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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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).