Incorporating tangent refinement in the Shake-and-Bake formalism

An alternative method for the calculation of joint probability distributions. Application to the expectation of the triplet invariant

This paper presents a completely new method for the calculation of expectations (and thus joint probability distributions) of structure factors or phase invariants. As an example, a first approximation of the expectation of the triplet invariant (up to a constant) is given and acomplexnumber is obtained. Instead of considering the atomic vector positions or reciprocal vectors as the fundamental random variables, the method samples over all functions (distributions) with a given number of atoms and given Patterson function. The aim of this paper was to explore the feasibility of the method, so the easiest problem was chosen: the calculation of the expectation value of the triplet invariant inP1. Calculation of the jointprobabilitydistribution of the triplet is not performed here but will be done in the future.

X-ray crystallographic studies of metalloproteins

Many proteins require metals for their physiological function. In combination with spectroscopic characterizations, X-ray crystallography is a very powerful method to correlate the function of protein-bound metal sites with their structure. Due to their special X-ray scattering properties, specific metals may be located in metalloprotein structures and eventually used for phasing the diffracted X-rays by the method of Multi-wavelength Anomalous Dispersion (MAD). How this is done is the principle subject of this chapter. Attention is also given to the crystallographic characterization of different oxidation states of redox active metals and to the complication of structural changes that may be induced by X-ray irradiation of protein crystals.

Relaxation of the resolution requirements for direct-methods phasing

Shake-and-bake phasing methods have permitted the ab initio solution of crystal structures containing more than 1000 independent non-H light atoms (C, N, O). The success of these procedures is critically dependent upon having diffraction data measured to at least 1.2 Å resolution. A new target function R(2)(φ(h)) is introduced into the shake-and-bake procedure along with a real difference map strategy whereby this resolution limit can be appreciably lowered toward 1.5 Å. These improvements, when applied to moderately high resolution data, may now allow one the possibility to solve structures that are twice as large as could have been solved previously.

Molecular replacement and high-throughput structure determination

We describe the philosophy of the MR method as implemented in the AMoRe package. Fast rotation and translation functions are first used to obtain a meaningful sampling of solution space, whose elements are subsequently assessed by using more robust criteria. The introduction of fast and accurate algorithms for screening a large number of possible solutions opened the way to automation, thus bringing MR methods to the realm of high-throughput structure determination. Selected examples are discussed to illustrate specific aspects of the method.

New developments in phase refinement

A longstanding problem in X-ray crystallography is that vital information regarding the crystal phases in missing from the experimental data that are gathered in the diffraction experiment. Prior knowledge needs to be introduced in order to resolve phase ambiguities whenever the diffraction data are not sufficient to unequivocally reconstruct the crystal phases through anomalous or isomorphous differences. Very recent developments include progress in the application of direct methods to small proteins and other compounds of a similar small size (Shake 'n' Bake, SHELXD, CRUNCH and SIR96), bias-free refinement through the gamma-correction (Solomon), improvements in the determination of phase probability distributions (SHARP) and automated atomic refinement (wARP).

The Shake-and-Bake structure determination of triclinic lysozyme

The crystal structure of triclinic lysozyme, comprised of 1,001 non-H protein atoms and approximately 200 bound water molecules, has been determined ab initio (using native data alone) by the "Shake-and-Bake" method by using the computer program SnB. This is the largest structure determined so far by the SnB program. Initial experiments, using default SnB parameters derived from studies of smaller molecules, were unsuccessful. In fact, such experiments produced electron density maps dominated by a single large peak. This problem was overcome by considering the choice of protocol used during the parameter-shift phase refinement. When each phase was subjected to a single shift of +/-157.5 degrees during each SnB cycle, an unusually high percentage of random trials (approximately 22%) yielded correct solutions within 750 cycles. This success rate is higher than that typically observed, even for much smaller structures.

Phasing methods for protein crystallography

The phase problem has been formulated as one of constrained global minimization and it leads to the minimal principle, which is the theoretical basis of 'Shake-and-Bake'--an algorithm for the automatic solution of the phase problem, ab initio. A related approach (termed 'Half-Baked') that, as in Shake-and-Bake, alternates phase refinement in reciprocal space with density modification in real space, has recently been formulated. The traditional techniques of direct methods have been integrated with isomorphous replacement and anomalous scattering and the first applications have been made. The accurate measurement of a limited number of structure invariants by means of multiple beam X-ray diffraction has become a reality. A feasibility study shows that, in combination with the direct method, the ability to measure the values of the structure invariants experimentally will strengthen existing techniques.