Modeling Structural Heterogeneity in Proteins from X-Ray Data

In a crystallographic experiment, a protein is precipitated to obtain a crystalline sample (crystal) containing many copies of the molecule. An electron density map (EDM) is calculated from diffraction images obtained from focusing X-rays through the sample at different angles. This involves iterative phase determination and density calculation. The protein conformation is modeled by placing the atoms in 3-D space to best match the electron density. In practice, the copies of a protein in a crystal are not exactly in the same conformation. Consequently the obtained EDM, which corresponds to the cumulative distribution of atomic positions over all conformations, is blurred. Existing modeling methods compute an "average" protein conformation by maximizing its fit with the EDM and explain structural heterogeneity in the crystal with a harmonic distribution of the position of each atom. However, proteins undergo coordinated conformational variations leading to substantial correlated changes in atomic positions. These variations are biologically important. This paper presents a sample-select approach to model structural heterogeneity by computing an ensemble of conformations (along with occupancies) that, collectively, provide a near-optimal explanation of the EDM. The focus is on deformable protein fragments, mainly loops and side-chains. Tests were successfully conducted on simulated and experimental EDMs.