Small molecule hydration energy and entropy from 3D-RISM

Implicit solvent models offer an attractive way to estimate the effects of a solvent environment on the properties of small or large solutes without the complications of explicit simulations. One common test of accuracy is to compute the free energy of transfer from gas to liquid for a variety of small molecules, since many of these values have been measured. Studies of the temperature dependence of these values (i.e. solvation enthalpies and entropies) can provide additional insights into the performance of implicit solvent models. Here, we show how to compute temperature derivatives of hydration free energies for the 3D-RISM integral equation approach. We have computed hydration free energies of 1123 small drug-like molecules (both neutral and charged). Temperature derivatives were also used to calculate hydration energies and entropies of 74 of these molecules (both neutral and charged) for which experimental data is available. While direct results have rather poor agreement with experiment, we have found that several previously proposed linear hydration free energy correction schemes give good agreement with experiment. These corrections also provide good agreement for hydration energies and entropies though simple extensions are required in some cases.

Revised AMBER parameters for bioorganic phosphates

We report AMBER force field parameters for biological simulations involving phosphorylation of serine, threonine or tyrosine. The initial parameters used RESP fitting for the atomic partial charges and standard values for all other parameters such as Lennard-Jones coefficients. These were refined with the aid of a thermodynamic cycle consisting of experimentally determined pKa values, solvation energies from molecular dynamics free energy simulations, and gas phase basicities from QM calculations. A polarization energy term was included to account for the charge density change between the gas-phase and solution, and solvation free energies were determined using thermodynamic integration. Parameter adjustment is required to obtain consistent thermodynamic results with better balanced electrostatic interactions between water and the phosphate oxygens. To achieve this we modified the phosphate oxygen radii. A thermodynamically consistent parameter set can be derived for monoanions and requires an increase of the van der Waals phosphate oxygen radii of approximately 0.09 Å. Larger, residue-specific radii appear to be needed for dianions. The revised parameters developed here should be of particular interest for environments where simulations of multiple protonation states may be of interest.

The delay-reduction hypothesis of conditioned reinforcement and punishment: Observing behavior

Pigeons responded in an observing-response procedure in which three fixed-interval components alternated. Pecking one response key produced food reinforcement according to a mixed schedule. Pecking the second (observing) key occasionally replaced the mixed-schedule stimulus with the stimulus correlated with the fixed-interval component then in effect. In Experiment 1, observing was best maintained by stimuli correlated with a reduction in mean time to reinforcement. That finding was consistent with the conditioned-reinforcement hypothesis of observing behavior. However, low rates of observing were also maintained by stimuli not representing delay reduction. Experiment 2 assessed the role of sensory reinforcement. It showed that response rate was higher when maintained by stimuli uncorrelated with reinforcement delay than when the stimuli were correlated with a delay increase. This latter result supports a symmetrical version of the conditioned-reinforcement hypothesis that requires suppression by stimuli correlated with an increase in time to reinforcement. The results were inconsistent with hypotheses stressing the reinforcing potency of uncertainty reduction.

Human observing: Maintained by stimuli correlated with reinforcement but not extinction

College students received points exchangeable for money (reinforcement) on a variable-time 60-second schedule that alternated randomly with an extinction component. Subjects were informed that responding would not influence either the rate or distribution of reinforcement. Instead, presses on either of two levers ("observing responses") produced stimuli. In each of four experiments, stimuli positively correlated with reinforcement and/or stimuli uncorrelated with reinforcement were each chosen over stimuli correlated with extinction. These results are consistent with prior results from pigeons in supporting the conditioned-reinforcement hypothesis of observing and in not supporting the uncertainty-reduction hypothesis.

Theory and applications of the generalized Born solvation model in macromolecular simulations

Generalized Born (GB) models provide an attractive way to include some thermodynamic aspects of aqueous solvation into simulations that do not explicitly model the solvent molecules. Here we discuss our recent experience with this model, presenting in detail the way it is implemented and parallelized in the AMBER molecular modeling code. We compare results using the GB model (or GB plus a surface-area based "hydrophobic" term) to explicit solvent simulations for a 10 base-pair DNA oligomer, and for the 108-residue protein thioredoxin. A slight modification of our earlier suggested parameters makes the GB results more like those found in explicit solvent, primarily by slightly increasing the strength of NH [bond] O and NH [bond] N internal hydrogen bonds. Timing and energy stability results are reported, with an eye toward using these model for simulations of larger macromolecular systems and longer time scales.

Continuum solvent molecular dynamics study of flexibility in interleukin-8

Generalized Born continuum solvent methods have been shown to provide a reasonable description of the equilibrium thermodynamics of aqueous solvation in a variety of applications to peptides, proteins, and nucleic acids. Here we study the performance of these methods in molecular dynamics simulations of interleukin-8, comparing nanosecond-length explicit solvent simulations with those using the generalized Born model. In general, the simulations show similar results, although movement away from the initial NMR-determined structure and average fluctuations about the mean are slightly higher for the continuum solvent results. In both simulations, the two helices that are packed on top of the core sheet move closer together, resulting in a structure that more closely resembles the X-ray structure. Principal-component (quasiharmonic) analysis is used to analyze the motions of these helices in both of the simulations and in the NMR ensemble of structures. Prospects for making more general use of continuum solvent models in protein dynamics simulations are discussed.

FeMo cofactor of nitrogenase: a density functional study of states M(N), M(OX), M(R), and M(I)

The M(N) S = (3)/(2) resting state of the FeMo cofactor of nitrogenase has been proposed to have metal-ion valencies of either Mo(4+)6Fe(2+)Fe(3+) (derived from metal hyperfine interactions) or Mo(4+)4Fe(2+)3Fe(3+) (from Mössbauer isomer shifts). Spin-polarized broken-symmetry (BS) density functional theory (DFT) calculations have been undertaken to determine which oxidation level best represents the M(N) state and to provide a framework for understanding its energetics and spectroscopy. For the Mo(4+)6Fe(2+)Fe(3+) oxidation state, the spin coupling pattern for several spin state alignments compatible with S = (3)/(2) were generated and assessed by energy and geometric criteria. The most likely BS spin state is composed of a Mo3Fe cluster with spin S(a) = 2 antiferromagnetically coupled to a 4Fe' cluster with spin S(b) = (7)/(2). This state has a low DFT energy for the isolated FeMoco cluster and the lowest energy when the interaction with the protein and solvent environment is included. This spin state also displays calculated metal hyperfine and Mössbauer isomer shifts compatible with experiment, and optimized geometries that are in excellent agreement with the protein X-ray data. Our best model for the actual spin-coupled state within FeMoco alters this BS state by a slight canting of spins and is analogous in several respects to that found in the 8Fe P-cluster in the same protein. The spin-up and spin-down components of the LUMO contain atomic contributions from Mo(4+) and the homocitrate and from the central prismane Fe sites and muS(2) atoms, respectively. This qualitative picture of the accepting orbitals for M(N) is consistent with observations from Mössbauer spectra of the one-electron reduced states. Similar calculations for the Mo(4+)4Fe(2+)3Fe(3+) oxidation state yield results that are in poorer agreement with experiment. Using the Mo(4+)6Fe(2+)Fe(3+) oxidation level as the most plausible resting state, the geometric, electronic and energetic properties of the one-electron redox transition to the oxidized state, M(OX), catalytically observed M(R) and radiolytically reduced M(I) states have also been explored.

Automated prediction of 15N, 13Calpha, 13Cbeta and 13C' chemical shifts in proteins using a density functional database

A database of peptide chemical shifts, computed at the density functional level, has been used to develop an algorithm for prediction of 15N and 13C shifts in proteins from their structure; the method is incorporated into a program called SHIFTS (version 4.0). The database was built from the calculated chemical shift patterns of 1335 peptides whose backbone torsion angles are limited to areas of the Ramachandran map around helical and sheet configurations. For each tripeptide in these regions of regular secondary structure (which constitute about 40% of residues in globular proteins) SHIFTS also consults the database for information about sidechain torsion angle effects for the residue of interest and for the preceding residue, and estimates hydrogen bonding effects through an empirical formula that is also based on density functional calculations on peptides. The program optionally searches for alternate side-chain torsion angles that could significantly improve agreement between calculated and observed shifts. The application of the program on 20 proteins shows good consistency with experimental data, with correlation coefficients of 0.92, 0.98, 0.99 and 0.90 and r.m.s. deviations of 1.94, 0.97, 1.05, and 1.08 ppm for 15N, 13Calpha, 13Cbeta and 13C', respectively. Reference shifts fit to protein data are in good agreement with 'random-coil' values derived from experimental measurements on peptides. This prediction algorithm should be helpful in NMR assignment, crystal and solution structure comparison, and structure refinement.

RNAMotif, an RNA secondary structure definition and search algorithm

RNA molecules fold into characteristic secondary and tertiary structures that account for their diverse functional activities. Many of these RNA structures are assembled from a collection of RNA structural motifs. These basic building blocks are used repeatedly, and in various combinations, to form different RNA types and define their unique structural and functional properties. Identification of recurring RNA structural motifs will therefore enhance our understanding of RNA structure and help associate elements of RNA structure with functional and regulatory elements. Our goal was to develop a computer program that can describe an RNA structural element of any complexity and then search any nucleotide sequence database, including the complete prokaryotic and eukaryotic genomes, for these structural elements. Here we describe in detail a new computational motif search algorithm, RNAMotif, and demonstrate its utility with some motif search examples. RNAMotif differs from other motif search tools in two important aspects: first, the structure definition language is more flexible and can specify any type of base-base interaction; second, RNAMotif provides a user controlled scoring section that can be used to add capabilities that patterns alone cannot provide.

Solution structure and dynamics of yeast elongin C in complex with a von Hippel-Lindau peptide

Elongin is a transcription elongation factor that stimulates the rate of elongation by suppressing transient pausing by RNA polymerase II at many sites along the DNA. It is heterotrimeric in mammals, consisting of elongins A, B and C subunits, and bears overall similarity to a class of E3 ubiquitin ligases known as SCF (Skp1-Cdc53 (cullin)-F-box) complexes. A subcomplex of elongins B and C is a target for negative regulation by the von Hippel-Lindau (VHL) tumor-suppressor protein. Elongin C from Saccharomyces cerevisiae, Elc1, exhibits high sequence similarity to mammalian elongin C. Using NMR spectroscopy we have determined the three-dimensional structure of Elc1 in complex with a human VHL peptide, VHL(157-171), representing the major Elc1 binding site. The bound VHL peptide is entirely helical. Elc1 utilizes two C-terminal helices and an intervening loop to form a binding groove that fits VHL(157-171). Chemical shift perturbation and dynamics analyses reveal that a global conformational change accompanies Elc1/VHL(157-171) complex formation. Moreover, the disappearance of conformational exchange phenomena on the microsecond to millisecond time scale within Elc1 upon VHL peptide binding suggests a role for slow internal motions in ligand recognition.

A novel view of pH titration in biomolecules

When individual titratable sites in a molecule interact with each other, their pH titration can be considerably more complex than that of an independent site described by the classical Henderson-Hasselbalch equation. We propose a novel framework that decomposes any complex titration behavior into simple standard components. The approach maps the set of N interacting sites in the molecule onto a set of N independent, noninteracting quasi-sites, each characterized by a pK'(a) value. The titration curve of an individual site in the molecule is a weighted sum of Henderson-Hasselbalch curves corresponding to the quasi-sites. The total protonation curve is the unweighted sum of these Henderson-Hasselbalch curves. We show that pK'(a) values correspond to deprotonation constants available from methods that can be used to assess total proton uptake or release, and establish their connection to protonation curves of individual residues obtained by NMR or infrared spectroscopy. The new framework is tested on a small molecule diethylenetriaminepentaacetate (DTPA) exhibiting nonmonotonic titration curves, where it gives an excellent fit to experimental data. We demonstrate that the titration curve of a site in a group of interacting sites can be accurately reconstructed, if titration curves of the other sites are known. The application of the new framework to the protein rubredoxin demonstrates its usefulness in calculating and interpreting complicated titration curves.

Generalized born models of macromolecular solvation effects

It would often be useful in computer simulations to use a simple description of solvation effects, instead of explicitly representing the individual solvent molecules. Continuum dielectric models often work well in describing the thermodynamic aspects of aqueous solvation, and approximations to such models that avoid the need to solve the Poisson equation are attractive because of their computational efficiency. Here we give an overview of one such approximation, the generalized Born model, which is simple and fast enough to be used for molecular dynamics simulations of proteins and nucleic acids. We discuss its strengths and weaknesses, both for its fidelity to the underlying continuum model and for its ability to replace explicit consideration of solvent molecules in macromolecular simulations. We focus particularly on versions of the generalized Born model that have a pair-wise analytical form, and therefore fit most naturally into conventional molecular mechanics calculations.

Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models

A historical perspective on the application of molecular dynamics (MD) to biological macromolecules is presented. Recent developments combining state-of-the-art force fields with continuum solvation calculations have allowed us to reach the fourth era of MD applications in which one can often derive both accurate structure and accurate relative free energies from molecular dynamics trajectories. We illustrate such applications on nucleic acid duplexes, RNA hairpins, protein folding trajectories, and protein-ligand, protein-protein, and protein-nucleic acid interactions.

NMR and molecular dynamics studies of the hydration of a zinc finger-DNA complex

The hydration of a high-affinity protein-DNA complex involving the three amino terminal zinc finger domains of transcription factor IIIA (TFIIIA) and a 15-base-pair DNA duplex was investigated by NMR spectroscopy and molecular dynamics (MD) simulations. Intermolecular nuclear Overhauser effects (NOEs) between protein and water provided an experimental basis for identifying potential sites of hydration. These initial assignments were evaluated with the aid of two, 2 ns MD simulations of the protein-DNA complex conducted with the explicit inclusion of water solvent. The two independent simulations produced similar trends in terms of water residence times around the solute, and these results were used to separate protein-water NOEs from alternate exchange-relayed cross peaks. Furthermore, only six of the 170 protons which failed to show intermolecular NOEs to solvent showed nearby long-resident water molecules in the MD simulations, illustrating an impressive level of agreement between theory and experiment. Analyses of the MD trajectories also allowed an examination of the role of water in recognition and binding affinity of the zinc fingers with DNA. The interface is well hydrated, characterized by direct contacts between the protein and DNA, as well as mediating water bridges. Approximately 18 water-mediated hydrogen bonds between the protein and DNA were observed on average. Roughly half of these were water molecules with long residence times that are most likely to be important for binding, since they involve residues which have been shown through biochemical studies to be crucial for protein-DNA binding. This level of atomic detail could not otherwise be established through the existing NMR and crystal structures of the TFIIIA-DNA complex.

The structural basis for in situ activation of DNA alkylation by duocarmycin SA

Duocarmycin SA is a member of a growing class of interesting lead compounds for chemotherapy, distinguished by the manner in which they bind to and react with DNA substrates. The first three-dimensional structure of a DNA adduct of an unnatural enantiomer from this family has been determined by (1)H NMR methods. Comparison to the previously determined structure of the natural enantiomer bound in the same DNA-binding site provides unique insights into the similarities and critical distinctions producing the respective alkylation products and site selectivities. The results also support the hypothesis that the duocarmycin SA alkylation reaction is catalyzed by the binding to DNA, and provide a deeper understanding of the structural basis for this unique mode of activation.

Interpretation of chemical shifts and coupling constants in macromolecules

Recent developments in NMR spectroscopy, along with advances in computational techniques, have produced new approaches to the interpretation of chemical shifts and spin-spin coupling constants in biomolecules. Quantum chemical studies of useful accuracy are now becoming more routine and are increasingly being used in conjunction with experimental studies to map out expected structural patterns for peptides and oligonucleotides. Topics of recent special interest include spin couplings across hydrogen bonds and patterns of chemical shift anisotropies, in both diamagnetic and paramagnetic proteins.

NMR solution structure of the inserted domain of human leukocyte function associated antigen-1

The interaction between the leukocyte function-associated antigen-1 (LFA-1) and the intercellular adhesion molecule is thought to be mediated primarily via the inserted domain (I-domain) in the alpha-subunit. The activation of LFA-1 is an early step in triggering the adhesion of leukocytes to target cells decorated with intercellular adhesion molecules. There is some disagreement in the literature over the respective roles of conformational changes in the I-domain and of divalent cations (Mg(2+), Mn(2+)) in the activation of LFA-1 for intercellular adhesion molecule binding. X-ray crystallographic structures of the I-domains of LFA-1 and Mac-1 in the presence and absence of cations show structural differences in the C-terminal alpha-helix; this change was proposed to represent the active and inactive conformations of the I-domain. However, more recent X-ray results have called this proposal into question. The solution structure of the Mg(2+) complex of the I-domain of LFA-1 has been determined by NMR methods, using a model-based approach to nuclear Overhauser enhancement spectroscopy peak assignment. The protein adopts the same structure in solution as that of the published I-domain X-ray structures, but the C-terminal region, where the X-ray structures are most different from each other, is different again in the solution structures. The secondary structure of this helix is well formed, but NMR relaxation data indicate that there is considerable flexibility present, probably consisting of breathing or segmental motion of the helix. The conformational diversity seen in the various X-ray structures could be explained as a result of the inherent flexibility of this C-terminal region and as a result of crystal contacts. Our NMR data are consistent with a model where the C-terminal helix has the potential flexibility to take up alternative conformations, for example, in the presence and absence of the intercellular adhesion molecule ligand. The role of divalent cations appears from our results not to be as a direct mediator of a conformational change that alters affinity for the ligand. Rather, the presence of the cation appears to be involved in some other way in ligand binding, perhaps by acting as a bridge to the ligand and by modulation of the charge of the binding surface.

Assessment of zinc finger orientations by residual dipolar coupling constants

Residual dipolar coupling constants measured in anisotropic solution contain information on orientations between internuclear vectors and the magnetic field, providing long-range information that may help determine the relative orientations of distinct domains in biomolecules. Here we describe the measurement and use of residual dipolar coupling restraints in the refinement of the structure of the complex of DNA with three zinc fingers of transcription factor IIIA (TFIIIA), measured in a DMPC/DHPC bicelle solution. These dipolar restraints were applied on a variety of orientations of the zinc finger domains (derived from crystallography, previous NMR studies, and systematic modeling) in order to examine the validity and sensitivity of using residual dipolar splittings to study interdomain orientations. The spread in interdomain angles between zinc fingers is reduced from 24 degrees to 9 degrees upon incorporation of dipolar restraints. However, the results also show that the ability to determine relative orientations is strongly dependent on the structural accuracy of the local domain structures.

Calculations of NMR dipolar coupling strengths in model peptides

Ab initio MP2 and density functional quantum chemistry calculations are used to explore geometries and vibrational properties of N-methylacetamide and of the alanine dipeptide with backbone angles characteristic of helix and sheet regions in proteins. The results are used to explore one-bond direct dipolar couplings for the N-H, C alpha-H alpha, C'-N, and C alpha-C' bonds, as well as for the two-bond C'-H interaction. Vibrational averaging affects these dipolar couplings, and these effects can be expressed as effective bond lengths that are 0.5-3% larger than the true bond lengths; bending and torsion vibrations have a bigger influence on the effective coupling than do stretching vibrations. Because of zero-point motion, these effects are important even at low temperature. Hydrogen bonding interactions at the amide group also increase the N-H effective bond length. Although vibrational contributions to effective bond lengths are small, they can have a significant influence on the extraction of order parameters from relaxation data, and a knowledge of relative bond lengths is needed when several types of dipolar couplings are to be simultaneously used for refinement. The present computational results are compared to both solid- and liquid-state NMR experiments. The analysis suggests that secondary structural elements in many proteins may be more rigid than is commonly thought.

Base-rate training without case cues reduces base-rate neglect

Base-rate neglect is a persistent phenomenon in which subjects do not place sufficient weight on the probabilities of occurrence of relevant events. Two experiments with college students support the hypothesis that base-rate neglect may be minimized by providing base-rate training in the absence of case, or witness, cues, prior to introducing (or reintroducing) these cues. In Experiment 1, the hypothesis was supported by both within-subjects and between-groups assessments; in Experiment 2, the hypothesis was supported while the effects of instructions and a correction procedure were found to be minimal. In Experiment 1, but not in Experiment 2, training with case cues present also reduced base-rate neglect, but this effect was not sufficient to account for the effect of cue-absent base-rate training. Correction trials led some subjects to detect that the task contingencies were random; however, neither this nor actually telling subjects after the experiment that the task was indeed random led invariably to subjects' describing the optimal strategy (which was to choose the richer alternative exclusively).

Continuum solvent studies of the stability of RNA hairpin loops and helices

We apply continuum solvent models to investigate the relative stability of various conformational forms for two RNA sequences, GGAC(UUCG)GUCC and GGUG(UGAA)CACC. In the first part, we compare alternate hairpin conformations to explore the reliability of these models to discriminate between different local conformations. A second part looks at the hairpin-duplex conversion for the UUCG sequence, identifying major contributors to the thermodynamics of a much large scale transition. Structures were taken as snapshots from multi-nanosecond molecular dynamics simulations computed in a consistent fashion using explicit solvent and with long-range electrostatics accounted for using the Particle-Mesh Ewald procedure. The electrostatic contribution to solvation energies were computed using both a finite-difference Poisson-Boltzmann (PB) model and a pairwise Generalized Born model; non-electrostatic contributions were estimated with a surface-area dependent term. To these solvation free energies were added the mean solute internal energies (determined from a molecular mechanics potential) and estimates of the solute entropy (from a harmonic analysis). Consistent with experiment and with earlier solvated molecular dynamics simulations, the UUCG hairpin was found to prefer conformers close to a recent NMR structure determination in preference to those from an earlier NMR study. Similarly, results for the UGAA hairpin favored an NMR-derived structure over that to be expected for a generic GNRA hairpin loop. Experimental free energies are not known for the hairpin/duplex conversion, but must be close to zero since hairpins are seen in solution and duplexes in crystals; out calculations find a value near zero and illustrate the expected interplay of solvation, salt effects and entropy in affecting this equilibrium.

Molecular dynamics and continuum solvent studies of the stability of polyG-polyC and polyA-polyT DNA duplexes in solution

Molecular dynamics simulation in explicit solvent and continuum solvent models are applied to investigate the relative stability of A- and B-form helices for two DNA sequences, dA10-dT10 and dG10-dC10 in three structural forms. One structural form is based on an unrestrained molecular dynamics (MD) trajectory starting from a canonical B-DNA structure, the second is based on a MD trajectory starting in a canonical B-DNA structure with the sugars constrained to be C2'-endo and the third simulation started from a canonical A-DNA structure with the sugars constrained to C3'-endo puckers. For the energetic analysis, structures were taken as snapshots from nanosecond length molecular dynamics simulations computed in a consistent fashion in explicit solvent, applying the particle mesh Ewald method and the Cornell et al. force field. The electrostatic contributions to solvation free energies are computed using both a finite-difference Poisson-Boltzmann model and a pairwise Generalized Born model. The non-electrostatic contributions to the solvation free energies are estimated with a solvent accessible surface area dependent term. To estimate the gas phase component of the relative free energy between the various structures, the mean solute internal energies (determined with the Cornell et al. molecular mechanics potential including all pairwise interactions within the solute) and estimates of the solute entropy (using a harmonic approximation) were used. Consistent with experiment, the polyG-polyC (GC) structures are found to be much more A-phillic than the polyA-polyT (AT) structures, the latter being quite A-phobic. The dominant energy components responsible for this difference comes from the internal and van der Waal energies. A perhaps less appreciated difference between the GC and AT rich sequences is suggested by the calculated salt dependence which demonstrates a significantly enhanced ability to drive GC rich sequences towards an A-form structure compared to AT rich sequences. In addition to being A-phobic, the AT structure also has a noticably larger helical repeat than GC and other mixed sequence duplexes, consistent with experiment. Analysis of the average solvent density from the trajectories shows hydration patterns in qualitative agreement with experiment and previous theoretical treatments.

The use of chemical shifts and their anisotropies in biomolecular structure determination

The existence of chemical shift dispersion is crucial for the application of NMR spectroscopy to biomolecules, but the direct interpretation of shift tensors in terms of structure and dynamics is often difficult. Proton shifts reflect environmental influences from nearby aromatic groups, metal sites or hydrogen-bonding partners. These effects can be reasonably modeled with empirical equations, but multiple contributions to shifts can be difficult to disentangle. Shifts for carbon and nitrogen generally reflect local bonding interactions, often in ways that allow the local structure to be inferred. The anisotropy of the shielding tensor is also of interest. It influences the resonance position in partially-ordered samples and has consequences for spin relaxation, even in isotropic systems. There has been recent progress in measuring and interpreting these anisotropies.

Calculations of proton-binding thermodynamics in proteins

Computational models of proton binding can range from the chemically complex and statistically simple (as in the quantum calculations) to the chemically simple and statistically complex. Much progress has been made in the multiple-site titration problem. Calculations have improved with the inclusion of more flexibility in regard to both the geometry of the proton binding and the larger scale protein motions associated with titration. This article concentrated on the principles of current calculations, but did not attempt to survey their quantitative performance. This is (1) because such comparisons are given in the cited papers and (2) because continued developments in understanding conformational flexibility and interaction energies will be needed to develop robust methods with strong predictive power. Nevertheless, the advances achieved over the past few years should not be underestimated: serious calculations of protonation behavior and its coupling to conformational change can now be confidently pursued against a backdrop of increasing understanding of the strengths and limitations of such models. It is hoped that such theoretical advances will also spur renewed experimental interest in measuring both overall titration curves and individual pKa values or pKa shifts. Exploration of the shapes of individual titration curves (as measured by Hill coefficients and other parameters) would also be useful in assessing the accuracy of computations and in drawing connections to functional behavior.

High-resolution solution structure of Bacillus subtilis IIAglc

The high-resolution solution structure of the phosphocarrier protein IIAglc from Bacillus subtilis is determined using 3D and 4D heteronuclear NMR methods. B. subtilis IIAglc contains 162 amino acid residues and is one of the larger proteins for which high-resolution solution structure has been determined by NMR methods. The structures have been calculated from a total of 2,232 conformational constraints. Comparison with the X-ray crystal structure indicates that the overall fold is the same in solution and in crystalline environments, although some local structural differences are observed. These occur largely in turns and loops, and mostly correspond to regions with high-temperature factors in the crystal structure. The N-terminus of IIAglc is disordered in solution. The active site is located in a concave region of the protein surface. The histidine, which accepts the phosphoryl group (His 83), interacts with a neighboring histidine (His 68) and is surrounded by hydrophobic residues.

Distributed torsion angle grid search in high dimensions: a systematic approach to NMR structure determination

Two complementary approaches for systematic search in torsion angle space are described for the generation of all conformations of polypeptides which satisfy experimental NMR restraints, hard-sphere van der Waals radii, and rigid covalent geometry. The first procedure is based on a recursive, tree search algorithm for the examination of linear chains of torsion angles, and uses a novel treatment to propagate the search results to neighboring regions so that the structural consequences of the restraints are fully realized. The second procedure is based on a binary combination of torsion vector spaces for connected submolecules, and produces intermediate results in Cartesian space for a more robust restraint analysis. Restraints for NMR applications include bounds on torsion angles and internuclear distances, including relational and degenerate restraints involving equivalent and nonstereoassigned protons. To illustrate these methods, conformation search results are given for the tetrapeptide APGA restrained to an idealized beta-turn conformation, an alanine octapeptide restrained to a right-handled helical conformation, and the structured region of the peptide SYPFDV.

Solution structure of the first three zinc fingers of TFIIIA bound to the cognate DNA sequence: determinants of affinity and sequence specificity

The high resolution solution structure of a protein containing the three amino-terminal zinc fingers of Xenopus laevis transcription factor IIIA (TFIIIA) bound to its cognate DNA duplex was determined by nuclear magnetic resonance spectroscopy. The protein, which is designated zf1-3, binds with all three fingers in the DNA major groove, with a number of amino acids making base-specific contacts. The DNA structure is close to B-form. Although the mode of interaction of zf1-3 with DNA is similar to that of zif268 and other structurally characterized zinc finger complexes, the TFIIIA complex exhibits several novel features. Each zinc finger contacts four to five base-pairs and the repertoire of known base contact residues is extended to include a tryptophan at position +2 of the helix (finger 1) and arginine at position +10 (finger 3). Sequence-specific base contacts are made over virtually the entire length of the finger 3 helix. Lysine and histidine side-chains involved in base recognition are dynamically disordered in the solution structure; in the case of lysine, in particular, this could significantly decrease the entropic cost of DNA binding. The TGEKP(N) linker sequences, which are highly flexible in the unbound protein, adopt ordered conformations on DNA binding. The linkers appear to play an active structural role in stabilization of the protein-DNA complex. Substantial protein-protein contact surfaces are formed between adjacent fingers. As a consequence of these protein-protein interactions, the orientation of finger 1 in the major groove differs from that of the other fingers. Contributions to high affinity binding by zf1-3 come from both direct protein-DNA contacts and from indirect protein-protein interactions associated with structural organization of the linkers and formation of well-packed interfaces between adjacent zinc fingers in the DNA complex. The structures provide a molecular level explanation for the large body of footprinting and mutagenesis data available for the TFIIIA-DNA complex.

High resolution solution structure of a DNA duplex alkylated by the antitumor agent duocarmycin SA

The three-dimensional solution structure of duocarmycin SA in complex with d-(G1ACTAATTGAC11).d-(G12TCATTAGTC22) has been determined by restrained molecular dynamics and relaxation matrix calculations using experimental NOE distance and torsion angle constraints derived from 1H NMR spectroscopy. The final input data consisted of a total of 858 distance and 189 dihedral angle constraints, an average of 46 constraints per residue. In the ensemble of 20 final structures, there were no distance constraint violations >0.06 A or torsion angle violations >0.8 degrees. The average pairwise root mean square deviation (RMSD) over all 20 structures for the binding site region is 0.57 A (average RMSD from the mean: 0.39 A). Although the DNA is very B-like, the sugar-phosphate backbone torsion angles beta, epsilon, and zeta are distorted from standard values in the binding site region. The structure reveals site-specific bonding of duocarmycin SA at the N3 position of adenine 19 in the AT-rich minor groove of the duplex and binding stabilization via hydrophobic interactions. Comparisons have been made to the structure of a closely related complex of duocarmycin A bound to an AT-rich DNA duplex. These results provide insights into critical aspects of the alkylation site selectivity and source of catalysis of the DNA alkylating agents, and the unusual stability of the resulting adducts.

Domain packing and dynamics in the DNA complex of the N-terminal zinc fingers of TFIIIA

The three N-terminal zinc fingers of transcription factor IIIA bind in the DNA major groove. Substantial packing interfaces are formed between adjacent fingers, the linkers lose their intrinsic flexibility upon DNA binding, and several lysine side chains implicated in DNA recognition are dynamically disordered.

Thermodynamics of a reverse turn motif. Solvent effects and side-chain packing

The linear pentapeptide, Ala-Tyr-cis-Pro-Tyr-Asp-NMA (AYPYD) is known to have a significant population of type VI turn conformers in aqueous solvent. We have carried out theoretical studies of the conformational energetics of this peptide using a potential of mean force (PMF) consisting of the AMBER/OPLS empirical potential energy function, a macroscopic electrostatic model of polar solvation, and a surface area-based model of non-polar solvation. Conformers were taken from molecular dynamics simulations reported elsewhere, or generated by a random search method reported here. The chain entropy of folding was calculated by a systematic search of accessible dihedral angle space. The intra-peptide component was found to strongly favor folding and was nearly cancelled by the polar solvation term which disfavored folding. The non-polar solvation term had little effect. Fluctuations about the average value of the PMF were small and in accord with estimates from a simple harmonic model. When applied to conformers generated by a random search, the PMF selected a conformer close to the NMR-determined structure as the lowest energy conformer. The conformer with the second-lowest energy was extended, but was found to fold rapidly to the turn state in a subsequent molecular dynamics study, and may be an important state on the folding-unfolding pathway. Averages of the PMF were combined with the entropy estimates to provide an estimate of the free energy of folding that is in reasonable agreement with experimental results. In terms of the interplay between backbone electrostatic interactions and the packing of apolar side-chains, this peptide provides a model for the energetics of protein folding, and therefore makes a useful test case for calculations.

Dynamics of a type VI reverse turn in a linear peptide in aqueous solution

BACKGROUND

Peptide sequences with aromatic groups flanking a cis-proline residue are known to have a high propensity for adopting compact structures in which the aromatic sidechains pack against the proline ring. In particular, the sequence Ser-Tyr-Pro-Phe-Asp-Val (and variants of this) is known by NMR to form a high proportion of type VI turns in aqueous solution. We set out to explore the energetic and dynamic features of such sequences using molecular dynamics simulation techniques.

RESULTS

The conformation properties of the linear pentapeptide NH3(+)-Ala-Tyr-cisPro-Tyr-Asp-NMA (cis-AYPYD) have been explored in three solvated molecular dynamics simulations. The first began from an NMR-derived model structure containing a type VIa turn and close-stacking interactions between the tyrosine and proline sidechains. During 20 ns of simulation, the peptide made transitions between type VIa and VIb turns, but did not 'unfold' to more extended conformers, consistent with the unusual stability for folded forms observed by NMR for this sequence. Distances monitored by nuclear Overhauser peaks and sidechain rotamer populations in the trajectory are in good agreement with NMR data. Two additional 5 ns trajectories were begun from more extended conformers. The first folded into a conformer much like the NMR-derived structure within 3 ns and remained folded for the remainder of the trajectory. The second was begun from a structure in which the sidechain orientations were deliberately misfolded relative to that required for turn formation; this structure did not make a transition to a turn-like state.

CONCLUSIONS

The kinetic stability of folded forms of AYPYD, along with the observation of spontaneous folding from an extended conformation, indicates that the special stability seen experimentally is reflected in computer simulations. The results provide new information about the stabilization of secondary structure in short peptides, particularly by aromatic-proline interactions, and offer a description of pathways of interconversion of type VIa and VIb turns.

NMR solution structure of Cu(I) rusticyanin from Thiobacillus ferrooxidans: structural basis for the extreme acid stability and redox potential

The solution structure of the Cu(I) form of the rusticyanin from Thiobacillus ferrooxidans has been calculated from a total of 1979 distance and dihedral angle constraints derived from 1H, 13C and 15N NMR spectra. The structures reveal two beta-sheets, one of six strands and one of seven strands that are tightly packed in a beta-barrel or beta-sandwich arrangement, and a short helix that extends on the outside of one of the sheets to form a second hydrophobic core. The copper coordination sphere is composed of the standard type I ligands (His2CysMet) in a distorted tetrahedral arrangement. The copper-binding site is located within a hydrophobic region at one end of the molecule, surrounded by a number of aromatic rings and hydrophobic residues. This configuration probably contributes to the acid stability of the copper site, since close association of the aromatic rings with the histidine ligands would sterically hinder their dissociation from the copper. An electrostatic analysis based on a comparison of the structures of rusticyanin and French bean plastocyanin shows that factors determining the high redox potential of rusticyanin include contributions from charged side-chains and from the disposition of backbone peptide dipoles, particularly in the 81 to 86 region of the sequence and the ligand cysteine residue. These interactions should also contribute to the acid stability by inhibiting protonation of His143.

Active site structure of Rieske-type proteins: electron nuclear double resonance studies of isotopically labeled phthalate dioxygenase from Pseudomonas cepacia and Rieske protein from Rhodobacter capsulatus and molecular modeling studies of a Rieske center

Continuous wave electron nuclear double resonance (CW ENDOR) spectra of [delta-15N,epsilon(-14)N]histidine-labeled phthalate dioxygenase (PDO) from Pseudomonas cepacia were recorded and found to be virtually identical to those previously recorded from [delta,epsilon-15N2]histidine-labeled protein [Gurbiel, R. J., Batie, C. J., Sivaraja, M., True, A. E., Fee, J. A., Hoffman, B. M., & Ballou, D. P. (1989) Biochemistry 28, 4861-4871]. Thus, the two histidine residues, previously shown to ligate one of the irons in the cluster [cf. Gurbiel et al. 1989)], both coordinate the metal at the N(delta) position of their imidazole rings. Pulsed ENDOR studies showed that the "remote", noncoordinating nitrogen of the histidine imidazole ring could be observed from the Rieske protein in a sample of Rhodobacter capsulatus cytochrome bc1 complex uniformly labeled with 15N but not in a sample of PDO labeled with [delta-15N,epsilon-14N]histidine, but this atom was easily observed with a sample of Rh. capsulatus cytochrome bc1 complex that had been uniformly labeled with 15N; this confirmed the conclusion from the CW ENDOR studies that ligation is exclusively via N(delta) for both ligands in the PDO center. Modifications in the algorithms previously used to simulate 14N ENDOR spectra permitted us to compute spectra without any constraints on the relative orientation of hyperfine and quadrupole tensors. This new algorithm was used to analyze current and previously published spectra, and slightly different values for the N-Fe-N angle and imidazole ring rotation angles are presented [cf. Gurbiel et al. (1989) Gurbiel, R. J., Ohnishi, T., Robertson, D. E., Daldal, F., and Hoffman, B. M. (1991) Biochemistry 30, 11579-11584]. This analysis has permitted us to refine the proposed structure of the [2Fe-2S] Rieske-type cluster and rationalize some of the properties of these novel centers. Although the spectra of cytochrome bc1 complex from Rh. capsulatus are of somewhat lower resolution than those obtained with samples of PDO, our analysis nevertheless permits the conclusion that the geometry of the cluster is essentially the same for all Rieske and Rieske-type proteins. Structural constraints inferred from the spectroscopic results permitted us to apply the principles of distance geometry to arrive at possible three-dimensional models of the active site structure of Rieske protein from Rh. capsulatus. Results from this test case indicate that similar procedures should be generally useful in metalloprotein systems. We also recorded the pulsed and CW ENDOR spectra of 57Fe-labeled PDO, and the resulting data were used to derive the full hyperfine tensors for both Fe(III) and Fe(II) ions, including their orientations relative to the g tensor. The A tensor of the ferric ion is nominally isotropic, while the A tensor of the ferrous ion is axial, having A(parallel) > A(perpendicular); both tensors are coincident with the observed g tensor, with A(parallel) of the ferrous ion lying along the maximum g-value, g1. These results were examined using refinements of existing theories of spin-coupling in [2Fe-2S]+ clusters, and it is concluded that current theories are not adequate to fully describe the experimental results.

Calibration of ring-current effects in proteins and nucleic acids

Density functional chemical shielding calculations are reported for methane molecules placed in a variety of positions near aromatic rings of the type found in proteins and nucleic acids. The results are compared to empirical formulas that relate these intermolecular shielding effects to magnetic anisotropy ('ring-current') effects and to electrostatic polarization of the C-H bonds. Good agreement is found between the empirical formulas and the quantum chemistry results, allowing a reassessment of the ring-current intensity factors for aromatic amino acids and nucleic acid bases. Electrostatic interactions contribute significantly to the computed chemical shift dispersion. Prospects for using this information in the analysis of chemical shifts in proteins and nucleic acids are discussed.

Pigeons' preference for variable-interval water reinforcement under widely varied water budgets

Water budget of pigeons was varied to assess the dependence of risk-sensitive preferences upon economic context such as has been reported for energy-budget manipulations with small animals in behavioral ecology research. Fixed- and variable-interval terminal-link water schedules reinforced choice between equal variable-interval initial-link schedules arranged on two pecking keys. While keeping a severely restrictive budget the same across three phases of the experiment, a contrasting distinct ample budget was arranged in each. To mimic typical methods in behavioral ecology studies, in each ample budget a more than three-fold increase in amount of water per reinforcer presentation was instituted simultaneously with significantly increased overall access to water. Total choice response rates plummeted in the ample budgets, and body weights either increased significantly or remained unchanged in different phases as expected by the nature of the different manipulations. Clear preferences for the variable-interval schedule were found throughout the experiment, except for rare instances of key bias. The results agree with similar operant food-reinforcement studies and extend conditions under which risk preference apparently does not depend upon economic context.

The structure of calcyclin reveals a novel homodimeric fold for S100 Ca(2+)-binding proteins

The S100 calcium-binding proteins are implicated as effectors in calcium-mediated signal transduction pathways. The three-dimensional structure of the S100 protein calcyclin has been determined in solution in the apo state by NMR spectroscopy and a computational strategy that incorporates a systematic docking protocol. This structure reveals a symmetric homodimeric fold that is unique among calcium-binding proteins. Dimerization is mediated by hydrophobic contacts from several highly conserved residues, which suggests that the dimer fold identified for calcyclin will serve as a structural paradigm for the S100 subfamily of calcium-binding proteins.

Structural basis for DNA bending by the architectural transcription factor LEF-1

Lymphoid enhancer-binding factor (LEF-1) and the closely related T-cell factor 1 (TCF-1) are sequence-specific and cell-type-specific DNA-binding proteins that play important regulatory roles in organogenesis and thymocyte differentiation. LEF-1 participates in regulation of the enhancer associated with the T cell receptor (TCR)-alpha gene by inducing a sharp bend in the DNA and facilitating interactions between Ets-1, PEBP2-alpha, and ATF/CREB, transcription factors bound at sites flanking the LEF-1 site. It seems that LEF-1 plays an architectural role in the assembly and function of this regulatory nucleoprotein complex. LEF-1 recognizes a specific nucleotide sequence through a high-mobility-group (HMG) domain. Proteins containing HMG domains bind DNA in the minor groove, bend the double helix, and recognize four-way junctions and other irregular DNA structures. Here we report the solution structure of a complex of the LEF-1 HMG domain and adjacent basic region with its cognate DNA. The structure reveals the HMG domain bound in the widened minor groove of a markedly distorted and bent double helix. The basic region binds across the narrowed major groove and contributes to DNA recognition.

Solution structure of carbonmonoxy myoglobin determined from nuclear magnetic resonance distance and chemical shift constraints

Solution NMR structures for sperm whale carbonmonoxy myoglobin have been calculated using 1301 distance restraints determined from nuclear Overhauser enhancement (NOE) measurements on 15N-labeled protein and chemical shift calculations for 385 protons. Starting structures included four crystal forms of myoglobin and 12 structures generated by metric matrix distance geometry. Refinements were also carried out using distance restraints alone. In general, the solution conformations are very close to the crystal structures, although the crystal structures are not consistent with some of the observed NOE connectivities. The solution structures are about as far apart from each other (as measured by backbone root-mean-square deviations) as they are from the crystal conformation. Inclusion of chemical shift restraints both tightened the spread of computed structures (especially in the heme pocket region) and led to structures that were closer to the X-ray conformation. The disposition of the side-chains near the heme group could in many cases be determined with considerable confidence, suggesting that a chemical shift analysis may be a useful adjunct to other sources of structural information available from NMR. In particular, this evidence suggests that the distal histidine residue is slightly displaced from the crystal conformation, but still inside the heme pocket at pH 5.6, that the side-chain of Leu89 is in contact with the heme ring but is probably disordered, and that the heme pocket where ligands bind is virtually identical in solution and in the crystal forms.

High-resolution solution structures of oxidized and reduced Escherichia coli thioredoxin

BACKGROUND

Thioredoxin participates in thiol-disulfide exchange reactions and both oxidized thioredoxin (disulfide form) and reduced thioredoxin (dithiol form) are found under physiological conditions. Previous structural studies suggested that the two forms were extremely similar, although significant functional and spectroscopic differences exist. We therefore undertook high-resolution solution structural studies of the two forms of Escherichia coli thioredoxin in order to detect subtle conformational differences.

RESULTS

The solution structures of reduced and oxidized thioredoxin are extremely similar. Backbone structure is largely identical in the two forms, with slight differences in the region of the active site, which includes Cys32 and Cys35. The side chain sulfur atom of Cys32 is tilted away from that of Cys35 in the reduced form of the protein to accommodate the increase in S-S distance that occurs upon reduction of the disulfide, but the chi 1 angles of the two cysteines remain the same in the two forms.

CONCLUSIONS

Only subtle conformational changes occur upon changing the oxidation state of the active site cysteines, including the positions of some side chains and in hydrogen bonding patterns in the active site region. Functional differences between the two forms are probably therefore related to differences in local conformational flexibility in and near the active site loop.

Analysis of proton chemical shifts in regular secondary structure of proteins

The contribution of peptide groups to H alpha and H beta proton chemical shifts can be modeled with empirical equations that represent magnetic anisotropy and electrostatic interactions [Osapay, K. and Case, D.A. (1991) J. Am. Chem. Soc., 113, 9436-9444]. Using these, a model for the 'random coil' reference state can be generated by averaging a dipeptide over energetically allowed regions of torsion-angle space. Such calculations support the notion that the empirical constant used in earlier studies arises from neighboring peptide contributions in the reference state, and suggest that special values be used for glycine and proline residues, which differ significantly from other residues in their allowed phi, psi-ranges. New constants for these residues are reported that provide significant improvements in predicted backbone shifts. To illustrate how secondary structure affects backbone chemical shifts we report calculations on oligopeptide models for helices, sheets and turns. In addition to suggesting a physical mechanism for the widely recognized average difference between alpha and beta secondary structures, these models suggest several additional regularities that should be expected: (a) H alpha protons at the edges of beta-sheets will have a two-residue periodicity; (b) the H alpha 2 and H alpha 3 protons of glycine residues will exhibit different shifts, particularly in sheets; (c) H beta protons will also be sensitive to local secondary structure, but in different directions and to a smaller extent than H alpha protons; (d) H alpha protons in turns will generally be shifted upfield, except those in position 3 of type I turns. Examples of observed shift patterns in several proteins illustrate the application of these ideas.