccine design problem
Fig 2
The graph encoding of the vaccine design problem.
Vertices represent epitopes and edge weights are design-dependent. By jointly modeling the epitope selection and vaccine assembly problem, we seek n subsets of vertices (n = 3 in the figure), each representing a separate polypeptide (blue, yellow and red in the figure), with the highest immunogenicity, whose simple tours start from and end in a placeholder node s, and are shorter than given limits in terms of the number of vertices k and edge-weight sum h. (a) The edge weights are simply ignored for epitope mixtures. (b) For string-of-beads, the edge weights represent the negative log-likelihood of being cleaved at the junction site of the two connecting epitopes, so that low total edge weight is achieved by selecting epitopes that are likely to be separated correctly upon proteasomal cleavage. (c) The weights in mosaic designs represent the added length to the mosaic vaccine once the two connecting epitopes are joined with maximum overlap, so that low total edge weight results in shorter polypeptides.