Chapter 2

 An Overview of Protein Crystallography

2.1 Introduction

The most common experimental means of obtaining a detailed model of a large molecule, allowing the resolution of individual atoms, is to interpret the diffraction of X-rays from many identical molecules in an ordered array like a crystal. This method is called single-crystal X-ray crystallography. As of January 2005, the Protein Data Bank (PDB), the world’s largest repository of macromolecular models obtained from experimental data (called experimental models), contains roughly 25,000 protein and nucleic-acid models determined by X-ray crystallography. In addition, the PDB holds roughly 4500 models, mostly proteins of fewer than 200 residues, that have been solved by nuclear magnetic resonance (NMR) spectroscopy, which provides a model of the molecule in solution, rather than in the crystalline state. (Because many proteins appear in multiple forms—for example, wild types and mutants, or solo and also as part of protein-ligand or multiprotein complexes—the number of unique proteins represented in the PDB is only a fraction of the almost 30,000 models.) Finally, there are theoretical models, either built by analogy with the structures of known proteins having similar sequence, or based on simulations of protein folding. (Theoretical models are available from databases other than the PDB.) All methods of obtaining models have their strengths and weaknesses, and they coexist happily as complementary methods. One of the goals of this book is to make users of crystallographic models aware of the strengths and weaknesses of X-ray crystallography, so that users’ expectations of the resulting models are in keeping with the limitations of crystallographic methods. Chapter 10 provides, in brief, complementary information about other types of models.

In this chapter, I provide a simplified overview of how researchers use the technique of X-ray crystallography to obtain models of macromolecules. Chapters 3 through 8 are simply expansions of the material in this chapter. In order to keep the language simple, I will speak primarily of proteins, but the concepts I describe apply to all macromolecules and macromolecular assemblies that possess ordered structure, including carbohydrates, nucleic acids, and nucleoprotein complexes like ribosomes and whole viruses.

2.1.1 Obtaining an image of a microscopic object

When we see an object, light rays bounce off (are diffracted by) the object and enter the eye through the lens, which reconstructs an image of the object and focuses it on the retina. In a simple microscope, an illuminated object is placed just beyond one focal point of a lens, which is called the objective lens. The lens collects light diffracted from the object and reconstructs an image beyond the focal point on the opposite side of the lens, as shown in Fig. 2.1.

For a simple lens, the relationship of object position to image position in Fig. 2.1 is (OF)(IF’) = (FL)(F’L). Because the distances FL and F’L are constants (but not necessarily equal) for a fixed lens, the distance OF is inversely proportional to the distance IF’. Placing the object just beyond the focal point F results in a magnified image produced at a considerable distance from F’ on the other side of the the lens, which is convenient for viewing. In a compound microscope, the most common type, an additional lens, the eyepiece, is added to magnify the image produced by the objective lens.

2.1.2 Obtaining images of molecules

In order for the object to diffract light and thus be visible under magnification, the wavelength (λ) of the light must be, roughly speaking, no larger than the object. Visible light, which is electromagnetic radiation with wavelengths of 400–700 nm (nm = 10–9 m), cannot produce an image of individual atoms in protein molecules, in which bonded atoms are only about 0.15 nm or 1.5 angstroms (Å = 10–10 m) apart. Electromagnetic radiation of this wavelength falls into the X-ray range, so X-rays are diffracted by even the smallest molecules. X-ray analysis of proteins seldom resolves the hydrogen atoms, so the protein models described in this book include elements on only the second and higher rows of the periodic table. The positions of all hydrogen atoms can be deduced on the assumption that bond lengths, bond angles, and conformational angles in proteins are just like those in small organic molecules.

Even though individual atoms diffract X-rays, it is still not possible to produce a focused image of a single molecule, for two reasons. First, X-rays cannot be focused by lenses. Crystallographers sidestep this problem by measuring the directions and strengths (intensities) of the diffracted X-rays and then using a computer to simulate an image-reconstructing lens. In short, the computer acts as the lens, computing the image of the object and then displaying it on a screen (Fig. 2.2).

Second, a single molecule is a very weak scatterer of X-rays. Most of the X-rays will pass through a single molecule without being diffracted, so the diffracted beams are too weak to be detected. Analyzing diffraction from crystals, rather than individual molecules, solves this problem. A crystal of a protein contains many ordered molecules in identical orientations, so each molecule diffracts identically, and the diffracted beams for all molecules augment each other to produce strong, detectable X-ray beams.

2.1.3 A thumbnail sketch of protein crystallography

In brief, determining the structure of a protein by X-ray crystallography entails growing high-quality crystals of the purified protein, measuring the directions and intensities of X-ray beams diffracted from the crystals, and using a computer to simulate the effects of an objective lens and thus produce an image of the crystal’s contents, like the small section of a molecular image shown in Fig. 2.3a. Finally, the crystallographer must interpret that image, which entails displaying it by computer graphics and building a molecular model that is consistent with the image (Fig. 2.3b).

The resulting model is often the only product of crystallography that the user sees. It is therefore easy to think of the model as a real entity that has been directly observed. In fact, our “view” of the molecule is quite indirect. Understanding just how the crystallographer obtains models of protein molecules from diffraction measurements is essential to fully understanding how to use models properly.

2.2 Crystals

2.2.1 The nature of crystals

Under certain circumstances, many molecular substances, including proteins, solidify to form crystals. In entering the crystalline state from solution, individual molecules of the substance adopt one or a few identical orientations. The resulting crystal is an orderly three-dimensional array of molecules, held together by noncovalent interactions. Figure 2.4 depicts such a crystalline array of molecules.

The lines in the figure divide the crystal into identical unit cells. The array of points at the corners or vertices of unit cells is called the lattice. The unit cell is the smallest and simplest volume element that is completely representative of the whole crystal. If we know the exact contents of the unit cell, we can imagine the whole crystal as an efficiently packed array of many unit cells stacked beside and on top of each other, more or less like identical boxes in a...