The sequence of 20 types of amino acid residues in a heteropolymer chain of a protein is believed to be the basis for the 3-D conformation (folded structure) that a protein assumes to serve its functions. We present a deterministic optimization method to design the sequence of a simplified model of proteins for a desired conformation. A design methodology developed for the topology optimization of compliant mechanisms is adapted here by converting the discrete combinatorial problem of protein sequence design to a continuous optimization problem. It builds upon our recent work which used a minimum energy criterion on a deterministic approach to protein design using continuous models. This paper focuses on the energy gap criterion, which is argued to be one of the most important characteristics determining the stable folding of a protein chain. The concepts, methodology, and illustrative examples are presented using HP models of proteins where only two types (H: hydrophobic and P: polar) of monomers are considered instead of 20. The highlight of the method presented in this paper is the drastic reduction in computational costs.

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