Optimal strategy for stabilizing protein folding intermediates

To manipulate the protein concentration at a certain functional state through chemical stabilizers is crucial for protein-related studies. It not only plays a key role in protein structure analysis and protein folding kinetics, but also affects protein functionality to a large extent and thus has wide applications in medicine, food industry, etc. However, due to concerns about side effects or financial costs of stabilizers, identifying optimal strategies for enhancing protein stability with a minimal amount of stabilizers is of great importance. Here, we prove that either for the fixed terminal time (including both finite and infinite cases) or for the free one, the optimal control strategy for stabilizing the folding intermediates with a linear strategy for stabilizer addition belongs to the class of bang-bang controls. The corresponding optimal switching time is derived analytically, whose phase diagram with respect to several key parameters is explored in detail. The bang-bang control will be broken when nonlinear strategies for stabilizer addition are adopted. Moreover, the above theory is applied to the stabilization of erythropoietin by ten different kinds of chemicals, providing theoretical guidance for the selection and rational usage of stabilizers. Our current study on optimal strategies for protein stabilizers not only offers deep insights into the general picture of protein folding kinetics but also provides valuable theoretical guidance on treatments for protein-related diseases in medicine.