Automating the Optimization of Catalytic Reaction Mechanism Parameters Using Basin-Hopping: A Proof of Concept

Parameter estimation is a crucial step for successful microkinetic modeling in catalysis. However, the large number of parameters to be optimized in order to match the experimental data is a bottleneck. In this regard, the global optimization algorithm Basin-Hopping is utilized to automate the typically time-extensive and error-prone task of manual fitting of kinetic parameters for a heterogeneous catalytic system. The stochastic approach of the Basin-Hopping algorithm to explore the kinetic parameter solution space coupled with local search methods makes it possible to screen the high-dimensional space for an optimal set of kinetic parameters giving the least residual between the simulated and the experimentally measured catalytic performance data. Our approach also ensures that only thermodynamically consistent solution candidates are explored at each optimization step. We utilize two example case studies in heterogeneous catalysis, namely, methane oxidation over a palladium catalyst and carbon monoxide methanation over a nickel catalyst, with corresponding detailed kinetic models to illustrate the applicability of the algorithm to efficiently fine-tune detailed kinetic models

Augmenting Basin-Hopping With Techniques From Unsupervised Machine Learning: Applications in Spectroscopy and Ion Mobility

Published by 'Frontiers in Chemistry' at 10.3389/fchem.2019.00519.Evolutionary algorithms such as the basin-hopping (BH) algorithm have proven to be useful for difficult non-linear optimization problems with multiple modalities and variables. Applications of these algorithms range from characterization of molecular states in statistical physics and molecular biology to geometric packing problems. A key feature of BH is the fact that one can generate a coarse-grained mapping of a potential energy surface (PES) in terms of local minima. These results can then be utilized to gain insights into molecular dynamics and thermodynamic properties. Here we describe how one can employ concepts from unsupervised machine learning to augment BH PES searches to more efficiently identify local minima and the transition states connecting them. Specifically, we introduce the concepts of similarity indices, hierarchical clustering, and multidimensional scaling to the BH methodology. These same machine learning techniques can be used as tools for interpreting and rationalizing experimental results from spectroscopic and ion mobility investigations (e.g., spectral assignment, dynamic collision cross sections). We exemplify this in two case studies: (1) assigning the infrared multiple photon dissociation spectrum of the protonated serine dimer and (2) determining the temperature-dependent collision cross-section of protonated alanine tripeptide.WH acknowledges funding from the Natural Sciences and Engineering Research Council (NSERC) of Canada in the form of a Discovery Grant and from the Province of Ontario in the form of an Early Researcher Award (ERA). CI acknowledges funding from NSERC in the form of a post graduate scholarship

Hopping between distant basins

We present and numerically analyse the Basin Hopping with Skipping (BH-S) algorithm for stochastic optimisation. This algorithm replaces the perturbation step of basin hopping (BH) with a so-called skipping mechanism from rare-event sampling. Empirical results on benchmark optimisation surfaces demonstrate that BH-S can improve performance relative to BH by encouraging non-local exploration, that is, by hopping between distant basins

A global optimization approach for searching low energy conformations of proteins

De novo protein structure prediction and understanding the protein folding mechanism is an outstanding challenge of Biological Physics. Relying on the thermodynamic hypothesis of protein folding it is expected that the native state of a protein can be found out if the global minimum of the free energy surface is found. To understand the energy landscape or the free energy surface is challenging. The structure and dynamics of proteins are the manifestations of the underlying potential energy surface. Here the potential energy function stands on a framework of all-atom representation and uses purely physics-based interactions. For the solvated proteins the effective free energy is defined as an implicit solvation model which includes the solvation free energy, along with a standard all-atom biomolecular forcefield. A major challenge is to search for the global minimum on this effective free energy surface. In this work the Minima Hopping Algorithm (MHOP) to find global minima on potential energy surfaces has been used for protein structure prediction or in general finding the lowest energy conformations of proteins. Here proteins have been studied both in vacuo and in the aqueous medium. For short peptides starting from a completely extended conformation we could find conformational minima which are very close to the experimentally observed structures

SPEEDING-UP A RANDOM SEARCH FOR THE GLOBAL MINIMUM OF A NON-CONVEX, NON-SMOOTH OBJECTIVE FUNCTION

The need to find the global minimum of a highly non-convex, non-smooth objective function over a high-dimensional and possibly disconnected, feasible domain, within a practical amount of computing time, arises in many fields. Such objective functions and/or feasible domains are so poorly-behaved that gradient-based optimization methods are useful only locally – if at all. Random search methods offer a viable alternative, but their convergence properties are not well-studied. The present work adapts a proof by Baba et al. (1977) to establish asymptotic convergence for Monotonic Basin Hopping, a random search method used in molecular modeling and interplanetary spacecraft trajectory optimization. In addition, the present work uses the framework of First Passage Times (the time required for the first arrival to within a very small distance of the global minimum) and Gamma distribution approximations to First Passage Time Densities, to study MBH convergence speed. The present work then provides analytically supported methods for speeding up Monotonic Basin Hopping. The speed-up methods are novel, complementary, and can be used separately or in combination. Their effectiveness is shown to be dramatic in the case of MBH operating on different highly non-convex, non-smooth objective functions and complicated feasible domains. In addition, explanations are provided as to why some speed-up methods are very effective on some highly non-convex, non-smooth objective functions having complicated feasible domains, but other methods are relatively ineffective. The present work is the first systematic study of the MBH convergence process and methods for speeding it up, as opposed to applications of MBH

Grammar-Aware Question-Answering on Quantum Computers

Natural language processing (NLP) is at the forefront of great advances in contemporary AI, and it is arguably one of the most challenging areas of the field. At the same time, with the steady growth of quantum hardware and notable improvements towards implementations of quantum algorithms, we are approaching an era when quantum computers perform tasks that cannot be done on classical computers with a reasonable amount of resources. This provides a new range of opportunities for AI, and for NLP specifically. Earlier work has already demonstrated a potential quantum advantage for NLP in a number of manners: (i) algorithmic speedups for search-related or classification tasks, which are the most dominant tasks within NLP, (ii) exponentially large quantum state spaces allow for accommodating complex linguistic structures, (iii) novel models of meaning employing density matrices naturally model linguistic phenomena such as hyponymy and linguistic ambiguity, among others. In this work, we perform the first implementation of an NLP task on noisy intermediate-scale quantum (NISQ) hardware. Sentences are instantiated as parameterised quantum circuits. We encode word-meanings in quantum states and we explicitly account for grammatical structure, which even in mainstream NLP is not commonplace, by faithfully hard-wiring it as entangling operations. This makes our approach to quantum natural language processing (QNLP) particularly NISQ-friendly. Our novel QNLP model shows concrete promise for scalability as the quality of the quantum hardware improves in the near future

From Single Neurons to Behavior in the Jellyfish Aurelia aurita

Jellyfish nerve nets provide insight into the origins of nervous systems, as both their taxonomic position and their evolutionary age imply that jellyfish resemble some of the earliest neuron-bearing, actively-swimming animals. Here we develop the first neuronal network model for the nerve nets of jellyfish. Specifically, we focus on the moon jelly Aurelia aurita and the control of its energy-efficient swimming motion. The proposed single neuron model disentangles the contributions of different currents to a spike. The network model identifies factors ensuring non-pathological activity and suggests an optimization for the transmission of signals. After modeling the jellyfish's muscle system and its bell in a hydrodynamic environment, we explore the swimming elicited by neural activity. We find that different delays between nerve net activations lead to well-controlled, differently directed movements. Our model bridges the scales from single neurons to behavior, allowing for a comprehensive understanding of jellyfish neural control

Conformational equilibria and spectroscopy of gas-phase homologous peptides from first principles

Peptides and proteins fulfil crucial tasks enabling and maintaining life. Their function is directly correlated with their three-dimensional structure, which is in turn determined by their chemical composition, the amino-acid sequence. Predicting the structure of a peptide based only on its sequence information is of fundamental interest. A fully first-principles treatment free of empirical parameters would be ideal. However, this presents an ongoing challenge, due to the large system size and conformational space of most peptides. In the present work, we address this challenge concentrating on the example of polyalanine-based peptides in the gas phase. Such studies under isolated conditions follow a bottom-up approach that allows one to investigate the intramolecular interactions important for secondary structure separate from environmental effects. Furthermore, direct benchmarks of theoretical structure predictions against experiment are facilitated. The peptide series Ac-Alan-Lys(H+), (n > 6), forms α-helices in the gas phase due to a favorable interaction of the helix dipole with the positive charge at the C-terminal lysine residue. Using this design principle as a template, we explore the impact of increased structural flexibility on the conformational space due to (i) sequence length [Ac-Alan-Lys(H+), n = 19], (ii) charge placement [Ac-Ala19-Lys(H+) versus Ac-Lys(H+)-Ala19], and (iii) backbone elongation of the monomer units as represented by β-amino acids [Ac-β2hAla6-Lys(H+)]. To address the large conformational space, we develop a three-step structure-search strategy employing an unprecedented first-principles screening effort. After pre-sampling of the conformational space using a force field, thousands of structures are optimized employing density-functional theory (DFT). For this, the PBE functional is used, coupled with a pairwise correction for van der Waals interactions. For the best few structure candidates, ab initio replica-exchange molecular-dynamics simulations are performed in order to refine the local structural environment. It is shown that these can yield lower-energy conformations and lead to rearrangements of the hydrogen-bonding network. In order to connect to experiment, collision cross sections are calculated that link to ion mobility-mass spectrometry. Furthermore, infrared spectra are derived from ab initio Born-Oppenheimer molecular-dynamics simulations accounting for anharmonicities within the classical-nuclei approximation. As expected, the 20-residue peptide Ac-Ala19-Lys(H+) forms helical structures. In contrast, placing the charge at the N-terminus [Ac-Lys(H+)-Ala19], leads to several different compact structures, which are close in energy. Such small energy differences present a challenge to the theoretical approach. Incorporating exact exchange and many-body van der Waals effects predicts the presence of only one dominant conformer, which is compatible with both experimental datasets. In comparison to Ac-Ala6-Lys(H+), the β-peptide Ac-β2hAla6-Lys(H+) exhibits increased conformational flexibility due to an extended monomer backbone. Out of the almost 15,000 structures optimized with DFT, no helical conformers are found in the low-energy regime. This is changed when considering vibrational free energy (300K, harmonic approximation), which strongly favors helical conformations due to softer vibrational modes. One possible structure candidate is the H16-helix, which is compatible with both experiments. It is a unique structure as it exhibits a hydrogen-bonding pattern equivalent to the helix of natural peptides. The systems considered here highlight the advances of current DFT functionals to address the large conformational space of peptides, but also the need for further development

Protein folding, structure prediction and aggregation studies using a free energy forcefield

Proteins are versatile molecules which perform multitude of functions in living organisms. The function of a protein depends on the precise three-dimensional structure which it attains under physiological conditions. Further, protein-protein interactions are responsible for many biochemical mechanisms in living organisms. Therefore the study of protein structure, protein folding and interactions is essential for understanding of biological processes. In recent years theoretical methods have increasingly complemented experiments in elucidating protein structure and function. This work pursues a denovo protein modeling approach based on Anfinsen’s thermodynamic hypothesis, which states that a protein in its native state is in thermodynamic equilibrium with its environment. The biologically active conformation thus corresponds to a global minimum of the free energy. We have developed a free-energy model for proteins (PFF02) in conjugation with efficient optimization methods for protein folding and structure prediction. With this approach a zinc finger motif was folded using an efficient evolutionary algorithm starting from an extended structure. In addition, we elucidated the folding characteristics of this protein by analyzing its energy landscape. We devised a de novo methodology for predicting the native structure of proteins, which was used to predict the structure of 27 targets in the CASP7 competition. Our method was quite successful for the free modeling targets. We investigated the aggregation of a fragment of amyloid beta protein, which is believed to play a key role in the aggregation of the full protein. A general computational scheme for protein-protein docking was developed and tested successfully for two protein dimers. Zusammenfassung Proteinfaltung, Strukturvorhersage und Protein-Aggregation mit einem Kraftfeld für die freie Energie: Proteine sind vielseitige Moleküle, die eine grosse Anzahl von Funktionen im lebenden Organismus erfüllen. Die Funktion eines Proteins wird von seiner genauen dreidimensionalen Struktur bestimmt, die unter physiologischen Bedingungen zumeist spontan angenommen wird. Darüber hinaus sind Protein-Proteinwechselwirkungen verantwortlich für viele biochemische Steuerungsmechanismen von Organismen. Aus diesem Grunde ist die Untersuchung von Proteinstrukturen, der Proteinfaltung und von Proteinwechselwirkungen wichtig für das Verständnis biologischer Vorgänge. In den vergangenen Jahren haben theoretische Methoden zunehmend experimentelle Untersuchungen zu Struktur und Funktion von Proteinen unterstützt. In dieser Arbeit wird ein Ansatz zur de-novo Proteinmodellierung verfolgt, der sich auf Anfinsens thermodynamische Hypothese stützt, nach der Proteine in ihrem nativen Zustand sich im thermodynamischen Gleichgewicht mit ihrer Umgebung befinden. Die biologisch aktive Konformation entspricht daher dem globalen Minimum der freien Energie. Wir entwickelten ein Modell für die freie Energie von Proteinen (PFF02) und effiziente Optimierungsverfahren für die Proteinfaltung und Strukturvorhersage. Mit diesem Ansatz wurde ein Zink-Finger Motiv aus der völlig entfalteten Struktur mittels eines effizienten evolutionären Algorithmus gefaltet. iv Darüber hinaus konnten wir die Faltungscharakteristika dieses Proteins durch die Analyse seiner Energielandschaft beschreiben. Wir entwickelten einen de-novo Ansatz zur Proteinstrukturvorhersage, mit dem wir die Struktur von 27 Proteinen im CASP7Wettbewerb vorhersagen konnten. Insbesondere für Proteine ohne Homologie zu bekannten Strukturen war unser Verfahren vergleichsweise erfolgreich. Schliesslich untersuchten wir die Aggregation eines Fragments des Beta-Amyloid Proteins, von dem man annimmt, dass es für die Aggregation des vollständigen Proteins eine entscheidende Rolle spielt. Darüber hinaus konnten wir ein Verfahren für das Protein-Docking entwickeln und an zwei Protein-Dimeren testen