Algorithms for the design of maximum hydropathic complementarity molecules

In this article, we address the problem of designing a string with optimal complementarity properties with respect to another given string according to a given criterion. The motivation comes from a drug design application, in which the complementarity between two sequences (proteins) is measured according to the values of the hydropathic coefficients associated with the sequence elements (amino acids). We present heuristic and exact optimization algorithms, and we report on some computational experiments on amino peptides taken from Semaphorin and human Interleukin-1β, which have already been investigated in the literature using heuristic algorithms. With our techniques, we proved the optimality of a known solution for Semaphorin-3A, and we discovered several other optimal and near-optimal solutions in a short computing time; we also found in fractions of a second an optimal solution for human interleukin-1β, whose complementary value is one order of magnitude better than previously known ones. The source code of a prototype C++ implementation of our algorithms is freely available for noncommercial use on the web. As a main result, we showed that in this context mathematical programming methods are more successful than heuristics, such as simulated annealing. Our algorithm unfolds its potential, especially when different measures could be used for scoring peptides, and is able to provide not only a single optimal solution, but a ranking of provable good ones; this ranking can then be used by biologists as a starting basis for further refinements, simulations, or in vitro experiments.