Conformational energy range of ligands in protein crystal structures: The difficult quest for accurate understanding

Abstract

In this review, we address a fundamental question: What is the range of conformational energies seen in ligands in protein-ligand crystal structures? This value is important biophysically, for better understanding the protein-ligand binding process; and practically, for providing a parameter to be used in many computational drug design methods such as docking and pharmacophore searches. We synthesize a selection of previously reported conflicting results from computational studies of this issue and conclude that high ligand conformational energies really are present in some crystal structures. The main source of disagreement between different analyses appears to be due to divergent treatments of electrostatics and solvation. At the same time, however, for many ligands, a high conformational energy is in error, due to either crystal structure inaccuracies or incorrect determination of the reference state. Aside from simple chemistry mistakes, we argue that crystal structure error may mainly be because of the heuristic weighting of ligand stereochemical restraints relative to the fit of the structure to the electron density. This problem cannot be fixed with improvements to electron density fitting or with simple ligand geometry checks, though better metrics are needed for evaluating ligand and binding site chemistry in addition to geometry during structure refinement. The ultimate solution for accurately determining ligand conformational energies lies in ultrahigh-resolution crystal structures that can be refined without restraints.

Keywords: X-ray crystallography; conformational energy; molecular modeling; protein binding; quality metrics; structure refinement; thermodynamics.

Figure 1

Potential energy surface of NH₂OH in the OPLS forcefield (Jorgensen et al., 1996) as a function of rotation around its central H-N-O-H bond. The global minimum conformation is marked with a red circle, and one of the local minima is marked with a yellow diamond. A hypothetical receptor-bound conformation is marked with a black + sign.

Figure 2

Values for the difference in conformational energy between the bound ligand conformation and the nearest local energy minimum, compared between literature data sets generated with different restrained minimization protocols: flat-bottomed restraints (Boström et al., 1998; Perola and Charifson, 2004), harmonic restraints (Butler et al., 2009), internal coordinate optimization with fixed torsions (Nicklaus et al., 1995; Sitzmann et al., 2012), and fitting to the electron density (Wlodek et al., 2006; Fu et al., 2011, 2012, 2013; Borbulevych et al., 2014). ‘Average’ refers to the average across all data sets for a given protocol and ‘max’ refers to the maximum value seen in any data set. Error bars indicate the standard deviation between data sets.

Figure 3

Values for the difference in conformational energy between the bound ligand conformation and the nearest local energy minimum, compared between literature data sets calculated at different levels of theory: molecular mechanics forcefields (Nicklaus et al., 1995; Boström et al., 1998; Perola and Charifson, 2004; Butler et al., 2009), the semi-empirical AM1 functional (Borbulevych et al., 2014), DFT (B3LYP) (Butler et al., 2009; Sitzmann et al., 2012), and MP2 (Fu et al., 2011, 2012, 2013). ‘Average’ refers to the average across all data sets for a given protocol and ‘max’ refers to the maximum value seen in any data set. Error bars indicate the standard deviation between data sets.

Figure 4

Values for the difference in conformational energy between the bound ligand conformation and the nearest local energy minimum, compared between literature data sets calculated in vacuum (Nicklaus et al., 1995; Boström et al., 1998; Wlodek et al., 2006; Butler et al., 2009; Sitzmann et al., 2012) or with different solvent modeling methods. Implicit solvent data sets are from (Perola and Charifson, 2004; Butler et al., 2009; Sitzmann et al., 2012), the explicit solvent data set is from (Foloppe and Chen, 2016), and high screening data sets (see text) are from (Vieth et al., 1998; Wlodek et al., 2006; Wang and Pang, 2007; Butler et al., 2009). ‘Average’ refers to the average across all data sets for a given protocol and ‘max’ refers to the maximum value seen in any data set. Error bars indicate the standard deviation between data sets.