A Continuous Protein Design Model Using Artificial Power Law in Topology Optimization

A continuous protein synthesis formulation based on the design principles applied to topology optimization problems is proposed in this paper. In contrast to conventional continuous protein design methods, the power law (PL) protein design formulation proposed in this paper can handle any number of residue types to accomplish the goal of protein synthesis, and hence provides a general continuous formulation for protein synthesis. Moreover, a discrete sequence with minimum energy can be determined by the PL design method as it inherits the feature of material penalization used in designing a structural topology. Since a continuous optimization method is implemented to solve the PL design formulation, the entire design process is more efficient and robust than conventional design methods employing stochastic or enumerative search methods. The performance of the proposed PL design formulation is explored by designing simple lattice protein models, for which an exhaustive search can be carried out to identify a sequence with minimum energy. We used residue probabilities as an initial guess for the design optimization to enhance the capability and efficiency of the PL design formulation. 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.