Comment on Stereochemical restraints revisited: how accurate are refinement targets and how much should protein structures be allowed to deviate from them? by Jaskolski, Gilski, Dauter & Wlodawer (2007)

Crystallographic refinement is an important subject. At the end of the 1980s, Petsko wrote that

it is well to remember that just over 10 years ago it was commonly felt that protein structures could not even be refined

(Ringe & Petsko, 1986). With the emergence of crystallographic programs, this seemingly impossible task has become routine and even automated.

The problem of aiding the refinement process with stereochemical constraints in the absence of sufficient experimental data is an important issue. Precisely for this reason, the paper by Jaskolski et al. (2007) is welcome and perhaps even overdue. It summarizes developments over the past several years, including the emergence of high-resolution protein crystallography and the explosive growth of the PDB. However, despite warnings that it is for `the cooks rather than the chefs', the paper does not discuss the wider ramifications of the problem, the elucidation of which might clearly benefit the `cooks'.

Among many positive aspects, the paper by Jaskolski et al. (2007) contains interesting observations that should be much more widely implemented, such as the scaling problem in the determination of cell dimensions that leads to protein models that are either `squeezed' or `expanded'. It would be important to follow this up with more studies and to resolve the issue of to what degree standard indexing methods introduce anisotropy in the scaling problem. It is also possible that the fastest growing crystal directions introduce more disorder, which results in less than perfect lattice-period determination. Well behaved stereochemical parameters, such as the C=O bond, may serve as a probe to indicate directional distortion.

The general recommendations of the paper, while not dramatic, appear to be well supported by other studies. However, several important factors not covered by Jaskolski and coworkers that are highly relevant to the problem of constraints and derivation of reliable protein models should be mentioned. We focus here on four factors (neglecting many others that are perhaps equally important), such as the dual (solid–liquid) nature of protein structure, context-dependent stereochemistry, the change of paradigm for protein-structure determination (classical–quantum) when higher resolution data are available and finally the approximate nature of symmetry.

In the last several years it has become rather obvious that proteins have a special nature that appears to be a non-ergodic glassy state that combines the features of two different states of matter: the solid and the liquid states (Fenimore et al., 2004; Teeter et al., 2001). This dual nature of proteins is reflected in protein crystal structures by two contrasting features. Firstly, the temperature factors behave in accord with a rigid-body motion (protein as a solid; Kuriyan & Weis, 1991). Secondly, this model always breaks down with excessive `motion' (high temperature factors) and the existence of disorder (protein as liquid). Jaskolski et al. (2007) are aware of the fact that most high-resolution structures have substantial disorder and try to separate ordered from disordered elements in order to draw their conclusions. However, it is not obvious at all that such idealities are unique or common to both dynamic and static structures.

There is no convincing experimental evidence that the idealities that the authors discuss have universal applicability, even for well ordered parts of the protein (solid-state components). In fact, there is emerging evidence that this is not the case (Esposito et al., 2000). Recent results suggest that protein stereochemistry is context-dependent. This view is illustrated by the correlation of the results obtained by Stec et al. (1995) with quantum-mechanical optimization of crambin. Such a comparison showed the systematic dependence of several parameters (Van Alsenoy et al., 1998) on the secondary structure (Fig. 1). The well established methodology of the χ² test also provided evidence that the distributions of some of the stereochemical parameters are not unimodal (Stec et al., 1995; Vlassi et al., 1998). Had Jaskolski and coworkers used this test, it would have confirmed non-Gaussian distributions of several other variables beyond those visible in Fig. 4 of their paper (the N—C^α—C angle). The elongation of the C=O bond as well as corrections to the C—N bond length and N—C^α—C angle have also been recommended by two previous studies (Stec et al., 1995; Vlassi et al., 1998).

Figure 1 The planar angles as obtained from a model of crambin refined at 0.83 Å resolution by the full-matrix least-squares method without constraints (the disordered elements were minimally constrained; Stec et al., 1995). The N—C^α—C theoretical curve represents the result of ab inito quantum-mechanical optimization as obtained by Van Alsenoy et al. (1998). There is a remarkable agreement between the high-resolution crystal structure and the result of the quantum-mechanical optimization. Below the curves, the excerpt from the PDB sequence viewer is shown to visualize the secondary structure (purple wavy line) and the disulfide bonds (green broken line). A clear correlation between the general behavior of the planar angles and the secondary-structure elements is visible.

The higher the resolution, the more disorder is observed, and the protein structure is less uniquely defined as a solid. Therefore, despite reaching higher apparent accuracy, it becomes more difficult to find the universality that the authors seek. At an average resolution (∼2 Å), the accuracy of the idealities is not essential to obtain a reliable protein model (the expected error in a model would be ∼0.2 Å). At high resolution the problem becomes complex and the highest resolution structures usually do not provide the needed resource [e.g., as mentioned in the paper, the questionable quality of crambin at 0.54 Å resolution (PDB code 1ejg ) as well as others]. At high resolution, methods such as least squares become less-than-perfect tools, because numerical implementation of matrix algebra methods does not handle singularities well. Atoms that are located closer than the resolution of the data are randomly shifted (sometimes at the cost of worsening R), leading to large stereochemical distortions. This particular problem calls for special methods that couple restraints with nonlinear optimization. For example, methods that combine ab initio quantum-mechanical optimization with crystallographic refinement are being developed, and such methods need to be mentioned (Yu et al., 2005; Zarychta et al., 2007; Volkov et al., 2007).

Finally, the symmetry of a crystal lattice is only as good as our conventions. The symmetry determination only holds up to the accuracy of our analysis as expressed in R_merge(sym), which is usually above 5% (significantly higher than the `small-molecule' standards). This leads us to believe that the symmetry of most deposited models in the PDB is not strictly obeyed, as the solvent is not expected to obey the ideal symmetry. In order to perform comparisons such as those attempted in this paper, it would be important to compare only the structures of proteins with similar size, the same space group and very well modeled solvent. The details of such a selection go beyond the analysis of Jaskolski and coworkers and beyond these remarks.

In conclusion, the paper by Jaskolski and coworkers is a valuable contribution to the complex subject of crystallographic refinement and a starting point for discussion on improving protein models in general (Furnham et al., 2006). Such a discussion has already been initiated by a valuable session (01.07 Computational Methods) of the recent American Crystallographic Association meeting in Salt Lake City, USA.