Conformational state matrices

Let the polymer chain be capable of assuming two different conformational states, coil and helix, the latter capable of binding iodine as I or I. Thus an amylose molecule may be described as a sequence of coil and helix sites, which for present purposes can each be taken to comprise approximately six glucose residues. Coil states can be denoted by c, unbound helix states by h, and helix states bound either to I or I by b. We define "complex" as any uninterrupted sequence of b states, regardless of length. Then in the usual fashion (3 ) we define the statistical weight matrix U indexed for sites i-1 and i as... 

Kim et al., 2006 Zhao et al., 2010). Infrequently, at the cost of the partial inactivation, covalent attachment leads to better enzyme stability because of the conformational changes induced by the covalent bonding of the enzyme residues to the matrix (Ma et al., 2009). However, it leads to structural changes and affects the entire molecule when it induces immobilization on a solid surface. The physicochemical properties may induce diverse conformational states in an immobilized enzyme (Lundqvist et al., 2004 Kelly et al., 2005). 

The statistical weight matrix constructed from the relative statistical weights permits the calculation of the partition function of a given sequence by matrix multiplication. The partition functions contribute to the evaluation of the conformational sequence probabilities P (i/n/ q> /), i.e. the probability to find a sequence of n residues in a specific conformational state q> starting at the i-th position of the chain. The results of these calculations can graphically be presented in the form of conformational probability profiles. 

The serial product in equation (6) imphes that the Uj need not all be identical. The only restriction on their relationship is that all pairs must be conformable for matrix multiplication. Conformabihty is ensured by the requirements expressed in the first two points before equation (4). Equation (6) can be used with chains in which different types of bonds are present, as in polyoxyethylene (14). It can also be used for chains in which not all bonds have the same number of rotational isomeric states, as in the polycarbonate of bisphenol A (15). 

Fig. 6 a) which, if repeated, is that of the 3 helical conformation which isotactic polypropylene, in common with most other isotactic polymers, is known to have in the crystalline state (Fig. 7). The calculations of Flory et al [75], using a three-state rotational isomeric state matrix treatment, showed that the mean... 

The free energy differences obtained from our constrained simulations refer to strictly specified states, defined by single points in the 14-dimensional dihedral space. Standard concepts of a molecular conformation include some region, or volume in that space, explored by thermal fluctuations around a transient equilibrium structure. To obtain the free energy differences between conformers of the unconstrained peptide, a correction for the thermodynamic state is needed. The volume of explored conformational space may be estimated from the covariance matrix of the coordinates of interest, = ((Ci [13, lOj. For each of the four selected conform-... 

Stereochemistry. - There has been a far infra-red spectroscopic study of ethyl phosphine,130 and in combination with X-ray fluorescence, further work completed on the conformational analysis of dialkylphenyl phosphines.131 The influence of water on the conformational equilibria of trimethyl phosphate has received attention.132 There has been a low temperature solid state and matrix isolation study of methyl phosphorodichi oridate,133 and a conformational study of polymorphic modifications of diphenyl-phosphinyl acetic acid hydrazide. 34... 

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