Oscillatory Active State of a Pd Nanocatalyst Identified by In Situ Capture of the Instantaneous Structure-Activity Change at the Atomic Scale.

Identifying the active phase with the highest activity, which is long-believed to be a steady state of the catalyst, is the basis of rational design of heterogeneous catalysis. In this work, we performed detailed in situ investigations, successfully capturing the instantaneous structure-activity change in oscillating Pd nanocatalysts during methane oxidation, which reveals an unprecedented oscillatory active state. Combining in situ quantitative environmental transmission electron microscopy and highly sensitive online mass spectrometry, we identified two distinct phases for the reaction: one where the Pd nanoparticles refill with oxygen, and the other, a period of abrupt pumping of oxygen and boosted methane oxidation within about 1 s. It is the rapid reduction process that shows the highest activity for total oxidation of methane, not a PdO or Pd steady state under the conditions applied here (methane:oxygen = 5:1). This observation challenges the traditional understanding of the active phase and requires a completely different strategy for catalyst optimization.

Analysis and interpretation of first passage time distributions featuring rare events.

In this contribution we consider theory and associated computational tools to treat the kinetics associated with competing pathways on multifunnel energy landscapes. Multifunnel landscapes are associated with molecular switches and multifunctional materials, and are expected to exhibit multiple relaxation time scales and associated thermodynamic signatures in the heat capacity. Our focus here is on the first passage time distribution, which is encoded in a kinetic transition network containing all the locally stable states and the pathways between them. This network can be renormalised to reduce the dimensionality, while exactly conserving the mean first passage time and approximately conserving the full distribution. The structure of the reduced network can be visualised using disconnectivity graphs. We show how features in the first passage time distribution can be associated with specific kinetic traps, and how the appearance of competing relaxation time scales depends on the starting conditions. The theory is tested for two model landscapes and applied to an atomic cluster and a disordered peptide. Our most important contribution is probably the reconstruction of the full distribution for long time scales, where numerical problems prevent direct calculations. Here we combine accurate treatment of the mean first passage time with the reliable part of the distribution corresponding to faster time scales. Hence we now have a fundamental understanding of both thermodynamic and kinetic signatures of multifunnel landscapes.

Combining experiment and energy landscapes to explore anaerobic heme breakdown in multifunctional hemoproteins.

To survive, many pathogens extract heme from their host organism and break down the porphyrin scaffold to sequester the Fe2+ ion via a heme oxygenase. Recent studies have revealed that certain pathogens can anaerobically degrade heme. Our own research has shown that one such pathway proceeds via NADH-dependent heme degradation, which has been identified in a family of hemoproteins from a range of bacteria. HemS, from Yersinia enterocolitica, is the main focus of this work, along with HmuS (Yersinia pestis), ChuS (Escherichia coli) and ShuS (Shigella dysenteriae). We combine experiments, Energy Landscape Theory, and a bioinformatic investigation to place these homologues within a wider phylogenetic context. A subset of these hemoproteins are known to bind certain DNA promoter regions, suggesting not only that they can catalytically degrade heme, but that they are also involved in transcriptional modulation responding to heme flux. Many of the bacterial species responsible for these hemoproteins (including those that produce HemS, ChuS and ShuS) are known to specifically target oxygen-depleted regions of the gastrointestinal tract. A deeper understanding of anaerobic heme breakdown processes exploited by these pathogens could therefore prove useful in the development of future strategies for disease prevention.

Triplet-Encoded Prebiotic RNA Aminoacylation.

The encoding step of translation involves attachment of amino acids to cognate tRNAs by aminoacyl-tRNA synthetases, themselves the product of coded peptide synthesis. So, the question arises─before these enzymes evolved, how were primordial tRNAs selectively aminoacylated? Here, we demonstrate enzyme-free, sequence-dependent, chemoselective aminoacylation of RNA. We investigated two potentially prebiotic routes to aminoacyl-tRNA acceptor stem-overhang mimics and analyzed those oligonucleotides undergoing the most efficient aminoacylation. Overhang sequences do not significantly influence the chemoselectivity of aminoacylation by either route. For aminoacyl-transfer from a mixed anhydride donor strand, the chemoselectivity and stereoselectivity of aminoacylation depend on the terminal three base pairs of the stem. The results support early suggestions of a second genetic code in the acceptor stem.

Analysing ill-conditioned Markov chains.

Discrete state Markov chains in discrete or continuous time are widely used to model phenomena in the social, physical and life sciences. In many cases, the model can feature a large state space, with extreme differences between the fastest and slowest transition timescales. Analysis of such ill-conditioned models is often intractable with finite precision linear algebra techniques. In this contribution, we propose a solution to this problem, namely partial graph transformation, to iteratively eliminate and renormalize states, producing a low-rank Markov chain from an ill-conditioned initial model. We show that the error induced by this procedure can be minimized by retaining both the renormalized nodes that represent metastable superbasins, and those through which reactive pathways concentrate, i.e. the dividing surface in the discrete state space. This procedure typically returns a much lower rank model, where trajectories can be efficiently generated with kinetic path sampling. We apply this approach to an ill-conditioned Markov chain for a model multi-community system, measuring the accuracy by direct comparison with trajectories and transition statistics. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Stable and scalable computation of state visitation probabilities in finite Markov chains.

We report an algorithm based on renormalization to compute the probability that a particular state, or set thereof, is visited along the first passage or transition paths between two endpoint states of a finite Markov chain. The procedure is numerically stable and does not require dense storage of the transition matrix.

Exploring energy landscapes for solid-state systems with variable cells at the extended tight-binding level.

The design of novel materials requires a theoretical understanding of dynamical processes in the solid state, including polymorphic transitions and associated pathways. The organization of the potential energy landscape plays a crucial role in such processes, which may involve changes in the periodic boundaries. This study reports the implementation of a general framework for periodic condensed matter systems in our energy landscape analysis software, allowing for variation in both the unit cell and atomic positions. This implementation provides access to basin-hopping global optimization, the doubly nudged elastic band procedure for identifying transition state candidates, the missing connection approach for multi-step pathways, and general tools for the construction and analysis of kinetic transition networks. The computational efficacy of the procedures is explored using the state-of-the-art semiempirical method GFN1-xTB for the first time in this solid-state context. We investigate the effectiveness of this level of theory by characterizing the potential energy and enthalpy landscapes of several systems, including silicon, CdSe, ZnS, and NaCl, and discuss further technical challenges, such as translational permutation of the cell. Despite the expected limitations of the semiempirical method, we find that the resulting energy landscapes provide useful insight into solid-state simulations, which will facilitate detailed analysis of processes such as defect and ion migration, including refinement at higher levels of theory.

Global analysis of energy landscapes for materials modeling: A test case for C60.

In this contribution, we employ computational tools from the energy landscape approach to test Gaussian Approximation Potentials (GAPs) for C60. In particular, we apply basin-hopping global optimization and explore the landscape starting from the low-lying minima using discrete path sampling. We exploit existing databases of minima and transition states harvested from previous work using tight-binding potentials. We explore the energy landscape for the full range of structures and pathways spanning from the buckminsterfullerene global minimum up to buckybowls. In the initial GAP model, the fullerene part of the landscape is reproduced quite well. However, there are extensive families of C1@C59 and C2@C58 structures that lie lower in energy. We succeeded in refining the potential to remove these artifacts by simply including two minima from the C2@C58 families found by global landscape exploration. We suggest that the energy landscape approach could be used systematically to test and improve machine learning interatomic potentials.

Archetypal landscapes for deep neural networks.

The predictive capabilities of deep neural networks (DNNs) continue to evolve to increasingly impressive levels. However, it is still unclear how training procedures for DNNs succeed in finding parameters that produce good results for such high-dimensional and nonconvex loss functions. In particular, we wish to understand why simple optimization schemes, such as stochastic gradient descent, do not end up trapped in local minima with high loss values that would not yield useful predictions. We explain the optimizability of DNNs by characterizing the local minima and transition states of the loss-function landscape (LFL) along with their connectivity. We show that the LFL of a DNN in the shallow network or data-abundant limit is funneled, and thus easy to optimize. Crucially, in the opposite low-data/deep limit, although the number of minima increases, the landscape is characterized by many minima with similar loss values separated by low barriers. This organization is different from the hierarchical landscapes of structural glass formers and explains why minimization procedures commonly employed by the machine-learning community can navigate the LFL successfully and reach low-lying solutions.

Energy Landscapes and Heat Capacity Signatures for Monomers and Dimers of Amyloid-Forming Hexapeptides.

Amyloid formation is a hallmark of various neurodegenerative disorders. In this contribution, energy landscapes are explored for various hexapeptides that are known to form amyloids. Heat capacity (CV) analysis at low temperature for these hexapeptides reveals that the low energy structures contributing to the first heat capacity feature above a threshold temperature exhibit a variety of backbone conformations for amyloid-forming monomers. The corresponding control sequences do not exhibit such structural polymorphism, as diagnosed via end-to-end distance and a dihedral angle defined for the monomer. A similar heat capacity analysis for dimer conformations obtained using basin-hopping global optimisation shows clear features in end-to-end distance versus dihedral correlation plots, where amyloid-forming sequences exhibit a preference for larger end-to-end distances and larger positive dihedrals. These results hold true for sequences taken from tau, amylin, insulin A chain, a de novo designed peptide, and various control sequences. While there is a little overall correlation between the aggregation propensity and the temperature at which the low-temperature CV feature occurs, further analysis suggests that the amyloid-forming sequences exhibit the key CV feature at a lower temperature compared to control sequences derived from the same protein.

Energy Landscapes of Carbon Clusters from Tight-Binding Quantum Potentials.

We calculate transformation pathways between fullerene and octahedral carbon clusters and between a buckyball and its bowl-shaped isomer. The energies and gradients are provided by efficient tight-binding potentials, which are interfaced to our Energy Landscape exploration software. From the global energy landscape, we extract the mechanistic and kinetic parameters as a function of temperature, and compare our results to selected density functional theory (DFT) (PBE/cc-pVTZ) benchmarks. Infrared spectra are calculated to provide data for experimental identification of the clusters and differentiation of their isomers. Our results suggest that the formation of buckyballs from a buckybowl will be suppressed at elevated temperatures (above around 5250 K) due to entropic effects, which may provide useful insight into the detection of cosmic fullerenes.

Structural transitions in the RNA 7SK 5' hairpin and their effect on HEXIM binding.

7SK RNA, as part of the 7SK ribonucleoprotein complex, is crucial to the regulation of transcription by RNA-polymerase II, via its interaction with the positive transcription elongation factor P-TEFb. The interaction is induced by binding of the protein HEXIM to the 5' hairpin (HP1) of 7SK RNA. Four distinct structural models have been obtained experimentally for HP1. Here, we employ computational methods to investigate the relative stability of these structures, transitions between them, and the effects of mutations on the observed structural ensembles. We further analyse the results with respect to mutational binding assays, and hypothesize a mechanism for HEXIM binding. Our results indicate that the dominant structure in the wild type exhibits a triplet involving the unpaired nucleotide U40 and the base pair A43-U66 in the GAUC/GAUC repeat. This conformation leads to an open major groove with enough potential binding sites for peptide recognition. Sequence mutations of the RNA change the relative stability of the different structural ensembles. Binding affinity is consequently lost if these changes alter the dominant structure.

Surface Chirality Influences Molecular Rotation upon Desorption.

Chiral surfaces offer great potential as a medium for enantioselective synthesis or separation, yet their dynamic enantiospecific interactions with adsorbates are not well understood. Here, the influence of chiral surfaces on the molecular rotations of desorbing molecules is investigated. Formic acid desorption from Cu{531} and Cu{110} serve as model systems for desorption processes of an achiral adsorbate from a chiral and an achiral surface. Our first-principles molecular dynamics study reveals a much larger and more directed angular momentum for molecules desorbing from the chiral surface and a clear preference for one sense of rotation. This result provides new insight into desorption and adsorption processes and propensities on chiral surfaces.

The energy landscapes of bidisperse particle assemblies on a sphere.

The interplay between crystalline ordering, curvature, and size dispersity make the packing of bidisperse mixtures of particles on a sphere a varied and complex phenomenon. These structures have functional significance in a broad range of systems, such as cellular organisation in spherical epithelia, catalytic activity in binary colloidosomes, and chemical activity in heterofullerenes. In this contribution, we elucidate the potential energy landscapes for systems of repulsive, bidisperse particles confined to the surface of a sphere. It is commonly asserted that particle size dispersity destroys ordered arrangements, leading to glassy landscapes. Surprisingly, across a range of compositions, we find highly ordered global minima. Moreover, a minority of small particles is able to passivate defects, stabilising bidisperse global minima relative to monodisperse systems. However, our landscape analysis also reveals that bidispersity introduces numerous defective, low-lying states that are expected to cause broken ergodicity in corresponding experimental and computational systems. Probing the global minimum structures further, particle segregation is energetically preferred at intermediate compositions, contrasting with the approximate icosahedral global packing at either end of the composition range. Finally, changing the composition has a dramatic effect on the heat capacity: systems with low-symmetry global minima have melting temperatures an order of magnitude lower than monodisperse or high-symmetry systems. This observation may provide a further example of the principle of maximum symmetry: higher symmetry global minima exhibit a larger energy separation from the minima that define the high-entropy phase-like region of configuration space, raising the transition temperature.

Development of ReaxFF Reactive Force Field for Aqueous Iron-Sulfur Clusters with Applications to Stability and Reactivity in Water.

Iron-sulfur clusters serve unique roles in biochemistry, geochemistry, and renewable energy technologies. However, a full theoretical understanding of their structures and properties is still lacking. To facilitate large-scale reactive molecular dynamics simulations of iron-sulfur clusters in aqueous environments, a ReaxFF reactive force field is developed, based on an extensive set of quantum chemical calculations. This force field compares favorably with the reference calculations on gas-phase species and significantly improves on a previous ReaxFF parametrization. We employ the new potential to study the stability and reactivity of iron-sulfur clusters in explicit water with constant-temperature reactive molecular dynamics. The aqueous species exhibit a dynamic, temperature-dependent behavior, in good agreement with previous much more costly ab initio simulations.

Crystal Structure Prediction for Benzene Using Basin-Hopping Global Optimization.

Organic molecules can be stable in distinct crystalline forms, known as polymorphs, which have significant consequences for industrial applications. Here, we predict the polymorphs of crystalline benzene computationally for an accurate anisotropic model parametrized to reproduce electronic structure calculations. We adapt the basin-hopping global optimization procedure to the case of crystalline unit cells, simultaneously optimizing the molecular coordinates and unit cell parameters to locate multiple low-energy structures from a variety of crystal space groups. We rapidly locate all the well-established experimental polymorphs of benzene, each of which corresponds to a single local energy minimum of the model. Our results show that basin-hopping can be both an efficient and effective tool for polymorphic crystal structure prediction, requiring no a priori experimental knowledge of cell parameters or symmetry.

Nearly reducible finite Markov chains: Theory and algorithms.

Finite Markov chains, memoryless random walks on complex networks, appear commonly as models for stochastic dynamics in condensed matter physics, biophysics, ecology, epidemiology, economics, and elsewhere. Here, we review exact numerical methods for the analysis of arbitrary discrete- and continuous-time Markovian networks. We focus on numerically stable methods that are required to treat nearly reducible Markov chains, which exhibit a separation of characteristic timescales and are therefore ill-conditioned. In this metastable regime, dense linear algebra methods are afflicted by propagation of error in the finite precision arithmetic, and the kinetic Monte Carlo algorithm to simulate paths is unfeasibly inefficient. Furthermore, iterative eigendecomposition methods fail to converge without the use of nontrivial and system-specific preconditioning techniques. An alternative approach is provided by state reduction procedures, which do not require additional a priori knowledge of the Markov chain. Macroscopic dynamical quantities, such as moments of the first passage time distribution for a transition to an absorbing state, and microscopic properties, such as the stationary, committor, and visitation probabilities for nodes, can be computed robustly using state reduction algorithms. The related kinetic path sampling algorithm allows for efficient sampling of trajectories on a nearly reducible Markov chain. Thus, all of the information required to determine the kinetically relevant transition mechanisms, and to identify the states that have a dominant effect on the global dynamics, can be computed reliably even for computationally challenging models. Rare events are a ubiquitous feature of realistic dynamical systems, and so the methods described herein are valuable in many practical applications.

Affinity-Selected Bicyclic Peptide G-Quadruplex Ligands Mimic a Protein-like Binding Mechanism.

The study of G-quadruplexes (G4s) in a cellular context has demonstrated links between these nucleic acid secondary structures, gene expression, and DNA replication. Ligands that bind to the G4 structure therefore present an excellent opportunity for influencing gene expression through the targeting of a nucleic acid structure rather than sequence. Here, we explore cyclic peptides as an alternative class of G4 ligands. Specifically, we describe the development of de novo G4-binding bicyclic peptides selected by phage display. Selected bicyclic peptides display submicromolar affinity to G4 structures and high selectivity over double helix DNA. Molecular simulations of the bicyclic peptide-G4 complexes corroborate the experimental binding strengths and reveal molecular insights into G4 recognition by bicyclic peptides via the precise positioning of amino acid side chains, a binding mechanism reminiscent of endogenous G4-binding proteins. Overall, our results demonstrate that selection of (bi)cyclic peptides unlocks a valuable chemical space for targeting nucleic acid structures.

Counterion-Trapped-Molecules: From High Polarity and Enriched IR Spectra to Induced Isomerization.

We report extensive computational studies of some novel intermolecular systems and their properties. Recombination of alkali-halide counterions separated by a noncovalently trapped hydrocarbon molecule is prevented by significant potential energy barriers, resulting in unusual metastable insertion complexes. These systems are extremely polar, while the inserted molecule is strongly counter-polarized, leading to significant cooperative nonadditivity effects. The compression and electric field produced by the counterions favours isomerization of the trapped molecule via a significant reduction of the barriers to bond rearrangement, in a field-induced mechanochemical process. The predicted IR intensity spectra clearly reflect (1) formation of the insertion complex, rather than simple attachment of alkali halide, and (2) isomerization of the trapped molecule, thus allowing experimental access to these events.

A multifunnel energy landscape encodes the competing α-helix and ß-hairpin conformations for a designed peptide.

Depending on the amino acid sequence, as well as the local environment, some peptides have the capability to fold into multiple secondary structures. Conformational switching between such structures is a key element of protein folding and aggregation. Specifically, understanding the molecular mechanism underlying the transition from an α-helix to a ß-hairpin is critical because it is thought to be a harbinger of amyloid assembly. In this study, we explore the energy landscape for an 18-residue peptide (DP5), designed by Araki and Tamura to exhibit equal propensities for the α-helical and ß-hairpin forms. We find that the degeneracy is encoded in the multifunnel nature of the underlying free energy landscape. In agreement with experiment, we also observe that mutation of tyrosine at position 12 to serine shifts the equilibrium in favor of the α-helix conformation, by altering the landscape topography. The transition from the α-helix to the ß-hairpin is a complex stepwise process, and occurs via collapsed coil-like intermediates. Our findings suggest that even a single mutation can tune the emergent features of the landscape, providing an efficient route to protein design. Interestingly, the transition pathways for the conformational switch seem to be minimally perturbed upon mutation, suggesting that there could be universal microscopic features that are conserved among different switch-competent protein sequences.