Structural model for an oligonucleotide containing a bulged guanosine by NMR and energy minimization

We present three-dimensional structural models for a DNA oligomer containing a bulged guanosine based on proton NMR data and energy minimization computations. The nonexchangeable proton resonances of the duplex 5'd(GATGGGCAG).d(CTGCGCCATC) are assigned by nuclear Overhauser effect spectroscopy (NOESY) and correlated spectroscopy connectivities, and the NMR spectrum is compared with that of a regular 8-mer of similar sequence, 5'd(GATGGCAG).d(CTGCCATC). Experimental proton-proton distances are obtained from NOESY spectra acquired with mixing times of 100, 150, and 200 ms. A refined three-dimensional structure for the bulge-containing duplex is calculated from regular B DNA starting coordinates by using the AMBER molecular mechanics program [Weiner, S. J., Kollman, P. A., Case, D. A., Singh, U. C., Ghio, C., Alagona, G., Profeta, S., & Weiner, P. (1984) J. Am. Chem. Soc. 106, 765-784]. We compare structures obtained by building the helix in three and four base pair increments with structures obtained by direct minimization of the entire nine base sequence, with and without experimental distance constraints. The general features of all the calculated structures are very similar. The helix is of the B family, with the extra guanine stacked into the helix, and the helix axis is bent by 18-23 degrees, in agreement with gel mobility data for bulge-containing sequences [Rice, J. A. (1987) Ph.D. Thesis, Yale University].     

Computation of mixed phosphatidylcholine-cholesterol bilayer structures by energy minimization.

The energetically preferred structures of dimyristoylphosphatidylcholine (DMPC)-cholesterol bilayers were determined at a 1:1 mole ratio. Crystallographic symmetry operations were used to generate planar bilayers of cholesterol and DMPC. Energy minimization was carried out with respect to bond rotations, rigid body motions, and the two-dimensional lattice constants. The lowest energy structures had a hydrogen bond between the cholesterol hydroxyl and the carbonyl oxygen of the sn-2 acyl chain, but the largest contribution to the intermolecular energy was from the nonbonded interactions between the flat alpha surface of cholesterol and the acyl chains of DMPC. Two modes of packing in the bilayer were found; in structure A (the global minimum), unlike molecules are nearest neighbors, whereas in structure B (second lowest energy) like-like intermolecular interactions predominate. Crystallographic close packing of the molecules in the bilayer was achieved, as judged from the molecular areas and the bilayer thickness. These energy-minimized structures are consistent with the available experimental data on mixed bilayers of lecithin and cholesterol, and may be used as starting points for molecular dynamics or other calculations on bilayers.     

Accurate flexible fitting of high-resolution protein structures into cryo-electron microscopy maps using coarse-grained pseudo-energy minimization

Cryo-electron microscopy (cryo-EM) has been widely used to explore conformational states of large biomolecular assemblies. The detailed interpretation of cryo-EM data requires the flexible fitting of a known high-resolution protein structure into a low-resolution cryo-EM map. To this end, we have developed what we believe is a new method based on a two-bead-per-residue protein representation, and a modified form of the elastic network model that allows large-scale conformational changes while maintaining pseudobonds and secondary structures. Our method minimizes a pseudo-energy which linearly combines various terms of the modified elastic network model energy with a cryo-EM-fitting score and a collision energy that penalizes steric collisions. Unlike previous flexible fitting efforts using the lowest few normal modes, our method effectively utilizes all normal modes so that both global and local structural changes can be fully modeled. We have validated our method for a diverse set of 10 pairs of protein structures using simulated cryo-EM maps with a range of resolutions and in the absence/presence of random noise. We have shown that our method is both accurate and efficient compared with alternative techniques, and its performance is robust to the addition of random noise. Our method is also shown to be useful for the flexible fitting of three experimental cryo-EM maps.     

Conformation of a bulge-containing oligomer from a hot-spot sequence by NMR and energy minimization

Two-dimensional nmr data on a bulge-containing oligodeoxyribonucleotide, 5'dGATGGGCAG.dCTGACCCATC, and a regular oligomer of similar sequence, 5'dGATGGCAG.dCTGCCATC, are presented. The nonexchangeable protons are assigned from sequential nuclear Overhauser effect spectroscopy (NOESY) connectivities. The two-dimensional NOE (NOESY) and correlated (COSY) spectra of the bulge-containing oligomer are compared to those of the perfect 8-mer. Experimental proton-proton distances are determined from NOESY spectra acquired with mixing times of 100, 150, and 200 ms, using comparable distances in the B-DNA region of the molecule as a calibration. With this approach, measured distances do not depend systematically on mixing time. Energy minimization techniques are used to calculate a three-dimensional structure for the bulge-containing oligomer in agreement with the nmr data. The helix is of the B family, with the extra adenine stacked into the helix, and the helix axis is bent by 20 degrees.     

Prediction of the structure of proteins using related structures,energy minimization and computer graphics

Insight into the functions and interactions of proteins may be gained by correlating a variety of types of experimental data (including kinetics, spectroscopy, biophysical measurements, among others) with three-dimensional structural models displayed and manipulated using interactive computer graphics. Although tertiary structures have been determined for a large number of proteins, one limiting factor in structure-function studies is the lack of availability of the structural coordinates of specific proteins for which other types of detailed experimental data are known. However, as the data base of known structures grows, it becomes more and more likely that the structure of a closely related protein will be available. Here we present a method for predicting structures by ( 1 ) careful alteration of a known structure of a homologous, functionally analogous protein followed by (2) energy minimization to optimize the predicted structure. This method provides a rapid and effective solution to the initial problem of obtaining a working structure for modeling studies.     

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.     

Global minimization of an off-lattice potential energy function using a chaperone-based refolding method

A global energy minimization method based on what is known about the mechanisms of the GroEL/GroES chaperonin system is applied to two 22-mers of an off-lattice protein model whose native states are beta-hairpins and which have structural similarity to short peptides known to interact strongly with the GroEL substrate binding domain. These model substrates have been used by other workers to test the effectiveness of a number of global minimization techniques, and are regarded as providing a significant challenge. The minimization method developed here is progressively elaborated from an initial simple form that targets exposed hydrophobic regions for unfolding to include a refolding phase that encourages the later recompactification of partly unfolded substrate; this refolding phase is seen to be crucial in the successful application of the method. The optimal handling of hydrophilic monomers within the model is also systematically explored, and it is seen that the best interpretation of their role is one that allows the chaperonin model to operate in "proofreading" mode whereby misfolded substrates are recognized by their surface exposure of a large proportion of hydrophobic monomers. The final version of the model allows native-like structures to be found quickly, on average for the two 22-mer substrates after 6 or 7 chaperone contacts. These results compare very favorably with those that have been obtained elsewhere using generic global minimization methods such as those based on thermal annealing. The paper concludes with a discussion of the place of the technique within the general category of hypersurface deformation methods for global minimization, and with suggestions as to how the chaperone-based method developed here could be elaborated so as to be effective on longer substrate chains that give rise to more complex tertiary structures in their native states.     

Pseudocontact shifts as constraints for energy minimization and molecular dynamics calculations on solution structures of paramagnetic metalloproteins

The pseudocontact shifts of NMR signals, which arise from the magnetic susceptibility anisotropy of paramagnetic molecules, have been used as structural constraints under the form of a pseudopotential in the SANDER module of the AMBER 4.1 molecular dynamics software package. With this procedure, restrained energy minimization (REM) and restrained molecular dynamics (RMD) calculations can be performed on structural models by using pseudocontact shifts. The structure of the cyanide adduct of the Met80Ala mutant of the yeast iso-1-cytochrome c has been used for successfully testing the calculations. For this protein, a family of structures is available, which was obtained by using NOE and pseudocontact shifts as constraints in a distance geometry program. The structures obtained by REM and RMD calculations with the inclusion of pseudocontact shifts are analyzed. Proteins 29:68–76, 1997. © 1997 Wiley-Liss, Inc.     

Automated minimization of steric clashes in protein structures

Molecular modeling of proteins including homology modeling, structure determination, and knowledge-based protein design requires tools to evaluate and refine three-dimensional protein structures. Steric clash is one of the artifacts prevalent in low-resolution structures and homology models. Steric clashes arise due to the unnatural overlap of any two nonbonding atoms in a protein structure. Usually, removal of severe steric clashes in some structures is challenging since many existing refinement programs do not accept structures with severe steric clashes. Here, we present a quantitative approach of identifying steric clashes in proteins by defining clashes based on the Van der Waals repulsion energy of the clashing atoms. We also define a metric for quantitative estimation of the severity of clashes in proteins by performing statistical analysis of clashes in high-resolution protein structures. We describe a rapid, automated, and robust protocol, Chiron, which efficiently resolves severe clashes in low-resolution structures and homology models with minimal perturbation in the protein backbone. Benchmark studies highlight the efficiency and robustness of Chiron compared with other widely used methods. We provide Chiron as an automated web server to evaluate and resolve clashes in protein structures that can be further used for more accurate protein design.     

Solution structure of murine epidermal growth factor determined by NMR spectroscopy and refined by energy minimization with restraints.

The solution structure of murine epidermal growth factor (mEGF) at pH 3.1 and a temperature of 28 degrees C has been determined from NMR data, using distance geometry calculations and restrained energy minimization. The structure determination is based on 730 conformational constraints derived from NMR data, including 644 NOE-derived upper bound distance constraints, constraints on the ranges of 32 dihedral angles based on measurements of vicinal coupling constants, and 54 upper and lower bound constraints associated with nine hydrogen bonds and the three disulfide bonds. The distance geometry interpretation of the NMR data is based on previously published sequence-specific 1H resonance assignments [Montelione et al. (1988) Biochemistry 27, 2235-2243], supplemented here with individual assignments for some side-chain amide, methylene, and isopropyl methyl protons. The molecular architecture of mEGF is the same as that described previously [Montelione et al. (1987) Proc. Natl. Acad. Sci. U.S.A. 84, 5226-5230], but the structure is overall more precisely determined by a more extensive set of NMR constraints. Analysis of proton NMR line widths, amide proton exchange rates, and side-chain 3J(H alpha-H beta) coupling constants provides evidence for internal motion in several regions of the mEGF molecule. Because mEGF is one member of a large family of homologous growth factors and protein domains for which X-ray crystal structures are not yet available, the atomic coordinates resulting from the present structure refinement (which we have deposited in the Brookhaven Protein Data Bank) are important data for understanding the structures of EGF-like proteins and for further detailed comparisons of these structures with mEGF.     

Protein contributions to redox potentials of homologous rubredoxins: an energy minimization study.

The energetic contributions of the protein to the redox potential in an iron-sulfur protein are studied via energy minimization, comparing homologous rubredoxins from Clostridium pasteurianum, Desulfovibrio gigas, Desulfovibrio vulgaris, and Pyrococcus furiosus. The reduction reaction was divided into 1) the change in the redox site charge without allowing the protein to respond and 2) the relaxation of the protein in response to the new charge state, focusing on the latter. The energy minimizations predict structural relaxation near the redox site that agrees well with that in crystal structures of oxidized and reduced P. furiosus rubredoxin, but underpredicts it far from the redox site. However, the relaxation energies from the energy-minimized structures agree well with those from the crystal structures, because the polar groups near the redox site are the main determinants and the charged groups are all located at the surface and thus are screened dielectrically. Relaxation energies are necessary for good agreement with experimentally observed differences in reduction energies between C. pasteurianum and the other three rubredoxins. Overall, the relaxation energy is large (over 500 mV) from both the energy-minimized and the crystal structures. In addition, the range in the relaxation energy for the different rubredoxins is large (300 mV), because even though the structural perturbations of the polar groups are small, they are very near the redox site. Thus the relaxation energy is an important factor to consider in reduction energetics.     

Translocation of a tRNA with an extended anticodon through the ribosome

Coordinated translocation of the tRNA-mRNA complex by the ribosome occurs in a precise, stepwise movement corresponding to a distance of three nucleotides along the mRNA. Frameshift suppressor tRNAs generally contain an extra nucleotide in the anticodon loop and they subvert the normal mechanisms used by the ribosome for frame maintenance. The mechanism by which suppressor tRNAs traverse the ribosome during translocation is poorly understood. Here, we demonstrate translocation of a tRNA by four nucleotides from the A site to the P site, and from the P site to the E site. We show that translocation of a punctuated mRNA is possible with an extra, unpaired nucleotide between codons. Interestingly, the NMR structure of the four nucleotide anticodon stem-loop reveals a conformation different from the canonical tRNA structure. Flexibility within the loop may allow conformational adjustment upon A site binding and for interacting with the four nucleotide codon in order to shift the mRNA reading frame.     

NMR structures of paramagnetic metalloproteins

Metalloproteins represent a large share of the proteome and many of them contain paramagnetic metal ions. The knowledge, at atomic resolution, of their structure in solution is important to understand processes in which they are involved, such as electron transfer mechanisms, enzymatic reactions, metal homeostasis and metal trafficking, as well as interactions with their partners. Formerly considered as unfeasible, the first structure in solution by nuclear magnetic resonance (NMR) of a paramagnetic protein was obtained in 1994. Methodological and instrumental advancements pursued over the last decade are such that NMR structure of paramagnetic proteins may be now routinely obtained. We focus here on approaches and problems related to the structure determination of paramagnetic proteins in solution through NMR spectroscopy. After a survey of the background theory, we show how the effects produced by the presence of a paramagnetic metal ion on the NMR parameters, which are in many cases deleterious for the detection of NMR spectra, can be overcome and turned into an additional source of structural restraints. We also briefly address features and perspectives given by the use of 13C-detected protonless NMR spectroscopy for proteins in solution. The structural information obtained through the exploitation of a paramagnetic center are discussed for some Cu2+ -binding proteins and for Ca2+ -binding proteins, where the replacement of a diamagnetic metal ion with suitable paramagnetic metal ions suggests novel approaches to the structural characterization of proteins containing diamagnetic and NMR-silent metal ions.     

TASSER-based refinement of NMR structures

The TASSER structure prediction algorithm is employed to investigate whether NMR structures can be moved closer to their corresponding X-ray counterparts by automatic refinement procedures. The benchmark protein dataset includes 61 nonhomologous proteins whose structures have been determined by both NMR and X-ray experiments. Interestingly, by starting from NMR structures, the majority (79%) of TASSER refined models show a structural shift toward their X-ray structures. On average, the TASSER refined models have a root-mean-square-deviation (RMSD) from the X-ray structure of 1.785 A (1.556 A) over the entire chain (aligned region), while the average RMSD between NMR and X-ray structures (RMSD(NMR_X-ray)) is 2.080 A (1.731 A). For all proteins having a RMSD(NMR_X-ray) >2 A, the TASSER refined structures show consistent improvement. However, for the 34 proteins with a RMSD(NMR_X-ray) <2 A, there are only 21 cases (60%) where the TASSER model is closer to the X-ray structure than NMR, which may be due to the inherent resolution of TASSER. We also compare the TASSER models with 12 NMR models in the RECOORD database that have been recalculated recently by Nederveen et al. from original NMR restraints using the newest molecular dynamics tools. In 8 of 12 cases, TASSER models show a smaller RMSD to X-ray structures; in 3 of 12 cases, where RMSD(NMR_X-ray) <1 A, RECOORD does better than TASSER. These results suggest that TASSER can be a useful tool to improve the quality of NMR structures.     

Prediction of geometrically feasible three-dimensional structures of pseudoknotted RNA through free energy estimation

Accurate free energy estimation is essential for RNA structure prediction. The widely used Turner''s energy model works well for nested structures. For pseudoknotted RNAs, however, there is no effective rule for estimation of loop entropy and free energy. In this work we present a new free energy estimation method, termed the pseudoknot predictor in three-dimensional space (pk3D), which goes beyond Turner''s model. Our approach treats nested and pseudoknotted structures alike in one unifying physical framework, regardless of how complex the RNA structures are. We first test the ability of pk3D in selecting native structures from a large number of decoys for a set of 43 pseudoknotted RNA molecules, with lengths ranging from 23 to 113. We find that pk3D performs slightly better than the Dirks and Pierce extension of Turner''s rule. We then test pk3D for blind secondary structure prediction, and find that pk3D gives the best sensitivity and comparable positive predictive value (related to specificity) in predicting pseudoknotted RNA secondary structures, when compared with other methods. A unique strength of pk3D is that it also generates spatial arrangement of structural elements of the RNA molecule. Comparison of three-dimensional structures predicted by pk3D with the native structure measured by nuclear magnetic resonance or X-ray experiments shows that the predicted spatial arrangement of stems and loops is often similar to that found in the native structure. These close-to-native structures can be used as starting points for further refinement to derive accurate three-dimensional structures of RNA molecules, including those with pseudoknots.     

Prediction of RNA secondary structure by free energy minimization

RNA secondary structure is often predicted from sequence by free energy minimization. Over the past two years, advances have been made in the estimation of folding free energy change, the mapping of secondary structure and the implementation of computer programs for structure prediction. The trends in computer program development are: efficient use of experimental mapping of structures to constrain structure prediction; use of statistical mechanics to improve the fidelity of structure prediction; inclusion of pseudoknots in secondary structure prediction; and use of two or more homologous sequences to find a common structure.     

Conformational studies of cyclic peptide structures in solution from 1H-Nmr data by distance geometry calculation and restrained energy minimization

The three-dimensional structure of a cyclic bouvardin analogue, cyclo (-Pro-MeTyr-Ala-MeTyr-MeTyr-D-Ala-) has been determined by distance geometry calculation and restrained energy minimization from nmr data. The preparation of the input for the distance geometry calculations, the modification of the amino acid library, and the analysis of the structures were done with the aid of a recently developed software package, GEOM. A great variety of different initial structures were explored to check the uniqueness of the determined solution structure. Calculations with 500 different initial structures and two different strategies led to a uniquely determined backbone conformation with a root mean square deviations value of 0.4 A. The backbone structure consists of two beta-turns, a beta-II turn at Pro1-MeTyr2, and a beta-VI turn at MeTyr4-MeTyr5. The efficiency of the two calculation strategies were compared in order to propose an optimal means for performing distance geometry calculations with cyclic structures.     

Conformational changes in the selectivity filter of the open-state KcsA channel: an energy minimization study

Potassium channels switch between closed and open conformations and selectively conduct K⁺ ions. There are at least two gates. The TM2 bundle at the intracellular site is the primary gate of KcsA, and rearrangements at the selectivity filter (SF) act as the second gate. The SF blocks ion flow via an inactivation process similar to C-type inactivation of voltage-gated K⁺ channels. We recently generated the open-state conformation of the KcsA channel. We found no major, possibly inactivating, structural changes in the SF associated with this massive inner-pore rearrangement, which suggests that the gates might act independently. Here we energy-minimize the open state of wild-type and mutant KcsA, validating in silico structures of energy-minimized SFs by comparison with crystallographic structures, and use these data to gain insight into how mutation, ion depletion, and K⁺ to Na⁺ substitution influence SF conformation. Both E71 or D80 protonations/mutations and the presence/absence of protein-buried water molecule(s) modify the H-bonding network stabilizing the P-loops, spawning numerous SF conformations. We find that the inactivated state corresponds to conformations with a partially unoccupied or an entirely empty SF. These structures, involving modifications in all four P-loops, are stabilized by H-bonds between amide H and carbonyl O atoms from adjacent P-loops, which block ion passage. The inner portions of the P-loops are more rigid than the outer parts. Changes are localized to the outer binding sites, with innermost site S4 persisting in the inactivated state. Strong binding by Na⁺ locally contracts the SF around Na⁺, releasing ligands that do not participate in Na⁺ coordination, and occluding the permeation pathway. K⁺ selectivity primarily appears to arise from the inability of the SF to completely dehydrate Na⁺ ions due to basic structural differences between liquid water and the “quasi-liquid” SF matrix.     

The evolution of plant social learning through error minimization

Plants have developed toxic chemical and physical defenses as a consequence of their co-evolution with herbivores. Humans, like other animal species, have evolved strategies to protect themselves from such plant dangers. For example, recent studies have shown that human infants exhibit a reluctance to manually explore plants and use social learning (SL) to acquire knowledge about plants. However, SL can also be costly under certain circumstances and there is reason to suspect this may be the case for plants. Some plant species are difficult to distinguish from one another. For example, some plants have evolved an adaptive strategy to fight against herbivorous threats, called Batesian mimicry, in which an edible plant mimics features of a poisonous plant to minimize the probability that it is consumed. When SL is prevalent in a population, by proliferating the knowledge about an edible mimic, SL also spreads the risk of consuming its poisonous counterpart. Here we propose a model describing different scenarios where SL is (a) favored, (b) ecologically stable, and (c) expected to evolve. Results show that SL is selected when the proportion of poisonous plants is high. However, this is only true if the edible mimic population is below a certain threshold and its selection depends on the capacity to minimize errors when differentiating edible mimics from their poisonous counterparts.