Predicting cavity formation free energy: how far is the Gaussian approximation valid?

We examine the range of validity of the Gaussian model for various water-like liquids whose intermolecular potentials differ from SPC/E water, to provide insight into the temperature dependence of the hydrophobic effect for small hard sphere solutes. We find that low compressibility liquids that have more close-packed network structures show much larger deviations from Gaussian fluctuations for low or zero occupancies relative to more compressible fluids with more open networks. Water appears to be a unique molecular fluid in possessing equilibrium density fluctuations that are faithfully described by the Gaussian theory. We ascribe this success to the fact, shown here, that the orientational correlations near a small hard sphere solute involve remarkably little reorganization from the bulk, which is a consequence of water's low solvent reorganization enthalpy and entropy.

Hydrogen bond strength and network structure effects on hydration of non-polar molecules.

We measure the solvation free energy, Δµ*, for hard spheres and Lennard-Jones particles in a number of artificial liquids made from modified water models. These liquids have reduced hydrogen bond strengths or altered bond angles. By measuring Δµ* for a number of state points at P = 1 bar and different temperatures, we obtain solvation entropies and enthalpies, which are related to the temperature dependence of the solubilities. By resolving the solvation entropy into the sum of the direct solute-solvent interaction and a term depending on the solvent reorganisation enthalpy we show that, although the hydrophobic effect in water at 300 K arises mainly from the small molecular size, its temperature dependence is anomalously low because the reorganisation enthalpy of liquid water is unusually small. We attribute this to the strong tetrahedral network which results from both the molecular geometry and the hydrogen bond strength.

Matching simulation and experiment: a new simplified model for simulating protein folding.

Simulations of simplified protein folding models have provided much insight into solving the protein folding problem. We propose here a new off-lattice bead model, capable of simulating several different fold classes of small proteins. We present the sequence for an alpha/beta protein resembling the IgG-binding proteins L and G. The thermodynamics of the folding process for this model are characterized using the multiple multihistogram method combined with constant-temperature Langevin simulations. The folding is shown to be highly cooperative, with chain collapse nearly accompanying folding. Two parallel folding pathways are shown to exist on the folding free energy landscape. One pathway contains an intermediate--similar to experiments on protein G, and one pathway contains no intermediates-similar to experiments on protein L. The folding kinetics are characterized by tabulating mean-first passage times, and we show that the onset of glasslike kinetics occurs at much lower temperatures than the folding temperature. This model is expected to be useful in many future contexts: investigating questions of the role of local versus nonlocal interactions in various fold classes, addressing the effect of sequence mutations affecting secondary structure propensities, and providing a computationally feasible model for studying the role of solvation forces in protein folding.

A global optimization strategy for predicting alpha-helical protein tertiary structure.

We present a global optimization strategy that incorporates predicted restraints in both a local optimization context and as directives for global optimization approaches, to predict protein tertiary structure for alpha-helical proteins. Specifically, neural networks are used to predict the secondary structure of a protein, restraints are defined as manifestations of the network with a predicted secondary structure and the secondary structure is formed using local minimizations on a protein energy surface, in the presence of the restraints. Those residues predicted to be coil, by the network, define a conformational sub-space that is subject to optimization using a global approach known as stochastic perturbation that has been found to be effective for Lennard-Jones clusters and homo-polypeptides. Our energy surface is an all-atom 'gas phase' molecular mechanics force field, that is combined with a new solvation energy function that penalizes hydrophobic group exposure. This energy function gives the crystal structure of four different alpha-helical proteins as the lowest energy structure relative to other conformations, with correct secondary structure but incorrect tertiary structure. We demonstrate this global optimization strategy by determining the tertiary structure of the A-chain of the alpha-helical protein, uteroglobin and of a four-helix bundle, DNA binding protein.

Evidence for microscopic, long-range hydration forces for a hydrophobic amino acid.

We have combined neutron solution scattering experiments with molecular dynamics simulation to isolate an excess experimental signal that is caused solely by N-acetyl-leucine-amide (NALA) correlations in aqueous solution. This excess signal contains information about how NALA molecule centers are correlated in water, and we show how these solute-solute correlations might be determined at dilute concentrations in the small angle region. We have tested qualitatively different pair distribution functions for NALA molecule centers-gas, cluster, and aqueous forms of gc(r)-and have found that the excess experimental signal is adequate enough to rule out gas and cluster pair distribution functions. The aqueous form of gc(r) that exhibits a solvent-separated minimum, and possibly longer-ranged correlations as well, is not only physically sound but reproduces the experimental data reasonably well. This work demonstrates that important information in the small angle region can be mined to resolve solute-solute correlations, their lengthscales, and thermodynamic consequences even at dilute concentrations. The hydration forces that operate on the microscopic scale of individual amino acid side chains, implied by the small angle scattering data, could have significant effects on the early stages of protein folding, on ligand binding, and on other intermolecular interactions.

Chemical bonding effects in the determination of protein structures by electron crystallography.

Scattering of electrons is affected by the distribution of valence electrons that participate in chemical bonding and thus change the electrostatic shielding of the nucleus. This effect is particularly significant for low-angle scattering. Thus, while chemical bonding effects are difficult to measure with small-unit cell materials, they can be substantial in the study of proteins by electron crystallography. This work investigates the magnitude of chemical bonding effects for a representative collection of protein fragments and a model ligand for nucleotide-binding proteins within the resolution range generally used in determining protein structures by electron crystallography. Electrostatic potentials were calculated by ab initio methods for both the test molecules and for superpositions of their free atoms. Differences in scattering amplitudes can be well over 10% in the resolution range below 5 A and are especially large in the case of ionized side chains and ligands. We conclude that the use of molecule-based scattering factors can provide a much more accurate representation of the low-resolution data obtained in electron crystallographic studies. The comparison of neutral and ionic structure factors at resolutions below 5 A can also provide a sensitive determination of charge states, important for biological function, that is not accessible from X-ray crystallographic measurements.

Redesigning the hydrophobic core of a model beta-sheet protein: destabilizing traps through a threading approach.

An off-lattice 46-bead model of a small all-beta protein has been recently criticized for possessing too many traps and long-lived intermediates compared with the folding energy landscape predicted for real proteins and models using the principle of minimal frustration. Using a novel sequence design approach based on threading for finding beneficial mutations for destabilizing traps, we proposed three new sequences for folding in the beta-sheet model. Simulated annealing on these sequences found the global minimum more reliably, indicative of a smoother energy landscape, and simulated thermodynamic variables found evidence for a more cooperative collapse transition, lowering of the collapse temperature, and higher folding temperatures. Folding and unfolding kinetics were acquired by calculating first-passage times, and the new sequences were found to fold significantly faster than the original sequence, with a concomitant lowering of the glass temperature, although none of the sequences have highly stable native structures. The new sequences found here are more representative of real proteins and are good folders in the T(f) > T(g) sense, and they should prove useful in future studies of the details of transition states and the nature of folding intermediates in the context of simplified folding models. These results show that our sequence design approach using threading can improve models possessing glasslike folding dynamics.

The importance of hydration for the kinetics and thermodynamics of protein folding: simplified lattice models.

BACKGROUND: Recent studies have proposed various sources for the origin of cooperativity in simplified protein folding models. Important contributions to cooperativity that have been discussed include backbone hydrogen bonding, sidechain packing and hydrophobic interactions. Related work has also focused on which interactions are responsible for making the free energy of the native structure a pronounced global minimum in the free energy landscape. In addition, two-flavor bead models have been found to exhibit poor folding cooperativity and often lack unique native structures. We propose a simple multibody description of hydration with expectations that it might modify the free energy surface in such a way as to increase the cooperativity of folding and improve the performance of two-flavor models. RESULTS: We study the thermodynamics and kinetics of folding for designed 36-mer sequences on a cubic lattice using both our solvation model and the corresponding model without solvation terms. Degeneracies of the native states are studied by enumerating the maximally compact states. The histogram Monte Carlo method is used to obtain folding temperatures, densities of states and heat capacity curves. Folding kinetics are examined by accumulating mean first-passage times versus temperature. Sequences in the proposed solvation model are found to have more unique ground states, fold faster and fold with more cooperativity than sequences in the nonsolvation model. CONCLUSIONS: We find that the addition of a multibody description of solvation can improve the poor performance of two-flavor lattice models and provide an additional source for more cooperative folding. Our results suggest that a better description of solvation will be important for future theoretical protein folding studies.

Differences in hydration structure near hydrophobic and hydrophilic amino acids.

We use molecular dynamics to simulate recent neutron scattering experiments on aqueous solutions of N-acetyl-leucine-amide and N-acetyl-glutamine-amide, and break down the total scattering function into contributions from solute-solute, solute-water, water-water, and intramolecular correlations. We show that the shift of the main diffraction peak to smaller angle that is observed for leucine, but not for glutamine, is attributable primarily to alterations in water-water correlations relative to bulk. The perturbation of the water hydrogen-bonded network extends roughly two solvation layers from the hydrophobic side chain surface, and is characterized by a distribution of hydrogen bonded ring sizes that are more planar and are dominated by pentagons in particular than those near the hydrophilic side chain. The different structural organization of water near the hydrophobic solute that gives rise to the inward shift in the main neutron diffraction peak under ambient conditions may also provide insight into the same directional shift for pure liquid water as it is cooled and supercooled.

Direct evidence for modified solvent structure within the hydration shell of a hydrophobic amino acid.

Neutron scattering experiments are used to determine scattering profiles for aqueous solutions of hydrophobic and hydrophilic amino acid analogs. Solutions of hydrophobic solutes show a shift in the main diffraction peak to smaller angle as compared with pure water, whereas solutions of hydrophilic solutes do not. The same difference for solutions of hydrophobic and hydrophilic side chains is also predicted by molecular dynamics simulations. The neutron scattering curves of aqueous solutions of hydrophobic amino acids at room temperature are qualitatively similar to differences between the liquid molecular structure functions measured for ambient and supercooled water. The nonpolar solute-induced expansion of water structure reported here is also complementary to recent neutron experiments where compression of aqueous solvent structure has been observed at high salt concentration.

Is water structure around hydrophobic groups clathrate-like?

The term "clathrate structure" is quantified for solvation of nonpolar groups by enumerating hydrogen-bonded ring sizes both in the solvation shell and through the shell-bulk interface and comparing it to a bulk control using the ST4 water model. For clathrate-like structure to be evident, the distributions along the hydrophobic surface are expected to be dominated by pentagons, with significant depletion of hexagons and larger polygons. While the distribution in this region is indeed distinguished by a large number of pentagons, there are significant contributions from hexagons and larger rings as well. Calculated polygon distributions through the shell-bulk interface indicate that when water structure is highly cooperative along the hydrophobic surface, hydrogen-bonded pathways leading back into bulk are then reduced. These results are qualitatively consistent with the observation that hydrophobicity is proportional to the nonpolar solute surface area.

Poly(L-alanine) as a universal reference material for understanding protein energies and structures.

We present a proposition, the "poly(L-alanine) hypothesis," which asserts that the native backbone geometry for any polypeptide or protein of M residues has a closely mimicking, mechanically stable, image in poly(L-alanine) of the same number of residues. Using a molecular mechanics force field to represent the relevant potential energy hypersurfaces, we have carried out calculations over a wide range of M values to show that poly(L-alanine) possesses the structural versatility necessary to satisfy the proposition. These include poly(L-alanine) representatives of minima corresponding to secondary and supersecondary structures, as well as poly(L-alanine) images for tertiary structures of the naturally occurring proteins bovine pancreatic trypsin inhibitor, crambin, ribonuclease A, and superoxide dismutase. The successful validation of the hypothesis presented in this paper indicates that poly(L-alanine) will serve as a good reference material in thermodynamic perturbation theory and calculations aimed at evaluating relative free energies for competing candidate tertiary structures in real polypeptides and proteins.

A strategy for finding classes of minima on a hypersurface: implications for approaches to the protein folding problem.

Locating the native structure of a given protein is a task made difficult by the complexity of the potential energy hypersurface and by the huge number of local minima it contains. We have explored a strategy (the "antlion" method) for hypersurface modification that suppresses all minima but that of the native structure. Transferrable penalty functions with general applicability for modifying a hypersurface to retain the desired minimum are identified, and two blocked oligopeptides (alanine dipeptide and tetrapeptide) are used for specific numerical illustration of the dramatic simplification that ensues. In addition, an intermediary role for neural networks to manage some aspects of the antlion strategy applied to large polypeptides and proteins is introduced.

Virtual rigid body dynamics.

An important direction in biological simulations is the development of methods that permit the study of larger systems and/or longer simulation time scales than is currently feasible by molecular dynamics. One such method designed with this objective in mind is stochastic boundary molecular dynamics (SBMD). SBMD was developed for the characterization of spatially localized processes in proteins, and has been shown to successfully reproduce structural and dynamical properties of these macromolecules, as compared to a molecular dynamics control simulation, when concerted or global motions are not present. The virtual rigid body dynamics method presented in this work extends the range of applicability of the SBMD method, by providing a framework to include these important long time scale conformational transitions. In this paper we describe the two-step implementation of the virtual rigid body model: first, the reduction of the full atomic representation to a reduced particle (virtual bond) model, and second, the propagation of the dynamics of flexibly connected rigid bodies containing virtual atom sites.