Electron density of proteins

The ab initio quality MEDLA electron densities of proteins [19] extend the scope of density domain analysis. 

Some recent developments concerning macromolecular quantum chemistry, especially the first linear-scaling method applied successfully for the ab initio quality quantum-chemistry computation of the electron density of proteins, have underlined the importance and the applicability of quantum chemistry-based approaches to molecular similarity. These methods, the linear-scaling numerical Molecular Electron Density Lego Approach (MEDLA) method [6 9] and the more advanced and more generally applicable linear-scaling macromolecular density matrix method called Adjustable Density Matrix Assembler or ADMA method [10,11], have been employed for the calculation of ab initio quality protein electron densities and other... 

Then this reaction field is incorporated into the MFCC Hamiltonians to generate the polarized electron density of protein. 

Fig. 8. A Ramachandran plot (37) indicating the overall geometrical quality of the structure of the Fepr protein from D. vulgaris at 1.7 A resolution. Some 94% of the residues lie within the most favored regions, 5.5% in the additional allowed regions, and only one residue, N303 on the border of a disallowed region. The electron density of this residue is very well defined (see text).

In more recent years, additional progress and new computational methodologies in macromolecular quantum chemistry have placed further emphasis on studies in transferability. Motivated by studies on molecular similarity [69-115] and electron density representations of molecular shapes [116-130], the transferability, adjustability, and additivity of local density fragments have been analyzed within the framework of an Additive Fuzzy Density Fragmentation (AFDF) approach [114, 131, 132], This AFDF approach, motivated by the early charge assignment approach of Mulliken [1, 2], is the basis of the first technique for the computation of ab initio quality electron densities of macromolecules such as proteins [133-141],... 

In fact, in a precise sense, no molecular fragment is rigorously transferable, although approximate transferability is an exceptionally useful and, if used judiciously, a valid approach within the limitations of the approximation. In particular, it is possible to define non-physical entities, such as fuzzy fragment electron densities, which do not exist as separate objects, yet they show much better transferability properties than actual, physically identifiable subsystems of well-defined, separate identity. This aspect of specially designed, custom- made , artificial subsystems of nearly exact additivity has been used to generate ab initio quality electron densities for proteins and other macromolecules. 

Bakhshi, A. K., P. Otto, C.-M. Liegener, E. Rehm, and J. Ladik. 1990. Modeling of Real 20-Component Protein Chains Determination of the Electronic Density of States of... 

Structures of actual enzyme-substrate complexes are generally difficult to determine, because the reaction occurs too quickly, but techniques now available occasionally enable study of these complexes [53]. Protein X-ray crystallography has several limitations, for example, it often gives little or no information about the positions of protons (because of the low electron density of hydrogen atoms) in a particular protein. This can cause prob-... 

The connectivity is not known for the seven-helix bundle of purple membrane protein (Henderson and Unwin, 1975), but on the basis of its resemblance to other antiparallel a proteins the most likely topologies would be either up-and-down or Greek key (see below). An analysis based on the sequence and the relative electron-densities of the helices (Engelman et ah, 1980) considers a left-handed up-and-down topology as the most probable model. 

For molecules of molecular weight above 20,000 g/mol, X-ray diffraction remains the only experimental approach available to obtain detailed and reliable three-dimensional atomic models. The major steps of the method include the obtention of large and well-ordered crystals, their exposure to X-rays and collection of diffraction data and the phasing of these data to obtain by Fourier analysis a three-dimensional view (or map) of the electron density of the molecule. Finally a three-dimensional atomic model of the protein is fitted like a hand in a glove within this map, using a kit containing all the available biochemical and spectroscopic information (Table 6.2). The reliability of the final atomic model is of course dependent on the qnality of the electron density map. This qnality depends on the number of X-ray data per atom and on the resolution and accnracy of these data, which in turn are highly dependent on the size and quality of the crystals. 

The isomorphous replacement method requires attachment of heavy atoms to protein molecules in the crystal. In this method, atoms of high atomic number are attached to the protein, and the coordinates of these heavy atoms in the unit cell are determined. The X-ray diffraction pattern of both the native protein and its heavy atom derivative(s) are determined. Application of the so-called Patterson function determines the heavy atom coordinates. Following the refinement of heavy atom parameters, the calculation of protein phase angles proceeds. In the final step the electron density of the protein is calculated. 

Solvent flatness. On average, protein crystals contain about 50% solvent, which on an atomic scale usually adopts a random, non-periodic structure within the crystal and hence is featureless within the averaged unit cell. Therefore, if we know the location of the solvent regions within a macro-molecular crystal, we already know a considerable part of the electron density (i.e. the part that is flat and featureless), and flattening the electron density of the solvent region can improve the density of our macromolecule of interest. 

Non-crystallographic symmetry. Many protein crystals contain multiple copies of one or more molecules within the asymmetric unit. Often the conformations of such chemically indistinguishable but crystallographically non-equivalent molecules are sufficiently alike to treat them as identical. In this case, we can improve the signal to noise ratio of the electron density of our molecule of interest by averaging the density of the multiple copies in the asymmetric unit. 

Electron density statistics. At high resolution we know the shape of the electron density of an atom, in which case we only need to know its exact location to reconstruct the electron density in its immediate vicinity. At lower resolution we can impose an expected shape on the uni- or multivariate distributions of electron density within the protein region in a procedure that is known as histogram matching. 

To be more precise about diffraction, when we direct an X-ray beam toward a crystal, the actual diffractors of the X rays are the clouds of electrons in the molecules of the crystal. Diffraction should therefore reveal the distribution of electrons, or the electron density, of the molecules. Electron density, of course, reflects the molecule s shape in fact, you can think of the molecule s boundary as a van der Waals surface, the surface of a cloud of electrons that surrounds the molecule. Because, as noted earlier, protein molecules are ordered, and because, in a crystal, the molecules are in an ordered array, the electron density in a crystal can be described mathematically by a periodic function. 

To compare apo- and holo-forms of proteins after both structures have been determined independently, crystallographers often compute difference Fourier syntheses (Chapter 7, Section IV.B), in which each Fourier term contains the structure-factor difference FAc>/c(-—F 0. A contour map of this Fourier series is called a difference map, and it shows only the differences between the holo-and apo- forms. Like the FQ — Fc map, the FAoio—F map contains both positive and negative density. Positive density occurs where the electron density of the holo-form is greater than that of the apo-form, so the ligand shows up clearly in positive density. In addition, conformational differences between holo- and apo-forms result in positive density where holo-protein atoms occupy regions that are unoccupied in the apo-form, and negative... 

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