The Effective Fragment Molecular Orbital Method for Fragments Connected by Covalent Bonds

We extend the effective fragment molecular orbital method (EFMO) into treating fragments connected by covalent bonds. The accuracy of EFMO is compared to FMO and conventional ab initio electronic structure methods for polypeptides including proteins. Errors in energy for RHF and MP2 are within 2 kcal/mol for neutral polypeptides and 6 kcal/mol for charged polypeptides similar to FMO but obtained two to five times faster. For proteins, the errors are also within a few kcal/mol of the FMO results. We developed both the RHF and MP2 gradient for EFMO. Compared to ab initio, the EFMO optimized structures had an RMSD of 0.40 and 0.44 {\AA} for RHF and MP2, respectively.Comment: Revised manuscrip

Characterizing Rhodopsin-Arrestin Interactions with the Fragment Molecular Orbital (FMO) Method

Arrestin binding to G protein-coupled receptors (GPCRs) plays a vital role in receptor signaling. Recently, the crystal structure of rhodopsin bound to activated visual arrestin was resolved using XFEL (X-ray free electron laser). However, even with the crystal structure in hand, our ability to understand GPCR-arrestin binding is limited by the availability of accurate tools to explore receptor-arrestin interactions. We applied fragment molecular orbital (FMO) method to explore the interactions formed between the residues of rhodopsin and arrestin. FMO enables ab initio approaches to be applied to systems that conventional quantum mechanical (QM) methods would be too compute-expensive. The FMO calculations detected 35 significant interactions involved in rhodopsin-arrestin binding formed by 25 residues of rhodopsin and 28 residues of arrestin. Two major regions of interaction were identified: at the C-terminal tail of rhodopsin (D330-S343) and where the "finger loop" (G69-T79) of arrestin directly inserts into rhodopsin active core. Out of these 35 interactions, 23 were mainly electrostatic and 12 hydrophobic in nature

Characterizing Protein-Protein Interactions with the Fragment Molecular Orbital Method

Proteins are vital components of living systems, serving as building blocks, molecular machines, enzymes, receptors, ion channels, sensors, and transporters. Protein-protein interactions (PPIs) are a key part of their function. There are more than 645,000 reported disease-relevant PPIs in the human interactome, but drugs have been developed for only 2% of these targets. The advances in PPI-focused drug discovery are highly dependent on the availability of structural data and accurate computational tools for analysis of this data. Quantum mechanical approaches are often too expensive computationally, but the fragment molecular orbital (FMO) method offers an excellent solution that combines accuracy, speed and the ability to reveal key interactions that would otherwise be hard to detect. FMO provides essential information for PPI drug discovery, namely, identification of key interactions formed between residues of two proteins, including their strength (in kcal/mol) and their chemical nature (electrostatic or hydrophobic). In this chapter, we have demonstrated how three different FMO-based approaches (pair interaction energy analysis (PIE analysis), subsystem analysis (SA) and analysis of protein residue networks (PRNs)) have been applied to study PPI in three protein-protein complexes

Analyzing GPCR-Ligand Interactions with the Fragment Molecular Orbital (FMO) Method

G-protein-coupled receptors (GPCRs) have enormous physiological and biomedical importance, and therefore it is not surprising that they are the targets of many prescribed drugs. Further progress in GPCR drug discovery is highly dependent on the availability of protein structural information. However, the ability of X-ray crystallography to guide the drug discovery process for GPCR targets is limited by the availability of accurate tools to explore receptor-ligand interactions. Visual inspection and molecular mechanics approaches cannot explain the full complexity of molecular interactions. Quantum mechanics (QM) approaches are often too computationally expensive to be of practical use in time-sensitive situations, but the fragment molecular orbital (FMO) method offers an excellent solution that combines accuracy, speed, and the ability to reveal key interactions that would otherwise be hard to detect. Integration of GPCR crystallography or homology modelling with FMO reveals atomistic details of the individual contributions of each residue and water molecule toward ligand binding, including an analysis of their chemical nature. Such information is essential for an efficient structure-based drug design (SBDD) process. In this chapter, we describe how to use FMO in the characterization of GPCR-ligand interactions

Rapid and Accurate Assessment of GPCR-Ligand Interactions Using the Fragment Molecular Orbital-Based Density-Functional Tight-Binding Method

The reliable and precise evaluation of receptor–ligand interactions and pair-interaction energy is an essential element of rational drug design. While quantum mechanical (QM) methods have been a promising means by which to achieve this, traditional QM is not applicable for large biological systems due to its high computational cost. Here, the fragment molecular orbital (FMO) method has been used to accelerate QM calculations, and by combining FMO with the density-functional tight-binding (DFTB) method we are able to decrease computational cost 1000 times, achieving results in seconds, instead of hours. We have applied FMO-DFTB to three different GPCR–ligand systems. Our results correlate well with site directed mutagenesis data and findings presented in the published literature, demonstrating that FMO-DFTB is a rapid and accurate means of GPCR–ligand interactions

Characterising Inter-helical Interactions of G Protein-Coupled Receptors with the Fragment Molecular Orbital Method

G-protein coupled receptors (GPCRs) are the largest superfamily of membrane proteins, regulating almost every aspect of cellular activity and serving as key targets for drug discovery. We have identified an accurate and reliable computational method to characterise the strength and chemical nature of the inter-helical interactions between the residues of transmembrane (TM) domains during different receptor activation states, something that cannot be characterised solely by visual inspection of structural information. Using the fragment molecular orbital (FMO) quantum mechanics method to analyse 35 crystal structures representing different branches of the class A GPCR family, we have identified 69 topologically-equivalent TM residues that form a consensus network of 51 inter-TM interactions, providing novel results that are consistent with and help to rationalise experimental data. This discovery establishes a comprehensive picture of how defined molecular forces govern specific inter-helical interactions which, in turn, support the structural stability, ligand binding and activation of GPCRs

Implementation of a Toffoli Gate with Superconducting Circuits

The quantum Toffoli gate allows universal reversible classical computation. It is also an important primitive in many quantum circuits and quantum error correction schemes. Here we demonstrate the realization of a Toffoli gate with three superconducting transmon qubits coupled to a microwave resonator. By exploiting the third energy level of the transmon qubit, the number of elementary gates needed for the implementation of the Toffoli gate, as well as the total gate time can be reduced significantly in comparison to theoretical proposals using two-level systems only. We characterize the performance of the gate by full process tomography and Monte Carlo process certification. The gate fidelity is found to be $68.5\pm0.5$%.Comment: 4 pages, 5figure

The nature of ferromagnetism in the chiral helimagnet Cr1/3NbS2

The chiral helimagnet Cr1/3NbS2 hosts exotic spin textures, whose influence on the magneto-transport properties make this material an ideal candidate for future spintronic applications. To date, the interplay between macroscopic magnetic and transport degrees of freedom is believed to result from a reduction in carrier scattering following spin order. Here, we present electronic structure measurements across the helimagnetic transition temperature TC that challenges this view. We show that the Fermi surface is comprised of strongly hybridized Nb- and Cr-derived electronic states, and that spectral weight close to the Fermi level increases anomalously as the temperature is lowered below TC. These findings are rationalized on the basis of first principle density functional theory calculations, which reveal a large nearest-neighbor exchange energy, suggesting the interaction between local spin moments and hybridized Nb- and Cr-derived itinerant states to go beyond the perturbative interaction of Ruderman-Kittel-Kasuya-Yosida, suggesting instead a mechanism rooted in a Hund’s exchange interaction

Estimating required information size by quantifying diversity in random-effects model meta-analyses

<p>Abstract</p> <p>Background</p> <p>There is increasing awareness that meta-analyses require a sufficiently large information size to detect or reject an anticipated intervention effect. The required information size in a meta-analysis may be calculated from an anticipated <it>a priori </it>intervention effect or from an intervention effect suggested by trials with low-risk of bias.</p> <p>Methods</p> <p>Information size calculations need to consider the total model variance in a meta-analysis to control type I and type II errors. Here, we derive an adjusting factor for the required information size under any random-effects model meta-analysis.</p> <p>Results</p> <p>We devise a measure of diversity (<it>D</it>²) in a meta-analysis, which is the relative variance reduction when the meta-analysis model is changed from a random-effects into a fixed-effect model. <it>D</it>²is the percentage that the between-trial variability constitutes of the sum of the between-trial variability and a sampling error estimate considering the required information size. <it>D</it>²is different from the intuitively obvious adjusting factor based on the common quantification of heterogeneity, the inconsistency (<it>I</it>²), which may underestimate the required information size. Thus, <it>D</it>²and <it>I</it>²are compared and interpreted using several simulations and clinical examples. In addition we show mathematically that diversity is equal to or greater than inconsistency, that is <it>D</it>²≥ <it>I</it>², for all meta-analyses.</p> <p>Conclusion</p> <p>We conclude that <it>D</it>²seems a better alternative than <it>I</it>²to consider model variation in any random-effects meta-analysis despite the choice of the between trial variance estimator that constitutes the model. Furthermore, <it>D</it>²can readily adjust the required information size in any random-effects model meta-analysis.</p