Conformational properties, computation

Due to the noncrystalline, nonequilibrium nature of polymers, a statistical mechanical description is rigorously most correct. Thus, simply hnding a minimum-energy conformation and computing properties is not generally suf-hcient. It is usually necessary to compute ensemble averages, even of molecular properties. The additional work needed on the part of both the researcher to set up the simulation and the computer to run the simulation must be considered. When possible, it is advisable to use group additivity or analytic estimation methods. 

The structures and conformational properties of a simple hemicarcerand, created earlier by Cram, see <96JA5590>, as well as the complexation and decomplexation with guest molecules have been computationally studied <96JA8056>. 

Molecules of the simpUcity of ethane or the complexity of proteins and DNA adopt different conformations. In the case of ethane this gives rise to the notion of a staggered and eclipsed bond, whereas proteins form an array of complex structural elements and DNA - the famous double hehx. The understanding of the conformational properties of small molecules is an important factor in computational approaches contributing to drug discovery. 

The conformational properties of various 1,1 -diheteroferrocenes (7-10) have been the subject of three computational studies using extended Huckel methods.19,46 471,1 -Diphosphaferrocene has also been studied using the Fenske-Hall approach.48 and an MS Xa method.46 Where they overlap, the four treatments are in reasonable qualitative agreement. 

The recent interest in substituted silane polymers has resulted in a number of theoretical (15-19) and spectroscopic (19-21) studies. Most of the theoretical studies have assumed an all-trans planar zig-zag backbone conformation for computational simplicity. However, early PES studies of a number of short chain silicon catenates strongly suggested that the electronic properties may also depend on the conformation of the silicon backbone (22). This was recently confirmed by spectroscopic studies of poly(di-n-hexylsilane) in the solid state (23-26). Complementary studies in solution have suggested that conformational changes in the polysilane backbone may also be responsible for the unusual thermochromic behavior of many derivatives (27,28). In order to avoid the additional complexities associated with this thermochromism and possible aggregation effects at low temperatures, we have limited this report to polymer solutions at room temperature. 

Stem, P. S., M. Chorev, M. Goodman, and A. T. Hagler. 1983. Computer Simulation of the Conformational Properties of Retro-Inverso Peptides. II Ab Initio Study, Spatial Electron Distribution, and Population Analysis of N-Formylglycine Methylamide, N-Formyl N -Acetyldiaminomethane, and N-Methylmalonamide. Biopolymers 22, 1901-1917. 

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. 

As is well known, the conformational properties of cyclohexane form one of the classical problems of conformational analysis (104) and have been the subject of numerous earlier computational studies (11, 41, 82,105-107). Cyclohexane shows a variety of very interesting conformational properties which make it an ideal candidate for illustrating key features of conformational calculations. 

Computer simulations of confined polymers have been popular for several reasons. For one, they provide exact results for the given model. In addition, computer simulations provide molecular information that is not available from either theory or experiment. Finally, advances in computers and simulation algorithms have made reasonably large-scale simulations of polymers possible in the last decade. In this section I describe computer simulations of polymers at surfaces with an emphasis on the density profiles and conformational properties of polymers at single flat surfaces. 

The previous result is an important one. It indicates that there can be yet another fruitful route to describe lipid bilayers. The idea is to consider the conformational properties of a probe molecule, and then replace all the other molecules by an external potential field (see Figure 11). This external potential may be called the mean-field or self-consistent potential, as it represents the mean behaviour of all molecules self-consistently. There are mean-field theories in many branches of science, for example (quantum) physics, physical chemistry, etc. Very often mean-field theories simplify the system to such an extent that structural as well as thermodynamic properties can be found analytically. This means that there is no need to use a computer. However, the lipid membrane problem is so complicated that the help of the computer is still needed. The method has been refined over the years to a detailed and complex framework, whose results correspond closely with those of MD simulations. The computer time needed for these calculations is however an order of 105 times less (this estimate is certainly too small when SCF calculations are compared with massive MD simulations in which up to 1000 lipids are considered). Indeed, the calculations can be done on a desktop PC with typical... 

From the density profiles one cannot really judge the effect of the double bonds the density profiles for membranes of saturated lipids are very similar to those of unsaturated ones. Therefore it is necessary to consider some of the conformational characteristics of the tails. It is possible to compute the order parameter profile for both the saturated and the unsaturated chains. The order parameter profile for the saturated chain closely follows the results presented in Figure 17 for DMPC membranes for both the SCF and the MD predictions. The order parameter profiles for the unsaturated chain closely follows the MC predictions, as discussed in Figure 9. A pronounced dip is found near the cis double bond. For this reason, we choose here to present complementary data about the conformational properties of the acyl chains. 

The method of mathematical simulation has many advantages, and is very close to the physical experiment. However the further development of this approach /a consideration of volume effects, reversible reactions and so onj can be rather difficult because it will reau.ire too much computer time, therefore it is expedient to search some simple analytical or semianalytical approximate approaches to the calculation of cross-linking kinetics and conformational properties of cross-linked macromolecules. The results obtained bv the Fonte Carlo calculation can serve as criteria of the accuracy of such approximation. 

Investigations of the conformational properties of the flavan-3-ols and oligomeric proanthocyanidins have hitherto involved a variety of molecular mechanics and molecular orbital computations in combination with crystal structures, time-resolved fluorescence, as well as and NMR methods. Representative references to all these techniques may be found in the papers listed in Refs. 241-247, 250. These NMR papers incidentally also represent the major contributions regarding the conformation of proanthocyanidins, and may be summarized in a conformational context by reference to the significant contributions of Hatano and Hemingway. 

Finally, it could be asked why it is so important to properly identify stereogenic centers and prefer them to helical units The main practical reason is that most molecules, when realistically described, e.g., by a crystal structure, contain numerous helical units and it is exceedingly difficult, particularly with a computer program, to sort out those that are invariant to physical conditions (see Section 1.1.1.). In general, it is advisable to base specification of stereogenic units on constitutional or configurational distinctions of ligands, as these are normally less affected by external conditions than conformational properties. 

Each of the N atoms or molecules in an MD simulation is treated as a point mass, and Newton s equations are integrated to compute the motion of these particles. A range of useful information, both microscopic and macroscopic, can be obtained from the motion of the ensemble of atoms, including transport coefficients, phase diagrams, and structural or conformational properties. MD simulations for complex physical systems often involve large system... 

---