Tests of an adaptive QM/MM calculation on free energy profiles of chemical reactions in solution.

We present reaction free energy calculations using the adaptive buffered force mixing quantum mechanics/molecular mechanics (bf-QM/MM) method. The bf-QM/MM method combines nonadaptive electrostatic embedding QM/MM calculations with extended and reduced QM regions to calculate accurate forces on all atoms, which can be used in free energy calculation methods that require only the forces and not the energy. We calculate the free energy profiles of two reactions in aqueous solution: the nucleophilic substitution reaction of methyl chloride with a chloride anion and the deprotonation reaction of the tyrosine side chain. We validate the bf-QM/MM method against a full QM simulation, and show that it correctly reproduces both geometrical properties and free energy profiles of the QM model, while the electrostatic embedding QM/MM method using a static QM region comprising only the solute is unable to do so. The bf-QM/MM method is not explicitly dependent on the details of the QM and MM methods, so long as it is possible to compute QM forces in a small region and MM forces in the rest of the system, as in a conventional QM/MM calculation. It is simple, with only a few parameters needed to control the QM calculation sizes, and allows (but does not require) a varying and adapting QM region which is necessary for simulating solutions.

Free energy surface reconstruction from umbrella samples using Gaussian process regression

We demonstrate how the Gaussian process regression approach can be used to efficiently reconstruct free energy surfaces from umbrella sampling simulations. By making a prior assumption of smoothness and taking account of the sampling noise in a consistent fashion, we achieve a significant improvement in accuracy over the state of the art in two or more dimensions or, equivalently, a significant cost reduction to obtain the free energy surface within a prescribed tolerance in both regimes of spatially sparse data and short sampling trajectories. Stemming from its Bayesian interpretation the method provides meaningful error bars without significant additional computation. A software implementation is made available on www.libatoms.org.

Free energy surface reconstruction from umbrella samples using Gaussian process regression II: Multiple collective variables

We demonstrate how a prior assumption of smoothness can be used to enhance the reconstruction of free energy profiles from multiple umbrella sampling simulations using the Bayesian Gaussian process regression approach. The method we derive allows the concurrent use of histograms and free energy gradients and can easily be extended to include further data. In Part I we review the necessary theory and test the method for one collective variable. We demonstrate improved performance with respect to the weighted histogram analysis method and obtain meaningful error bars without any significant additional computation. In Part II we consider the case of multiple collective variables and compare to a reconstruction using least squares fitting of radial basis functions. We find substantial improvements in the regimes of spatially sparse data or short sampling trajectories. A software implementation is made available on www.libatoms.org.

Surface attachment of protein fibrils via covalent modification strategies.

Chemical control of surface functionality and topography is an essential requirement for many technological purposes. In particular, the covalent attachment of monomeric proteins to surfaces has been the object of intense studies in recent years, for applications as varied as electrochemistry, immuno-sensing, and the production of biocompatible coatings. Little is known, however, about the characteristics and requirements underlying surface attachment of supramolecular protein nanostructures. Amyloid fibrils formed by the self-assembly of peptide and protein molecules represent one important class of such structures. These highly organized beta-sheet-rich assemblies are a hallmark of a range of neurodegenerative disorders, including Alzheimer's disease and type II diabetes, but recent findings suggest that they have much broader significance, potentially representing the global free energy minima of the energy landscapes of proteins and having potential applications in material science. In this paper, we describe strategies for attaching amyloid fibrils formed from different proteins to gold surfaces under different solution conditions. Our methods involve the reaction of sulfur containing small molecules (cystamine and 2-iminothiolane) with the amyloid fibrils, enabling their covalent linkage to gold surfaces. We demonstrate that irreversible attachment using these approaches makes possible quantitative analysis of experiments using biosensor techniques, such as quartz crystal microbalance (QCM) assays that are revolutionizing our understanding of the mechanisms of amyloid growth and the factors that determine its kinetic behavior. Moreover, our results shed light on the nature and relative importance of covalent versus noncovalent forces acting on protein superstructures at metal surfaces.

Population of nonnative states of lysozyme variants drives amyloid fibril formation.

The propensity of protein molecules to self-assemble into highly ordered, fibrillar aggregates lies at the heart of understanding many disorders ranging from Alzheimer's disease to systemic lysozyme amyloidosis. In this paper we use highly accurate kinetic measurements of amyloid fibril growth in combination with spectroscopic tools to quantify the effect of modifications in solution conditions and in the amino acid sequence of human lysozyme on its propensity to form amyloid fibrils under acidic conditions. We elucidate and quantify the correlation between the rate of amyloid growth and the population of nonnative states, and we show that changes in amyloidogenicity are almost entirely due to alterations in the stability of the native state, while other regions of the global free-energy surface remain largely unmodified. These results provide insight into the complex dynamics of a macromolecule on a multidimensional energy landscape and point the way for a better understanding of amyloid diseases.

Evaluating boundary dependent errors in QM/MM simulations.

Hybrid quantum mechanics/molecular mechanics (QM/MM) simulations provide a powerful tool for studying chemical reactions, especially in complex biochemical systems. In most works to date, the quantum region is kept fixed throughout the simulation and is defined in an ad hoc way based on chemical intuition and available computational resources. The simulation errors associated with a given choice of the quantum region are, however, rarely assessed in a systematic manner. Here we study the dependence of two relevant quantities on the QM region size: the force error at the center of the QM region and the free energy of a proton transfer reaction. Taking lysozyme as our model system, we find that in an apolar region the average force error rapidly decreases with increasing QM region size. In contrast, the average force error at the polar active site is considerably higher, exhibits large oscillations and decreases more slowly, and may not fall below acceptable limits even for a quantum region radius of 9.0 A. Although computation of free energies could only be afforded until 6.0 A, results were found to change considerably within these limits. These errors demonstrate that the results of QM/MM calculations are heavily affected by the definition of the QM region (not only its size), and a convergence test is proposed to be a part of setting up QM/MM simulations.

A study of capacitance-voltage characteristics of lead zirconate titanate ferroelectric thin films and their usage to investigate polarization and coercive field.

Capacitance-voltage (C-V) characteristics of lead zirconate titanate (PZT) thin films with a thickness of 130 nm were measured between 300 and 533 K. The transition between ferroelectric and paraelectric phases was revealed to be of second order in our case, with a Curie temperature at around 450 K. A linear relationship was found between the measured capacitance and the inverse square root of the applied voltage. It was shown that such a relationship could be fitted well by a universal expression of C/A = k(V+V(0))(-1/2) and that this expression could be derived by expanding the Landau-Devonshire free energy at an effective equilibrium position of the Ti/Zr ion in a PZT unit cell. By using the derived equations in this work, the free energy parameters for an individual material can be obtained solely from the corresponding C-V data, and the temperature dependences of both remnant polarization and coercive voltage are shown to be in quantitative agreement with the experimental data.

Measuring the kinetics of amyloid fibril elongation using quartz crystal microbalances.

Kinetic measurements of amyloid growth provide insight into the free energy landscape of this supramolecular process and are crucial in the search for potent inhibitors of the main disorders with which it is associated, including Alzheimer's and Parkinson's diseases and Type II diabetes. In recent years, a new class of surface-bound biosensor assays, e.g., those based on surface plasmon resonance (SPR) and the quartz crystal microbalance (QCM) have been established as extremely valuable tools for kinetic measurements of amyloid formation. Here we describe detailed protocols of how QCM techniques can be used to monitor the elongation of amyloid fibrils in real time and to study the influence of external factors on the kinetics of amyloid growth with unprecedented accuracy.

Nested sampling for materials: the case of hard spheres

The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by studying the three dimensional hard sphere model. Having obtained the partition function, we show how easy it is to calculate the compressibility and the free energy as functions of the packing fraction and local order, verifying that the transition to crystallinity has a very small barrier, and that the entropic contribution of jammed states to the free energy is negligible for packing fractions above the phase transition. We quantify the previously proposed schematic phase diagram and estimate the extent of the region of jammed states. We find that within our samples, the maximally random jammed configuration is surprisingly disordered.

Twisting transition between crystalline and fibrillar phases of aggregated peptides

We study two distinctly ordered condensed phases of polypeptide molecules, amyloid fibrils and amyloidlike microcrystals, and the first-order twisting phase transition between these two states. We derive a single free-energy form which connects both phases. Our model identifies relevant degrees of freedom for describing the collective behavior of supramolecular polypeptide structures, reproduces accurately the results from molecular dynamics simulations as well as from experiments, and sheds light on the uniform nature of the dimensions of different peptide fibrils. © 2012 American Physical Society.

Topologically invariant reaction coordinates for simulating multistate chemical reactions.

Evaluating free energy profiles of chemical reactions in complex environments such as solvents and enzymes requires extensive sampling, which is usually performed by potential of mean force (PMF) techniques. The reliability of the sampling depends not only on the applied PMF method but also the reaction coordinate space within the dynamics is biased. In contrast to simple geometrical collective variables that depend only on the positions of the atomic coordinates of the reactants, the E(gap) reaction coordinate (the energy difference obtained by evaluating a suitable force field using reactant and product state topologies) has the unique property that it is able to take environmental effects into account leading to better convergence, a more faithful description of the transition state ensemble and therefore more accurate free energy profiles. However, E(gap) requires predefined topologies and is therefore inapplicable for multistate reactions, in which the barrier between the chemically equivalent topologies is comparable to the reaction activation barrier, because undesired "side reactions" occur. In this article, we introduce a new energy-based collective variable by generalizing the E(gap) reaction coordinate such that it becomes invariant to equivalent topologies and show that it yields more well behaved free energy profiles than simpler geometrical reaction coordinates.

Magneto-Optical Imaging of Superconductors for Liquid Hydrogen Applications

Restricted deposits of fossil fuels and ecological problems created by their extensive use require a transition to renewable energy resources and clean fuel free from emissions of CO2. This fuel is likely to be liquid hydrogen. An important feature of liquid hydrogen is that it allows wide use of superconductivity. Superconductors provide compactness, high efficiency, savings in energy and a range of new applications not possible with other materials. The benefits of superconductivity justify use of low temperatures and facilitate development of fossil-free energy economy. The widespread use of superconductors requires a simple and reliable technique to monitor their properties. Magneto-optical imaging (MOI) is currently the only direct technique allowing visualization of the superconducting properties of materials. We report the application of this technique to key superconducting materials suitable for the hydrogen economy: MgB2 and high temperature superconductors (HTS) in bulk and thin-film form. The study shows that the MOI technique is well suited to the study of these materials. It demonstrates the advantage of HTS at liquid hydrogen temperatures and emphasizes the benefits of MgB2, in particular. © 2012 Springer Science+Business Media New York.