Phases molecular replacement

Molecular replacement is where the phases of a known structure are used to determine the structure of a protein that may be identical but crystallized in a different space group or may adopt essentially the same structure (e.g., a homologous protein). Essentially, the calculations find the rotation and translation of the molecule that work with the phases to produce an interpretable electron density map. 

Stability implies a resistance to change, and may be defined qualitatively in those terms. In the specific case at hand, stability is defined as resistance to molecular or chemical disturbance. This requirement recognizes that a flocculated dispersion may be more stable than a peptized dispersion from the standpoint of its future behavior. A physically stable dispersion is one which will not undergo molecular replacements at the interface between the dispersed solid and the continuous phase. 

Equations (8) are based on the assumption of plug flow in each phase but one may take account of any axial mixing in each liquid phase by replacing the molecular thermal conductivities fc, and ku with the effective thermal conductivities /c, eff and kn eff in the definition of the Peclet numbers. The evaluation of these conductivity terms is discussed in Section II,B,1. The wall heat-transfer terms may be defined as... 

The molecular replacement method assumes similarity of the unknown structure to a known one. This is the most rapid method but requires the availability of a homologous protein s structure. The method relies on the observation that proteins which are similar in their amino acid sequence (homologous) will have very similar folding of their polypeptide chains. This method also relies on the use of Patterson functions. As the number of protein structure determinations increases rapidly, the molecular replacement method becomes extremely useful for determining protein phase angles. 

Once a suitable crystal is obtained and the X-ray diffraction data are collected, the calculation of the electron density map from the data has to overcome a hurdle inherent to X-ray analysis. The X-rays scattered by the electrons in the protein crystal are defined by their amplitudes and phases, but only the amplitude can be calculated from the intensity of the diffraction spot. Different methods have been developed in order to obtain the phase information. Two approaches, commonly applied in protein crystallography, should be mentioned here. In case the structure of a homologous protein or of a major component in a protein complex is already known, the phases can be obtained by molecular replacement. The other possibility requires further experimentation, since crystals and diffraction data of heavy atom derivatives of the native crystals are also needed. Heavy atoms may be introduced by covalent attachment to cystein residues of the protein prior to crystallization, by soaking of heavy metal salts into the crystal, or by incorporation of heavy atoms in amino acids (e.g., Se-methionine) prior to bacterial synthesis of the recombinant protein. Determination of the phases corresponding to the strongly scattering heavy atoms allows successive determination of all phases. This method is called isomorphous replacement. 

Several steps were needed to determine the structure of the core particle to higher resolution (Fig. Id). The X-ray phases of the low-resolution models were insufficient to extend the structure to higher resolution, since the resolution of the early models of the NCP was severely limited by disorder in the crystals. The disorder was presumed to derive from both the random sequences of the DNA and from heterogeneity of the histone proteins caused by variability in post-translational modification of the native proteins. One strategy for developing an atomic position model of the NCP was to develop a high-resolution structure of the histone core. This structure could then be used with molecular replacement techniques to determine the histone core within the NCP and subsequently identify the DNA in difference Fourier electron density maps. 

Fig. 2. The histone octamer. The 3.1 A X-ray diffraction data model of Arents et al. [20] is shown in secondary structure cartoon format. The core of the histone octamer is well defined, but more than 30% of the histone sequence is in regions without secondary structure. These are unfortunately the most interesting regions in terms of epigenetic signaling. 25% of the molecule located in the N-terminal tails (and the C-termini of H2A) in the 3.1 A octamer structure has no interpretable electron density. Despite these limitations, this structure is sufficient to use as a starting model for molecular replacement phasing of the NCP. (Image courtesy of E. Moudrianakis.)...

One major problem crystallographers have to deal with is the so-called phase problem, which states that of the two components of an irrational Figure (magnitude and phase) only the magnitude can be measured. A technique called molecular replacement is an approach to deal with this problem [131]. 

The possibility and feasibility of molecular replacement was demonstrated by Rossmann and colleagues in the 1960s, as part of an effort to use non-crystallographic synnmetry to solve the phase problem for macromolecules (Rossmann, 1990). 

In practice, recombination of structure factors involves first weighting of the phases of the modified structure factors in a resolution dependent fashion, according to their estimated accuracy or probability. Every phase also has an experimental probability (determined by experimental phasing techniques and/or molecular replacement). The two distributions are combined by multiplication, and the new phase is calculated from this combined probability distribution. The measured associated structure factor amplitude is then scaled by the probability of the phase, and we have our set of recombined structure factors. 

The most demanding element of macromolecular crystallography (except, perhaps, for dealing with macromolecules that resist crystallization) is the so-called phase problem, that of determining the phase angle ahkl for each reflection. In the remainder of this chapter, I will discuss some of the common methods for overcoming this obstacle. These include the heavy-atom method (also called isomorphous replacement), anomalous scattering (also called anomalous dispersion), and molecular replacement. Each of these techniques yield only estimates of phases, which must be improved before an interpretable electron-density map can be obtained. In addition, these techniques usually yield estimates for a limited number of the phases, so phase determination must be extended to include as many reflections as possible. In Chapter 7,1 will discuss methods of phase improvement and phase extension, which ultimately result in accurate phases and an interpretable electron-density map. 

V. Molecular replacement Related proteins as phasing models... 

The crystallographer can sometimes use the phases from structure factors of a known protein as initial estimates of phases for a new protein. If this method is feasible, then the crystallographer may be able to determine the structure of the new protein from a single native data set. The known protein in this case is referred to as a phasing model, and the method, which entails calculating initial phases by placing a model of the known protein in the unit cell of the new protein, is called molecular replacement. 

In words, the desired electron-density function is a Fourier series in which term hkl has amplitude IFobsl, which equals (7/, /)1/2, the square root of the measured intensity Ihkl from the native data set. The phase ot hkl of the same term is calculated from heavy-atom, anomalous dispersion, or molecular replacement data, as described in Chapter 6. The term is weighted by the factor whU, which will be near 1.0 if ct hkl is among the most highly reliable phases, or smaller if the phase is questionable. This Fourier series is called an Fobs or Fo synthesis (and the map an Fo map) because the amplitude of each term hkl is iFobsl for reflection hkl. 

Because ALBP is related to several proteins of known structure, molecular replacement is an attractive option for phasing. The choice of a phasing model is simple here just pick the one with the amino-acid sequence most similar to ALBP, which is myelin P2 protein. Solution of rotation and translation functions refers to the search for orientation and position of the phasing model (P2) in the unit cell of ALBP. The subsequent paper provides more details. 

Plate 13 ALBP electron-density map calculated with molecular-replacement phases before any refinement, shown with the final model. Compare with Plate 2, which shows the final electron-density map in the same region. (For discussion, see Chapter 8.)... 

A way to get round collecting and processing image sets for each new ligand tested was to use the phases from the original PTX experiment to process the diffraction amplitudes recorded for new drugs in the Zn sheets. As discussed above, this is not a new concept. The techniques molecular replacement (MR) and phase switching are often employed in X-ray crystal structure determination when actual phases aren t known [32], The application and results of these experiments are described herein. 

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