Alignment statistics

Altschul, S. F., and Gish, W. (1996). Local alignment statistics. Methods Enzymol. 266, 460-480. 

Altschul SF, Gish W. Local alignment statistics. Meth Enzymol 1996 266 460-480. 

The phases formed by liquid crystals may be classified according to the structure existing in the liquid. In nematic liquid crystals the molecules have their long axes aligned statistically parallel to one another within macroscopic volumes of the phase, but they have no positional order, as shown schematically in Fig. 8.5(a). This statistically averaged direction defines a unique direction in the liquid crystal and the unit vector in this direction is known as the director. At a sufficiently high temperature the nematic structure breaks down to give a true liquid. 

After an alignment of a set of molecules known to bind to the same receptor a comparative molecular field analysis CoMFA) makes it possible to determine and visuahze molecular interaction regions involved in hgand-receptor binding [51]. Further on, statistical methods such as partial least squares regression PLS) are applied to search for a correlation between CoMFA descriptors and biological activity. The CoMFA descriptors have been one of the most widely used set of descriptors. However, their apex has been reached. 

KK Koretke, Z Luthey-Schulten, PG Wolynes. Self-consistently optimized statistical mechanical energy functions for sequence structure alignment. Protein Sci 5 1043-1059, 1996. 

Metallurgists originally, and now materials scientists (as well as solid-state chemists) have used erystallographic methods, certainly, for the determination of the structures of intermetallic compounds, but also for such subsidiary parepistemes as the study of the orientation relationships involved in phase transformations, and the study of preferred orientations, alias texture (statistically preferential alignment of the crystal axes of the individual grains in a polycrystalline assembly) however, those who pursue such concerns are not members of the aristocracy The study of texture both by X-ray diffraction and by computer simulation has become a huge sub-subsidiary field, very recently marked by the publication of a major book (Kocks el al. 1998). 

S. Blenk, H. Ehrentraut, W. Muschik. Statistical foundation of macroscopic balances for liquid crystals in alignment tensor formulation. Physica A 77 119-138, 1991. 

Any given molecule has only one of the three possible alignments of -CH2Br spins, but in a large collection of molecules, all three spin states are represented in a 1 2 1 statistical ratio. We therefore find that the neighboring -CFIj protons come into resonance at three slightly different values of the applied field, and we see a 1 2 1 triplet in the NMR spectrum. One resonance is a little above where it... 

This branch of bioinformatics is concerned with computational approaches to predict and analyse the spatial structure of proteins and nucleic acids. Whereas in many cases the primary sequence uniquely specifies the 3D structure, the specific rules are not well understood, and the protein folding problem remains largely unsolved. Some aspects of protein structure can already be predicted from amino acid content. Secondary structure can be deduced from the primary sequence with statistics or neural networks. When using a multiple sequence alignment, secondary structure can be predicted with an accuracy above 70%. 

Molecular orientation increases the crystallization rate for two reasons the statistical probability of chain segments becoming suitably aligned to form a nucleus is increased and the entropic difference between the molten and crystalline states is reduced, which increases the driving force towards crystallization. 

The maximum search function is designed to locate intensity maxima within a limited area of x apace. Such information is important in order to ensure that the specimen is correctly aligned. The user must supply an initial estimate of the peak location and the boundary of the region of interest. Points surrounding this estimate are sampled in a systematic pattern to form a new estimate of the peak position. Several iterations are performed until the statistical uncertainties in the peak location parameters, as determined by a linearized least squares fit to the intensity data, are within bounds that are consistent with their estimated errors. 

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