The Solution of the Phase Problem by the Isomorphous Replacement Method

Abstract

As we have seen in Chapter 4 the electron density in a crystal can be obtained by calculating the Fourier summation:

$$ \rho (xyz) = \frac{1}{V}\sum\limits_{{hkl}} {\left| {F(hkl)} \right|\exp \left[ { - 2\pi i(hx + ky + lz) + ia(hkl)} \right]} $$

((7.1))

in which |F(h k l)| is the structure factor amplitude of reflection (h k l), including the temperature factor, and α(h k l) is the phase angle. x, y, and z are coordinates in the unit cell. From the diffraction pattern the values of I(h k l) are obtained after applying the correction factors L, P, and A. Because I(h k l) = |F(h k l)|² the amplitudes |F(h k l)| can be found. Unfortunately, no information is available on the phase angles. In principle, four techniques exist for solving the phase problem in protein X-ray crystallography:

• 1. The isomorphous replacement method, which requires the attachment of heavy atoms (atoms with high atomic number) to the protein molecules in the crystal.

• 2. The multiple wavelength anomalous diffraction method. It depends on the presence of sufficiently strong anomalously scattering atoms in the protein structure itself. Anomalous scattering occurs if the electrons in an atom cannot be regarded as free electrons.

• 3. The molecular replacement method for which the similarity of the unknown structure to an already known structure is a prerequisite.

• 4. Direct methods, the methods of the future, still in a stage of development toward practical application for proteins.