Optimization of Multistate Energies by Tree Search): A provable and efficient protein design algorithm to optimize binding affinity and specificity with respect to sequence

(Constrained Optimization of Multi-state Energies by Tree Search): A provable and efficient protein design algorithm to optimize binding affinity and specificity with respect to sequence. Section A provides a highly simplified, " toy " example of a multistate protein design calculation to demonstrate the operation of comets. Section B provides details of the methods used to compute lower bounds for LMEs over sequence spaces. Section C provides details on the protein design runs described in Section 3 of the main text. Let us introduce a highly simplified, " toy " example to explain the algorithm. Say we are designing a peptide inhibitor for a protein, " targetin, " involved in some disease. We want our peptide to not bind a related protein, " offtargetin, " because this binding would cause toxicity. However, we do have a peptide (say, a natural product) that binds both targetin and offtargetin, and we have crystal structures of this peptide with both targetin (structure T) and offtargetin (structure O). Thus, we set up a multistate design as follows. There will be four states: peptide bound to targetin (structure T), unbound peptide in targetin-binding conformation (peptide from structure T), peptide bound to offtargetin (structure O), and unbound peptide in offtargetin-binding conformation (peptide from structure O). These states will be called T-bound, T-unbound, O-bound, and O-unbound respectively. We will optimize the binding energy for the peptide-targetin interaction, which is the difference between the T-bound and T-unbound state energies. We will constrain binding energy for the peptide-offtargetin interaction to be worse than a threshold E u : say, 10 kcal/mol worse than the wild-type binding energy. We will also constrain the unbound state to be stable, by demanding that the average of the T-unbound and O-unbound state energies be at most 10 kcal/mol worse than wild type. All of these constraints, and the objective function, are simple LMEs.