Free kick instead of cross-validation in maximum-likelihood refinement of macromolecular crystal structures.

Jure Pražnikar,Dušan Turk

doi:10.1107/s1399004714021336

Abstract

The refinement of a molecular model is a computational procedure by which the atomic model is fitted to the diffraction data. The commonly used target in the refinement of macromolecular structures is the maximum-likelihood (ML) function, which relies on the assessment of model errors. The current ML functions rely on cross-validation. They utilize phase-error estimates that are calculated from a small fraction of diffraction data, called the test set, that are not used to fit the model. An approach has been developed that uses the work set to calculate the phase-error estimates in the ML refinement from simulating the model errors via the random displacement of atomic coordinates. It is called ML free-kick refinement as it uses the ML formulation of the target function and is based on the idea of freeing the model from the model bias imposed by the chemical energy restraints used in refinement. This approach for the calculation of error estimates is superior to the cross-validation approach: it reduces the phase error and increases the accuracy of molecular models, is more robust, provides clearer maps and may use a smaller portion of data for the test set for the calculation of Rfree or may leave it out completely.

Highlights

Structural biology has immensely impacted our understanding of biological processes by providing insight into molecular structures at the atomic level
The structures of actinidin (Baker, 1980), Crotalus atrox phospholipase A2 (Keith et al, 1981), stefin B (Stubbs et al, 1990), thaumatin (Ko et al, 1994) and choline and its polyalanine (Figs. 1b and 1d) model were refined using the ML approach with cross-validation (ML CV), ML noCV and ML free-kick refinement (ML FK) target functions against data truncated to 2.0 Aresolution with different fractions of test data
An overview of the coordinate (Figs. 1a and 1b) and phase (Figs. 1c and 1d) errors demonstrates that the ML CV target function strongly depends on the size of the test portion of data and that the lowest deviations from the reference structure are exhibited by the structures refined using the ML FK target

Summary

Introduction

Structural biology has immensely impacted our understanding of biological processes by providing insight into molecular structures at the atomic level. The oldest and most widely used approach, which has delivered the majority of structural data to date, is macromolecular crystallography. After diffraction data have been measured and the phase problem has been solved, structural models are built, rebuilt and refined to best interpret the measured data. Every macromolecular model from the last few decades has been subjected to crystallographic refinement, in which the positions of individual atoms are fitted to experimental observations to make the model represent the data in the best way possible. In the 1980s, an initial attempt to use the maximum-likelihood (ML) target function (Lunin & Urzhumtsev, 1984) was unsuccessful because the phase-error estimates were too low. Use of the partial free data concept (Lunin & Skovoroda, 1995) showed that the refinement was successful. ML refinement has been widely adopted by the

Methods

Results

Conclusion