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While an order o tensor can be thought of as a multi-dimensional array of dimension o in a given frame of reference (or basis), it must also transform in a specific manner when the basis is transformed ... Angular similarities are displayed in polar coordinates, with 0 o meaning no angular difference. ...arXiv:2006.14163v1 fatcat:vtdkdnla6nal5m4zbhr2b65kia
The sigma-1 receptor is a poorly understood integral membrane protein expressed in most cells and tissues in the human body. It has been shown to modulate the activity of other membrane proteins such as ion channels and G protein-coupled receptors, and ligands targeting the sigma-1 receptor are currently in clinical trials for treatment of Alzheimer's disease, ischemic stroke, and neuropathic pain. Despite its importance, relatively little is known regarding sigma-1 receptor function at thedoi:10.1101/333765 fatcat:uy5t4ahslngwteade4633o62ym
more »... cular level. Here, we present crystal structures of the human sigma-1 receptor bound to the classical antagonists haloperidol and NE-100, as well as the agonist (+)-pentazocine, at crystallographic resolutions of 3.1 A, 2.9 A, and 3.1 A respectively. These structures reveal a unique binding pose for the agonist. The structures and accompanying molecular dynamics (MD) simulations demonstrate that the agonist induces subtle structural rearrangements in the receptor. In addition, we show that ligand binding and dissociation from sigma-1 is a multistep process, with extraordinarily slow kinetics limited by receptor conformational change. We use MD simulations to reconstruct a ligand binding pathway that requires two major conformational changes. Taken together, these data provide a framework for understanding the molecular basis for agonist action at sigma-1.
Journal of Vision
Preliminary results of this study were presented in a conference paper (Dror, Leung, Willsky, & Adelson, 2001 ). ... By taking advantage of the regularity of real-world illumination statistics, we have developed a system for classifying reflectance robustly under unknown everyday illumination conditions Dror, 2002) ...doi:10.1167/4.9.11 pmid:15493972 fatcat:yl4lygz3sjggdnpcxalkbhcofe
Journal of Vision
, & Adelson (2001) and Dror (2002) for a more thorough account]. ... This is consistent with the example of the pearlescent sphere above, and our previous report (Fleming, Dror, & Adelson, 2001) . Figure 5 further demonstrates the effects of changing context. ...doi:10.1167/3.5.3 pmid:12875632 fatcat:te67coiuxzak3b7bm2k6cmh3dq
Representing and reasoning about 3D structures of macromolecules is emerging as a distinct challenge in machine learning. Here, we extend recent work on geometric vector perceptrons and apply equivariant graph neural networks to a wide range of tasks from structural biology. Our method outperforms all reference architectures on three out of eight tasks in the ATOM3D benchmark, is tied for first on two others, and is competitive with equivariant networks using higher-order representations andarXiv:2106.03843v2 fatcat:3uhjvnsrwjdyrghcb4c66c7vx4
more »... erical harmonic convolutions. In addition, we demonstrate that transfer learning can further improve performance on certain downstream tasks. Code is available at https://github.com/drorlab/gvp-pytorch.
Drug Discovery Today
It is increasingly appreciated that the rates at which drugs associate with and dissociate from receptorsthe binding kinetics -directly impact drug efficacy and safety. The molecular determinants of drugreceptor binding kinetics remain poorly understood, however, especially when compared with the wellknown factors that affect binding affinity. The rational modulation of kinetics during lead optimization thus remains challenging. We review some of the key factors thought to control drug-receptordoi:10.1016/j.drudis.2013.02.007 pmid:23454741 fatcat:iqta53cmabaztbnhfvithz3jye
more »... binding kinetics at the molecular level -molecular size, conformational fluctuations, electrostatic interactions and hydrophobic effects -and discuss several possible approaches for the rational design of drugs with desired binding kinetics.
We determined particle positions by placing the reported crystal structure of the 213-residue protein Catechol O-Methyltransferase ͑PDB code 1vid͒ 26 in a water bath ͑neutralized with the appropriate number ...doi:10.1063/1.2191489 pmid:16709099 fatcat:rht3d7rmnbgmhkzn2kwpzl2afu
Lecture Notes in Computer Science
a b o ve 1 cycle/ . ... Second, mean correlator response for most natural images peaks at a velocity o f 3 5 t o 4 0 /s. ...doi:10.1007/3-540-45482-9_50 fatcat:poxalic3xvdhbmurzw5j77nfpa
., 2016; Dror et al., 2012; Faraldo-Gomez and Forrest, 2011; Fukuda et al., 2015; Lee et al., 2016; Li et al., 2015; Watanabe et al., 2010) . ...doi:10.1016/j.cell.2017.03.010 pmid:28340354 pmcid:PMC5557413 fatcat:d2dongtdgvdvzpfyig7sgujk3m
Molecular dynamics (MD) simulations have become a powerful and popular method for the study of protein allostery, the widespread phenomenon in which a stimulus at one site on a protein influences the properties of another site on the protein. By capturing the motions of a protein's constituent atoms, simulations can enable the discovery of allosteric binding sites and the determination of the mechanistic basis for allostery. These results can provide a foundation for applications includingdoi:10.1371/journal.pcbi.1004746 pmid:27285999 pmcid:PMC4902200 fatcat:olv67vwnirgvlgm6e7uplgeejm
more »... nal drug design and protein engineering. Here, we provide an introduction to the investigation of protein allostery using molecular dynamics simulation. We emphasize the importance of designing simulations that include appropriate perturbations to the molecular system, such as the addition or removal of ligands or the application of mechanical force. We also demonstrate how the bidirectional nature of allostery-the fact that the two sites involved influence one another in a symmetrical mannercan facilitate such investigations. Through a series of case studies, we illustrate how these concepts have been used to reveal the structural basis for allostery in several proteins and protein complexes of biological and pharmaceutical interest. PLOS Computational Biology |
Molecular dynamics (MD) simulations that capture the spontaneous binding of drugs and other ligands to their target proteins can reveal a great deal of useful information, but most drug-like ligands bind on time scales longer than those accessible to individual MD simulations. Adaptive sampling methods-in which one performs multiple rounds of simulation, with the initial conditions of each round based on the results of previous rounds-offer a promising potential solution to this problem. Nodoi:10.1021/acs.jctc.8b00913 pmid:30645108 pmcid:PMC6795214 fatcat:qgsw6c7ipvhcjdstb5msc64vja
more »... rehensive analysis of the performance gains from adaptive sampling is available for ligand binding, however, particularly for protein-ligand systems typical of those encountered in drug discovery. Moreover, most previous work presupposes knowledge of the ligand's bound pose. Here we outline existing methods for adaptive sampling of the ligand-binding process and introduce several improvements, with a focus on methods that do not require prior knowledge of the binding site or bound pose. We then evaluate these methods by comparing them to traditional, long MD simulations for realistic protein-ligand systems. We find that adaptive sampling simulations typically fail to reach the bound pose more efficiently than traditional MD. However, adaptive sampling identifies multiple potential binding sites more efficiently than traditional MD and also provides better characterization of binding pathways. We explain these results by showing that protein-ligand binding is an example of an exploration-exploitation dilemma. Existing adaptive sampling methods for ligand binding in the absence of a known bound pose vastly favor the broad exploration of protein-ligand space, sometimes failing to sufficiently exploit intermediate states as they are discovered. We suggest potential avenues for future research to address this shortcoming.
of the b2-Adrenergic Receptor Ron O. Dror, Daniel H. Arlow, Paul Maragakis, Thomas J. Mildorf, Albert C. Pan, Huafeng Xu, David W. Borhani, David E. Shaw. D. E. Shaw Research, New York, NY, USA. ...doi:10.1016/j.bpj.2011.11.1317 fatcat:wwba2qcajjhq7bn2talsywrkoi
Molecular dynamics simulations provide a vehicle for capturing the structures, motions, and interactions of biological macromolecules in full atomic detail. The accuracy of such simulations, however, is critically dependent on the force fieldthe mathematical model used to approximate the atomic-level forces acting on the simulated molecular system. Here we present a systematic and extensive evaluation of eight different protein force fields based on comparisons of experimental data withdoi:10.1371/journal.pone.0032131 pmid:22384157 pmcid:PMC3285199 fatcat:bh5onbdi3bdotdez54pttjl2vy
more »... r dynamics simulations that reach a previously inaccessible timescale. First, through extensive comparisons with experimental NMR data, we examined the force fields' abilities to describe the structure and fluctuations of folded proteins. Second, we quantified potential biases towards different secondary structure types by comparing experimental and simulation data for small peptides that preferentially populate either helical or sheet-like structures. Third, we tested the force fields' abilities to fold two small proteins-one a-helical, the other with b-sheet structure. The results suggest that force fields have improved over time, and that the most recent versions, while not perfect, provide an accurate description of many structural and dynamical properties of proteins.
Discovering the functional mechanisms of biological systems frequently requires information that challenges the spatial and temporal resolution limits of current experimental techniques. Recent dramatic methodological advances have made all-atom molecular dynamics (MD) simulations an ever more useful partner to experiment because MD simulations capture the atomic resolution behavior of biological systems on timescales spanning 12 orders of magnitude, covering a spatiotemporal domain wheredoi:10.1085/jgp.200910373 pmid:20513757 pmcid:PMC2888062 fatcat:yqbrpjcg3ravziupmkjk6wff7m
more »... mental characterization is often difficult if not impossible. We present here our perspective on the mechanistic insights that a scientistin particular, a membrane protein physiologist-might garner by complementing experiments with atomistic MD simulations. Drawing on case studies from our work, we illustrate the diversity of membrane proteins amenable to study by MD and the types of discoveries one can make through simulation. We discuss the strengths and limitations of MD as a tool for physiologists, and we speculate on advances that such simulations may enable in the coming years. Why simulate? What might a physiologist gain by supplementing the usual experimental tools-cell lines, patch clamp rig, spectrometers, and the like-with atomistic MD simulations? Foremost is the ability to probe the biological system of interest, which may be anything from an individual protein to a large biological assembly, across a very broad range of timescales at high spatial resolution (Fig. 1 ). An all-atom MD simulation typically comprises thousands to millions of individual atoms representing, for example, all the atoms of a membrane protein and of the surrounding lipid bilayer and water bath (Fig. 2) . The simulation progresses in a series of short, discrete time steps; the force on each atom is computed at each time step, and the position and velocity of each atom are then updated according to Newton's laws of motion. Each atom in the system Correspondence to David E. Shaw: David.Shaw@DEShawResearch.com Abbreviations used in this paper: AQP0, aquaporin 0; 2 AR, 2 -adrenergic receptor; GPCR, G protein-coupled receptor; MD, molecular dynamics. under study is thus followed intimately: its position in space, relative to all the other atoms, is known at all times during the simulation. This exquisite spatial resolution is accompanied by the unique ability to observe atomic motion over an extremely broad range of timescales-12 orders of magnitude-from 1 femtosecond (10 15 s), less than the time it takes for a chemical bond to vibrate, to >1 ms (10 3 s), the time it takes for some proteins to fold, for a substrate to be actively transported across a membrane, or for an action potential to be initiated by the opening of voltage-gated sodium channels. MD simulations thus allow access to a spatiotemporal domain that is difficult to probe experimentally (Fig. 1) . Simulations can be particularly valuable for membrane proteins, for which experimental characterization of structural dynamics tends to be challenging. How might this ability to "see" the atoms of a biological system moving over time truly be useful? First, one can observe qualitative behavior, such as the mechanism of permeation through membrane channels. Second, one can probe systems quantitatively, for example, determining the conductance of a single water or ion channel (Fig. 2) . Third, simulations often allow one to generate novel mechanistic hypotheses, sometimes based simply on straightforward observation: as Yogi Berra once said, "You can observe a lot by watching." Fourth, simulations of perturbed or mutated molecular systems can be used to test specific hypotheses originating from experiment, computation, or theory. The power of MD simulations is further augmented by the ability to model molecules that cannot easily be constructed experimentally. A wide variety of physiological processes are amenable to study at the atomic level by MD simulation. Examples relevant to membrane protein function include the active transport of solutes across bilayers by antiporters and symporters; the passive transport of water, ions, Perspectives on: Molecular dynamics and computational methods
an overall O(N) or O(N ln N) method. ... N ln N) computation, multigrid requires O(N) computation. ...doi:10.1063/1.1839571 pmid:15740304 fatcat:mi3lu72g6zdyzalnsi5fjspg44
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