Flexible molecules, representation

Isomers that differ by their chemical constitution are constitutionally isomeric. As traditionally defined, stereoisomers are molecules with the same chemical constitution that differ with respect to the relative spatial arrangement of their constituent atoms. Since many types of flexible molecules exist whose shape rapidly change with time and that are not adequately representable by any geometric model, stereoisomers must be defined as follows, without reference to molecular geometry ... 

Elementary geometry and the associated theory of point group symmetry are still the main mathematical tools of stereochemistry, despite the increasing importance of flexible molecules that are not adequately representable by rigid geometric models [10, 11, 35]. 

Cartesian coordinates are a convenient alternative representation for a spatial distribution function. Being uniform over the local space, the data structure obtained is easy to represent (access), to normalize, and to visualize. Use of a Cartesian representation becomes a necessity for complex or very flexible molecules. The principal drawbacks of this coordinate system are the size of the data structure it generates (typically about 1,000,000 elements), its inherent inefficiency (since the grid size is determined by the shortest dimension of the smallest feature one hopes to capture), and the fact that its sampling pattern is usually not commensurate with the structures one wants to represent (which can cause artificial surface features or textures when visualized). Obtaining sufficiently well-averaged results in more distant volume elements can be a problem if the examination of more subtle secondary features is desired. See Figures 7, 8 and 9 for examples of SDFs that have utilized Cartesian coordinates. 

Clark, D.E., Willett, P. and Kenny, P. (1992). Pharmacophoric Pattern Matching in Files of Three-Dimensional Chemical Structures Use of Smoothed-Bounded Distance Matrices for the Representation and Searching of Conformationally-Flexible Molecules. J.MoLGraphics, 10,194-204. 

Almond et investigated how aqueous dynamical simulations of flexible molecules can be compared against NMR data. The methodology compares state-of-the-art NMR residual dipolar coupling, NOESY and relaxation, to molecular dynamics simulations in water over several nanoseconds. In contrast to many previous applications of residual dipolar couplings in structure investigation of biomolecules, the approach described here uses MD simulations to provide a dynamic representation of the molecules. 

Clark DE, Willett P, Kenny PW. Pharmacophoric pattern matching in files of three-dimensional chemical structures use of bounded distance matrices for the representation and searching of conformationally flexible molecules. J Mol Graph 1992 10 194-204. 

Dunn WJ, Hopfinger AJ. 3D QSAR of flexible molecules using tensor representation. In Kubinyi H, Folkers G, Martin YC, eds. 3D QSAR in Drug Design. Vol. 3. Recent Advances. Dordrecht Kluwer/ESCOM, 1998 167-182. 

The dimensions of a linear flexible molecule in solution can be readily calculated using an extension of the random walk concept first introduced to describe the movement of gas molecules. The influence of chain connections, bond lengths, bond angles and short- and long-range steric interactions can all be introduced into the calculation. The random walk problem readily lends itself to computer-based numerical methods and it is possible to generate pictorial representations which reflect the chemical constitution of the backbone polymer and the interactions of the polymer with itself and the solvent. 

Generalized Formalism of Three-Dimensional Quantitative Structure-Property Relationship Analysis for Flexible Molecules Using Tensor Representation. 

Glick M, Grant GH, Richards WG (2002) Docking of flexible molecules using multiscale ligand representations. J Med Chem 45 4639-4646... 

Leherte L, Meurice N, Vercauteren DP (2005) Influence of conformation on the representation of small flexible molecules at low resolution alignment of endothiapepsin ligands. J Comput Aided Mol Des 19 525-549... 

An alternative and much more flexible approach is represented hy the STAR file format [L48, 149, which can be used for building self-describing data files. Additionally, special dictionaries can be constructed, which specify more precisely the contents of the eorresponding data files. The two most widely used such dictionaries (and file formats) arc the CIF (Crystallographic Information File) file format [150] - the International Union of Crystallography s standard for representation of small molecules - and mmCIF [151], which is intended as a replacement for the PDB format for the representation of macromolecular structures,... 

This kind of perfect flexibility means that C3 may lie anywhere on the surface of the sphere. According to the model, it is not even excluded from Cj. This model of a perfectly flexible chain is not a realistic representation of an actual polymer molecule. The latter is subject to fixed bond angles and experiences some degree of hindrance to rotation around bonds. We shall consider the effect of these constraints, as well as the effect of solvent-polymer interactions, after we explore the properties of the perfectly flexible chain. Even in this revised model, we shall not correct for the volume excluded by the polymer chain itself. 

The formalism that we have set up to describe chain flexibility readily lends itself to the problem of hindered rotation. Figure 1.8a shows a sawhorse representation of an ethane molecule in which the angle of rotation around the bond is designated by electron repulsion between the atoms bonded to... 

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