HOGVAX: Exploiting epitope overlaps to maximize population coverage in vaccine design with application to SARS-CoV-2.

The efficacy of epitope vaccines depends on the included epitopes as well as the probability that the selected epitopes are presented by the major histocompatibility complex (MHC) proteins of a vaccinated individual. Designing vaccines that effectively immunize a high proportion of the population is challenging because of high MHC polymorphism, diverging MHC-peptide binding affinities, and physical constraints on epitope vaccine constructs. Here, we present HOGVAX, a combinatorial optimization approach for epitope vaccine design. To optimize population coverage within the constraint of limited vaccine construct space, HOGVAX employs a hierarchical overlap graph (HOG) to identify and exploit overlaps between selected peptides and explicitly models the structure of linkage disequilibrium in the MHC. In a SARS-CoV-2 case study, we demonstrate that HOGVAX-designed vaccines contain substantially more epitopes than vaccines built from concatenated peptides and predict vaccine efficacy in over 98% of the population with high numbers of presented peptides in vaccinated individuals.

Genome Rearrangements on Multigenomic Models: Applications of Graph Convexity Problems.

Genome rearrangements are events where large blocks of DNA exchange pieces during evolution. The analysis of such events is a tool for understanding evolutionary genomics, in whose context many rearrangement distances have been proposed, based on finding the minimum number of rearrangements to transform one genome into another, using some predefined operation. However, when more than two genomes are considered, we have new challenging problems. Studying such problems from a combinatorial point of view has been shown to be a useful tool to approach such problems, for example, the reconstruction of phylogenetic trees. We focus on genome rearrangement problems related to graph convexity. Such an approach is in connection with some other well-known studies on multigenomic models, for example, those based on the median and on the closest string. We propose an association between graph convexities and genome rearrangements in such a way that graph convexity problems deal with input sets of vertices and try to answer questions concerning the closure of such inputs. The concept of closure is useful for studies on genome rearrangement by suggesting mechanisms to reduce the genomic search space. Regarding the computational complexity, and considering the Hamming distance on strings, we solve the following problems: decide if a given set is convex; compute the interval and the convex hull of a given set; and determine the convexity number, interval number, and hull number of a Hamming graph. All such problems are solved for three types of convexities: geodetic, monophonic, and P3. Considering the Cayley distance on permutations, we solve the convexity number and interval determination problems for the geodetic convexity.

Reduced-Size Integer Linear Programming Models for String Selection Problems: Application to the Farthest String Problem.

We present integer programming models for some variants of the farthest string problem. The number of variables and constraints is substantially less than that of the integer linear programming models known in the literature. Moreover, the solution of the linear programming-relaxation contains only a small proportion of noninteger values, which considerably simplifies the rounding process. Numerical tests have shown excellent results, especially when a small set of long sequences is given.