## Info

Sum(Best Energies for nj) = (-2 + -2 + 1 + -3) = -6 Sum(Worst Energies for n^) = (-1 + -1 + 0 + -5) = -7

Sum(Best Energies for nj) = (-2 + -2 + 1 + -3) = -6 Sum(Worst Energies for n^) = (-1 + -1 + 0 + -5) = -7

FIGuRE 17.3 (see color insert following page 178) Example of dead-end elimination (DEE). The basic principle of the DEE algorithm is that some rotamers can be proven never to be in the GMEC, by identification of another rotamer to which it would always be favorable to switch. In the simplest form, rotamer j at position n (nj) can be eliminated by rotamer k at position n (nk) if the best energy conformation of nj is worse than the worst energy conformation of nk. This calculation is easy to perform. First, a pair-wise matrix of energies is tabulated. In this table, the individual interaction energies of nj and nk with each possible rotamer at every other position is calculated, along with the self energy (the energy of nj or nk with the backbone template). In this example, there are three other positions: p, q, and r. Then the best possible total energy for nj is calculated, regardless of the interaction energies among p, q, and r. The worst possible total energy for nk is calculated, also regardless of the interactions among p, q, and r. In this example, nkeliminates nj from the GMEC, because the energetically worst combination of p, q, r for nk (p2, q^, r2) is still better than the best combination of p, q, r for nj (pt, q2, r4). The computational power of DEE can be seen by the fact that this table required only pairwise 24 energies to be calculated, whereas enumeration would require 120 (2*3*5*4) energies to be calculated.

more easily said than done, as mutation of the many residues to even the surface of a protein can lead to significant destabilization. DeGrado and colleagues have used computational design to resurface the exterior of two proteins with sufficient hydro-philic character to promote water solubility, while minimizing the disruptive actions of mutation to the global structure. Their redesigns of the potassium channel KcsA (Slovic et al. 2004) and phospholamban (Slovic et al. 2003) were based on either crystal structures or models assembled from individual subunits of the wild-type proteins. Of course, the "catch-22" is that the structure in the native environment is needed to apply computational design and produce a water-soluble version, but this requires a large quantity of the protein. Hopefully, with a combination of predictive techniques for protein folding and homology modeling, it may be possible to design solubilized versions of membrane proteins for which there are no available structures (Roosild and Choe 2005).

Example: Nucleic Acids

Unlike nucleic acid hybridization, which can be predicted from the simple Watson-Crick base-pair recognition code, the sequence specificity of DNA-binding proteins cannot be easily predicted from the primary sequence of the protein. This is because recognition interfaces in proteins are constructed from complex stereochemical surfaces influenced by a combination of van der Waals, hydrogen bonding, solvation, and electrostatic forces. In theory, altering DNA-binding specificity in a protein is little different from altering its specificity for a small molecule, a peptide, or another protein. The limiting step is parameterization of the interactions between protein atoms and DNA atoms (Havranek et al. 2004). Baker and colleagues tested these parameters by altering the DNA recognition sequence specificity of the endonuclease I-MsoI (Ashworth et al. 2006). They redesigned the specificity of the enzyme by first screening in silico for base changes that would disrupt DNA binding by the wild-type enzyme. Two base substitutions (one each on the "left" and "right" sides of the symmetry dyad) were predicted to ablate binding to the wild-type protein. Computational redesign of the amino acids surrounding these bases suggested that just two mutations to the protein (K28L and T83R) could restore binding (Figure 17.4). Cleavage specificity, activity, and binding affinity of the redesigned protein are on par with the wild-type protein for its cognate sequence, and the crystal structure of the complex superimposes well with the predicted structure.

FIGURE 17.4 (see color insert following page 178) Designed DNA-binding protein (Ashworth et al. 2006). The left panel shows the structure of the wild-type (MsoI) enzyme in complex with wild-type DNA (from 2FLD.pdb). The G-C base pair is shown in the center, and important side chains from the protein are shown as sticks. The right panel shows the designed enzyme in complex with the mutant DNA (from 1M5X.pdb). The G-C base pair has been mutated to C-G. Notice that the Lys and Thr in the wild-type (yellow) that form hydrogen bonds with the DNA bases are mutated to Val and Arg in the designed enzyme to provide new van der Waals and hydrogen bonds.

FIGURE 17.4 (see color insert following page 178) Designed DNA-binding protein (Ashworth et al. 2006). The left panel shows the structure of the wild-type (MsoI) enzyme in complex with wild-type DNA (from 2FLD.pdb). The G-C base pair is shown in the center, and important side chains from the protein are shown as sticks. The right panel shows the designed enzyme in complex with the mutant DNA (from 1M5X.pdb). The G-C base pair has been mutated to C-G. Notice that the Lys and Thr in the wild-type (yellow) that form hydrogen bonds with the DNA bases are mutated to Val and Arg in the designed enzyme to provide new van der Waals and hydrogen bonds.

Example: Peptides

Computational design can also be used to alter the interaction between full-length proteins and small peptides. Calmodulin (CaM) is a calcium-modulated protein expressed in all eukaryotic cells that binds and regulates a large number of other proteins (many of which are enzymes) in response to fluctuating intracellular calcium levels. CaM binds up to four Ca2+ ions and then undergoes a conformational change that greatly increases its affinity for various peptides (which are helical pep-tide domains of target proteins). This conformational change, when coupled with fluorescent proteins such as GFP, has been exploited to create genetically encoded calcium indicators (GECIs), which are very useful for monitoring calcium flux in neurons (Kotlikoff 2007). However, there are potential problems with CaM-based GECIs binding to endogenous cellular proteins, and it would thus be desirable to create a more specific CaM-peptide pairing. It has been hypothesized that the broad target specificity of CaM may be the result of its conformational flexibility, and that the abundance of methionines within the CaM-peptide interface makes for an accommodating binding site. Shifman and Mayo aimed to increase the specificity of CaM for one of its peptides, smooth muscle myosin light chain kinase (smMLCK), by redesigning CaM to minimize the free energy of the CaM-smMLCK complex (Shifman and Mayo 2002; Shifman and Mayo 2003). The affinity of the redesigned CaM (with eight mutations) for smMLCK is similar to that of the wild-type protein, and the affinity for other peptides is reduced by up to 86-fold.

Palmer and colleagues pursued a more complicated strategy for altering the specificity of the CaM-smMLCK interaction (Palmer et al. 2006). They first introduced "knobs" or "bumps" into the peptide and calculated free energies of interaction with wild-type CaM to determine whether binding of wild-type CaM to the mutant peptide would be destabilized compared to binding of the wildtype peptide. Then with the most destabilizing "knob" mutation in the peptide, four or five of the surrounding residues of CaM were redesigned (with "holes") to accommodate the protrusion, resulting in variants that form specific cognate pairs i^WM