Structure Calculation Algorithms

Structure calculation algorithms in general assume that the experimental list of restraints is completely free of errors. This is usually true only in the final stages of a structure calculation, when all errors (e.g., in the assignment of chemical shifts or NOEs) have been identified, often in a laborious iterative process. Many effects can produce inconsistent or incorrect restraints, e.g., artifact peaks, imprecise peak positions, and insufficient error bounds to correct for spin diffusion. 

The structure of this chapter is as follows Section 2.2 introduces the various types of conformational constraints used in NMR structure calculations. Section 2.3 is devoted to modern structure calculation algorithms. Section 2.4 gives an account of the general principles and the practice of automated NOESY assignment. 

For use in a structure calculation, geometric conformational constraints have to be derived from suitable conformation-dependent NMR parameters. These geometric constraints should, on the one hand, convey to the structure calculation as much as possible of the structural information inherent in the NMR data, and, on the other hand, be simple enough to be used efficiently by the structure calculation algorithms. NMR parameters with a clearly understood physical relation to a corresponding geometric parameter... 

Molecular mechanics methods are not generally applicable to structures very far from equilibrium, such as transition structures. Calculations that use algebraic expressions to describe the reaction path and transition structure are usually semiclassical algorithms. These calculations use an energy expression fitted to an ah initio potential energy surface for that exact reaction, rather than using the same parameters for every molecule. Semiclassical calculations are discussed further in Chapter 19. 

The HE, GVB, local MP2, and DFT methods are available, as well as local, gradient-corrected, and hybrid density functionals. The GVB-RCI (restricted configuration interaction) method is available to give correlation and correct bond dissociation with a minimum amount of CPU time. There is also a GVB-DFT calculation available, which is a GVB-SCF calculation with a post-SCF DFT calculation. In addition, GVB-MP2 calculations are possible. Geometry optimizations can be performed with constraints. Both quasi-Newton and QST transition structure finding algorithms are available, as well as the SCRF solvation method. 

The first problem of the theory of the intramolecular reactions is a calculation of dimensions of the intramolecularly cross-linked coils as a function of the degree of cross-linking. For the analytical calculation of such dependence one needs to know all possible topological structures for any number of cross-linkages and to have the calculation algorithm for each of... 

Here, we review how the development of SAXS as a structural technique is driven by advances in computer algorithms that allow to reconstruct low-resolution electron density maps ab initio from scattering profiles. In addition, we delineate how these low-resolution models can be used in free energy electrostatics calculations. Finally, we discuss how one can exploit the hierarchical nature of RNA folding by combining the low resolution, global information provided by SAXS with local information on RNA structure, from either experiments or state-of-the-art RNA structure prediction algorithms, to further increase the resolution and quality of models obtained from SAXS. 

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