Flexibility of molecules

Figure 15 describes the decrease in the flexibility f of the macromolecules during melt stretching (corresponding to an increase in /3m) with x. According to Flory s criterion, the diminution of the flexibility of molecules to the value of f < 0.63 leads to a spontaneous transition of the system into the state of parallel order. It can be seen in Fig. 15 that f = 0. is attained at x = 30 or o = 0.6 x 107 n/m2 at these stresses, the melt is organized into a nematic state. 

Fluorescence polarization measurements can thus provide useful information on molecular mobility, size, shape and flexibility of molecules, fluidity of a medium, and order parameters (e.g. in a lipid bi layer)2 . 

In particular St levik s conformational study of a series of halogenated propanes has contributed to our understanding of the flexibility of molecules with two axes of internal rotation. The coexistence of as many as three conformers has been found in several instances. For these halopropanes the structures of the coexisting conformers have been determined as well as their mole fractions. The molecules are quite rigid, and from the study of the u-values the conclusion has been drawn that the torsional potentials are harmonic in the minimum regions. 

RDCs belong to the so-called anisotropic NMR parameters which cannot be observed in isotropically averaged samples as, for example, is the case in liquids. Besides RDCs, a number of other anisotropic parameters can be used for structure elucidation, like residual chemical shift anisotropy, residual quad-rupolar couplings for spin-1 nuclei, or pseudo-contact shifts in paramagnetic samples. Here, we will focus on RDCs where we give a brief introduction into the dipolar interaction, then into the averaging effects with the description by the alignment tensor and concepts to deal with the flexibility of molecules. For the other anisotropic NMR parameters, we refer the reader to ref 19 for an introduction and to refs. 6-8 for a detailed description. 

The description of the averaging in Equation (1) is by no means trivial, and the development of corresponding models for an effective inclusion of flexibility of molecules on various time scales is still an ongoing field of research. We therefore will start out with the most simple case, the averaging of a completely rigid molecule, before going into effects of conformational averaging. 

The screening software SPECITOPE, developed by Schnecke et al.156, uses distance matrix comparisons as a first filter step. Elowever, flexibility of molecules is not modeled by distance intervals. Instead, a weighting scheme is defined to scale down the contributions of more flexible atom pairs in the overall score. In addition, a special optimizer is added that allows the removal of protein-ligand steric clashes after the placement calculation. 

Manipulation of computer models is much superior to the use of traditional physical models (os lung as the electricity is flowing). Mathematical models using quantum mechanics or force field methcxls (.see below) better account for the inherent flexibility of molecules than do hard sphere phy.sic al mcxlcls. In addition, it is easy to superimpose one or mon molecular models on a computer and to color each stnictun ... 

Palm et al. [3] took into account the flexibility of molecules by using molecular mechanics to calculate an averaged PSA according to a Boltzmann distribution. Later Clark [4,5] found that the use of a representative conformation was sufficient for the calculation of reliable PSA values. Ertl [6] developed a method to calculate PSA as the sum of fragment contributions and proposed a topological PSA (TPSA). The advantage of TPSA is that it can be directly calculated from the 2D chemical structure, which makes the calculation rapid and reproducible. 

To derive this submatrix, vhich collects structural and electronic features responsible for activity, the flexibility of molecules is taken into account by choosing some tolerance limits for variation of diagonal (Ai) and off-diagonal (A2 for bonded atoms and A3 for nonbonded atoms) elements. Then, to decide vhich features are responsible for activity, two probabilistic functions are used ... 

Then, queries are generated covering all possible triplets of PPP types and geometrical interatomic distances (i.e., 5916 geometrically valid queries) and used to search the molecules in the analyzed data set. To account for conformational flexibility of molecules, a tolerance is associated with each point-point distance. Finally, the molecular descriptor is obtained as a bit string indicating the queries (i.e., pharmacophores) hit by the compound. For each pharmacophore, it is possible to identify not only if a compound or database of compounds can express it, but also how many times it can express. 

Molecular similarity indices can be optimized by fixing one molecule and translating and rotating the other one until their similarity reaches an optimum. This ASP-implemented procedure constitutes another promising tool for the rational alignment of molecules in 3D space, also considering the flexibility of molecules [1075]. 

Plasticizer properties are determined by their chemical structure because they are affected by the polarity and flexibility of molecules. The polarity and flexibility of plasticizer molecules determine their... 

The correct explanation of this result by Kuhn is one of the first triumphs of the statistical theory of polymer chains. He was well aware of the developments in structural chemistry that explained the flexibility of molecules in terms of rotation about single bonds. Since polymers are molecules, rota-... 

A flexible molecule is one that can adopt many different shapes, or conformations. The study of the three-dimensional shapes of molecules is called conformational analysis. This chapter will introduce only the most basic principles of conformational analysis, which we will use to analyze the flexibility of molecules. To simplify our discussion, we will explore compounds that lack a functional group, called alkanes and cycloalkanes. Analysis of these compounds will enable us to understand how molecules achieve flexibility. Specifically, we will explore how alkanes and cycloalkanes change their three-dimensional shape as a result of the rotation of C—C single bonds. 

Conformational flexibility of molecules in solution and their effect on the vibrational and electronic spectra, which in turn determine the nonlinear optical responses. 

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