In the early twentieth century the course of modern structural biology was set when Max von Laue realized that the magnitude of the wavelength of x-ray beams was in the range of the spacings between atoms in crystals and

Introduction 403 Restrained Simulations 407

Formulation of Restraints in MD Simulations 407 Time-and Ensemble-Averaging 409 Timescale of the Dynamic Properties to be Represented by the Ensemble 411

NMR Data Used in Restrained MD Simulations 412 ps-ns Dynamics from 15N Relaxation Experiments (S 2-Order Parameters) 412 µs-ms Dynamics from PRE Experiments 416 ms-ks Dynamics from Hydrogen Exchange Experiments 419

Concluding Remarks 423 References 423

molecules. is realization lead to the development of x-ray di raction as a technique for structure determination, beginning with his description of the di raction behavior of a copper(II) sulfate crystal together with his technicians Walter Friedrich and Paul Knipping in 1912 (Friedrich, Knipping, and von Laue 1912). Bringing the famous Bragg’s law into play, William Lawrence Bragg and his father William Henry Bragg made the connection between the di raction pattern and the structure of atoms in crystal lattices of simple salt crystals shortly after (Bragg 1913a, b). Although the basic instruments needed to structurally characterize the more complicated macromolecular biopolymers that dene life were available, the world of biological science had to wait until the 1950s for those tools to be applied by Rosalid Franklin, Raymond Gosling, James Watson, and Francis Crick to determine the helical structure of deoxyribonucleic acid (DNA) (Franklin and Gosling 1953; Watson and Crick 1953). After solving the phase problem that becomes severe for large, highly structurally heterogeneous, and nonsymmetric objects, the rst three-dimensional structures of proteins were reported for myoglobin and hemoglobin by John Kendrew in 1958 (Kendrew et al. 1958, 1960) and Max Perutz in 1960 (Perutz et al. 1960). ey mark the hour of birth for modern structural biology that is now able to describe macromolecules at atomic resolution. To date, x-ray crystallography has produced countless three-dimensional structures of proteins, dominates the entries in the Protein Data Bank (PDB) (>85%) and has given valuable insight into many biological processes.