Spatial restraints

Direct interception refers to a sieve-type mechanism in which contaminants larger than the filter pore size are directly trapped by the filter. This sieve retention mechanism of particle arrest is the mechanism of choice and occurs owing to geometric or spatial restraint. This type of particle arrest is considered to be absolute, that is, it is independent of filtration conditions. 

Figure 3 Model building by Modeller [31], First, spatial restraints in the form of atomic distances and dihedral angles are extracted from the template stmcture(s). The alignment is used to determine equivalent residues between the target and the template. The restraints are combined into an objective function. Finally, the model for the target is optimized until a model that best satisfies the spatial restraints is obtained. This procedure is technically similar to the one used in structure determination by NMR.

In the second step, the spatial restraints and the CHARMM22 force field tenns enforcing proper stereochemistry [80,81] are combined into an objective function. The general form of the objective function is similar to that in molecular dynamics programs such as CHARMM22 [80]. The objective function depends on the Cartesian coordinates of —10,000 atoms (3D points) that form a system (one or more molecules) ... 

Figure 4 Sample spatial restraint m Modeller. A restraint on a given C -C , distance, d, is expressed as a conditional probability density function that depends on two other equivalent distances (d = 17.0 and d" = 23.5) p(dld, d"). The restraint (continuous line) is obtained by least-squares fitting a sum of two Gaussian functions to the histogram, which in turn is derived from many triple alignments of protein structures. In practice, more complicated restraints are used that depend on additional information such as similarity between the proteins, solvent accessibility, and distance from a gap m the alignment.

Because modeling by satisfaction of spatial restraints can use many different types of information about the target sequence, it is perhaps the most promising of all comparative modeling techniques. One of the strengths of modeling by satisfaction of spatial restraints... 

A Sail, TL Blundell. Comparative protein modelling by satisfaction of spatial restraints. J Mol Biol 234 779-815, 1993. 

Sali, A. and Blundell, T. L. (1993) Comparative protein modeUing by satisfaciion of spatial restraints. /. Mol. Biol. 234, 779-815. 

Build entire protein from spatial restraints drawn from known structure(s) and sequence alignment (e.g., MODELLER [16, 17]). 

Sali, Blundell, MODELLER CHARMM + Satisfaction of spatial restraints... 

The third method, satisfaction of spatial restraints, adopts a rather different approach to the problem One possible method that would fall into this category would be distance geometry, with the distance constraints being derived from related template structures,... 

Sali A and T L Blundell 1993 Comparative Protein Modelling by Satisfaction of Spatial Restraints Journal of Molecular Biology 234.779-815. 

Analysis of protein structure has led to the discovery of many rules and filters, all of which should be included in a protein structure prediction method, but are largely ignored in fragment assembly methods. Spatial restraint methods ° allow a more flexible approach to protein structure prediction and naturally include much of the known information that can be used to restrain a model. 

MODELLER [49] builds models of three-dimensional structures of proteins by satisfaction of spatial restraints distances and dihedral angles in the target sequence, stereochemical restraints such as bond length and bond angle obtained from the CHARMM forcefield, and statistical preferences of dihedral angles and non-bonded atomic distances obtained from a representative set of all known protein structures. The model is then calculated by an optimization method relying... 

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