Conformation space

Metzler W J, Hare D R and Pardi A 1989 Limited sampling of conformational space by the distance geometry algorithm implications for structures generated from NMR data Bioohemistry 2S 7045-52... 

Simulations of the dynamic motion of proteins aim at sampling relevant portions of the conformational space accessible to the proteins under the influence of environmental variables such as temperature, pressure, and pH. We... 

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-... 

A similar algorithm has been used to sample the equilibrium distribution [p,(r )] in the conformational optimization of a tetrapeptide[5] and atomic clusters at low temperature.[6] It was found that when g > 1 the search of conformational space was greatly enhanced over standard Metropolis Monte Carlo methods. In this form, the velocity distribution can be thought to be Maxwellian. 

Other methods which are applied to conformational analysis and to generating multiple conformations and which can be regarded as random or stochastic techniques, since they explore the conformational space in a non-deterministic fashion, arc genetic algorithms (GA) [137, 1381 simulation methods, such as molecular dynamics (MD) and Monte Carlo (MC) simulations 1139], as well as simulated annealing [140], All of those approaches and their application to generate ensembles of conformations arc discussed in Chapter II, Section 7.2 in the Handbook. 

As the number of conformations increases exponentially with the number of rotatable bonds, for most molecules it is not feasible to take all possible conformations into account. However, a balanced sampling of the conformational space should be ensured if only subsets arc being considered. In order to restrict the number of geometries output, while retaining a maximum of conformational diversity, ROTATE offers the possibility of classifying the remaining conformations, i.c., similar conformations can be combined into classes. The classification is based on the RMS deviation between the conformations, either in Cartesian (RMS y 7if [A]) or torsion space in [ ], The RMS threshold, which decides whether two... 

A molecular dynamics simulation samples the phase space of a molecule (defined by the position of the atoms and their velocities) by integrating Newton s equations of motion. Because MD accounts for thermal motion, the molecules simulated may possess enough thermal energy to overcome potential barriers, which makes the technique suitable in principle for conformational analysis of especially large molecules. In the case of small molecules, other techniques such as systematic, random. Genetic Algorithm-based, or Monte Carlo searches may be better suited for effectively sampling conformational space. 

Molecular dynamics simulations are el ficient for searching the conformational space of medium-sized molecules and peptides. Different protocols can increase the elTicieiicy of the search and reduce the computer time needed to sample adequately the available conformations. 

High temperature searches of conformational space (see Quenched Dynamics" on page 78), can produce unwanted conformational changes, such as cis-tmnx peptide flips, ring inversions, and other changes that you cannot reverse easily by geometry optimization. You can use restraints to prevent these changes. 

The choice of bctiling lirnc depends on ibc purpose of llic molecular dynarn ics simulation. If the sim u lalioti is for con form aliori al search es. lb e b catin g step is not critical for a successfti I calculation, The healing step may be rapid lo induce large structural changes that provide access to more of tbc conformational space. 

The book is organised so that some of the techniques discussed in later chapters refer to material discussed earlier, though I have tried to make each chapter as independent of the ofhers as possible. Some readers may therefore be pleased to know that it is not essential to completely digest the chapters on quantum mechanics and molecular mechanics in order to read about methods for searching conformational space Readers with experience in one or more areas may, of course, wish to be more selective. 

Fig. 9.8 The intramolecular parameters that may be checked when exploring the conformational space of a ring system.

One way to describe the conformation of a molecule other than by Cartesian or intern coordinates is in terms of the distances between all pairs of atoms. There are N(N - )/ interatomic distances in a molecule, which are most conveniently represented using a N X N S5munetric matrix. In such a matrix, the elements (i, j) and (j, i) contain the distant between atoms i and and the diagonal elements are all zero. Distance geometry explort conformational space by randomly generating many distance matrices, which are the converted into conformations in Cartesian space. The crucial feature about distance geometi (and the reason why it works) is that it is not possible to arbitrarily assign values to ti... 

Exploring Conformational Space Using Simulation Methods... 

The Monte Carlo and molecular dynamics simulation methods can be used to explor the conformational space of molecules. During such a simulation the system is able t... 

Fig. 9.19 Schematic illustration of an energy surface. A high-temperature molecular dynamics simulation may be ah to ooercome very high energy barriers and so explore conformational space. On minimisation, the appropriate minimum energy conformation is obtained (arrcrws).

Dmparison of various methods for searching conformational space has been performed cycloheptadecane (C17H34) [Saunders et al. 1990]. The methods compared were the ematic search, random search (both Cartesian and torsional), distance geometry and ecular dynamics. The number of unique minimum energy conformations found with 1 method within 3 kcal/mol of the global minimum after 30 days of computer processing e determined (the study was performed in 1990 on what would now be considered a / slow computer). The results are shown in Table 9.1. 

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