Stereochemistrybased Design

Methodology

Geometry-based approaches dominated the field of computational design until the mid-1990s, when a number of significant achievements made stereochemically complex problems addressable. More sophisticated semiempirical molecular mechanical potentials ("force fields") increased the accuracy of predictions, while new search algorithms and more powerful computers increased the combinatorial complexity that could be covered. Force fields typically comprise functions to quantify the steric, hydrogen bonding, and electrostatic interactions between pairs of atoms, a solvation term that quantifies the hydrophobic effect, and a variety of statistical or ad hoc terms.

While elementary descriptions of these interactions have been available since the mid-1980s (Brooks et al. 1983; Weiner et al. 1984), it has recently been discovered that seemingly minor, but critical adjustments are required to make accurate distinctions among highly similar structures. (For a comprehensive review of force field development, see Park et al. 2004.) One such adjustment is modification of the Lennard-Jones potential—a simple mathematical model of the London dispersion (van der Waals) force that represents the equilibrium balance of long-range attraction and short-range repulsion between atoms—to decrease the overemphasis of minor clashes. This can be done by decreasing the van der Waals radii (Dahiyat et al. 1997), stretching the van der Waals well (Looger et al. 2001), or using a linear (instead of r12) repulsive term (Kortemme et al. 2002).

Substantial improvements to the quantitation of hydrogen bond energies have also been made. New angle dependence terms have been formulated by analyzing ideal hydrogen bond geometry (Dahiyat et al. 1997), and an empirically guided hydrogen bond energy function has been created by structural bioinformatics analysis of hydrogen bonds in high-resolution structures combined with quantum mechanical modeling (Kortemme et al. 2003). Furthermore, the contribution of water-mediated hydrogen bonds has been described quantitatively (Jiang et al. 2005). In some designs, a "hydrogen bond inventory" has been included to penalize nonsatisfaction of this important term (Looger et al. 2003). The electrostatic component of atomic interactions has often been modulated by varying the dielectric constant to account for observed differences between electrostatic interactions at the surface or in the core of proteins (for review, see Schutz and Warshel 2001). The distance-dependence term can be modified to more heavily weight shorter-range interactions (Selzer and Schreiber 1999), and recently, a pairwise-decom-posable Poisson-Boltzmann function has been developed (Marshall et al. 2005). Another significant change to the potential function has been the addition of an empirical term that gives some amino acids preference over others, based on a statistical analysis of the backbone-dependent internal free energies of amino-acid rotamers (Kortemme and Baker 2002; Kuhlman and Baker 2000). Finally, quantum mechanics has been used to better estimate rotamer energies (Renfrew et al. 2007). Together, these modifications of the force field are leading to more complicated, but more accurate, quantitation of biophysical associations.

Stereochemistry-based design requires not only accurate force fields, but also methods for finding a combination of amino acids to produce a properly complementary surface from an astronomically large number of possible sequences. For the most part, three algorithms have been used in recent years: dead-end elimination (DEE), simulated annealing (SA, including Metropolis Monte Carlo), and fast and accurate side-chain topology and energy refinement (FASTER). DEE is an exact, deterministic algorithm that can quickly and drastically reduce the combinatorial complexity of the inverse folding problem. DEE in its original (Desmet et al. 1992) and generalized forms (Goldstein 1994; Gordon and Mayo 1998; Looger and Hellinga 2001) uses the pairwise-decomposability of the potential function to place upper and lower bounds on the energies of single side chains, removing those that provably cannot be members of the global minimum energy conformation (GMEC) (Figure 17.3). FASTER (Desmet et al. 2002) is a modified greedy algorithm that has been a major driving force in the radical redesign of some proteins. It functions by iteratively optimizing single protein positions or position clusters, in the context of a fixed combination of rotamers at the remaining positions. SA is an older technique, but many of the most impressive feats of computational protein design have resulted from its use to search sequence space (Baker 2006). SA searches a fitness landscape via a biased random walk: Energetically favorable moves are accepted, and unfavorable ones are accepted with a probability that decreases as the computation proceeds over time. The slower the rate of decrease (the "annealing"), the more likely the algorithm is to find an optimal or near-optimal state.

The advent of both accurate force fields and advanced methods for searching sequence space has made the design of complex stereochemical surfaces possible. Following, we highlight some of the more significant achievements in computational modulation of protein structure and interactions. This is not an exhaustive list, but rather an example of the diversity of problems that have been addressed.

Example: Integral Membrane Proteins

One of the first principles discovered by analysis of protein structures is that proteins fold such that the interior is primarily hydrophobic, while the exterior is primarily hydrophilic. Transmembrane (TM) proteins are an exception to this rule, as the exteriors of the membrane-embedded portion match the hydrophobic environment of the membrane. Many TM proteins (especially G-protein coupled receptors) are key drug targets, playing essential roles in biological processes including signal transduction, ion conductance, and small molecule transport; thus they are of significant commercial interest. The design of new drugs would be greatly assisted by the ability to produce TM membrane proteins more reliably and with higher yield. In theory, one could make a water-soluble version of a transmembrane protein by simply redecorating the exterior facing hydrophobic side chains with hydrophilic ones. However, it is

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