Isomers and Energy Landscapes of Perchlorate-Water Clusters and a Comparison to Pure Water and Sulfate-Water Clusters.

Hydrated ions are crucially important in a wide array of environments, from biology to the atmosphere, and the presence and concentration of ions in a system can drastically alter its behavior. One way in which ions can affect systems is in their interactions with proteins. The Hofmeister series ranks ions by their ability to salt-out proteins, with kosmotropes, such as sulfate, increasing their stability and chaotropes, such as perchlorate, decreasing their stability. We study hydrated perchlorate clusters as they are strongly chaotropic and thus exhibit different properties than sulfate. In this study we simulate small hydrated perchlorate clusters using a basin-hopping geometry optimization search with empirical potentials. We compare topological features of these clusters to data from both computational and experimental studies of hydrated sulfate ions and draw some conclusions about ion effects in the Hofmeister series. We observe a patterning conferred to the water molecules within the cluster by the presence of the perchlorate ion and compare the magnitude of this effect to that observed in previous studies involving sulfate. We also investigate the influence of the overall ionic charge on the low-energy structures adopted by these clusters.

Chiral effects on helicity studied via the energy landscape of short (D, L)-alanine peptides.

The homochirality of natural amino acids facilitates the formation of regular secondary structures such as α-helices and ß-sheets. Here, we study the relationship between chirality and backbone structure for the example of hexa-alanine. The most stable stereoisomers are identified through global optimisation. Further, the energy landscape, a database of connected low-energy local minima and transition points, is constructed for various neutral and zwitterionic stereoisomers of hexa-alanine. Three order parameters for partial helicity are applied and metric disconnectivity graphs are presented with partial helicity as a metric. We also apply the Zimm-Bragg model to derive average partial helicities for Ace-(L-Ala)6-NHMe, Ace-(D-Ala-L-Ala)3-NHMe, and Ace-(L-Ala)3-(D-Ala)3-NHMe from the database of local minima and compare with previous studies.

Visualizing energy landscapes with metric disconnectivity graphs.

The visualization of multidimensional energy landscapes is important, providing insight into the kinetics and thermodynamics of a system, as well the range of structures a system can adopt. It is, however, highly nontrivial, with the number of dimensions required for a faithful reproduction of the landscape far higher than can be represented in two or three dimensions. Metric disconnectivity graphs provide a possible solution, incorporating the landscape connectivity information present in disconnectivity graphs with structural information in the form of a metric. In this study, we present a new software package, PyConnect, which is capable of producing both disconnectivity graphs and metric disconnectivity graphs in two or three dimensions. We present as a test case the analysis of the 69-bead BLN coarse-grained model protein and show that, by choosing appropriate order parameters, metric disconnectivity graphs can resolve correlations between structural features on the energy landscape with the landscapes energetic and kinetic properties.

Symmetrisation schemes for global optimisation of atomic clusters.

Locating the global minima of atomic and molecular clusters can be a difficult optimisation problem. Here we report benchmarks for procedures that exploit approximate symmetry. This strategy was implemented in the GMIN program following a theoretical analysis, which explained why high-symmetry structures are more likely to have particularly high or particularly low energy. The analysis, and the corresponding algorithms, allow for approximate point group symmetry, and can be combined with basin-hopping and genetic algorithms. We report results for 38-, 75-, and 98-atom Lennard-Jones clusters, which are all multiple-funnel systems. Exploiting approximate symmetry reduces the mean time taken to locate the global minimum by up to two orders of magnitude, with smaller improvements in efficiency for LJ(55) and LJ(74), which correspond to simpler single-funnel energy landscapes.

First principles predictions of thermophysical properties of refrigerant mixtures.

We present pair potentials for fluorinated methanes and their dimers with CO(2) based on ab initio potential energy surfaces. These potentials reproduce the experimental second virial coefficients of the pure fluorinated methanes and their mixtures with CO(2) without adjustment. Ab initio calculations on trimers are used to model the effects of nonadditive dispersion and induction. Simulations using these potentials reproduce the experimental phase-coexistence properties of CH(3)F within 10% over a wide range of temperatures. The phase coexistence curve of the mixture of CH(2)F(2) and CO(2) is reproduced with an error in the mole fractions of both phases of less than 0.1. The potentials described here are based entirely on ab initio calculations, with no empirical fits to improve the agreement with experiment.

Additive and nonadditive models of vapor-liquid equilibrium in CO2 from first principles.

We describe quantum-chemical calculations on dimers of CO(2) and use the results to develop first-principles models for Gibbs ensemble Monte Carlo simulations of the phase coexistence curve. Isotropic pairwise potentials are insufficient to model the phase behavior and overestimate the binding in liquid CO(2) by 4 kJ mol(-1). An anisotropic treatment of the atoms in the pairwise potential reduces the strength of the binding by approximately 0.5 kJ mol(-1). We use ab initio calculations on trimers of CO(2) to assess the strength of nonadditive interactions. Including nonadditive dispersion in Gibbs ensemble simulations gives an enthalpy of vaporization within 1.5 kJ mol(-1) of the experimental value over a wide range of temperatures.

Search strategies in structural bioinformatics.

Optimisation problems pervade structural bioinformatics. In this review, we describe recent work addressing a selection of bioinformatics challenges. We begin with a discussion of research into protein structure comparison, and highlight the utility of Kolmogorov complexity as a measure of structural similarity. We then turn to research into de novo protein structure prediction, in which structures are generated from first principles. In this endeavour, there is a compromise between the detail of the model and the extent to which the conformational space of the protein can be sampled. We discuss some developments in this area, including off-lattice structure prediction using the great deluge algorithm. One strategy to reduce the size of the search space is to restrict the protein chain to sites on a regular lattice. In this context, we highlight the use of memetic algorithms, which combine genetic algorithms with local optimisation, to the study of simple protein models on the two-dimensional square lattice and the face-centred cubic lattice.

Calculations on the electronic excited states of ureas and oligoureas.

We report CASPT2 calculations on the electronic excited states of several ureas. For monoureas, we find an electric dipole forbidden n --> pi* transition between 180 and 210 nm, dependent on the geometry and substituents of the urea. We find two intense pinb --> pi* transitions between 150 and 210 nm, which account for the absorptions seen in the experimental spectra. The n' --> pi* and pib --> pi* transitions are at wavelengths below 125 nm, which is below the lower limit of the experimental spectra. Parameter sets modeling the charge densities of the electronic transitions have been derived and permit calculations on larger oligoureas, using the exciton matrix method. For glycouril, a urea dimer, both the CASPT2 method and the matrix method yield similar results. Calculations of the electronic circular dichroism spectrum of an oligourea containing eight urea groups indicate that the experimental spectrum cannot be reproduced without the inclusion of electronic excitations involving the side chains. These calculations are one of the first attempts to understand the relationship between the structure and excited states of this class of macromolecule.

Structures and Energy Landscapes of Hydrated Sulfate Clusters.

The sulfate ion is the most kosmotropic member of the Hofmeister series, but the chemical origins of this effect are unclear. We present a global optimization and energy landscape mapping study of microhydrated sulfate ions, SO4(2-)(H2O)n, in the size range 3 ≤ n ≤ 50. The clusters are modeled using a rigid-body empirical potential and optimized using basin-hopping Monte Carlo in conjunction with a move set including cycle inversions to explore hydrogen bond topologies. For clusters containing a few water molecules (n ≤ 6) we are able to reproduce ab initio global minima, either as global minima of the empirical potential, or as low-energy isomers. This result justifies applications to larger systems. Experimental studies have shown that dangling hydroxyl groups are present on the surfaces of pure water clusters, but absent in hydrated sulfate clusters up to n ≈ 43. Our global optimization results agree with this observation, with dangling hydroxyl groups absent from the low-lying minima of small clusters, but competitive in larger clusters.

Energy Landscapes and Global Optimization of Self-Assembling Cyclic Peptides.

Self-assembled cyclic peptide nanotubes have attracted much attention because of their antimicrobial properties. Here, we present calculations on the formation of cyclic peptide dimers using basin-hopping and discrete path sampling. We present an analysis of the basin-hopping move sets that most efficiently explore the conformations of cyclic peptides. Group rotation moves, in which sections of the ring are rotated as a rigid body, are the most effective for cyclic peptides containing up to 20 residues. For cyclic peptide dimers, we find that a combination of group rotation intramolecular moves and rigid body intermolecular moves performs well. Discrete path sampling calculations on the cyclic peptide dimers show significant differences in the dimerization of hexa- and octapeptides.

Exploring the Energy Landscapes of Cyclic Tetrapeptides with Discrete Path Sampling.

Cyclic tetrapeptides are an important class of biologically active molecules that exhibit interesting conformational dynamics, with slow interconversion of several different structures. We present calculations on their energy landscapes using discrete path sampling. In acyclic peptides and large cyclic peptides, isomers containing cis-peptide groups are much less stable than the all-trans isomers and separated from them by large barriers. Strain in small cyclic peptides causes the cis and trans isomers to be closer in energy and separated by much lower barriers. If d-amino acids or proline residues are introduced, isomers containing cis-peptides become more stable than the all-trans structures. We also show that changing the polarity of the solvent has a significant effect on the energy landscapes of cyclic tetrapeptides, causing changes in the orientations of the peptide groups and in the degree of intramolecular hydrogen bonding.

Protein structure optimization with a "Lamarckian" ant colony algorithm.

We describe the LamarckiAnt algorithm: a search algorithm that combines the features of a "Lamarckian" genetic algorithm and ant colony optimization. We have implemented this algorithm for the optimization of BLN model proteins, which have frustrated energy landscapes and represent a challenge for global optimization algorithms. We demonstrate that LamarckiAnt performs competitively with other state-of-the-art optimization algorithms.

Computational and experimental investigations into the conformations of cyclic tetra-α/ß-peptides.

We present a combined computational and experimental study of the energy landscapes of cyclic tetra-α/ß-peptides. We have performed discrete path sampling calculations on a series of cyclic tetra-α/ß-peptides to obtain the relative free energies and barriers to interconversion of their conformers. The most stable conformers of cyclo-[(ß-Ala-Gly)2] contain all-trans peptide groups. The relative energies of the cis isomers and the cis-trans barriers are lower than in acyclic peptides but not as low as in the highly strained cyclic α-peptides. For cyclic tetra-α/ß-peptides containing a single proline residue, of the type cyclo-[ß-Ala-Xaa-ß-Ala-Pro], the energy landscapes show that the most stable isomers containing cis and trans ß-Ala-Pro have similar free energies and are separated by barriers of approximately 15 kcal mol(-1). We show that the underlying energy landscapes of cyclo-[ß-Ala-Lys-ß-Ala-Pro] and cyclo-[ß-Ala-Ala-ß-Ala-Pro] are similar, allowing the substitution of the flexible side chain of Lys with Ala to reduce the computational demand of our calculations. However, the steric bulk of the Val side chain in cyclo-[ß-Ala-Val-ß-Ala-Pro] affects the conformations of the ring, leading to significant differences between its energy landscape and that of cyclo-[ß-Ala-Ala-ß-Ala-Pro]. We have synthesized the cyclic peptide cyclo-[ß-Ala-Lys-ß-Ala-Pro], and NMR spectroscopy shows the presence of conformers that interconvert slowly on the NMR time scale at temperatures up to 80 °C. Calculated circular dichroism (CD) spectra for the proposed major isomer of cyclo-[ß-Ala-Ala-ß-Ala-Pro] are in good agreement with the experimental spectra of cyclo-[ß-Ala-Lys-ß-Ala-Pro], suggesting that the Ala cyclic tetrapeptide is a viable model for the Lys analogue.

Energy landscape and global optimization for a frustrated model protein.

The three-color (BLN) 69-residue model protein was designed to exhibit frustrated folding. We investigate the energy landscape of this protein using disconnectivity graphs and compare it to a Go model, which is designed to reduce the frustration by removing all non-native attractive interactions. Finding the global minimum on a frustrated energy landscape is a good test of global optimization techniques, and we present calculations evaluating the performance of basin-hopping and genetic algorithms for this system. Comparisons are made with the widely studied 46-residue BLN protein. We show that the energy landscape of the 69-residue BLN protein contains several deep funnels, each of which corresponds to a different ß-barrel structure.

Charge-transfer transitions in protein circular dichroism calculations.

Charge-transfer transitions in proteins play a key role in many biophysical processes, from the behavior of redox proteins to photochemical reactions. We present ab initio calculations on a model dipeptide and more approximate calculations of the electronic excited states of proteins which, taken together, provide the most definitive assignment and characterization of charge-transfer transitions in proteins to date. We have calculated from first principles the electronic circular dichroism (CD) spectra of 31 proteins on the basis of their structures. Compared to previous studies, we achieve more accurate calculated CD spectra between 170 and 190 nm, owing mainly to the importance in alpha-helices of a charge-transfer transition from the lone pair on one peptide group to the pi* orbital on the next peptide group.

First-principles calculations of protein circular dichroism in the far-ultraviolet and beyond.

Understanding the relationship between the amino acid sequence of a protein and its unique, compact three-dimensional structure is one of the grand challenges in molecular biophysics. One exciting approach to the protein-folding problem is fast time-resolved spectroscopy in the ultra-violet (UV). Time-resolved electronic circular dichroism (CD) spectroscopy offers resolution on a nanosecond (or faster) timescale, but does not provide the spatial resolution of techniques like X-ray crystallography or NMR. There is a need to underpin fast timescale spectroscopic studies of protein folding with a stronger theoretical foundation. We review some recent studies in this regard and briefly highlight how modern quantum chemical models of aromatic groups have improved the accuracy of calculations of protein CD spectra near-UV. On the other side of the far-UV, we describe calculations indicating that charge-transfer transitions are likely to be responsible for bands observed in the vacuum UV in protein CD.

Lattice models of peptide aggregation: evaluation of conformational search algorithms.

We present a series of conformational search calculations on the aggregation of short peptide fragments that form fibrils similar to those seen in many protein mis-folding diseases. The proteins were represented by a face-centered cubic lattice model with the conformational energies calculated using the Miyazawa-Jernigan potential. The searches were performed using algorithms based on the Metropolis Monte Carlo method, including simulated annealing and replica exchange. We also present the results of searches using the tabu search method, an algorithm that has been used for many optimization problems, but has rarely been used in protein conformational searches. The replica exchange algorithm consistently found more stable structures then the other algorithms, and was particularly effective for the octamers and larger systems.

Aromatic 4-tetrahydropyranyl and 4-quinuclidinyl cations. Linking Prins with Cope and Grob.

The chair 4-tetrahydropyranyl cation and the 4-quinuclidinyl cation are shown to be energy minima and to be delocalized, with exceptionally long CH2CH2 bonds, according to B3LYP/6-31G* calculations; the implications for Prins cyclizations, Cope rearrangements, and Grob fragmentations are discussed.

A sequential molecular mechanics/quantum mechanics study of the electronic spectra of amides.

We report gas-phase electronic spectra of formamide, N-methyformamide, acetamide, and N-methylacetamide at 300 K calculated using a combination of classical molecular dynamics and time-dependent density functional theory (TDDFT). In comparison to excitation energies computed using the global minima structures, the valence npi* and pi(nb)pi* states show a significant red-shift of 0.1-0.35 eV, while smaller shifts are found for the n3s and pi(nb)3s Rydberg states. In this work, we have identified the physical origin of these shifts arising from variations of the molecular structure. We present simple relationships between key geometrical parameters and spectral shifts. Consequently, electronic spectra can be generated directly from ground-state structures, without additional quantum chemical calculations. The electronic spectrum of formamide in aqueous solution is computed using TDDFT using an explicit solvent model. This provides a quantitative determination of the condensed-phase spectrum. In general, this study shows that temperature effects can change the predicted excitation energies significantly and demonstrates how electronic spectra at elevated temperatures can be computed in a computationally efficient way.

The azulene-to-naphthalene rearrangement revisited: a DFT study of intramolecular and radical-promoted mechanisms.

Intramolecular and radical-promoted mechanisms for the rearrangement of azulene to naphthalene are assessed with the aid of density functional calculations. All intramolecular mechanisms have very high activation energies (>/=350 kJ mol(-1) from azulene) and so can only be competitive at temperatures above 1000 degrees C. Two radical-promoted mechanisms, the methylene walk and spiran pathways, dominate the reaction below this temperature. The activation energy for an orbital symmetry-allowed mechanism via a bicyclobutane intermediate is 382 kJ mol(-1). The norcaradiene-vinylidene mechanism that has been proposed in order to explain the formation of small amounts of 1-phenyl-1-buten-3-ynes from flash thermolysis of azulene has an activation energy of 360 kJ mol(-1); subtle features of the B3LYP/6-31G(d) energy surface for this mechanism are discussed. All intermediates and transition states on the spiran and methylene walk radical-promoted pathways have been located at the B3LYP/6-31G(d) level. Interconversion of all n-H-azulyl radicals via hydrogen shifts was also examined, and hydrogen shifts around the five-membered ring are competitive with the mechanisms leading to rearrangement to naphthalene, but those around the seven-membered ring are not. Conversion of a tricyclic radical to the 9-H-naphthyl radical is the rate-limiting transition state on the spiran pathway, and lies 164.0 kJ mol(-1) above that of the 1-H-azulyl radical. The transition state for the degenerate hydrogen shift between the 9-H-azulyl and 10-H-azulyl radicals is 7.4 kJ mol(-1) lower. Partial equilibration of the intermediates in the spiran pathway via this shift may therefore occur, and this can account for the surprising formation of 1-methylnaphthalene from 2-methylazulene. The rate-limiting transition state for the methylene walk pathway involves the concerted transfer of a methylene group from one ring to the other and lies 182.3 kJ mol(-1) above that of the 1-H-azulyl radical. It is shown that rearrangement via a combination of 31% methylene walk and 69% spiran pathways can account semiquantitatively for all the products from 1-(13)C-azulene, 9-(13)C-azulene, and 4,7-(13)C(2)-azulene, in addition to accounting for the products from methylazulenes, and the formation of naphthalene-d(0) and -d(2) from azulene-4-d. It is also pointed out that a small extension to the spiran pathway could provide an alternative explanation for the formation of 1-phenyl-1-buten-3-ynes.