Mark T. Oakley

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.

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.

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 Go̅ 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 β-barrel structure.

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.

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

We present a combined computational and experimental study of the energy landscapes of cyclic tetra-α/β-peptides. We have performed discrete path sampling calculations on a series of cyclic tetra-α/β-peptides to obtain the relative free energies and barriers to interconversion of their conformers. The most stable conformers of cyclo-[(β-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/β-peptides containing a single proline residue, of the type cyclo-[β-Ala-Xaa-β-Ala-Pro], the energy landscapes show that the most stable isomers containing cis and trans β-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-[β-Ala-Lys-β-Ala-Pro] and cyclo-[β-Ala-Ala-β-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-[β-Ala-Val-β-Ala-Pro] affects the conformations of the ring, leading to significant differences between its energy landscape and that of cyclo-[β-Ala-Ala-β-Ala-Pro]. We have synthesized the cyclic peptide cyclo-[β-Ala-Lys-β-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-[β-Ala-Ala-β-Ala-Pro] are in good agreement with the experimental spectra of cyclo-[β-Ala-Lys-β-Ala-Pro], suggesting that the Ala cyclic tetrapeptide is a viable model for the Lys analogue.

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.

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.

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.

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.

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.