Build-up procedures

Gibson K D and H A Scheraga 1987. Revised Algorithms for the Build-up Procedure for Predicting lAotein Conformations by Energy Minimization, journal of Computational Chemistry 8 826-834. 

M Vasquez, ElA Scheraga. Calculation of protein conformation by the build-up procedure. Application to bovine pancreatic trypsin inhibitor using limited simulated nuclear magnetic resonance data. J Biomol Struct Dyn 5 705-755, 1988. 

According to this scheme an atom of sulphur, for example, with sixteen electrons, would have an electronic configuration of 2, 4, 4, 6 (Bohr [1923]). The main feature of the building-up procedure was Bohr s assumption that the stationary states would also exist in the next atom, obtained by the addition of a further electron. He also assumed that the number of stationary states would remain unchanged apart from any additional states of the newly introduced electron. In other words the assumption was one of the existence of sharp stationary states, and their retention on adding both an electron and a proton to an atom. To quote Bohr ... 

At the basis of the building up procedure used by Bohr there lies the adiabatic principle introduced by Ehrenfest [1917]. 

The pharmacophore build-up procedure is similar to that in Catalyst HipHop. Two-point pharmacophores characterized by the two features and a binned dis-... 

The globular protein human leukocyte interferon (containing 156 residues) is being treated by the build-up procedure.146 Thus far, approximately two thirds of the molecule has been built up. 

Another globular protein, bovine pancreatic trypsin inhibitor (BPTI), has also been treated by the build-up procedure however, because of a limitation on computer time when the calculation on this protein was carried out, a limited set of simulated NMR distance constraints (taken from the known X-ray structure225) was used226-227 to reduce the number of conformations... 

M. Vasquez and H. A. Scheraga, J. Biomol. Struct. Dyn., 5, 70S (1988). Calculation of Protein Conformation by the Build-up Procedure. Application to Bovine Pancreatic Trypsin Inhibitor Using Limited Simulated Nuclear Magnetic Resonance Data. 

Obviously, a combination of the different methods described above that takes advantage of each individual approach can be used. Lee et al. [20] proposed to combine the build-up procedure and genetic algorithms. 

Gibson KD, Scheraga HA. Revised algorithms for the build-up procedure for predicting protein conformations by energy minimization. J Comput Chem 1987 8 826-834. 

K. D. Gibson and H. A. Scheraga, / Comput. Chem. 8(6), 826 (1987). Revised Algorithms for the Build-Up Procedure for Predicting Protein Conformations by Energy Minimization. 

To summarise, the building up procedure we have used is called the Aufbau principle. Each electron occupies one electron state, represented by four quantum numbers, one of which represents the spin of the electron. Each orbital can contain two... 

Aufbau procedure n. The procedure of starting at the lowest of a set of energy levels and gradually adding electrons to progressively higher levels building-up procedure. 

By use of a build-up procedure, in which small energy-minimized fragments were combined (with subsequent energy-minimization of the resulting large fragments), it was possible to compute the structure of the 20-residue membrane-bound portion of melittin [36]. The computed structure (Fig. 5) is in satisfactory agreement with experiment [37, 38]. 

The idea behind the build-up procedure is illustrated in figure 2. As shown in Roslbf et al,(2001), the order in which the products are inserted has impact on the quality of the schedule obtained. It is therefore of use to use the same reordering, or post processing, strategy as proposed in the same paper. When all products are inserted, some are released and the system is rescheduled. This improves the quality of the solution, as the elements already scheduled can not change place in the sequence during the build-up. 

We shall now see how the concepts we have introduced apply to other homo-nuclear diatomic molecules, such as N2 and O2, and diatomic ions such as. In line with the building-up procedure, we first consider the molecular orbitals that can be formed from the valence orbitals and do not (at this stage) worry about how many electrons are available. 

The transfer matrix S controls the transformation of connectivity states between successive lines, its /yth element being equal to the number of ways to transit connectivity state i at a given line can evolve to state j at the subsequent line of the build-up procedure, or zero otherwise. Thus, the state of line m -1- 1 is determined from the application of the operator S to line m. 

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