Analysis of experimental time-resolved crystallographic data by singular value decomposition

Abstract

Singular value decomposition (SVD) separates time-dependent crystallographic data into time-independent and time-dependent components. Procedures for the effective application of SVD to time-resolved macromolecular crystallographic data have yet to be explored systematically. Here, the applicability of SVD to experimental crystallographic data is tested by analyzing 30 time-resolved Laue data sets spanning a time range of nanoseconds to milliseconds through the photocycle of the E46Q mutant of photoactive yellow protein. The data contain random and substantial systematic errors, the latter largely arising from crystal-to-crystal variation. The signal-to-noise ratio of weighted difference electron-density maps is significantly improved by the SVD flattening procedure. Application of SVD to these flattened maps spreads the signal across many of the 30 singular vectors, but a rotation of the vectors partitions the large majority of the signal into only five singular vectors. Fitting the time-dependent vectors to a sum of simple exponentials suggests that a chemical kinetic mechanism can describe the time-dependent structural data. Procedures for the effective SVD analysis of experimental time-resolved crystallographic data have been established and emphasize the necessity for minimizing systematic errors by modification of the data-collection protocol.