Computational Comparison Studies of Quadratic Assignment Like Formulations for the In Silico Sequence Selection Problem in De Novo Protein Design

In this paper an O(n²) mathematical formulation for in silico sequence selection in de novo protein design proposed by Klepeis et al. (2003, 2004), in which the number of additional variables and linear constraints scales with the square of the number of binary variables, is compared to three O(n) formulations. It is found that the O(n²) formulation is superior to the O(n) formulations on most sequence search spaces. The superiority of the O(n²) formulation is due to the reformulation linearization techniques (RLTs), since the O(n²) formulation without RLTs is found to be computationally less efficient than the O(n) formulations. In addition, new algorithmic enhancing components of RLTs with inequality constraints, triangle inequalities, and Dead-End Elimination (DEE) type preprocessing are added to the O(n²) formulation. The current best O(n²) formulation, which is the original formulation from Klepeis et al. (2003, 2004) plus DEE type preprocessing, is proposed for in silico sequence search. For a test problem with a search space of 3.4×10⁴⁵ sequences, this new improved model is able to reduce the required CPU time by 67%.