On the complexity of Engh and Huber refinement restraints: the angle τ as example

The Engh and Huber parameters for bond lengths and bond angles have been used uncontested in macromolecular structure refinement from 1991 until very recently, despite critical discussion of their ubiquitous validity by many authors. An extensive analysis of the backbone angle τ (N-C(α)-C) illustrates that the Engh and Huber parameters can indeed be improved and a recent study [Tronrud et al. (2010), Acta Cryst. D66, 834-842] confirms these ideas. However, the present study of τ shows that improving the Engh and Huber parameters will be considerably more complex than simply making the parameters a function of the backbone ϕ, ψ angles. Many other aspects, such as the cooperativity of hydrogen bonds, the bending of secondary-structure elements and a series of biophysical aspects of the 20 amino-acid types, will also need to be taken into account. Different sets of Engh and Huber parameters will be needed for conceptually different refinement programs.