On the construction of model Hamiltonians for adiabatic quantum computation and its application to finding low energy conformations of lattice protein models

In this report, we explore the use of a quantum optimization algorithm for obtaining low energy conformations of protein models. We discuss mappings between protein models and optimization variables, which are in turn mapped to a system of coupled quantum bits. General strategies are given for constructing Hamiltonians to be used to solve optimization problems of physical/chemical/biological interest via quantum computation by adiabatic evolution. As an example, we implement the Hamiltonian corresponding to the Hydrophobic-Polar (HP) model for protein folding. Furthermore, we present an approach to reduce the resulting Hamiltonian to two-body terms gearing towards an experimental realization.Comment: 35 pages, 8 figure

Classical Ising model test for quantum circuits

We exploit a recently constructed mapping between quantum circuits and graphs in order to prove that circuits corresponding to certain planar graphs can be efficiently simulated classically. The proof uses an expression for the Ising model partition function in terms of quadratically signed weight enumerators (QWGTs), which are polynomials that arise naturally in an expansion of quantum circuits in terms of rotations involving Pauli matrices. We combine this expression with a known efficient classical algorithm for the Ising partition function of any planar graph in the absence of an external magnetic field, and the Robertson-Seymour theorem from graph theory. We give as an example a set of quantum circuits with a small number of non-nearest neighbor gates which admit an efficient classical simulation.Comment: 17 pages, 2 figures. v2: main result strengthened by removing oracular settin

Efficient Reconstruction of Metabolic Pathways by Bidirectional Chemical Search

One of the main challenges in systems biology is the establishment of the metabolome: a catalogue of the metabolites and biochemical reactions present in a specific organism. Current knowledge of biochemical pathways as stored in public databases such as KEGG, is based on carefully curated genomic evidence for the presence of specific metabolites and enzymes that activate particular biochemical reactions. In this paper, we present an efficient method to build a substantial portion of the artificial chemistry defined by the metabolites and biochemical reactions in a given metabolic pathway, which is based on bidirectional chemical search. Computational results on the pathways stored in KEGG reveal novel biochemical pathways

Key interactions by conserved polar amino acids located at the transmembrane helical boundaries in Class B GPCRs modulate activation, effector specificity and biased signalling in the glucagon-like peptide-1 receptor

Class B GPCRs can activate multiple signalling effectors with the potential to exhibit biased agonism in response to ligand stimulation. Previously, we highlighted key TM domain polar amino acids that were crucial for the function of the GLP-1 receptor, a key therapeutic target for diabetes and obesity. Using a combination of mutagenesis, pharmacological characterisation, mathematical and computational molecular modelling, this study identifies additional highly conserved polar residues located towards the TM helical boundaries of Class B GPCRs that are important for GLP-1 receptor stability and/or controlling signalling specificity and biased agonism. This includes (i) three positively charged residues (R3.30227, K4.64288, R5.40310) located at the extracellular boundaries of TMs 3, 4 and 5 that are predicted in molecular models to stabilise extracellular loop 2, a crucial domain for ligand affinity and receptor activation; (ii) a predicted hydrogen bond network between residues located in TMs 2 (R2.46176), 6 (R6.37348) and 7 (N7.61406 and E7.63408) at the cytoplasmic face of the receptor that is important for stabilising the inactive receptor and directing signalling specificity, (iii) residues at the bottom of TM 5 (R5.56326) and TM6 (K6.35346 and K6.40351) that are crucial for receptor activation and downstream signalling; (iv) residues predicted to be involved in stabilisation of TM4 (N2.52182 and Y3.52250) that also influence cell signalling. Collectively, this work expands our understanding of peptide-mediated signalling by the GLP-1 receptor

Sectoral Transformations in Neo-Patrimonial Rentier States: Tourism Development and State Policy in Egypt

This article challenges claims that liberalising state regulated markets in developing countries may induce lasting economic development. The analysis of the rise of tourism in Egypt during the last three decades suggests that the effects of liberalisation and structural adjustment are constrained by the neo-patrimonial character of the Egyptian political system. Since the decline of oil rent revenues during the 1980s tourism development was the optimal strategy to compensate for the resulting fiscal losses. Increasing tourism revenues have helped in coping with macroeconomic imbalances and in avoiding more costly adjustment of traditional economic sectors. Additionally, they provided the private elite with opportunities to generate large profits. Therefore, sectoral transformations due to economic liberalisation in neo-patrimonial Rentier states should be described as a process, which has led to the diversification of external rent revenues, rather than to a general downsizing of the Rentier character of the economy

Computational Treatment of Metalloproteins

Metalloproteins present a considerable challenge for modeling, especially when the starting point is far from thermodynamic equilibrium. Examples include formidable problems such as metalloprotein folding and structure prediction upon metal addition, removal, or even just replacement; metalloenzyme design, where stabilization of a transition state of the catalyzed reaction in the specific binding pocket around the metal needs to be achieved; docking to metal-containing sites and design of metalloenzyme inhibitors. Even more conservative computations, such as elucidations of the mechanisms and energetics of the reaction catalyzed by natural metalloenzymes, are often nontrivial. The reason is the vast span of time and length scales over which these proteins operate, and thus the resultant difficulties in estimating their energies and free energies. It is required to perform extensive sampling, properly treat the electronic structure of the bound metal or metals, and seamlessly merge the required techniques to assess energies and entropies, or their changes, for the entire system. Additionally, the machinery needs to be computationally affordable. Although a great advancement has been made over the years, including some of the seminal works resulting in the 2013 Nobel Prize in chemistry, many aforementioned exciting applications remain far from reach. We review the methodology on the forefront of the field, including several promising methods developed in our lab that bring us closer to the desired modern goals. We further highlight their performance by a few examples of applications

Optimal scaling factors for CM1 and CM3 atomic charges in RM1‐based aqueous simulations

Scaling factors for atomic charges derived from the RM1 semiempirical quantum mechanical wavefunction in conjunction with CM1 and CM3 charge models have been optimized by minimizing errors in absolute free energies of hydration, ΔG(hyd) , for a set of 40 molecules. Monte Carlo statistical mechanics simulations and free energy perturbation theory were used to annihilate the solutes in gas and in a box of TIP4P water molecules. Lennard-Jones parameters from the optimized potentials for liquid simulations-all atom (OPLS-AA) force field were utilized for the organic compounds. Optimal charge scaling factors have been determined as 1.11 and 1.14 for the CM1R and CM3R methods, respectively, and the corresponding unsigned average errors in ΔG(hyd) relative to experiment were 2.05 and 1.89 kcal/mol. Computed errors in aniline and two derivatives were particularly large for RM1 and their removal from the data set lowered the overall errors to 1.61 and 1.75 kcal/mol for CM1R and CM3R. Comparisons are made to the AM1 method which yielded total errors in ΔG(hyd) of 1.50 and 1.64 kcal/mol for CM1A*1.14 and CM3A*1.15, respectively. This work is motivated by the need for a highly efficient yet accurate quantum mechanical (QM) method to study condensed-phase and enzymatic chemical reactions via mixed QM and molecular mechanical (QM/MM) simulations. As an initial test, the Menshutkin reaction between NH(3) and CH(3) Cl in water was computed using a RM1/TIP4P-Ew/CM3R procedure and the resultant ΔG(‡) , ΔG(rxn) , and geometries were in reasonable accord with other computational methods; however, some potentially serious shortcomings in RM1 are discussed