Proteins are molecules that possess the rare property of self-assembling into compact little machines that move. And not just any kind of jiggling and wiggling motions but clean mechanical motion, like the gears on a bike, or the winch of a crane.

The dynamic nature of proteins was not appreciated for a long time due partly to the difficulty of measure fast protein motions and partly to the prevalence of X-ray structures. For a long time, the principal method for determining the molecular structure of a protein was through the analysis of X-ray diffraction patterns of proteins trapped in crystalline form. This gave the impression that protein molecules existed in discrete static states. In reality, many proteins are highly dynamic structures, where the static structure of an X-ray structure represents an artifically constrained conformation due to the formation of the crystalline lattice.

Today, there are many beautiful NMR experiments that can measure microscopic fluctuations in a protein in solution at room temperature. Work is in progress to measure large motions in proteins directly.

Still, understanding the motion of a protein seems like a perfect fit for computer simulation. There is a pretty solid consensus that molecular dynamics simulations is a reliable method for simulating protein molecules. Sadly the ability to simulate a protein molecule faithfully using molecular dynamics far outstrips our ability to see any useful motions in our simulation. It just takes too damn long to simulate a protein to the time-scale required to see anything interesting.

Approximations that work well in protein studies are rare but in recent years, a really neat approximation technique has been developed that models really large motions in proteins.

The method is the Gaussian Network Model (GNM) approximation, which has been developed in large part by Ivet Bahar from the University of Pittsburg.

The pre-cursor to the GNM is Normal Mode Analysis. Normal Mode Analysis is a bastardization of molecular mechanics that uses the classical-mechanics idea that the minimum of any potential can be approximated as a harmonic function. Near the minimum, forces act like springs. One can calculate the springs that approximate the global minimum of a protein using atomic force-fields taken from molecular dynamics simulations.

Unfortunately, the energy minimum of a protein modeled with atomic force fields is really unstable, and produce lots of spurious local minimum.

The genius of the Gaussian Network Model is to strip down the atomic interactions to just the essential ones that allow the protein to be modeled as a clean system of springs. Instead of modeling the full complement of atomic interactions, springs are only applied between entire residues – either between the Cα atoms, or between Cα and Cβ atoms that are in contact.

This level of approximation is sparse enough to produce network of springs that consistently produce clean cooperative motion. The network of springs in a GNM is a tractable mechanical system, amenable to complete analysis. From this network, one can calculate all the modes of vibrations. Each mode consists of the network of springs making one unique vibrational motion. You can classify each mode by its frequency – how long the motion takes to make one bouncy spring motion. It is assumed that the largest, slowest vibration, correspond to the intrinsic global motion of the protein.

There exists a lot of evidence to suggest that these motions are real. One immediate success of the GNM has been to predict the B-factors of many protein structures. In a talk by Valerie Dagett, she remarked that in her unfolding simulations, the unfolding motions invariably resembled motions predicted by GNM’s.

Ivet Bahar has built a beautiful web interface to help you calculate the GNM modes of vibration for the protein of your choice, with a java applet animation of course!

The GNM is very good at identifying hinge regions in a large protein. Indeed, there is an even simpler version of the GNM, called FIRST that analyzes only the connectivity of the network of springs to identify the hinge regions in a protein.

One spectacular example of a GNM calculation is the analysis of the HIV reverse transcriptase [1]. This is a huge, multi-domain complex that moves cooperatively to process RNA to make new DNA. The following is a movie of the motion:

But for me, the most impressive application of GNM is the recent calculation of an entire virus capsid [2]. The virus capsid is made up of hundreds of proteins that form the protective casing for a nasty piece of viral DNA. The virus capsid is known to exist in an immature form with a given symmetry. On maturation, the capsid changes into a different symmetry.

In a tour-de-force calculation, the entire capsid is simulated with GNM, using a clever approximation of simulating only 1 in every 6 residues to generate the network of springs. The slowest mode of this mind-boggingly massive complex had a collective motion that switched from the symmetry of the immature to the mature form:

References:

[1]: “Collective dynamics of HIV-1 reverse transcriptase: Examination of Flexibility and Enzyme Function”
I. Bahar, B. Erman, R. L. Jernigan, A. R. Atilgan, & D. Covell J. Mol. Biol. 285, 1023-1037, (1999)

[2]: A.J. Rader, Daniel H. Vlad and Ivet Bahar, Structure (Camb), 2005 Mar;13(3):413-21 , 2005.