Single topology description

Figure 3 Mutation of a ligand Asp into Asn in solution and bound to a protein, (a) Thermodynamic cycle, (b) Dual topology description a hybrid ligand with two side chains. Blocks are used to define the hybrid energy function [Eq. (14)]. Only the ligand is shown the environment is either solvent or the solvated protein, (c) Single-topology description.

A single topology description should be used for systems in which mutations of atom types are made that are not likely to lead to different conformations. The one-to-one correspondence in a single topology description usually leads to smaller statistical error because at any time during tbe simulation a single set of coordinates is present. 

Figure 2.2 Selected families (DDj(aj)) of density domains of the water molecule, as calculated with the GAUSSIAN 90 ab initio program [253] and the GSHAPE 90 molecular shape analysis program [254], using a 6-3IG basis set. There are only two topologically different types of families of density domains either a single density domain, or a family of three density domains. The sequence of topologically distinct cases provides a topological description of chemical bonding.

The most frequently used single-determinant descriptions of the magnetic systems incorporate spin polarization effects through spin-symmetry breaking of the molecular orbitals. Since the next section is devoted to comparisons between the predictions of the topological approaches and the results of non-empirical calculations, which are performed along the Unrestricted Density Functional Theory (UDFT) approximation, it is worth recalling briefly the main features of the spin polarization phenomenon. 

Most of the antiparallel /3 domains have their sheets wrapped around into a cylinder, or barrel, shape. None of the antiparallel barrels has as symmetrical or as continuously hydrogen-bonded a cylindrical sheet as the singly wound parallel fi barrels of triosephos-phate isomerase and pyruvate kinase dl however, antiparallel barrels are very much more common. Because of gaps in the hydrogenbonding, some of these structures have been described as two /3 sheets facing each other (e.g., Schiffer et al., 1973 Blake et al., 1978 Harrison et al., 1978). Our reasons for treating them all as barrels are that the gap positions are sometimes different in domains that are probably related, and that the barrel description yields very much simpler and more unified topologies. 

The analytical description of this fold catastrophe is obtained by replacing p(r) by a function of the single behaviour coordinate and parametrized by a single control parameter v, denoting displacements from the catastrophe point along the reaction coordinate. The topological behaviour of p(r) in the... 

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