Ensembles of conformations

Obtaining an Ensemble of Conformations What is Conformational Analysis ... 

Many approaches and methods for the generation of multiple conformations have been developed and published since the early 1980s. Below we describe briefly some of the basic concepts and methods of automatic conformer generation. However, interested readers are referred to Chapter 11, Section 7.2 in the Handbook, where the approaches to automatic generation of ensembles of conformations and the program systems that have been developed are described in detail. 

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. 

From the complete ensembles of conformations found by the CICADA analysis of the pentasaccharide, H- H distances have been calculated.These distances (not shown here) can be compared to the interesidual H- H distances estimated from the NOE build-up rates of the corresponding cross-peaks in the 2D NOESY spectra, to be made un future experiments. 

THE EXPANDED DENATURED STATE AN ENSEMBLE OF CONFORMATIONS TRAPPED IN A LOCALLY ENCODED TOPOLOGICAL SPACE... 

When a protein reversibly unfolds in solution, it enters a large and diverse ensemble of conformations known as the denatured state. Studies of this reaction over the past 40 years have suggested it is a single,... 

The most important feature of the information in dipolar couplings is that it is independent of distance. The data can be envisioned as reflecting the relative orientation of pairs of bond vectors, with the intervening distance having no effect (Meiler et al., 2000). Thus dipolar couplings can potentially provide a method for characterizing the structure of denatured proteins, provided that the denatured state ensemble of conformations retains several levels of nonrandomness. 

This simple three-state model of protein folding, shown schematically in Figure 7, ascribes a separate force to shaping the structure of each state. Local steric interactions trap the protein chain in a large ensemble of conformations with the correct topology hydrophobic interactions drive the chain to a smaller, more compact subset of conformations then dispersion forces supply the enthalpy loss required to achieve a relatively fixed and rigid ensemble of native conformations. 

The fraction of Pn conformer in denatured proteins can be roughly estimated from the work of Park et al. (1997). They analyzed the data of Drake et al. (1988) on poly(Lys) over the temperature range of —100 to +80°C plus their own data on the peptide AcYEAAAKEAPAKEAAAKANMHs at temperatures from 0° to 90°C. They used a two-state model, justified by the tight isodichroic points observed in each system, and derived limiting 222 nm ellipticity values of +9500 deg cm2 dmol-1 for the Pn conformation and —5560 deg cm2 dmol-1 for the high-temperature ensemble of conformers. This leads to Eq. (1) (Bienkiewicz etal., 2000) ... 

A solvated MD simulation is performed to determine an ensemble of conformations for the molecule of interest. This ensemble is then used to calculate the terms in this equation. Vm is the standard molecular mechanics energy for each member of the ensemble (calculated after removing the solvent water). G PB is the solvation free energy calculated by numerical integration of the Poisson-Boltzmann equation plus a simple surface energy term to estimate the nonpolar free energy contribution. T is the absolute temperature. S mm is the entropy, which is estimated using... 

For example, the representation of 5 requires information on the configuration about both C-atoms as well as the statement of at least one dihedral angle, e.g., <5(Cla—C-cfcp— Cl ) = — 60°. If a polycentric molecule corresponds to the equilibrium of an ensemble of conformations, one could describe it with the dihedral angles of all participating conformations, or neglect the conformational aspect and use the configurations as the characteristic class feature of the ensemble. Except for conformation analytic problems, the latter treatment suffices for the solution of chemical problems. 

The latter exists as only one achiral polycentric configuration. For systems like 10 there are not only achiral rigid models 10b and 10d but also chiral ones, 10a and 10a, as well as 10c and 10c where the observable achirality must be interpreted by looking at the whole ensemble of conformations. Such systems are achiral, because the enantiomeric conformations are mutually interconvertible via achiral conformations and occur at equal equilibrium concentrations. 

The obtained ensembles of conformers for 2-4 that quantitatively reproduce the experimental data are shown in Fig. 10a. These ensembles were... 

Fig. 10 a MD-tar ensembles of conformers for 2-4. The experimental ensemble corresponding to 1 in the free state (reft) is shown for comparison, b Structures representative of the main conformational families present in solution for neomycin-B derivatives 2 (left) and 3 (right) superimposed on the X-Ray structure of paromomycin in the complex with ribosomal RNA, according to X-Ray data. The maximum 4>/ U deviations (for each glycosidic linkage) is shown. Unit IV is omitted for simplicity... 

This algorithm will generate the ensemble of conformations at thermodynamic equilibrium, if the conformational variations introduced in step 1 (the so-called moves ) are sufficient to cover all possible regions of conformational space and are locally reversible. It is easy to understand that feature of the Metropolis procedure the transition probability into the higher energy state is given by the Boltzmann factor, the transition probability into the lower energy state is one. The relative population of the two states is then the ratio of the transition probabilities, thus the Boltzmann factor this is the outcome expected from thermodynamics. 

Many peptides have no well-defined conformation, but exist as an ensemble of conformers, especially in aqueous solution. Unordered peptides have a characteristic strong negative CD band in the 195-200 nm region and a weaker feature in the 220 nm region that may be either positive or negative [shown in Figure 9 for poly(Lys) 94] poly(Ser) 150l and poly(Lys-Leu)192 ]. 

Fiqu re 19.17 Reduction of the folding funnel to a conventional reaction coordinate diagram. This reconciles the classical view of a pathway with the new view of an energy landscape and an ensemble of conformations. [After W. A. Eaton, P. A. Thompson, C. K. Chan, S. Hagen, and J. Hofrichter, Structure 4,1133 (1996).]... 

Quasar not only considers one conformer per molecule but also represents each molecule by an ensemble of conformers in different orientations and protonation states (called fourth dimension [21]), thereby reducing the bias associated with the choice of the bioactive conformation. The fifth dimension refers to the possibility to consider an ensemble of different induced-fit models [22] and the sixth dimension allows for the simulation of local induced H-bond flip-flop and various solvation effects [23]. 

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