Molecular replacement

Molecular replacement[1] (or MR) is a method of solving the phase problem in X-ray crystallography. MR relies upon the existence of a previously solved protein structure which is similar to our unknown structure from which the diffraction data is derived. This could come from a homologous protein, or from the lower-resolution protein NMR structure of the same protein.[2]

The first goal of the crystallographer is to obtain an electron density map, density being related with diffracted wave as follows: ${\displaystyle \rho (x,y,z)={\frac {1}{V}}\sum _{h}\sum _{k}\sum _{l}|F_{hkl}|\exp(2\pi i(hx+ky+lz)+i\Phi (hkl)).}$

With usual detectors the intensity ${\displaystyle I=F\cdot F^{*}}$ is being measured, and all the information about phase (${\displaystyle \Phi }$) is lost. Then, in the absence of phases (Φ), we are unable to complete the shown Fourier transform relating the experimental data from X-ray crystallography (in reciprocal space) to real-space electron density, into which the atomic model is built. MR tries to find the model which fits best experimental intensities among known structures.