Free Energy Structure Research Articles

Assessing the reliability of RNA folding using statistical mechanics

We have analyzed the base-pairing probability distributions of 16 S and 16 S-like, and 23 S and 23 S-like ribosomal RNAs of Archaea, Bacteria, chloroplasts, mitochondria and Eukarya, as predicted by the partition function approach for RNA folding introduced by McCaskill. A quantitative analysis of the reliability of RNA folding is done by comparing the base-pairing probability distributions with the structures predicted by comparative sequence analysis (comparative structures). We distinguish two factors that show a relationship to the reliability of RNA minimum free energy structure. The first factor is the dominance of one particular base-pair or the absence of base-pairing for a given base within the base-pairing probability distribution (BPPD). We characterize the BPPD per base, including the probability of not base-pairing, by its Shannon entropy ( S). The S value indicates the uncertainty about the base-pairing of a base: low S values result from BPPDs that are strongly dominated by a single base-pair or by the absence of base-pairing. We show that bases with low S values have a relatively high probability that their minimum free energy (MFE) structure corresponds to the comparative structure. The BPPDs of prokaryotes that live at high temperatures (thermophilic Archaea and Bacteria) have, calculated at 37°C, lower S values than the BPPDs of prokaryotes that live at lower temperatures (mesophilic and psychrophilic Archaea and Bacteria). This reflects an adaptation of the ribosomal RNAs to the environmental temperature. A second factor that is important to consider with regard to the reliability of MFE structure folding is a variable degree of applicability of the thermodynamic model of RNA folding for different groups of RNAs. Here we show that among the bases that show low S values, the Archaea and Bacteria have similar, high probabilities (0.96 and 0.94 in 16 S and 0.93 and 0.91 in 23 S, respectively) that the MFE structure corresponds to the comparative structure. These probabilities are lower in the chloroplasts (16 S 0.91, 23 S 0.79), mitochondria (16 S-like 0.89, 23 S-like 0.69) and Eukarya (18 S 0.81, 28 S 0.86).

Studies on the surface free energy and surface structure of PTFE film treated with low temperature plasma

The surface free energy and surface structure of poly(tetrafluoroethylene) (PTFE) film treated with low temperature plasma in O2, Ar, He, H2, NH3, and CH4 gases are studied. The contact angles of the samples were measured, and the critical surface tension γc (Zisman) and γc (max) were determined on the basis of the Zisman's plots. Furthermore, the values of nonpolar dispersion force γas, dipole force γbs, and hydrogen bonding force γcs to the surface tensions for the plasma-treated samples were evaluated by the extended Fowkes equation. Mainly because of the contribution of polar force, the surface free energy and surface wettability of PTFE film which was treated with H2, He, NH3, Ar, and CH4 for a short time increased greatly. Electron spectroscopy for chemical analysis (ESCA) shows that the reason was the decrease of fluorine and the increase of oxygen or nitrogen polar functional group on the surface of PTFE. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 63: 1733–1739, 1997

Interfaces between coexisting phases of polymer mixtures: Comparison between Monte Carlo simulations and theoretical predictions

AbstractLarge scale Monte Carlo investigations of the interface between A‐rich and B‐rich phases of symmetric binary (AB) polymer mixtures are presented, using the bond fluctuation model of flexible chains with NA=NB=N=32 effective monomers. The temperature range studied, 0.144<T/Tc0.759, includes both the strong and the weak segregation limit. Interfacial free energy and interfacial structure are studied, and compared to predictions based on the selfconsistent field theory. Also the broadening of the interfacial width due to capillary waves is considered, and finite size effects due to the confinement of interfaces in thin films of polymer blends are discussed.

Efficiency of monte carlo minimization procedures and their use in analysis of NMR data obtained from flexible peptides

The Monte Carlo minimization (MCM) method of Li and Scheraga is an efficient tool for generating low energy minimized structures of peptides, in particular the global energy minimum (GEM). In a recent article we proposed an enhancement to MCM, called the free energy Monte Carlo minimization (FMCM) procedure. With FMCM the conformational search is carried out with respect to the harmonic free energy, which approximates the free energy of the potential energy wells around the energy minimized structures (these wells are called localized microstates). In this work we apply both methods to the pentapeptide Leu-enkephalin described by the potential energy function ECEPP, and study their efficiency in identifying the GEM structure as well as the global harmonic free energy (GFM) structure. We also investigate the efficiency of these methods to generate localized microstates, which pertain to different energy and harmonic free energy intervals above the GEM and GFM, respectively. Such microstates constitute an important ingredient of our statistical mechanical methodology for analyzing nuclear magnetic resonance data of flexible peptides. Aspects of this methodology related to the stability properties of the localized microstates are examined. © 1997 by John Wiley & Sons, Inc.

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.

Experimental verification of the secondary structures of guide RNA-pre-mRNA chimaeric molecules in Trypanosoma brucei.

RNA editing in kinetoplastid organisms is an RNA-processing reaction that adds and deletes U nucleotides at specific sites in mitochondrial pre-mRNAs. The edited sequence is specified by guide RNAs and the processing presumably occurs within a high-molecular-mass ribonucleoprotein complex containing several enzymatic activities. Although the mechanism is not currently known, potential intermediates or by-products of the editing process are chimaeric RNAs where guide (g) RNAs are covalently attached, via their non-encoded U-tail, to their cognate pre-mRNAs. We determined the secondary structures of three different ATPase 6 chimaeras of Trypanosoma brucei using a set of structure-sensitive chemical and enzymatic probes. The experiments revealed a bipartite domain structure consisting of a gRNA/pre-mRNA interaction hairpin and an independently folding mRNA stem/loop in all three RNAs. The connecting U-tail was a determinant for the length of the interaction stems with the oligo(U) nucleotides base pairing to internal gRNA sequences. The probed structures have calculated delta G27o values of -92 kJ/ mol to -134 kJ/mol, somewhat less stable than the predicted minimal free energy structures and support previously proposed models for the interaction between gRNAs and pre-mRNAs. Optical melting studies indicated additional, higher order structural features for all three molecules with four defined melting transition between 10 degrees C and 90 degrees C. A comparison of CD spectra in the absence and presence of mitochondrial protein extracts demonstrated no gross structural changes of the RNA structures induced by the association with polypeptides.

Free energy and cluster structure in the coexistence region of the restricted primitive model

The method of thermodynamic integration is used to determine the free energy of the restricted primitive model of electrolytes along two subcritical isotherms. The densities of liquid-gas coexistence derived from these data are found to be in good agreement with recent estimates from Gibbs ensemble Monte Carlo calculations. The difficulties of the free energy approach—which reside in the necessity of obtaining extremely accurate free energy values at near critical temperatures—is stressed. A detailed account is given of the clustering properties of the ions in the vapor phase, including cluster populations and energies, as well as intercluster contributions to the thermodynamic properties. The validity of several cluster theories for the free energy is investigated.

Quantitative structure-free energy relationship for the dehalogenation of halogenated aromatic compounds

The structure-reactivity relationship for the biodegradation of various classes of halogenated aromatic compounds was studied. The results indicated that free energies of these dehalogenations could be estimated accurately. Microorganisms conserve energy for growth by routing electrons in the form of H 2 from anaerobic environments to halogenated aromatic compounds as electron acceptors. In order to develop a calculable method of quantitative structure-reactivity and estimate the degree of dehalogenation of compounds, a number of available molecular descripors were correlated to the free energies of the reaction, the best correlation was obtained using the descriptors 〈1〉 energy of the heighest ocupied molecular orbital 〈2〉 molecular connectivity of the substrates.

Free energies of interfaces from quasi-harmonic theory: A critical appraisal

A critical assessment is given of the quasi-harmonic approximation, and various approximations to the quasi-harmonic approximation, with regard to predicting the free energy and atomic structure of grain boundaries in silicon at elevated temperatures. The quasi-harmonic results are compared with those obtained by molecular dynamics and thermodynamic integration. It is found that the quasi-harmonic approximation yields accurate excess free energies and atomic structures of grain boundaries at 1,000 K. The anharmonic contribution to the free energy that is absent in the quasi-harmonic contribution is virtually the same at a grain boundary in Si and in the perfect crystal. The second-moment and Einstein approximations to the full quasi-harmonic theory yield unreliable free energies, but reasonably accurate atomic structures. However, excess free energies are quite well described by the Einstein model. It is concluded that the quasi-harmonic approximation works remarkably well in silicon. The simplest approximations to the phonon density of states lead to unreliable results for the free energy, but cancellation of errors occurs to a large extent when excess free energies are computed.

Prediction of alternative RNA secondary structures based on fluctuating thermodynamic parameters.

In this paper we present a new method for predicting a set of RNA secondary structures that are thermodynamically favored in RNA folding simulations. This method uses a large number of 'simulated energy rules' (SER) generated by perturbing the free energy parameters derived experimentally within the range of the experimental errors. The structure with the lowest free energy is computed for each SER. Structural comparisons are used to avoid multiple generation of similar structures. Computed structures are evaluated using the energy distribution of the lowest free energy structures derived in the simulation. Predicted be graphically displayed with their occurring frequencies in the simulation by dot-plot representations. On average, about 90% of phylogenetic helixes in the known models of tRNA, Group I self-splicing intron, and Escherichia coli 16 S rRNA, were predicted using the method.

A comparison of optimal and suboptimal RNA secondary structures predicted by free energy minimization with structures determined by phylogenetic comparison

This article describes the latest version of an RNA folding algorithm that predicts both optimal and suboptimal solutions based on free energy minimization. A number of RNA's with known structures deduced from comparative sequence analysis are folded to test program performance. The group of solutions obtained for each molecule is analysed to determine how many of the known helixes occur in the optimal solution and in the best suboptimal solution. In most cases, a structure about 80% correct is found with a free energy within 2% of the predicted lowest free energy structure.

Current research problems and opportunities in the vapor phase synthesis of diamond and cubic boron nitride

Current research problems in the chemical-vapor deposition (CVD) of diamond and cubic-boron nitride (c-BN) include efforts to rationalize the formation of well-crystallized diamond as part of efforts to achieve several important goals. Among these is well-crystallized c-BN by CVD, improved diamond crystal perfection important to many applications, the large-area heteroepitaxial growth of diamond (or c-BN), and possibly, new composites and superlattice materials not heretofore thought possible. It is argued that the synthesis of diamond is not inconsistent with thermodynamic analysis, provided the influence of relevant surface chemistries and the nonequilibrium nature of materials synthesis are taken into account, and that the phase composition of the solid is determined in large measure by the lowest free-energy structure of its surface during growth. From linear irreversible thermodynamics it follows that crystal perfection and the nature of the growth surface during deposition will be determined by how far from equilibrium the system is held and whether or not a locally stable stationary state is maintained during deposition. The greater the departure from equilibrium, the higher the defect levels expected, implying that the growth of relatively defect-free diamond will require a close approach to equilibrium. Much of the experimental data available are shown to be consistent with this approach, including difficulties with using methods successful for diamond to grow c-BN. Although the diamond growth surface can be stabilized by the chemisorption of hydrogen, a similar stabilization of the surfaces of c-BN is at best problematic, and new chemistries may be needed to achieve its synthesis. Similarly, the heteroepitaxial growth of diamond may require not only the provision of a suitable surface template or lattice match but, also, a compatible interfacial chemistry for the stabilization of sp3 hybridized carbon.

Spin glass properties of a class of mean-field models

A class of mean-field models for spin glasses, in which the magnitude of the Onsager term is controlled to interpolate between the TAP equations for the SK model and the 'naive' mean-field (NMF) equations, is introduced. The authors examine the number of metastable states and the related parameters of the models. For the NMF model the spin glass susceptibility is also evaluated numerically. The results indicate that the rugged free energy structure and the marginal stability of the spin glass phase are common properties of these mean-field models, and that the Onsager term plays a minor role on yielding these novel spin glass properties.

A new method to find a set of energetically optimal RNA secondary structures

We present a computer method to determine nucleic acid secondary structures. It is based on three steps: 1) the search for all possible helical regions relied on a mathematical approach derived from the convolution theorem; it uses a tetradimensional complex vector representation of the bases along the sequence; 2) a 'tree' search for a set of minimum free energy structures, by the aid of an approximate energy evaluation to reduce the computer time requirements; 3) the exact calculation and refinement of the energies. A method to introduce the experimental data and reach an arrangement between them and the free energy minimization criterion is shown. In order to demonstrate the confidence of the program a test on four RNA sequences is performed. The method has computer time requirement proportional to N2, where N is the length of the sequence and retrieves a set of optimal free energy structures.

TAP free energy structure of SK spin glasses

The structure of the TAP free energy of SK spin glasses of finite sizes is studied numerically. The extrapolation of the results to the thermodynamic limit indicates that a solution of the TAP equations correspondings to a saddle point on the boundary beyond which the validity condition of the TAP free energy no longer holds.

The role of surface free energy and lattice structure in the cathodic protection of Al-Zn-Hg alloy

The enhanced cathodic protection characteristic of Al-Zn-Hg compared with aluminium or Al-Zn alloy has been looked at from a structural point of view. The surface free energies of these metals and alloys have been calculated from their atomic spacings and Young's moduli. Atomic spacings were obtained from Debye-Scherrer powder diffraction studies and Young's moduli from stress-strain curves. It has shown that al-Zn-Hg has the lowest surface free energy, leading to a film with reduced thickness and reduced metal/oxide bond strength. These factors in turn result in the better cathodic protection properties of Al-Zn-Hg alloy.

Crystal structure and melting in a cell model. I. Solvable lattices and isomorphisms

The free energy and crystal structure of some particular cases of a cell model of melting are obtained. These include (i) a class of one-dimensional cases with interactions extending to many neighbouring cells, (ii) the plane hexagonal, bcc and triangular lattices with nearest-neighbour interactions, (iii) a case of the plane, square lattice with first- and second-neighbour (diagonal) interactions, and others. The solutions for the simple cubic lattices in all dimensions were obtained in a previous paper (abstr. A46569 of 1971). It is shown that some of the 2, 3, etc dimensional cases are closely related ('isomorphic') to one-dimensional cases.

Studies on the stabilizing forces of simple RNA viruses: II. Stability, dissociation and reassembly of cucumber mosaic virus

The stability properties of cucumber mosaic virus were investigated in relation to those of two other, well-described, icosahedral RNA viruses of similar geometry; the cowpea chlorotic mottle virus and the turnip yellow mosaic virus. High concentrations of neutral salts caused the dissociation of cucumber mosaic virus into its constituent RNA and protein subunits irrespective of the pH of the solution. At low ionic strength the effect of pH on the infectivity and the sedimentation behavior of the virus was tested between pH 4.0 and 8.5. No effect was noticed in this range, but significant change became evident at pH 9.8 and was complete at pH 10.45. The products of this alkaline treatment were a mixture of slower sedimenting nucleoproteins. The RNA inside cucumber mosaic virus was accessible to pancreatic ribonuclease. There was little or no pH-dependence of the ribonuclease susceptibility. Under no circumstances were protein capsids of cucumber mosaic virus ever obtained, neither by degradation of the virion, reassembly of the protein subunits, nor directly from the infected plant. These stability properties of cucumber mosaic virus are strikingly different from those of cowpea chlorotic mottle virus and turnip yellow mosaic virus, as reported in the literature, and indicate the possession of only weak inter-protein subunit linkages, or their total absence. Cucumber mosaic virus could be reversibly dissociated by varying the concentration of lithium chloride in its solutions. The reassembled virus was shown to be identical to cucumber mosaic virus in its physical properties, in its reaction with cucumber mosaic virus antiserum, and in the degree of its sensitivity to ribonuclease. The infectivity of the reassembled virus was almost as high as the infectivity of the untreated virus. Cucumber mosaic virus protein combined with great efficiency with turnip yellow mosaic virus RNA of different molecular conformations and size. Fragmented turnip yellow mosaic virus RNA (molecular weight 60,000) combined to yield particles with the sedimentation properties of cucumber mosaic virus ( S 20, w about 93 s); full size turnip yellow mosaic virus RNA gave particles with sedimentation rates of about 130 s. The presence of RNA was mandatory for the reassembly of cucumber mosaic virus protein subunits. No reaggregation of alkali-converted cucumber mosaic virus could be achieved. Salt-dissociated cucumber mosaic virus failed to reassemble in a normal fashion below pH 5, where insoluble nucleoprotein precipitates were formed, or above pH 10, where slower sedimenting nucleoproteins were obtained. These nucleoproteins also could not be assembled further into virus-like particles, and might represent minimum free-energy structures resulting from a less specific interaction of the different sized RNA species of cucumber mosaic virus with protein subunits. Cucumber mosaic virus probably derives its stability from relatively strong ionic linkages between nucleic acid-phosphate residues functioning as a polyanion, and basic amino-acid residues of the protein which function as a polycation.