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Stiles PJ, Gray CG. Improved Hodgkin-Huxley type model for neural action potentials. EUROPEAN BIOPHYSICS JOURNAL : EBJ 2021; 50:819-828. [PMID: 34181052 DOI: 10.1007/s00249-021-01547-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Revised: 05/09/2021] [Accepted: 05/10/2021] [Indexed: 06/13/2023]
Abstract
The simple Goldman-Hodgkin-Katz model for resting-state membrane potentials has been generalized to provide a new nonlinear theoretical model for action potentials in perfused axons. Our minimalistic model appeals naturally to physically based electrodiffusion principles to describe electric-current densities inside sodium and potassium-ion channels whereas the 1952 Hodgkin-Huxley model describes such current densities in an ad hoc way. Although the two models share similar schemes for the kinetics of ion-channel gating, our relaxation times for channel gating are simpler, being independent of membrane potential. Like the theoretical model of Hodgkin and Huxley, based primarily on experimental data at [Formula: see text], our dynamical system behaves as a 4-dimensional resonator exhibiting subthreshold oscillations. Although our present analysis refers to experiments at [Formula: see text], re-parameterizations of this model should permit consideration of action potentials at alternative temperatures. The predicted speed of propagating action potentials in giant axons of squid at [Formula: see text] is in excellent agreement with the Hodgkin-Huxley experimental value at [Formula: see text]. In cases where our model predictions differ from those of the Hodgkin-Huxley model, new experiments will be required to determine which model is more accurate.
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Affiliation(s)
- P J Stiles
- Department of Molecular Sciences, Macquarie University, Sydney, NSW, Australia.
| | - C G Gray
- Department of Physics, University of Guelph, Guelph, ON, Canada
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Cabezas F, Mascayano C. Docking, steered molecular dynamics, and QSAR studies as strategies for studying isoflavonoids as 5-, 12-, and 15-lipoxygenase inhibitors. J Biomol Struct Dyn 2018; 37:1511-1519. [PMID: 29624122 DOI: 10.1080/07391102.2018.1461687] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
Lipoxygenases (LOX) are enzymes that catalyze polyunsaturated fatty acid peroxidation and have a non-heme iron atom located in their active site. They are implicated in the arachidonic acid pathway and involved in inflammation, fever, pain production, and in the origins of several diseases such as cancer, asthma, and psoriasis. The search for inhibitors of these enzymes has emerged in the last years, and isoflavonoids have a broad spectrum of biological activity with low cytotoxicity. Our previous results have shown that isoflavonoids inhibited different LOX isoforms in vitro. For this reason, we studied the most important interactions that govern the potency and selectivity of some isoflavones and isoflavans toward different LOX isoforms using computational methods. The docking results have shown that all the molecules can be located in different zones in the LOX active site. Steered molecular dynamics indicated that selectivity was present at the cavity entry, but not at its exit. We also observed the correlation between the potential mean force and the best (HIR-303) and worst inhibitors (IR-213) in 5-LOX. Finally, structure-activity relationship (QSAR) studies showed a good correlation between theoretical IC50 values and experimental data for 5-LOX and 12-LOX with 96 and 95%, respectively, and a lower correlation for 15-LOX (79%). Conclusively, pharmacophore analysis showed that our proposed molecules should possess a donor-acceptor and aromatic centers to encourage interactions in the active site.
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Affiliation(s)
- Francisco Cabezas
- a Laboratorio de Simulación Molecular y Diseño Racional de Fármacos, Facultad de Química y Biología, Departamento de Ciencias del Ambiente , Universidad de Santiago de Chile , Santiago , Chile
| | - Carolina Mascayano
- a Laboratorio de Simulación Molecular y Diseño Racional de Fármacos, Facultad de Química y Biología, Departamento de Ciencias del Ambiente , Universidad de Santiago de Chile , Santiago , Chile
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Stock P, Monroe JI, Utzig T, Smith DJ, Shell MS, Valtiner M. Unraveling Hydrophobic Interactions at the Molecular Scale Using Force Spectroscopy and Molecular Dynamics Simulations. ACS NANO 2017; 11:2586-2597. [PMID: 28267918 DOI: 10.1021/acsnano.6b06360] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Interactions between hydrophobic moieties steer ubiquitous processes in aqueous media, including the self-organization of biologic matter. Recent decades have seen tremendous progress in understanding these for macroscopic hydrophobic interfaces. Yet, it is still a challenge to experimentally measure hydrophobic interactions (HIs) at the single-molecule scale and thus to compare with theory. Here, we present a combined experimental-simulation approach to directly measure and quantify the sequence dependence and additivity of HIs in peptide systems at the single-molecule scale. We combine dynamic single-molecule force spectroscopy on model peptides with fully atomistic, both equilibrium and nonequilibrium, molecular dynamics (MD) simulations of the same systems. Specifically, we mutate a flexible (GS)5 peptide scaffold with increasing numbers of hydrophobic leucine monomers and measure the peptides' desorption from hydrophobic self-assembled monolayer surfaces. Based on the analysis of nonequilibrium work-trajectories, we measure an interaction free energy that scales linearly with 3.0-3.4 kBT per leucine. In good agreement, simulations indicate a similar trend with 2.1 kBT per leucine, while also providing a detailed molecular view into HIs. This approach potentially provides a roadmap for directly extracting qualitative and quantitative single-molecule interactions at solid/liquid interfaces in a wide range of fields, including interactions at biointerfaces and adhesive interactions in industrial applications.
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Affiliation(s)
- Philipp Stock
- Department for Interface Chemistry and Surface Engineering, Max-Planck-Institut für Eisenforschung GmbH , D-40237 Düsseldorf, Germany
| | - Jacob I Monroe
- Department of Chemical Engineering, University of California Santa Barbara , Santa Barbara, California 93106-5080, United States
| | - Thomas Utzig
- Department for Interface Chemistry and Surface Engineering, Max-Planck-Institut für Eisenforschung GmbH , D-40237 Düsseldorf, Germany
| | - David J Smith
- Department of Chemical Engineering, University of California Santa Barbara , Santa Barbara, California 93106-5080, United States
| | - M Scott Shell
- Department of Chemical Engineering, University of California Santa Barbara , Santa Barbara, California 93106-5080, United States
| | - Markus Valtiner
- Department for Interface Chemistry and Surface Engineering, Max-Planck-Institut für Eisenforschung GmbH , D-40237 Düsseldorf, Germany
- Department for Physical Chemistry, Technische Universität Bergakademie Freiberg , D-09599 Freiberg, Germany
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Nategholeslam M, Gray CG, Tomberli B. Stiff Spring Approximation Revisited: Inertial Effects in Nonequilibrium Trajectories. J Phys Chem B 2017; 121:391-403. [DOI: 10.1021/acs.jpcb.6b08701] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
| | - C. G. Gray
- Guelph-Waterloo
Physics Institute and Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1, Canada
- Department
of Physics and Biophysics Interdepartmental Group, University of Guelph, Guelph, Ontario N1G 2W1, Canada
| | - Bruno Tomberli
- Department
of Physics and Biophysics Interdepartmental Group, University of Guelph, Guelph, Ontario N1G 2W1, Canada
- Department
of Physics, Capilano University, North Vancouver, British
Columbia V7J 3H5, Canada
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Sprenger KG, Pfaendtner J. Strong Electrostatic Interactions Lead to Entropically Favorable Binding of Peptides to Charged Surfaces. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2016; 32:5690-5701. [PMID: 27181161 DOI: 10.1021/acs.langmuir.6b01296] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Thermodynamic analyses can provide key insights into the origins of protein self-assembly on surfaces, protein function, and protein stability. However, obtaining quantitative measurements of thermodynamic observables from unbiased classical simulations of peptide or protein adsorption is challenging because of sampling limitations brought on by strong biomolecule/surface binding forces as well as time scale limitations. We used the parallel tempering metadynamics in the well-tempered ensemble (PTMetaD-WTE) enhanced sampling method to study the adsorption behavior and thermodynamics of several explicitly solvated model peptide adsorption systems, providing new molecular-level insight into the biomolecule adsorption process. Specifically studied were peptides LKα14 and LKβ15 and trpcage miniprotein adsorbing onto a charged, hydrophilic self-assembled monolayer surface functionalized with a carboxylic acid/carboxylate headgroup and a neutral, hydrophobic methyl-terminated self-assembled monolayer surface. Binding free energies were calculated as a function of temperature for each system and decomposed into their respective energetic and entropic contributions. We investigated how specific interfacial features such as peptide/surface electrostatic interactions and surface-bound ion content affect the thermodynamic landscape of adsorption and lead to differences in surface-bound conformations of the peptides. Results show that upon adsorption to the charged surface, configurational entropy gains of the released solvent molecules dominate the configurational entropy losses of the bound peptide. This behavior leads to an apparent increase in overall system entropy upon binding and therefore to the surprising and seemingly nonphysical result of an apparent increased binding free energy at elevated temperatures. Opposite effects and conclusions are found for the neutral surface. Additional simulations demonstrate that by adjusting the ionic strength of the solution, results that show the expected physical behavior, i.e., peptide binding strength that decreases with increasing temperature or is independent of temperature altogether, can be recovered on the charged surface. On the basis of this analysis, an overall free energy for the entire thermodynamic cycle for peptide adsorption on charged surfaces is constructed and validated with independent simulations.
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Affiliation(s)
- K G Sprenger
- Department of Chemical Engineering, University of Washington , Seattle, Washington 98195-1750, United States
| | - Jim Pfaendtner
- Department of Chemical Engineering, University of Washington , Seattle, Washington 98195-1750, United States
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Zhang Z, Santos AP, Zhou Q, Liang L, Wang Q, Wu T, Franzen S. Steered molecular dynamics study of inhibitor binding in the internal binding site in dehaloperoxidase-hemoglobin. Biophys Chem 2016; 211:28-38. [DOI: 10.1016/j.bpc.2016.01.003] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2015] [Revised: 12/24/2015] [Accepted: 01/12/2016] [Indexed: 10/22/2022]
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Abstract
Calcium binding and dissociation within the cardiac thin filament (CTF) is a fundamental regulator of normal contraction and relaxation. Although the disruption of this complex, allosterically mediated process has long been implicated in human disease, the precise atomic-level mechanisms remain opaque, greatly hampering the development of novel targeted therapies. To address this question, we used a fully atomistic CTF model to test both Ca(2+) binding strength and the energy required to remove Ca(2+) from the N-lobe binding site in WT and mutant troponin complexes that have been linked to genetic cardiomyopathies. This computational approach is combined with measurements of in vitro Ca(2+) dissociation rates in fully reconstituted WT and cardiac troponin T R92L and R92W thin filaments. These human disease mutations represent known substitutions at the same residue, reside at a significant distance from the calcium binding site in cardiac troponin C, and do not affect either the binding pocket affinity or EF-hand structure of the binding domain. Both have been shown to have significantly different effects on cardiac function in vivo. We now show that these mutations independently alter the interaction between the Ca(2+) ion and cardiac troponin I subunit. This interaction is a previously unidentified mechanism, in which mutations in one protein of a complex indirectly affect a third via structural and dynamic changes in a second to yield a pathogenic change in thin filament function that results in mutation-specific disease states. We can now provide atom-level insight that is potentially highly actionable in drug design.
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Neale C, Pomès R. Sampling errors in free energy simulations of small molecules in lipid bilayers. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2016; 1858:2539-2548. [PMID: 26952019 DOI: 10.1016/j.bbamem.2016.03.006] [Citation(s) in RCA: 75] [Impact Index Per Article: 9.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2015] [Revised: 03/01/2016] [Accepted: 03/02/2016] [Indexed: 12/14/2022]
Abstract
Free energy simulations are a powerful tool for evaluating the interactions of molecular solutes with lipid bilayers as mimetics of cellular membranes. However, these simulations are frequently hindered by systematic sampling errors. This review highlights recent progress in computing free energy profiles for inserting molecular solutes into lipid bilayers. Particular emphasis is placed on a systematic analysis of the free energy profiles, identifying the sources of sampling errors that reduce computational efficiency, and highlighting methodological advances that may alleviate sampling deficiencies. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.
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Affiliation(s)
- Chris Neale
- Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, 110 8th St, Troy, New York 12180-3590, USA
| | - Régis Pomès
- Molecular Structure and Function, The Hospital for Sick Children, 686 Bay Street, Toronto, Ontario M5G 0A4, Canada; Department of Biochemistry, University of Toronto, 101 College Street, Toronto, Ontario M5G 1L7, Canada.
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Tchaicheeyan O, Meirovitch E. Polar Versus Non-polar Local Ordering at Mobile Sites in Proteins: Slowly Relaxing Local Structure Analysis of (15)N Relaxation in the Third Immunoglobulin-Binding Domain of Streptococcal Protein G. J Phys Chem B 2016; 120:386-95. [PMID: 26731631 DOI: 10.1021/acs.jpcb.5b10244] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We developed recently the slowly relaxing local structure (SRLS) approach for studying restricted motions in proteins by NMR. The spatial restrictions have been described by potentials comprising the traditional L = 2, K = 0, 2 spherical harmonics. However, the latter are associated with non-polar ordering whereas protein-anchored probes experience polar ordering, described by odd-L spherical harmonics. Here we extend the SRLS potential to include the L = 1, K = 0, 1 spherical harmonics and analyze (15)N-(1)H relaxation from the third immunoglobulin-binding domain of streptococcal protein G (GB3) with the polar L = 1 potential (coefficients c0(1) and c1(1)) or the non-polar L = 2 potential (coefficients c0(2) and c2(2)). Strong potentials, with ⟨c0(1)⟩ ∼ 60 for L = 1 and ⟨c0(2)⟩ ∼ 20 for L = 2 (in units of kBT), are detected. In the α-helix of GB3 the coefficients of the rhombic terms are c1(1) ∼ c2(2) ∼ 0; in the preceding (following) chain segment they are ⟨c1(1)⟩ ∼ 6 for L = 1 and ⟨c2(2)⟩ ∼ 14 for L = 2 (⟨c1(1)⟩ ∼ 3 for L = 1 and ⟨c2(2)⟩ ∼ 7 for L = 2). The local diffusion rate, D2, lies in the 5 × 10(9)-1 × 10(11) s(-1) range; it is generally larger for L = 1. The main ordering axis deviates moderately from the N-H bond. Corresponding L = 1 and L = 2 potentials and probability density functions are illustrated for residues A26 of the α-helix, Y3 of the β1-strand, and L12 of the β1/β2 loop; they differ considerably. Polar/orientational ordering is shown to be associated with GB3 binding to its cognate Fab fragment. The polarity of the local ordering is clearly an important factor.
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Affiliation(s)
- Oren Tchaicheeyan
- The Mina and Everard Goodman Faculty of Life Sciences, Bar-Ilan University , Ramat-Gan 52900 Israel
| | - Eva Meirovitch
- The Mina and Everard Goodman Faculty of Life Sciences, Bar-Ilan University , Ramat-Gan 52900 Israel
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