The tradition in design of relying upon pairwise-decomposable energy functions limits the kind of biochemical understanding that can be incorporated into the design process. If, as I suggested in Chapter 1, protein design takes its scientific worth from its insis-
Figure 3.1: A TIM Barrel Protein.PDB ID: 1TIM. The core of the TIM barrel is com- posed of eight parallelβ-strands, forming a cylindricalβ-sheet. Because the sheet wraps around on itself, it does not leave any backbone hydrogen bonding groups unsatisfied and exposed to solvent to form unwanted aggregates. A helical region connects each
β strand to the next. The middle view is through the center of the barrel with theβ- strands coming out of the page and theα-helical connections between the strands going into the page. TIM barrels appear frequently; often in enzyme proteins. One of the de- sign goals in the ongoing Protein Design Project is the redesign of a TIM barrel protein to perform novel catalytic activity. Images created with Mage and Render3D (Merritt and Bacon, 1997).
tence that designers explicitly state and test the current biochemical understanding of protein energetics, then the requirement that energy functions be pairwise decom- posable detracts from design’s worth. Current biochemical understanding of protein stability cannot be expressed in a pairwise decomposable fashion. The rule (Fleming and Rose, 2005) that “buried hydrogen bonding groups form intra-molecular hydrogen bonds” cannot be captured as a sum of pair interactions.
For the most part, protein designers have avoided the problems associated with satisfying buried hydrogen bonding groups by packing cores with hydrophobic groups alone. If there are no buried hydrogen bonding groups, then none end up unsatisfied. There are two ways to prevent hydrogen bonding groups from ending up in protein cores: explicitly forbid them by only considering hydrophobic amino acids for buried residues (Dahiyat and Mayo, 1997b), or implicitly forbid hydrophilics from the core by including a solvation model (e.g. the Lazaridis-Karplus solvation model [1999]) that penalizes the approach of any atom towards a hydrophilic group (Kuhlman et al., 2002; Kuhlman et al., 2003) and thereby penalizes the presence of a hydrophilic group in the core. However, some design instances require burial of hydrogen bonding groups: for instance in enzyme design, the ligand that needs to be buried inside the enzyme’s active site will likely contain hydrogen bonding groups. If a ligand’s buried hydroxyl group is not satisfied by a hydrogen bond to the protein, the stability of the enzyme/ligand complex will be lower, diminishing the effectiveness of the enzyme.
There are two key exceptions to the observation that designers prohibit hydrophilic amino acids from the core, and they both are involved in ensuring hydrogen bond sat- isfaction for buried ligands (Looger et al., 2003; Dwyer et al., 2004). In both of these cases, the designers filtered the designed structures that resulted from the optimiza- tion of a pairwise decomposable energy function in a post-processing step. The filters examined, among other things, the number of buried unsatisfied hydrogen bonding groups. They discarded designs that contained several unsatisfied hydrogen bonding groups. The problem with this approach, as demonstrated in Chapter 8, is that opti- mizing according to one function and filtering according to a second function produces sub-optimal designs.
The effect of solvent on a protein’s stability is non-pairwise decomposable for a second reason. If solvation free energy is understood in Dill’s framework as hydrophobic groups ordering water around them so that the waters’ hydrogen atoms can hydrogen- bond with the rest of the solvent (Dill, 1990), then the solvation free energy of a protein conformation is a function of the amount of solvent-accessible hydrophobic surface area
and the solvation stability of a protein conformation is a function of the amount of buried hydrophobic surface area. While significant effort has gone into expressing hydrophobic surface area burial in terms of rotamer-pair burials (Street and Mayo, 1998; Zhang et al., 2004), these efforts nonetheless produce artifacts suggesting that hydrophobic surfaces near the protein’s surface are not fully buried when they in fact are and suggesting that hydrophilic surfaces are buried when they remain sufficiently solvent accessible.
These artifacts do not show up in core redesigns, when everything is completely solvent inaccessible anyway; however, they have a dramatic effect on the design of protein/protein interfaces. Protein interfaces bury significant amounts of hydrophobic surface areas (Janin and Chothia, 1990; Waksman et al., 1993); they also contain many buried hydrogen bonds. The pairwise decomposability requirement has hindered interface design.
Incorporation of non-pairwise decomposable energy functions into design software has proven difficult. For starters, the dead-end elimination theorems require the energy function they optimize be pairwise decomposable. Moreover, frameworks for optimiza- tion by simulated annealing that rely on the precomputation and tabulation of pair energies cannot incorporate non-pairwise decomposable energy functions as simply an- other term.
This dissertation describes the optimization of one non-pairwise decomposable en- ergy function with dynamic programming in the context of the hydrogen placement problem (Chapter 4), the optimization of a different non-pairwise decomposable energy function into simulated annealing for protein design (Chapter 8), and the groundwork I have laid in the Rosetta molecular modeling program for the optimization of future non-pairwise decomposable energy functions (Chapter 5).