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Malgaretti P, Harting J. Closed Formula for Transport across Constrictions. ENTROPY (BASEL, SWITZERLAND) 2023; 25:470. [PMID: 36981357 PMCID: PMC10047801 DOI: 10.3390/e25030470] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/03/2023] [Revised: 03/01/2023] [Accepted: 03/05/2023] [Indexed: 06/18/2023]
Abstract
In the last decade, the Fick-Jacobs approximation has been exploited to capture transport across constrictions. Here, we review the derivation of the Fick-Jacobs equation with particular emphasis on its linear response regime. We show that, for fore-aft symmetric channels, the flux of noninteracting systems is fully captured by its linear response regime. For this case, we derive a very simple formula that captures the correct trends and can be exploited as a simple tool to design experiments or simulations. Lastly, we show that higher-order corrections in the flux may appear for nonsymmetric channels.
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Affiliation(s)
- Paolo Malgaretti
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy, Forschungszentrum Jülich, 90429 Erlangen, Germany
| | - Jens Harting
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy, Forschungszentrum Jülich, 90429 Erlangen, Germany
- Department of Chemical and Biological Engineering and Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 90429 Erlangen, Germany
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Guardiani C, Cecconi F, Chiodo L, Cottone G, Malgaretti P, Maragliano L, Barabash ML, Camisasca G, Ceccarelli M, Corry B, Roth R, Giacomello A, Roux B. Computational methods and theory for ion channel research. ADVANCES IN PHYSICS: X 2022; 7:2080587. [PMID: 35874965 PMCID: PMC9302924 DOI: 10.1080/23746149.2022.2080587] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Accepted: 05/15/2022] [Indexed: 06/15/2023] Open
Abstract
Ion channels are fundamental biological devices that act as gates in order to ensure selective ion transport across cellular membranes; their operation constitutes the molecular mechanism through which basic biological functions, such as nerve signal transmission and muscle contraction, are carried out. Here, we review recent results in the field of computational research on ion channels, covering theoretical advances, state-of-the-art simulation approaches, and frontline modeling techniques. We also report on few selected applications of continuum and atomistic methods to characterize the mechanisms of permeation, selectivity, and gating in biological and model channels.
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Affiliation(s)
- C. Guardiani
- Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Rome, Italy
| | - F. Cecconi
- CNR - Istituto dei Sistemi Complessi, Rome, Italy and Istituto Nazionale di Fisica Nucleare, INFN, Roma1 section. 00185, Roma, Italy
| | - L. Chiodo
- Department of Engineering, Campus Bio-Medico University, Rome, Italy
| | - G. Cottone
- Department of Physics and Chemistry-Emilio Segrè, University of Palermo, Palermo, Italy
| | - P. Malgaretti
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, Erlangen, Germany
| | - L. Maragliano
- Department of Life and Environmental Sciences, Polytechnic University of Marche, Ancona, Italy, and Center for Synaptic Neuroscience and Technology, Istituto Italiano di Tecnologia, Genova, Italy
| | - M. L. Barabash
- Department of Materials Science and Nanoengineering, Rice University, Houston, TX 77005, USA
| | - G. Camisasca
- Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Rome, Italy
- Dipartimento di Fisica, Università Roma Tre, Rome, Italy
| | - M. Ceccarelli
- Department of Physics and CNR-IOM, University of Cagliari, Monserrato 09042-IT, Italy
| | - B. Corry
- Research School of Biology, The Australian National University, Canberra, ACT 2600, Australia
| | - R. Roth
- Institut Für Theoretische Physik, Eberhard Karls Universität Tübingen, Tübingen, Germany
| | - A. Giacomello
- Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Rome, Italy
| | - B. Roux
- Department of Biochemistry & Molecular Biology, University of Chicago, Chicago IL, USA
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Malgaretti P, Harting J. Transport of neutral and charged nanorods across varying-section channels. SOFT MATTER 2021; 17:2062-2070. [PMID: 33475112 DOI: 10.1039/d0sm02045a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We study the dynamics of neutral and charged rods embedded in varying-section channels. By means of systematic approximations, we derive the dependence of the local diffusion coefficient on both the geometry and charge of the rods. This microscopic insight allows us to provide predictions for the permeability of varying-section channels to rods with diverse lengths, aspect ratios and charge. Our analysis shows that the dynamics of charged rods is sensitive to the geometry of the channel and that their transport can be controlled by tuning both the shape of the confining walls and the charge of the rod. Interestingly, we find that the channel permeability does not depend monotonically on the charge of the rod. This opens the possibility of a novel mechanism to separate charged rods.
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Affiliation(s)
- Paolo Malgaretti
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany and Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, Fürther Straße 248, 90429 Nürnberg, Germany.
| | - Jens Harting
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, Fürther Straße 248, 90429 Nürnberg, Germany. and Department of Chemical and Biological Engineering and Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Fürther Straße 248, 90429 Nürnberg, Germany
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Glatzel F, Janssen M, Härtel A. Reversible heat production during electric double layer buildup depends sensitively on the electrolyte and its reservoir. J Chem Phys 2021; 154:064901. [PMID: 33588538 DOI: 10.1063/5.0037218] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Several modern technologies for energy storage and conversion are based on the screening of electric charge on the surface of porous electrodes by ions in an adjacent electrolyte. This so-called electric double layer (EDL) exhibits an intricate interplay with the electrolyte's temperature that was the focus of several recent studies. In one of them, Janssen et al. [Phys. Rev. Lett. 119, 166002 (2017)] experimentally determined the ratio Qrev/Wel of reversible heat flowing into a supercapacitor during an isothermal charging process and the electric work applied therein. To rationalize that data, here, we determine Qrev/Wel within different models of the EDL using theoretical approaches such as density functional theory (DFT) as well as molecular dynamics simulations. Applying mainly the restricted primitive model, we find quantitative support for a speculation of Janssen et al. that steric ion interactions are key to the ratio Qrev/Wel. Here, we identified the entropic contribution of certain DFT functionals, which grants direct access to the reversible heat. We further demonstrate how Qrev/Wel changes when calculated in different thermodynamic ensembles and processes. We show that the experiments of Janssen et al. are explained best by a charging process at fixed bulk density or in a "semi-canonical" system. Finally, we find that Qrev/Wel significantly depends on parameters such as pore and ion size, salt concentration, and valencies of the cations and anions of the electrolyte. Our findings can guide further heat production measurements and can be applied in studies on, for instance, nervous conduction, where reversible heat is a key element.
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Affiliation(s)
- Fabian Glatzel
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - Mathijs Janssen
- Mechanics Division, Department of Mathematics, University of Oslo, 0316 Oslo, Norway
| | - Andreas Härtel
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
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Catacuzzeno L, Sforna L, Franciolini F, Eisenberg RS. Multiscale modeling shows that dielectric differences make NaV channels faster than KV channels. J Gen Physiol 2021; 153:211724. [PMID: 33502441 PMCID: PMC7845922 DOI: 10.1085/jgp.202012706] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2020] [Revised: 11/22/2020] [Accepted: 12/18/2020] [Indexed: 12/31/2022] Open
Abstract
The generation of action potentials in excitable cells requires different activation kinetics of voltage-gated Na (NaV) and K (KV) channels. NaV channels activate much faster and allow the initial Na+ influx that generates the depolarizing phase and propagates the signal. Recent experimental results suggest that the molecular basis for this kinetic difference is an amino acid side chain located in the gating pore of the voltage sensor domain, which is a highly conserved isoleucine in KV channels but an equally highly conserved threonine in NaV channels. Mutagenesis suggests that the hydrophobicity of this side chain in Shaker KV channels regulates the energetic barrier that gating charges cross as they move through the gating pore and control the rate of channel opening. We use a multiscale modeling approach to test this hypothesis. We use high-resolution molecular dynamics to study the effect of the mutation on polarization charge within the gating pore. We then incorporate these results in a lower-resolution model of voltage gating to predict the effect of the mutation on the movement of gating charges. The predictions of our hierarchical model are fully consistent with the tested hypothesis, thus suggesting that the faster activation kinetics of NaV channels comes from a stronger dielectric polarization by threonine (NaV channel) produced as the first gating charge enters the gating pore compared with isoleucine (KV channel).
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Affiliation(s)
- Luigi Catacuzzeno
- Department of Chemistry, Biology and Biotechnology, University of Perugia, Perugia, Italy
| | - Luigi Sforna
- Department of Chemistry, Biology and Biotechnology, University of Perugia, Perugia, Italy
| | - Fabio Franciolini
- Department of Chemistry, Biology and Biotechnology, University of Perugia, Perugia, Italy
| | - Robert S Eisenberg
- Department of Physiology and Biophysics, Rush University, Chicago, IL.,Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL
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Malgaretti P, Janssen M, Pagonabarraga I, Rubi JM. Driving an electrolyte through a corrugated nanopore. J Chem Phys 2019; 151:084902. [DOI: 10.1063/1.5110349] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Affiliation(s)
- Paolo Malgaretti
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany
- IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - Mathijs Janssen
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany
- IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - Ignacio Pagonabarraga
- Departament de Fisica de la Materia Condensada, Universitat de Barcelona, Carrer Martí i Franqués, 08028 Barcelona, Spain
- CECAM, Centre Européeen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lausanne, Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland
- Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain
| | - J. Miguel Rubi
- Departament de Fisica de la Materia Condensada, Universitat de Barcelona, Carrer Martí i Franqués, 08028 Barcelona, Spain
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Gußmann F, Roth R. Bubble gating in biological ion channels: A density functional theory study. Phys Rev E 2017; 95:062407. [PMID: 28709278 DOI: 10.1103/physreve.95.062407] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2017] [Indexed: 06/07/2023]
Abstract
We study the behavior of a waterlike liquid inside the gate of a biological ion channel following the basic geometry of the well studied potassium channel KcsA. We calculate the three-dimensional density distribution ρ(r) of the liquid within the framework of classical density functional theory and observe the formation of a low density region (bubble) when the gate is narrow. This observation corresponds to a finite-size form of capillary evaporation and supports the so-called bubble-gate theory. From the density profile we also compute the energy landscape of the gate and the energy required to change the gate from a closed (narrow) to an open (wide) state and vice versa.
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Affiliation(s)
- Florian Gußmann
- Institut für Theoretische Physik, Universität Tübingen, D-72076 Tübingen, Germany and Max-Planck Institut für Intelligente Systeme, Heisenbergstrasse 3, D-70569 Stuttgart, Germany
| | - Roland Roth
- Institut für Theoretische Physik, Universität Tübingen, D-72076 Tübingen, Germany
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