A continuous protein synthesis formulation based on the design principles developed for structural topology optimization is proposed in this paper. Unlike conventional continuous protein design methods, the Power Law-based (PL) design formulation proposed in this paper enables using any number of residue types to accomplish the goal of protein synthesis and hence provides a continuous protein design formulation applicable to any general protein design problems. Moreover, a discrete sequence with minimum energy can be synthesized by the PL design method as it inherits the feature of material penalization used for the topology optimization. Since a continuous optimization method is implemented to solve the PL design formulation, the entire design process is more efficient and robust than the conventional design methods employing a stochastic or enumerative search process. The performance of the PL design formulation is demonstrated by designing simple lattice protein models for which an exhaustive search can be carried out to identify the sequence with minimum energy. The comparison with the exchange replica method indicates that the PL design method is millions of times more efficient than the conventional stochastic protein design method.

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