Secondary structure parameters

The branching angles chemical nature (geometry) of the branch juncture, whereas the rotational angles steric effects and hydrogen bonding. 

The influence of molecular weight distribution, (which also refers to the secondary structure parameters), on the behaviour of solutions as well as the method of determination will now be discussed. By preparing two polyethylene oxide samples with different molecular weight distributions = 1.6 and... 

The characterization of the covalent arrangement of the monomers within one polymer chain and within the mixture of polymer chains refers to the secondary structure parameters as well as branching (long and short chain branches). 

There is some confusion in using Bayes rule on what are sometimes called explanatory variables. As an example, we can try to use Bayesian statistics to derive the probabilities of each secondary structure type for each amino acid type, that is p( x r), where J. is a, P, or Y (for coil) secondary strucmres and r is one of the 20 amino acids. It is tempting to writep( x r) = p(r x)p( x)lp(r) using Bayes rule. This expression is, of course, correct and can be used on PDB data to relate these probabilities. But this is not Bayesian statistics, which relate parameters that represent underlying properties with (limited) data that are manifestations of those parameters in some way. In this case, the parameters we are after are 0 i(r) = p( x r). The data from the PDB are in the form of counts for y i(r), the number of amino acids of type r in the PDB that have secondary structure J.. There are 60 such numbers (20 amino acid types X 3 secondary structure types). We then have for each amino acid type a Bayesian expression for the posterior distribution for the values of xiiry. 

A common use of statistics in structural biology is as a tool for deriving predictive distributions of strucmral parameters based on sequence. The simplest of these are predictions of secondary structure and side-chain surface accessibility. Various algorithms that can learn from data and then make predictions have been used to predict secondary structure and surface accessibility, including ordinary statistics [79], infonnation theory [80], neural networks [81-86], and Bayesian methods [87-89]. A disadvantage of some neural network methods is that the parameters of the network sometimes have no physical meaning and are difficult to interpret. 

For example, Stolorz et al. [88] derived a Bayesian formalism for secondary structure prediction, although their method does not use Bayesian statistics. They attempt to find an expression for / ( j. seq) = / (seq j.)/7( j.)//7(seq), where J. is the secondary structure at the middle position of seq, a sequence window of prescribed length. As described earlier in Section II, this is a use of Bayes rule but is not Bayesian statistics, which depends on the equation p(Q y) = p(y Q)p(Q)lp(y), where y is data that connect the parameters in some way to observables. The data are not sequences alone but the combination of sequence and secondary structure that can be culled from the PDB. The parameters we are after are the probabilities of each secondary structure type as a function of the sequence in the sequence window, based on PDB data. The sequence can be thought of as an explanatory variable. That is, we are looking for... 

JE Gibrat, J Garnier, B Robson. Eurther developments of protein secondary structure prediction using information theory. New parameters and consideration of residue pairs. J Mol Biol 198 425-443, 1987. 

Such differences in the secondary structure behavior with respect to temperature can be explained by suggesting that molecular close packing of proteins in the film is the main parameter responsible for the thermal stability. In fact, as in the case of BR, we have close packing of molecules even in the solution (membrane fragments) there are practically no differences in the CD spectra of BR solution at least tiU 75°C (denaturation takes place only for the sample heated to 90°C). RC in solution begins to be affected even at 50°C and is completely denatured at 75°C, for the solution contains separated molecules. 

Several local labels need to be measured, usually one-by-one in individual samples in the case of 19F-NMR. The combined set of anisotropic NMR parameters then allows one to re-construct the geometry of the entire peptide and to determine its alignment in the membrane, as illustrated in Fig. 1 [35-37, 47, 48]. The only prerequisite is that the 19F-labelled moiety has to be rigidly attached to the peptide backbone, and that the peptide assumes a well-defined secondary structure. Provided that a sufficient number of local orientational constraints can be measured... 

Solid state 2H NMR parameters are almost exclusively governed by the quadrupole interaction with the electric field gradient (EFG) tensor at the deuteron site.1 8 The EFG is entirely intramolecular in nature. Thus molecular order and mobility are monitored through the orientation of individual C-2H bond directions. Therefore, 2H NMR is a powerful technique for studying local molecular motions. It enables us to discriminate different types of motions and their correlation times over a wide frequency range. Dynamics of numerous polymers has been examined by solid state 2H NMR.1 3,7,9 Dynamic information on polypeptides by NMR is however limited,10 26 although the main-chain secondary structures of polypeptides in the solid have been extensively evaluated by 13C and 15N CP/MAS NMR.27,28... 

Typically, residues from secondary structural elements such as a-helices or yS-sheets may be fitted to a simple one-parameter (S2) model with low residuals. Since increased mobility reduces R2 rates in general, increased R2 values well above those otherwise found... 

An interesting aspect of many structural phase transitions is the coupling of the primary order parameter to a secondary order parameter. In transitions of molecular crystals, the order parameter is coupled with reorientational or libration modes. In Jahn-Teller as well as ferroelastic transitions, an optical phonon or an electronic excitation is coupled with strain (acoustic phonon). In antiferrodistortive transitions, a zone-boundary phonon (primary order parameter) can induce spontaneous polarization (secondary order parameter). Magnetic resonance and vibrational spectroscopic methods provide valuable information on static as well as dynamic processes occurring during a transition (Owens et ai, 1979 Iqbal Owens, 1984 Rao, 1993). Complementary information is provided by diffraction methods. 

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