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Energy Terms (energy + term)
Selected AbstractsSmectic A liquid crystal configurations with interface defectsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2001M. Carme Calderer We study planar energy minimizing configurations of smectic A liquid crystal materials and classify the corresponding defect structures. We investigate focal conic configurations in wedge, non-parallel plates, funnel-shaped domains, and non-concentric annuli. The application of the stability condition for focal conics is relevant to the specification of the location of the interfacial defects. Self-similar structures are discussed for a class of solutions with the same bulk energy. We propose surface energies terms to serve as selection mechanisms of particular self-similar configurations. We also show how the modelling of chevron texture naturally arises in the present framework. Copyright © 2001 John Wiley & Sons, Ltd. [source] On searching in, sampling of, and dynamically moving through conformational space of biomolecular systems: A reviewJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 2 2008Markus Christen Abstract Methods to search for low-energy conformations, to generate a Boltzmann-weighted ensemble of configurations, or to generate classical-dynamical trajectories for molecular systems in the condensed liquid phase are briefly reviewed with an eye to application to biomolecular systems. After having chosen the degrees of freedom and method to generate molecular configurations, the efficiency of the search or sampling can be enhanced in various ways: (i) efficient calculation of the energy function and forces, (ii) application of a plethora of search enhancement techniques, (iii) use of a biasing potential energy term, and (iv) guiding the sampling using a reaction or transition pathway. The overview of the available methods should help the reader to choose the combination that is most suitable for the biomolecular system, degrees of freedom, interaction function, and molecular or thermodynamic properties of interest. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008 [source] Different types of hydrogen bonds: correlation analysis of interaction energy components,JOURNAL OF PHYSICAL ORGANIC CHEMISTRY, Issue 8 2005Slawomir J. Grabowski Abstract Ab initio calculations at the MP2/6,311++G(d,p) level of approximation were performed for the following complexes: (C2H2)2, FH···OCH2, NF3H+···HBeH, H3N···HF, NH4+···HBeH, NH4+···HBeF, (H2O)2, FH···C2H2, (FHF),, FH···OH2, FH···HLi, HCCH···OH2 and HOH···NH3. The decomposition of the interaction energy for these H-bonded dimers was performed, showing that electrostatic and delocalization energy terms are the most important attractive components and together with the repulsive exchange energy term they are the main energy components. Correlation analysis was also applied together with factor analysis, supporting the energetic results of calculations. Copyright © 2005 John Wiley & Sons, Ltd. [source] The effect of a surface energy term on the distribution of phases in an elastic medium with a two-well elastic potentialMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 2 2002Michael Bildhauer Abstract We consider the problem of minimizing among functions u:,d,,,,d, u,,,=0, and measurable subsets E of ,. Here fh+, f, denote quadratic potentials defined on ,¯×{symmetric d×d matrices}, h is the minimum energy of fh+ and ,(u) is the symmetric gradient of the displacement field u. An equilibrium state û, Ê of J(u,E) is called one-phase if E=, or E=,, two-phase otherwise. For two-phase states, ,,,E,,, measures the effect of the separating surface, and we investigate the way in which the distribution of phases is affected by the choice of the parameters h,,, ,>0. Additional results concern the smoothness of two-phase equilibrium states and the behaviour of inf J(u,E) in the limit ,,0. Moreover, we discuss the case of additional volume force potentials, and extend the previous results to non-zero boundary values. Copyright © 2002 John Wiley & Sons, Ltd. [source] Physical,chemical determinants of coil conformations in globular proteinsPROTEIN SCIENCE, Issue 6 2010Lauren L. Perskie Abstract We present a method with the potential to generate a library of coil segments from first principles. Proteins are built from ,-helices and/or ,-strands interconnected by these coil segments. Here, we investigate the conformational determinants of short coil segments, with particular emphasis on chain turns. Toward this goal, we extracted a comprehensive set of two-, three-, and four-residue turns from X-ray,elucidated proteins and classified them by conformation. A remarkably small number of unique conformers account for most of this experimentally determined set, whereas remaining members span a large number of rare conformers, many occurring only once in the entire protein database. Factors determining conformation were identified via Metropolis Monte Carlo simulations devised to test the effectiveness of various energy terms. Simulated structures were validated by comparison to experimental counterparts. After filtering rare conformers, we found that 98% of the remaining experimentally determined turn population could be reproduced by applying a hydrogen bond energy term to an exhaustively generated ensemble of clash-free conformers in which no backbone polar group lacks a hydrogen-bond partner. Further, at least 90% of longer coil segments, ranging from 5- to 20 residues, were found to be structural composites of these shorter primitives. These results are pertinent to protein structure prediction, where approaches can be divided into either empirical or abinitio methods. Empirical methods use database-derived information; abinitio methods rely on physical,chemical principles exclusively. Replacing the database-derived coil library with one generated from first principles would transform any empirically based method into its corresponding abinitio homologue. [source] Sharp interface limit for invariant measures of a stochastic Allen-Cahn equationCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2010Hendrik Weber The invariant measure of a one-dimensional Allen-Cahn equation with an additive space-time white noise is studied. This measure is absolutely continuous with respect to a Brownian bridge with a density that can be interpreted as a potential energy term. We consider the sharp interface limit in this setup. In the right scaling this corresponds to a Gibbs-type measure on a growing interval with decreasing temperature. Our main result is that in the limit we still see exponential convergence towards a curve of minimizers of the energy if the interval does not grow too fast. In the original scaling, the measure is concentrated on configurations with precisely one jump. © 2010 Wiley Periodicals, Inc. [source] Thermal performance of juvenile Atlantic Salmon, Salmo salar L.FUNCTIONAL ECOLOGY, Issue 6 2001B. JONSSON Summary 1,Experimental data for maximum growth and food consumption of Atlantic Salmon (Salmo salar L.) parr from five Norwegian rivers situated between 59 and 70°N were analysed and modelled. The growth and feeding models were also applied to groups of Atlantic Salmon growing and feeding at rates below the maximum. The data were fitted to the Ratkowsky model, originally developed for bacterial growth. 2,The rates of growth and food consumption varied significantly among populations but the variation appeared unrelated to thermal conditions in the river of population origins. No correlation was found between the thermal conditions and limits for growth, thermal growth optima or maximum growth, and hypotheses of population-specific thermal adaptation were not supported. Estimated optimum temperatures for growth were between 16 and 20 °C. 3, Model parameter estimates differed among growth-groups in that maximum growth and the performance breadth decreased from fast to slow growing individuals. The optimum temperature for growth did not change with growth rate. 4, The model for food consumption (expressed in energy terms) peaked at 19,21 °C, which is only slightly higher than the optimal temperature for growth. Growth appeared directly related to food consumption. Consumption was initiated ,2 °C below the lower temperature for growth and terminated ,1·5 °C above the upper critical temperature for growth. Model parameter estimates for consumption differed among growth-groups in a manner similar to the growth models. 5,By combining the growth and consumption models, growth efficiencies were estimated. The maximum efficiencies were high, 42,58%, and higher in rivers offering hostile than benign feeding and growth opportunities. [source] On coupling the Reynolds-averaged Navier,Stokes equations with two-equation turbulence model equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2006Seungsoo Lee Abstract Two methods for coupling the Reynolds-averaged Navier,Stokes equations with the q,, turbulence model equations on structured grid systems have been studied; namely a loosely coupled method and a strongly coupled method. The loosely coupled method first solves the Navier,Stokes equations with the turbulent viscosity fixed. In a subsequent step, the turbulence model equations are solved with all flow quantities fixed. On the other hand, the strongly coupled method solves the Reynolds-averaged Navier,Stokes equations and the turbulence model equations simultaneously. In this paper, numerical stabilities of both methods in conjunction with the approximated factorization-alternative direction implicit method are analysed. The effect of the turbulent kinetic energy terms in the governing equations on the convergence characteristics is also studied. The performance of the two methods is compared for several two- and three-dimensional problems. Copyright © 2005 John Wiley & Sons, Ltd. [source] One-body energy decomposition schemes revisited: Assessment of Mulliken-, Grid-, and conventional energy density analyses,INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 11 2009Yasuaki Kikuchi Abstract We propose a new energy density analysis (EDA) that evaluates atomic contributions of all energy terms, i.e., the kinetic, nuclear-attraction, Coulomb, and Hartree,Fock (HF) exchange and density functional theory (DFT) exchange-correlation energies using the Mulliken-type partitioning. Although widely used DFT exchange-correlation functionals are nonlinear expressions in terms of density, they are decomposed into atomic contributions by focusing the linear part of the density. Numerical assessment on Mulliken-EDA, Grid-EDA, and conventional EDA has been carried out for the G2-1 set. Correlations between HF and DFT exchanges demonstrate that a consistent partitioning of all energy terms is essential for EDA. These numerical results confirm that the present Mulliken-EDA offers a more reasonable picture for the atomization process. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Improved pKa prediction: Combining empirical and semimicroscopic methodsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 15 2008Gernot Kieseritzky Abstract Using three different methods we tried to compute 171 experimentally known pKa values of ionizable residues from 15 different proteins and compared the accuracies of computed pKa values in terms of the root mean square deviation (RMSD) from experiment. One method is based on a continuum electrostatic model of the protein including conformational flexibility (KBPLUS). The others are empirical approaches with PROPKA deploying physically motivated energy terms with adjustable parameters and PKAcal using an empirical function with no physical basis. PROPKA reproduced the pKa values with highest overall accuracy. Differentiating the data set into weakly and strongly shifted experimental pKa values, however, we found that PROPKA's accuracy is better if the pKa values are weakly shifted but on equal footing with that of KBPLUS for more strongly shifted values. On the other hand, PKAcal reproduces strongly shifted pKa values badly but weakly shifted values with the same accuracy as PROPKA. We tested different consensus approaches combining data from all three methods to find a general procedure for most accurate pKa predictions. In most of the cases we found that the consensus approach reproduced experimental data with better accuracy than any of the individual methods alone. © 2008 Wiley Periodicals, Inc. J Comput Chem 2008 [source] Molecular dynamics simulation in the grand canonical ensembleJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 10 2007Hossein Eslami Abstract An extended system Hamiltonian is proposed to perform molecular dynamics (MD) simulation in the grand canonical ensemble. The Hamiltonian is similar to the one proposed by Lynch and Pettitt (Lynch and Pettitt, J Chem Phys 1997, 107, 8594), which consists of the kinetic and potential energies for real and fractional particles as well as the kinetic and potential energy terms for material and heat reservoirs interacting with the system. We perform a nonlinear scaling of the potential energy parameters of the fractional particle, as well as its mass to vary the number of particles dynamically. On the basis of the equations of motion derived from this Hamiltonian, an algorithm has been proposed for MD simulation at constant chemical potential. The algorithm has been tested for the ideal gas, for the Lennard,Jones fluid over a wide range of temperatures and densities, and for water. The results for the low-density Lennard,Jones fluid are compared with the predictions from a truncated virial equation of state. In the case of the dense Lennard,Jones fluid and water our predicted results are compared with the results reported using other available methods for the calculation of the chemical potential. The method is also applied to the case of vapor-liquid coexistence point predictions. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007 [source] Atom,atom partitioning of total (super)molecular energy: The hidden terms of classical force fieldsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 1 2007M. Rafat Abstract Classical force fields describe the interaction between atoms that are bonded or nonbonded via simple potential energy expressions. Their parameters are often determined by fitting to ab initio energies and electrostatic potentials. A direct quantum chemical guide to constructing a force field would be the atom,atom partitioning of the energy of molecules and van der Waals complexes relevant to the force field. The authors used the theory of quantum chemical topology to partition the energy of five systems [H2, CO, H2O, (H2O)2, and (HF)2] in terms of kinetic, Coulomb, and exchange intra-atomic and interatomic contributions. The authors monitored the variation of these contributions with changing bond length or angle. Current force fields focus only on interatomic interaction energies and assume that these purely potential energy terms are the only ones that govern structure and dynamics in atomistic simulations. Here the authors highlight the importance of self-energy terms (kinetic and intra-atomic Coulomb and exchange). © 2006 Wiley Periodicals, Inc. J Comput Chem 2007 [source] Prediction of pKa shifts in proteins using a combination of molecular mechanical and continuum solvent calculationsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 15 2004Bernd Kuhn Abstract The prediction of pKa shifts of ionizable groups in proteins is of great relevance for a number of important biological phenomena. We present an implementation of the MM-GBSA approach, which combines molecular mechanical (MM) and generalized Born (GB) continuum solvent energy terms, to the calculation of pKa values of a panel of nine proteins, including 69 individual comparisons with experiment. While applied so far mainly to the calculation of biomolecular binding free energies, we show that this method can also be used for the estimation of protein pKa shifts, with an accuracy around 1 pKa unit, even for strongly shifted residues. Our analysis reveals that the nonelectrostatic terms that are part of the MM-GBSA free energy expression are important contributors to improved prediction accuracy. This suggests that most of the previous approaches that focus only on electrostatic interactions could be improved by adding other nonpolar energy terms to their free energy expression. Interestingly, our method yields best accuracy at protein dielectric constants of ,int = 2,4, which is in contrast to previous approaches that peak at higher ,int , 8. An important component of our procedure is an intermediate minimization step of each protonation state involving different rotamers and tautomers as a way to explicitly model protein relaxation upon (de)protonation. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 1865,1872, 2004 [source] Comparison of linear-scaling semiempirical methods and combined quantum mechanical/molecular mechanical methods for enzymic reactions.JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 14 2002Abstract QM/MM methods have been developed as a computationally feasible solution to QM simulation of chemical processes, such as enzyme-catalyzed reactions, within a more approximate MM representation of the condensed-phase environment. However, there has been no independent method for checking the quality of this representation, especially for highly nonisotropic protein environments such as those surrounding enzyme active sites. Hence, the validity of QM/MM methods is largely untested. Here we use the possibility of performing all-QM calculations at the semiempirical PM3 level with a linear-scaling method (MOZYME) to assess the performance of a QM/MM method (PM3/AMBER94 force field). Using two model pathways for the hydride-ion transfer reaction of the enzyme dihydrofolate reductase studied previously (Titmuss et al., Chem Phys Lett 2000, 320, 169,176), we have analyzed the reaction energy contributions (QM, QM/MM, and MM) from the QM/MM results and compared them with analogous-region components calculated via an energy partitioning scheme implemented into MOZYME. This analysis further divided the MOZYME components into Coulomb, resonance and exchange energy terms. For the model in which the MM coordinates are kept fixed during the reaction, we find that the MOZYME and QM/MM total energy profiles agree very well, but that there are significant differences in the energy components. Most significantly there is a large change (,16 kcal/mol) in the MOZYME MM component due to polarization of the MM region surrounding the active site, and which arises mostly from MM atoms close to (<10 Å) the active-site QM region, which is not modelled explicitly by our QM/MM method. However, for the model where the MM coordinates are allowed to vary during the reaction, we find large differences in the MOZYME and QM/MM total energy profiles, with a discrepancy of 52 kcal/mol between the relative reaction (product,reactant) energies. This is largely due to a difference in the MM energies of 58 kcal/mol, of which we can attribute ,40 kcal/mol to geometry effects in the MM region and the remainder, as before, to MM region polarization. Contrary to the fixed-geometry model, there is no correlation of the MM energy changes with distance from the QM region, nor are they contributed by only a few residues. Overall, the results suggest that merely extending the size of the QM region in the QM/MM calculation is not a universal solution to the MOZYME- and QM/MM-method differences. They also suggest that attaching physical significance to MOZYME Coulomb, resonance and exchange components is problematic. Although we conclude that it would be possible to reparameterize the QM/MM force field to reproduce MOZYME energies, a better way to account for both the effects of the protein environment and known deficiencies in semiempirical methods would be to parameterize the force field based on data from DFT or ab initio QM linear-scaling calculations. Such a force field could be used efficiently in MD simulations to calculate free energies. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 1314,1322, 2002 [source] Quantum chemical geometry optimizations in proteins using crystallographic raw dataJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 11 2002Ulf Ryde Abstract A method is developed for the combination of quantum chemical geometry optimizations and crystallographic structure refinement. The method is implemented by integrating the quantum chemical software Turbomole with the crystallographic software Crystallography and NMR System (CNS), using three small procedures transferring information between the two programs. The program (COMQUM-X)is used to study the binding of the inhibitor N -methylmesoporphyrin to ferrochelatase, and we show that the method behaves properly and leads to an improvement of the structure of the inhibitor. It allows us to directly quantify in energy terms how much the protein distort the structure of the bound inhibitor compared to the optimum vacuum structure (4,6 kJ/mol). The approach improves the standard combined quantum chemical and molecular mechanics (QC/MM) approach by guaranteeing that the final structure is in accordance with experimental data (the reflections) and avoiding the risk of propagating errors in the crystal coordinates. The program can also be seen as an improvement of standard crystallographic refinement, providing an accurate empirical potential function for any group of interest. The results can be directly interpreted in standard crystallographic terms (e.g., R factors or electron density maps). The method can be used to interpret crystal structures (e.g., the protonation status of metal-bound water molecules) and even to locally improve them. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 1058,1070, 2002 [source] New energy terms for reduced protein models implemented in an off-lattice force fieldJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 12 2001Tommi Hassinen Abstract Parameterization and test calculations of a reduced protein model with new energy terms are presented. The new energy terms retain the steric properties and the most significant degrees of freedom of protein side chains in an efficient way using only one to three virtual atoms per amino acid residue. The energy terms are implemented in a force field containing predefined secondary structure elements as constraints, electrostatic interaction terms, and a solvent-accessible surface area term to include the effect of solvation. In the force field the main-chain peptide units are modeled as electric dipoles, which have constant directions in ,-helices and ,-sheets and variable conformation-dependent directions in loops. Protein secondary structures can be readily modeled using these dipole terms. Parameters of the force field were derived using a large set of experimental protein structures and refined by minimizing RMS errors between the experimental structures and structures generated using molecular dynamics simulations. The final average RMS error was 3.7 Å for the main-chain virtual atoms (C, atoms) and 4.2 Å for all virtual atoms for a test set of 10 proteins with 58,294 amino acid residues. The force field was further tested with a substantially larger test set of 608 proteins yielding somewhat lower accuracy. The fold recognition capabilities of the force field were also evaluated using a set of 27,814 misfolded decoy structures. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1229,1242, 2001 [source] Different types of hydrogen bonds: correlation analysis of interaction energy components,JOURNAL OF PHYSICAL ORGANIC CHEMISTRY, Issue 8 2005Slawomir J. Grabowski Abstract Ab initio calculations at the MP2/6,311++G(d,p) level of approximation were performed for the following complexes: (C2H2)2, FH···OCH2, NF3H+···HBeH, H3N···HF, NH4+···HBeH, NH4+···HBeF, (H2O)2, FH···C2H2, (FHF),, FH···OH2, FH···HLi, HCCH···OH2 and HOH···NH3. The decomposition of the interaction energy for these H-bonded dimers was performed, showing that electrostatic and delocalization energy terms are the most important attractive components and together with the repulsive exchange energy term they are the main energy components. Correlation analysis was also applied together with factor analysis, supporting the energetic results of calculations. Copyright © 2005 John Wiley & Sons, Ltd. [source] Molecular Modeling and Receptor-Dependent (RD) 3D-QSAR Approach to a Set of Antituberculosis DerivativesMOLECULAR INFORMATICS, Issue 11-12 2009Fernanda, Kerly, Mesquita Pasqualoto Abstract In this study, receptor-dependent (RD) 3D-QSAR models were built for a set of thirty-seven isoniazid derivatives bound to the enoyl-acp reductase from M. tuberculosis, called InhA (PDB entry code 1zid). Ligand-receptor (L-R) molecular dynamics (MD) simulations [500,000 steps; the step size was 0.001,ps (1,fs)] were carried out at 310,K (biological assay temperature). The hypothesized active conformations resulting from a previously reported receptor-independent (IR) 4D-QSAR analysis were used as the molecular geometries of each ligand in this structure-based L-R binding research. The dependent variable is the reported MIC values against M. tuberculosis var. bovis. The independent variables (descriptors) are energy terms of a modified first-generation AMBER force field combined with a hydration shell aqueous solvation model. Genetic function approximation (GFA) formalism and partial least squares (PLS) regression were employed as the fitting functions to develop 3D-QSAR models. The bound ligand solvation energy, the sum of electrostatic and hydrogen bonding energies of the unbound ligand, the bending energy of the unbound ligand, the electrostatic intermolecular L-R energy, and the change in hydrogen bonding energy upon binding were found as important energy contributions to the binding process. The 3D-QSAR model at 310,K has good internal and external predictability and may be regarded as representative of the binding process of ligands to InhA. [source] Physical,chemical determinants of coil conformations in globular proteinsPROTEIN SCIENCE, Issue 6 2010Lauren L. Perskie Abstract We present a method with the potential to generate a library of coil segments from first principles. Proteins are built from ,-helices and/or ,-strands interconnected by these coil segments. Here, we investigate the conformational determinants of short coil segments, with particular emphasis on chain turns. Toward this goal, we extracted a comprehensive set of two-, three-, and four-residue turns from X-ray,elucidated proteins and classified them by conformation. A remarkably small number of unique conformers account for most of this experimentally determined set, whereas remaining members span a large number of rare conformers, many occurring only once in the entire protein database. Factors determining conformation were identified via Metropolis Monte Carlo simulations devised to test the effectiveness of various energy terms. Simulated structures were validated by comparison to experimental counterparts. After filtering rare conformers, we found that 98% of the remaining experimentally determined turn population could be reproduced by applying a hydrogen bond energy term to an exhaustively generated ensemble of clash-free conformers in which no backbone polar group lacks a hydrogen-bond partner. Further, at least 90% of longer coil segments, ranging from 5- to 20 residues, were found to be structural composites of these shorter primitives. These results are pertinent to protein structure prediction, where approaches can be divided into either empirical or abinitio methods. Empirical methods use database-derived information; abinitio methods rely on physical,chemical principles exclusively. Replacing the database-derived coil library with one generated from first principles would transform any empirically based method into its corresponding abinitio homologue. [source] Building native protein conformation from NMR backbone chemical shifts using Monte Carlo fragment assemblyPROTEIN SCIENCE, Issue 8 2007Haipeng Gong Abstract We have been analyzing the extent to which protein secondary structure determines protein tertiary structure in simple protein folds. An earlier paper demonstrated that three-dimensional structure can be obtained successfully using only highly approximate backbone torsion angles for every residue. Here, the initial information is further diluted by introducing a realistic degree of experimental uncertainty into this process. In particular, we tackle the practical problem of determining three-dimensional structure solely from backbone chemical shifts, which can be measured directly by NMR and are known to be correlated with a protein's backbone torsion angles. Extending our previous algorithm to incorporate these experimentally determined data, clusters of structures compatible with the experimentally determined chemical shifts were generated by fragment assembly Monte Carlo. The cluster that corresponds to the native conformation was then identified based on four energy terms: steric clash, solvent-squeezing, hydrogen-bonding, and hydrophobic contact. Currently, the method has been applied successfully to five small proteins with simple topology. Although still under development, this approach offers promise for high-throughput NMR structure determination. [source] Electrostatic screening and backbone preferences of amino acid residues in urea-denatured ubiquitinPROTEIN SCIENCE, Issue 2 2007Franc Avbelj Abstract Local structures in denatured proteins may be important in guiding a polypeptide chain during the folding and misfolding processes. Existence of local structures in chemically denatured proteins is a highly controversial issue. NMR parameters [coupling constants 3J(H,,HN) and chemical shifts] of chemically denatured proteins in general deviate little from their values in small peptides. These peptides were presumed to be completely unstructured; therefore, it was considered that chemically denatured proteins are random coils. But recent experimental studies show that small peptides adopt relatively stable structures in aqueous solutions. Small deviations of the NMR parameters from their values in small peptides may thus actually indicate the existence of local structures in chemically denatured proteins. Using NMR data and theoretical predictions we show here that fluctuating ,-strands exist in urea-denatured ubiquitin (8 M urea at pH 2). Residues in such ,-strands populate more frequently the left side of the broad , region of ,,, space. Urea-denatured ubiquitin contains no detectable ,-sheet secondary structures; nevertheless, the fluctuating ,-strands in urea-denatured ubiquitin coincide to the ,-strands in the native state. Formation of ,-strands is in accord with the electrostatic screening model of unfolded proteins. The free energy of a residue in an unfolded protein is in this model determined by the local backbone electrostatics and its screening by backbone solvation. These energy terms introduce strong electrostatic coupling between neighboring residues, which causes cooperative formation of ,-strands in denatured proteins. We propose that fluctuating ,-strands in denatured proteins may serve as initiation sites to form fibrils. [source] | ||||||||||||||||