Linked-Atom Least-Squares

Lactones, nomenclature, 105 Linked-Atom Least-Squares analysis, 319 Lithium gellan, 386 Luteic acid, 8... 

Linked-atom least-squares refinements of fibrous structures were introduced by Arnott and Wonacott (24) in 1966 and since then have been used to refine a wide range of polymers including polyesters (24,26,27) polypeptides (28,29,30,31,32), polynucleotides (33), and polysaccharides (34-45). Earlier analyses involved mainly eqn. (xxiii) but since 1975 eqn. (xxiv) has been preferred (25). Fig. 7 illustrates a scheme for systematic structure analyses based on fiber diffraction data. 

The phase problem and the problem of arbitration. Fibrous structures are usually made up of linear polymers with helical conformations. Direct or experimental solution of the X-ray phase problem is not usually possible. However, the extensive symmetry of helical molecules means that the molecular asymmetric unit is commonly a relatively small chemical unit such as one nucleotide. It is therefore not difficult to fabricate a preliminary model (which incidently provides an approximate solution to the phase problem) and then to refine this model to provide a "best" solution. This process, however, provides no assurance that the solution is unique. Other stereochemically plausible models may have to be considered. Fortunately, the linked-atom least-squares approach provides a very good framework for objective arbitration independent refinements of competing models can provide the best models of each kind the final values of n or its components (eqn. xxiv) provide measures of the acceptability of various models these measures of relative acceptability can be compared using standard statistical tests (4) and the decision made whether or not a particular model is significantly superior to any other. 

Table 1. Values of Variable Parameters Obtained by Linked-Atom Least-Squares Refinement of Different /3-DNA Models...

For electron diffraction of the unpolymerized dimer, microscopic single crystals were obtained from a dilute hexane solution at 4 C. The structure refinement was carried out using the linked atom least-squares (LALS) program (developed by Arnott and coworkers (12) ) on 19 unique reflections. The unit cell Is... 

Diffraction patterns obtained by Davies and Baldwin [12] indicated that poly d(A-T).poly d(A-T) could assume a conformation with axial periodicity about 24.5 A which they named D-DNA. Similar diffraction patterns were obtained from poly d(I-C).poly d(I-C) by Mitsui et al. [46]. They proposed a novel left-handed double helix with anti-parallel strands and Watson-Crick base-pairs. This eightfold helix contained sugars with an unusual pucker and the bases were placed about 2 A behind the helix axis i.e. on the opposite side from the position of the base-pairs in the A form of DNA. Arnott et al. [47] obtained better quality D-form diffraction patterns from poly d(A-T).poly d(A-T) which they analysed using the linked atom least squares technique. They rejected the left-handed model of Mitsui et al. [46] and claimed... 

The Linked Atom Least Squares (LALS) program (18,19) by Arnott and coauthors is used at several institutions, including Purdue, where it was developed, and Case Western Reserve University, where it was used by Gardner and Blackwell. It is best Implemented on a large computer the Control Data Corporation supercomputer at Purdue handles it very rapidly. Setting up a new model with LALS is more complicated than with the other programs, but LALS appears to provide realistic molecular flexibility. 

Linked-Atom-Least-Squares Procedure. Molecular models having... 

The Linked-Atom Least-Squares (LALS) procedure (44) was used to generate molecular models of cellotetraose. The glucose residues were kept in the standard Cj conformation all bond angles cmd bond lengths were fixed at standard values (43). The constrained model of the crystal structure was optimized against both X-ray data and non-covalent interatomic interactions, as described by Smith and Arnott (44). 

Campbell, P.J.S. and S. Amott. 1978. LAIS A linked-atom least-squares reciprocal-space refinement system incorporating stereochemical restraints to supplement sparse diffraction. Acta Crystallographica. Section A 34 3-11. 

Fig. 1. The chain conformation of the collagen molecule, showing a single chain and a triple helix. Obtained through a linked atom, least-squares refinement of X-ray data obtained from dried kangaroo tail tendon. Hydrogen atoms not attached to the main chain have been omitted. From Ref 5 with permission.

Crystal Structure of Wild and Domestic Silk Fibres Using Linked-Atom Least-Squares Method... 

Molecular Model. Amino acid analyses of all these three silk fibroins show a uniformly high content of alanine ([Ala] ). There is an option in linked-atom least-squares (LALS) program to indicate two molecular chains by defining the constraints for only one of them. Here, the geometry for Ala is for the D-Ala and not L-Ala. The molecular conformation must satisfy both the sterical and mathematical requirements. Hence, we have chosen initial

main chain was constructed with appropriate helical parameters together with bond lengths and angles. 

Sangappa S, Mahesh S, Somashekar R. Crystal structure of raw pure Mysore silk fibre based on (Ala-Gly)n-Ser-Gly peptide sequence using linked-atom-least-squares method,/ Biosci, 30(2), 259-268,2005. 

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