Low-energy Domains Research Articles

Evidence for kinetic effects in the folding of large RNA molecules

When RNA secondary structures predicted by free energy minimization programs are compared with the structures obtained by phylogenetic comparison it is found that there are often substantial differences. Here we consider a sample of large RNA molecules including 16S and 23S ribosomal RNA, and RNaseP RNA, and compare the minimum free energy and phylogenetic structures for domains of different size within the molecule. The pattern of differences between the structures is consistent with the idea that the native structures are influenced by the kinetics of the folding process, rather than solely by free energy minimization. It is found that the free energy of small domains in the phylogenetic structure of size 100 bases or less is usually much lower (i.e., more stable) than the average value of the minimum free energy of typical domains of corresponding size, whereas the reverse is true for large domains. We interpret these results using a picture of the folding process where short range secondary structure elements form first, which gradually rearrange to form domains of larger and larger size. Once low free energy domains of a moderate size are formed, these structures will remain trapped, because free energy barriers associated with structural rearrangement will be too large. The result is a structure containing small low free energy domains linked by a few longer range helices which fit in as best they can at a later stage of folding. We also discuss other possible causes of error in the predicted minimum free energy structures, and conclude that the difference between the minimum free energy and the phylogenetic structures cannot simply be put down to errors in the free energy parameters used in the model.

Conformations of disaccharides by empirical force field calculations. Part V: Conformational maps of β-gentiobiose in an optimized consistent force field

A recently optimized set of potential energy functions is used to investigate the conformational flexibility of the beta-(1-->6) glycosidic linkage in beta-gentiobiose. Relaxed Ramachandran maps in vacuo are presented in the torsional angles phi and omega, with torsional angle psi allowed to relax freely, as are all other internal degrees of freedom. The study reveals two almost iso-energetic low energy domains in (phi, psi, omega) space, and cross-sections in the low-energy domains at omega = -60 degrees and omega = 60 degrees show that more than 60% and 70% respectively of the area of the conformational maps are accessible within 40 kJ mol-1. The molecular structure in the crystal, including the exoanomeric effect, is well reproduced. The structure belongs to the potential energy well which includes the global potential energy minimum in vacuo. The most profound structural difference between the crystal structure and the calculated global minimum in vacuo is the 20 degrees deviation of the psi torsional angle (24 degrees from perfect trans). It occurs in the most flexible glucosidic degree of freedom, psi, and is caused by optimization of the hydrogen bonding network and not by the exoanomeric effect.

Structural aspects of Ca2+ binding by acyclic peptides: low-energy conformational domains and molecular dynamics of N-acetyl-L-prolyl-D-alanyl-L-alanine-N'-methylamide.

We have applied random-search, energy minimization and molecular dynamics simulations to investigate the structural aspects of the interaction of N-acetyl-L-prolyl-D-alanyl-L-alanine-N'-methylamide with Ca2+. Spectral data on related peptides had suggested that the beta-turn conformation might be a prerequisite for the binding of cation ion by such short linear peptides. In order to relate the conformational characteristics with the Ca(2+)-binding affinities of these peptides, the molecular events involved in cation binding need to be understood. We have addressed this problem in this study by using a systematic approach that involved the following steps. First, a random search technique was used to generate a large population of conformers for the free peptide in the absence of Ca2+. Next, the energies of these conformers were computed. Conformations with energies within 4 kcal/mol of the global minimum were analysed and found to fall into four main groups characterized by the presence of different types of hydrogen-bonded structures including single and consecutive beta-turns. The energies for interconversion of conformers from one group to another were computed and found to be relatively small (< 10 kcal/mol). Finally, molecular dynamics of the peptide at 300K in the presence of Ca2+ were used to simulate the cation binding process. Starting points for these simulations were generated by placing the ion in the vicinity of two molecules of the peptide. The simulation results showed that the conformers with two consecutive beta-turns led to the formation of a stable 2:1 (peptide:Ca2+) sandwich complex in agreement with earlier experimental observations on similar linear peptides. While the starting conformation of the peptide in the consecutive beta-turn structure allowed for the proper orientation of three carbonyl oxygen atoms for chelation to the metal ion, the dynamics of complex formation rearranged the peptide structure substantially, leading to the formation of an 8-coordinated Ca2+ complex in a dodecahedral spatial arrangement. Thus, based on the energetics of the structures and processes involved, the present study demonstrates that: a) peptide-Ca2+ complex formation is initiated by conformers adopting consecutive beta-turn structures which subsequently go over to a significantly different conformation found in the complex; and, b) The facile interconversion between the low-energy conformers in the different groups would help shift the equilibrium population towards the consecutive beta-turn structure during the complex formation.

Characterization of low-energy conformational domains for Met-enkephalin

An extensive exploration of the conformational hypersurface of Met-enkephalin has been carried out, in order to characterize different low-energy conformational domains accessible to this pentapeptide. The search strategy used consisted of two steps. First, systematic nested rotations were performed using the ECEPP potential. Ninety-two low-energy structures were found and minimized using the CHARMm potential. High and low-temperature molecular dynamics trajectories were then computed for the lowest energy structures in an interative fashion until no lower energy conformers could be found. The same search strategy was used in these studies simulating three different environments, a distance-dependent dielectric epsilon = r, and two constant dielectrics epsilon = 10 and epsilon = 80. The lowest energy structure found in a distance-dependent dielectric is a Gly-Gly beta-II'-type turn. All other structures found for epsilon = r within 10 kcal/mol of this lowest energy structure are also bends. In the more polar environments, the density of conformational states is significantly larger compared to the apolar media. Moreover, fewer hydrogen bonds are formed in the more polar environments, which increases the flexibility of the peptide and results in less structured conformers. Comparisons are made with previous calculations and experimental results.

Low-energy conformational domains of polypeptides, characterized by a random-search and minimization procedure

In the framework of molecular mechanics conformational energy calculations, a random-search and minimization procedure is presented to characterize low-energy domains of polypeptidic structures. Rather than striving for global minima, populations of conformers are randomly generated, and their energy is minimized in order to study their intrinsic properties. The application to the opioid peptide Met-Enkephalin allowed the identification of low-energy domains that are compared with previous results of conformational studies on this molecule. Our method gives a complete overview of the conformational behaviour of the polypeptide under study, including previously reported structures as determined from experimental and theoretical studies. To illustrate the usefulness of this method to determine bioactive peptidic structures and their active conformers, the application to geometrically constrained chemotactic tripeptides is presented. Keywords: peptides, conformation, theoretical prediction.

Low density expansion of the nucleon-nucleus optical-model potential

The optical-model potential for nucleon-nucleus scattering is studied within the framework of the Green function approach to the many-body problem. The optical potential is identified with the self-energy, for which an expansion in terms of irreducible graphs exists. We propose to group the diagrams of this expansion according to the number of independent hole lines and to sum the graphs within each class. This procedure essentially amounts to an expansion in powers of the density and is closely related to the Bethe-Brueckner expansion for the binding energy of nuclear matter. We show that the same convergence parameter appears in both expansions. The one-and two-hole line contributions are studied in detail, numerical estimates are provided and compared with experiment. At low energy, our expansion can be related to the calculation of the optical potential within the framework of nuclear reactions (e.g., using doorway states). At high energy one is led in a natural way to the expressions derived from multiple scattering theory. Thus the hole-line expansion ties together the low and high energy domains of the optical potential. Hole line expansions for the momentum distribution and the total energy are derived from the expansion of the self-energy. The self-consistency requirement is discussed. The present study is restricted to nuclear matter but most results apply to finite nuclei as well.

Models for High-Energy Processes

Recent developments in the concepts and models used to describe high-energy collisions of fundamental particles are reviewed. The areas of appreciable activity in research in high-energy physics are surveyed briefly and the general framework for the description of processes at high energies is outlined. There follows a sampling of recent experimental data designed to show the extent and detail of present-day experimental results. Recent applications of Regge pole models are reviewed with emphasis on the difficulties as well as the successes of models employing only Regge poles. The various multiple-scattering models are then discussed and correlated by means of the methods of Glauber. The connection of these models with amplitudes having branch cuts in the angular-momentum plane (Regge cuts) is described, as well as some comparisons with experiment. Finite energy sum rules as a means of relating the low-energy and high-energy domains are discussed in some detail. Next, the far-reaching concept of duality whereby the direct-channel resonances are (in some sense) the crossed-channel Regge exchanges is described, along with the related ideas of exchange degeneracy, the special role of the Pomeranchon Regge pole, and duality diagrams. An explicit realization of duality is achieved in the Veneziano model. This model is discussed in some detail for the relatively simple and interesting example of pion-pion scattering. Brief mention is also made of the extensions of the Veneziano model to the $n$-particle amplitude, attempts at unitarization, and various applications. The topic of multiparticle final states is covered relatively briefly with emphasis on the applications of double Regge pole exchange to three-body final states, the calculation of proton and pion energy and angular distributions in proton-proton collisions by means of the multi-Regge exchange model, and the generation of self-consistent Regge singularities with the multi-Regge exchange model and unitarity. The final section of the review concerns recent results on pion-pion scattering phase shifts and also $K\ensuremath{-}\ensuremath{\pi}$ phase shifts, and some remarks on theorems connecting decay correlations of resonances with the mechanism of production. The literature survey ended, with a few exceptions, in May 1969.