INDEX three-dimensional structure

Enzymes are excellent catalysts for two reasons great specificity and high turnover rates. With but few exceptions, all reac tions in biological systems are catalyzed by enzymes, and each enzyme usually catalyzes only one reaction. For most of the important enzymes and other proteins, the amino-acid sequences and three-dimensional structures have been determined. When the molecular struc ture of an enzyme is known, a precise molecular weight could be used to state concentration in molar units. However, the amount is usually expressed in terms of catalytic activity because some of the enzyme may be denatured or otherwise inactive. An international unit (lU) of an enzyme is defined as the amount capable of producing one micromole of its reaction product in one minute under its optimal (or some defined) reaction conditions. Specific activity, the activity per unit mass, is an index of enzyme purity. 

But the champion is vitamin B12, a complicated cobalt complex with a three-dimensional structure of great intricacy. No chemist would learn this structure but would look it up in an advanced textbook of organic chemistry. You will find it in such books in the index under vitamin B12 and not under its systematic name. We do not even know what its systematic name might be and we are not very interested. 

The topological state index (T ) of an atom represents the position of the atom in the scaffold of the molecular structure in relation to aU other atoms of the molecule (hut based on topology, i.e., on the connectivity and not on the three-dimensional structure) [54], Chemically and topologically equivalent atoms have identical indices. 

Note that power-law behaviour is prevalent at gelation. This has been proposed to be due to a fractal or self-similar character of the gel. Note that the exponent )f is termed the fractal dimension. For any three-dimensional structure D = 3) the exponent Df<3 (where Df < 3 indicates an open structure and Df= 3 indicates a dense strucmre). Also Muthu-kumar (Muthukumar and Winter, 1986, Muthukumar, 1989) and Takahashi et al. (1994) show explicitly the relationship between fractal dimension (Df) and power-law index of viscoelastic behaviour (n). Interestingly, more recent work (Altmann, 2002) has also shown a direct relationship between the power-law behaviour and the mobility of chain relaxations, which will be discussed further in Chapter 6. 

The aim of the ProFunc [57,58] server is to help identify the likely biochemical function of a protein from its three-dimensional structure. It uses a series of methods, including fold matching, residue conservation, surface cleft analysis, and functional 3D templates, to identify both the protein s likely active site and possible homologues in the PDB. (http //www. ebi. ac. uk/ thornton- srv/databases/profunc/index, html)... 

An important factor in the progress of bioinformatics has been the constant increase in computer speed and memory capacity of desktop computers and the increasing sophistication of data processing techniques. The computation power of common personal computers has increased within 12 years approximately 100-fold in processor speed, 250-fold in RAM memory space and 500-fold or more in hard disk space, while the price has nearly halved. This enables acquisition, transformation, visuahsation and interpretation of large amounts of data at a fraction of the cost compared to 12 years ago. Presently, bioanalytical databases are also growing quickly in size and many databases are directly accessible via the Internet One of the first chemical databases to be placed on the Internet was the Brookha-ven protein data bank, which contains very valuable three-dimensional structural data of proteins. The primary resource for proteomics is the ExPASy (Expert Protein Analysis System) database, which is dedicated to the analysis of protein sequences and structures and contains a rapidly growing index of 2D-gel electrophoresis maps. Some primary biomolecular database resources compiled from spectroscopic data are given in Tab. 14.1. 

Jy. They can be evaluated by procedures suggested by Haidar and Mahadevan (2000b) for linear and nrailinear, two- or three-dimensional structures. Once the coordinates of the design point y are evaluated with a preselected convergence criteritMi, the reliability index (3 can be evaluated as ... 

A worldwide repository for the processing and distribution of three-dimensional biologic macromolecular structure data.) The Protein Kinase Resource http //pkr.sdsc.edu/html/index. shtml... 

Electron crystallography of textured samples can benefit from the introduction of automatic or semi-automatic pattern indexing methods for the reconstruction of the three-dimensional reciprocal lattice from two-dimensional data and fitting procedures to model the observed diffraction pattern. Such automatic procedures had not been developed previously, but it is the purpose of this study to develop them now. All these features can contribute to extending the limits of traditional applications such as identification procedures, structure determination etc. 

Since the variation of any physical property in a three dimensional crystal is a periodic function of the three space coordinates, it can be expanded into a Fourier series and the determination of the structure is equivalent to the determination of the complex Fourier coefficients. The coefficients are indexed with the vectors of the reciprocal lattice (one-to-one relationship). In principle the expansion contains an infinite number of coefficients. However, the series is convergent and determination of more and more coefficients (corresponding to all reciprocal lattice points within a sphere, whose radius is given by the length of a reciprocal lattice vector) results in a determination of the stmcture with better and better spatial resolution. Both the amplitude and the phase of the complex number must be determined for any Fourier coefficient. The amplitudes are determined from diffraction... 

In an effort to understand if HAMs are, in any way, different from LAMs (low activity molecules), we extended this survey to compounds published between 1991 and 2002, as indexed in WOMBAT [26]. This database [27] contains 4927 unique structures with at least one measured activity better than 1 nM (HAMs), and 34028 unique structures with at least one activity less than 1 XM (LAMs). Between HAMs and LAMs, 1080 molecules are common, that is, they have at least one activity above 1 nM and at least one activity below 1 XM. This is not uncommon for, for example, highly selective molecules. We did not exclude these from either set since we monitor trends, not exact figures. We studied these trends using 2-D-(two-dimensional) descriptors, that is, descriptors that do not use information related to the three-dimensional characteristics of model compounds. These descriptors can be classified as follows ... 

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