Dealing with structural variability in molecular replacement and crystallographic refinement through normal-mode analysis

Abstract

Normal-mode analysis (NMA) can be used to generate multiple structural variants of a given template model, thereby increasing the chance of finding the molecular-replacement solution. Here, it is shown that it is also possible to directly refine the amplitudes of the normal modes against experimental data (X-ray or cryo-EM), generalizing rigid-body refinement methods by adding just a few additional degrees of freedom that sample collective and large-amplitude movements. It is also argued that the situation where several (conformations of) models are present simultaneously in the crystal can be studied with adjustable occupancies using techniques derived from statistical thermodynamics and already used in molecular modelling.

Figure 1

Elastic network representation of the glutamine-binding protein 1ggg, as output by NOMAD-Ref (Lindahl et al., 2006 ▶). This figure was drawn with PyMOL (DeLano, 2002 ▶).

Figure 2

Influence of a steeper and steeper harmonic potential for the closed form compared with a constant harmonic curve for the open form on the crossing point between the two curves. The closed form is represented by a family of harmonic curves on the right and the open form is on the left with just one harmonic curve. It can be seen that the steeper the potential of the closed form, the closer the crossing point to the closed form. At a constant temperature (horizontal line), the amplitude of the movement away from the equilibrium position is smaller for steeper potentials.

Figure 3

Overlap coefficient O_k (see equation 3) for low-frequency modes (k = 1–106) for the open and closed forms of the glutamine-binding protein (PDB codes 1ggg and 1wdn). The cumulated score is also represented (dashed line).

Figure 4

Refinement in an envelope: the case of adenylate kinase (PDB codes 1ake and 4ake). Left, the open form (CA trace) and its envelope at 10 Å resolution (cyan). Right, the refined open form (CA trace) in the envelope of the closed form at 10 Å resolution (cyan).

Figure 5

Mean field refinement of the weights of 25 different models against diffraction data calculated solely from model 20. The flowchart of the algorithm (see Koehl & Delarue, 1994, 1996 ▶) is shown, with an inset representing the result of the mean field refinement of amplitudes (continuous line) and comparison with a normal conjugate-gradient refinement (dashed line).