Normal Mode Analysis as a Routine Part of a Structural Investigation

Abstract

Normal mode analysis (NMA) is a technique that can be used to describe the flexible states accessible to a protein about an equilibrium position. These states have been shown repeatedly to have functional significance. NMA is probably the least computationally expensive method for studying the dynamics of macromolecules, and advances in computer technology and algorithms for calculating normal modes over the last 20 years have made it nearly trivial for all but the largest systems. Despite this, it is still uncommon for NMA to be used as a component of the analysis of a structural study. In this review, we will describe NMA, outline its advantages and limitations, explain what can and cannot be learned from it, and address some criticisms and concerns that have been voiced about it. We will then review the most commonly used techniques for reducing the computational cost of this method and identify the web services making use of these methods. We will illustrate several of their possible uses with recent examples from the literature. We conclude by recommending that NMA become one of the standard tools employed in any structural study.

Keywords: X-ray crystallography; crystal structure; elastic network model; normal mode analysis; protein dynamics.

Figure 1

Illustration of the application ofNMA using an elastic network model to hen egg-white lysozyme (PDB ID 6lyz). (a) The lysozyme structure in cyan as a cartoon ribbon is overlaid with the elastic network model used for NMA. The C${}_{\alpha }$ atoms are shown as green spheres. All C${}_{\alpha }$ atoms within a radius of 7.3 Å are connected by black lines. (b) Lysozyme’s well-known hinge-bending motion is captured by the lowest-frequency non-zero mode. In this illustration, the arrows show the direction of motion, with longer arrows indicating greater motion.

Figure 2

An illustration of how the conformational change between the open and substrate-bound forms of LivJ can be described using only a few low-frequency modes. The NMA was carried out on the open, unbound form of LivJ using the offline form of ElNémo [20,68]. In both panels, the unbound form is shown in purple, the substrate-bound form is shown in green, and the valine substrate is shown as Van der Waals spheres. (a) Most of the substrate-bound conformation can be reproduced by applying the lowest-frequency mode to the open form. The magenta structure shows the results of applying only the lowest-frequency mode to the open form of LivJ. The RMSD between this conformation and the substrate-bound form is 2.3 Å as compared to 6.5 Å between the open and substrate-bound forms. (b) The closed form can be even more closely approximated using a combination of five of the lowest-frequency modes (cyan). The RMSD between this form and the substrate-bound form is only 1.5 Å.