Conformational variables

The essential slow modes of a protein during a simulation accounting for most of its conformational variability can often be described by only a few principal components. Comparison of PGA with NMA for a 200 ps simulation of bovine pancreatic trypsic inhibitor showed that the variation in the first principal components was twice as high as expected from normal mode analy-si.s ([Hayward et al. 1994]). The so-called essential dynamics analysis method ([Amadei et al. 1993]) is a related method and will not be discussed here. 

However, the B.E.T. and modificated B.E.T as well as isotherm of d Arcy and Watt fit the experimental data only in some range of the relative humidities up to about 80-85%. At the same time the adsorption in the interval 90-100% is of great interest for in this interval the A— B conformational transition, which is of biological importance, takes place [17], [18]. This disagreement can be the result of the fact that the adsorbed water molecules can form a regular lattice, structure of which depends on the conformation of the NA. To take into account this fact we assume that the water binding constants depend on the conformational variables of the model, i.e ... 

Fig. 1. The dependence of the stable stationary values of the adsorption and conformational variables on the control parameter, Xe. a-total adsorption per the mole of the nucleotides, b-the probability of finding of an arbitrary NA unit in the A form, c-the probability of finding of an arbitrary NA unit in the B-form. Param-(ders values used to obtain numerical results Vmi = 3,nL = 15.4, = 3.24,6° =...

Fig. 2. The dependence of the stable stationary values of the adsorption and conformational variables on the control parameter, for 0 < < 0.9. a-total adsorption...

Here and below, T , 1, , and e, i, j = 1,. . . , 5, denote atomic position vectors, atom-atom distances, and the corresponding unit vectors, respectively. In order to construct a correctly closed conformation, variables qi,. . . , q4 are considered independent, and the last valence angle q is computed from Eq. (7) as follows. Variables qi,.. ., q4 determine the orientation of the plane of q specified by vector 634 and an in-plane unit vector 6345 orthogonal to it. In the basis of these two vectors, condition (7) results in... 

The situation is different for other examples—for example, the peptide hormone glucagon and a small peptide, metallothionein, which binds seven cadmium or zinc atoms. Here large discrepancies were found between the structures determined by x-ray diffraction and NMR methods. The differences in the case of glucagon can be attributed to genuine conformational variability under different experimental conditions, whereas the disagreement in the metallothionein case was later shown to be due to an incorrectly determined x-ray structure. A re-examination of the x-ray data of metallothionein gave a structure very similar to that determined by NMR. 

Many of the conformational properties of peptide systems, including protein conformation, can be approximated in terms of the local interactions encountered in dipeptides, where the two torsional angles 4> (N-C(a)) and < i (C(a)-C ) are the main conformational variables. N-acetyl N -methyl alanine amide, shown in Fig. 7.11, is a model dipeptide that has been the subject of numerous computational studies. 

By using conformationally variable Cp ligands such as C5H4Pr1, change in the dominant mode of propylene polymerization from isotactic to syndiotactic was accomplished by varying the reaction temperature [172]. 

Since the catalyst is large and has a high degree of conformational variability, the ab initio molecular dynamics simulations have been used to provide an initial scan of the potential energy surfaces. This approach has been previously applied to study homogeneous catalytic systems [47, 52-54],... 

Figure 1. Potential energy values as some (unspecified) conformational variable is changed. A represents a local (false) minimum and C represents the global minimum (assuming that all other variable parameters are also in the least energetic conformations).

The double hehx of the DNA can only to a first approximation be considered a linear, rod-like structure with the typical coordinates of B-DNA. Actually DNA possesses considerable flexibility and conformational variability. The flexibihty and structural polymorphism of DNA are prerequisites for many of the regulatory processes on the DNA level (review Harrington, 1994 Alleman and Egli, 1997). Local deviation from the classical B-structure of DNA, as well as bending of the DNA, are observed in many protein-DNA complexes. 

Fig. 11.2. Conformational variables of pair interactions shown on a ball-and-stick model of a protein segment, a, b amino acids c, d atom types r spatial distance (treated in discrete intervals) k separ ation along die sequence (=5 here).

Fig. 11.3. Conformational variables for surface potentials shown on a ball-and- stick model of a protein. a amino acid c atom type s number of protein Ca atoms (black) within a sphere of radius R. Here, s = 19.

The aims of studies on the first three groups have been broadly similar - principally elucidation of the origins of metal ion selectivity and investigation of the conformational variability. All of the studies were reasonably successful in reproducing observed structures or in rationalizing the differences predicted on the basis of gas phase calculations and those determined in the solid state or solution. 

Figure 4.2 The poly(di- -propyl-siloxane) chain, showing the conformational variability of the propyl side chains.10 Reproduced by permission of the American Chemical Society.

Mayer, B. Zhang, X. Nau, W.M. and Marconi, G. (2001) Co-conformational Variability of Cyclodextrin Complexes Studied by Induced Circular Dichroism of Azoalkanes, J. Am. Chem. Soc. 123, 5240-5248. 

The stability of polynucleotide systems and the conformational variability of nucleic acids are governed, inter alia, by noncovalent interactions [1], They lead to the... 

Abstract The discussion of relaxation and diffusion of macromolecules in very concentrated solutions and melts of polymers showed that the basic equations of macromolecular dynamics reflect the linear behaviour of a macromolecule among the other macromolecules, so that one can proceed further. Considering the non-linear effects of viscoelasticity, one have to take into account the local anisotropy of mobility of every particle of the chains, introduced in the basic dynamic equations of a macromolecule in Chapter 3, and induced anisotropy of the surrounding, which will be introduced in this chapter. In the spirit of mesoscopic theory we assume that the anisotropy is connected with the averaged orientation of segments of macromolecules, so that the equation of dynamics of the macromolecule retains its form. Eventually, the non-linear relaxation equations for two sets of internal variables are formulated. The first set of variables describes the form of the macromolecular coil - the conformational variables, the second one describes the internal stresses connected mainly with the orientation of segments. 

The set of internal variables is usually determined when considering a particular system in more detail. For concentrated solutions and melts of polymers, for example, a set of relaxation equation for internal variables were determined in the previous chapter. One can see that all the internal variables for the entangled systems are tensors of the second rank, while, to describe viscoelasticity of weakly entangled systems, one needs in a set of conformational variables xfk which characterise the deviations of the form and size of macromolecular coils from the equilibrium values. To describe behaviour of strongly entangled systems, one needs both in the set of conformational variables and in the other set of orientational variables w fc which are connected with the mean orientation of the segments of the macromolecules. 

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