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Nicholson S, Minh DDL, Eisenberg R. H-Bonds in Crambin: Coherence in an α-Helix. ACS OMEGA 2023; 8:13920-13934. [PMID: 37091420 PMCID: PMC10116620 DOI: 10.1021/acsomega.3c00181] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/17/2023] [Accepted: 02/23/2023] [Indexed: 05/03/2023]
Abstract
We applied coherence analysis-used by engineers to identify linear interactions in stochastic systems-to molecular dynamics simulations of crambin, a thionin storage protein found in Abyssinian cabbage. A key advantage of coherence over other analyses is that it is robust, independent of the properties, or even the existence of probability distributions often relied on in statistical mechanics. For frequencies between 0.391 and 5.08 GHz (corresponding reciprocally to times of 2.56 and 0.197 ns), the displacements of oxygen and nitrogen atoms across α-helix H-bonds are strongly correlated, with a coherence greater than 0.9; the secondary structure causes the H-bonds to effectively act as a spring. Similar coherence behavior is observed for covalent bonds and other noncovalent interactions including H-bonds in β-sheets and salt bridges. In contrast, arbitrary pairs of atoms that are physically distant have uncorrelated motions and negligible coherence. These results suggest that coherence may be used to objectively identify atomic interactions without subjective thresholds such as H-bond lengths angles and angles. Strong coherence is also observed between the average position of adjacent leaves (groups of atoms) in an α-helix, suggesting that the harmonic analysis of classical molecular dynamics can successfully describe the propagation of allosteric interactions through the structure.
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Affiliation(s)
- Stanley Nicholson
- Department
of Chemistry, Illinois Institute of Technology, Chicago, Illinois 60616, United States
| | - David D. L. Minh
- Department
of Applied Mathematics, Illinois Institute
of Technology, Chicago, Illinois 60616, United States
| | - Robert Eisenberg
- Department
of Applied Mathematics, Illinois Institute
of Technology, Chicago, Illinois 60616, United States
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Eisenberg B. Setting Boundaries for Statistical Mechanics. MOLECULES (BASEL, SWITZERLAND) 2022; 27:molecules27228017. [PMID: 36432117 PMCID: PMC9696510 DOI: 10.3390/molecules27228017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Revised: 10/21/2022] [Accepted: 11/08/2022] [Indexed: 11/22/2022]
Abstract
Statistical mechanics has grown without bounds in space. Statistical mechanics of noninteracting point particles in an unbounded perfect gas is widely used to describe liquids like concentrated salt solutions of life and electrochemical technology, including batteries. Liquids are filled with interacting molecules. A perfect gas is a poor model of a liquid. Statistical mechanics without spatial bounds is impossible as well as imperfect, if molecules interact as charged particles, as nearly all atoms do. The behavior of charged particles is not defined until boundary structures and values are defined because charges are governed by Maxwell's partial differential equations. Partial differential equations require boundary structures and conditions. Boundary conditions cannot be defined uniquely 'at infinity' because the limiting process that defines 'infinity' includes such a wide variety of structures and behaviors, from elongated ellipses to circles, from light waves that never decay, to dipolar fields that decay steeply, to Coulomb fields that hardly decay at all. Boundaries and boundary conditions needed to describe matter are not prominent in classical statistical mechanics. Statistical mechanics of bounded systems is described in the EnVarA system of variational mechanics developed by Chun Liu, more than anyone else. EnVarA treatment does not yet include Maxwell equations.
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Affiliation(s)
- Bob Eisenberg
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA;
- Department of Physiology and Biophysics, Rush University Medical Center, Chicago, IL 60612, USA
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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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Boda D, Valiskó M, Gillespie D. Modeling the Device Behavior of Biological and Synthetic Nanopores with Reduced Models. ENTROPY 2020; 22:e22111259. [PMID: 33287027 PMCID: PMC7711659 DOI: 10.3390/e22111259] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/12/2020] [Revised: 10/30/2020] [Accepted: 11/02/2020] [Indexed: 01/08/2023]
Abstract
Biological ion channels and synthetic nanopores are responsible for passive transport of ions through a membrane between two compartments. Modeling these ionic currents is especially amenable to reduced models because the device functions of these pores, the relation of input parameters (e.g., applied voltage, bath concentrations) and output parameters (e.g., current, rectification, selectivity), are well defined. Reduced models focus on the physics that produces the device functions (i.e., the physics of how inputs become outputs) rather than the atomic/molecular-scale physics inside the pore. Here, we propose four rules of thumb for constructing good reduced models of ion channels and nanopores. They are about (1) the importance of the axial concentration profiles, (2) the importance of the pore charges, (3) choosing the right explicit degrees of freedom, and (4) creating the proper response functions. We provide examples for how each rule of thumb helps in creating a reduced model of device behavior.
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Affiliation(s)
- Dezső Boda
- Department of Physical Chemistry, University of Pannonia, P.O. Box 158, H-8201 Veszprém, Hungary;
- Correspondence: ; Tel.: +36-88-624-000 (ext. 6041)
| | - Mónika Valiskó
- Department of Physical Chemistry, University of Pannonia, P.O. Box 158, H-8201 Veszprém, Hungary;
| | - Dirk Gillespie
- Department of Physiology and Biophysics, Rush University Medical Center, Chicago, IL 60612, USA;
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Mádai E, Valiskó M, Boda D. Application of a bipolar nanopore as a sensor: rectification as an additional device function. Phys Chem Chem Phys 2019; 21:19772-19784. [PMID: 31475284 DOI: 10.1039/c9cp03821c] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
We model and simulate a nanopore sensor that selectively binds analyte ions. This binding leads to the modulation of the local concentrations of the ions of the background electrolyte (KCl), and, thus, to the modulation of the ionic current flowing through the pore. The nanopore's wall has a bipolar charge pattern with a larger positive buffer region determining the anions as the main charge carriers and a smaller negative binding region containing binding sites. This charge pattern proved to be an appropriate one as shown by a previous comparative study of varying charge patterns (Mádai et al. J. Mol. Liq., 2019, 283, 391-398.). Binding of the positive analyte ions attracts more anions in the pore thus increasing the current. The asymmetric nature of the pore results in an additional device function, rectification. Our model, therefore, is a dual response device. Using a reduced model of the nanopore studied by a hybrid computer simulation method (Local Equilibrium Monte Carlo coupled with the Nernst-Planck equation) we show that we can create a sensor whose underlying mechanisms are based on the changes in the local electric field as a response to changing thermodynamic conditions. The change in the electric field results in changes in the local ionic concentrations (depletion zones), and, thus, changes in ionic currents.
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Affiliation(s)
- Eszter Mádai
- Department of Material- and Geo-Sciences, Technische Universität Darmstadt, Petersenstr. 23, D-64287 Darmstadt, Germany
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Valiskó M, Matejczyk B, Ható Z, Kristóf T, Mádai E, Fertig D, Gillespie D, Boda D. Multiscale analysis of the effect of surface charge pattern on a nanopore's rectification and selectivity properties: From all-atom model to Poisson-Nernst-Planck. J Chem Phys 2019; 150:144703. [PMID: 30981242 DOI: 10.1063/1.5091789] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
We report a multiscale modeling study for charged cylindrical nanopores using three modeling levels that include (1) an all-atom explicit-water model studied with molecular dynamics, and reduced models with implicit water containing (2) hard-sphere ions studied with the Local Equilibrium Monte Carlo simulation method (computing ionic correlations accurately), and (3) point ions studied with Poisson-Nernst-Planck theory (mean-field approximation). We show that reduced models are able to reproduce device functions (rectification and selectivity) for a wide variety of charge patterns, that is, reduced models are useful in understanding the mesoscale physics of the device (i.e., how the current is produced). We also analyze the relationship of the reduced implicit-water models with the explicit-water model and show that diffusion coefficients in the reduced models can be used as adjustable parameters with which the results of the explicit- and implicit-water models can be related. We find that the values of the diffusion coefficients are sensitive to the net charge of the pore but are relatively transferable to different voltages and charge patterns with the same total charge.
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Affiliation(s)
- Mónika Valiskó
- Department of Physical Chemistry, University of Pannonia, P.O. Box 158, H-8201 Veszprém, Hungary
| | - Bartłomiej Matejczyk
- Department of Mathematics, University of Warwick, CV4 7AL Coventry, United Kingdom
| | - Zoltán Ható
- Department of Physical Chemistry, University of Pannonia, P.O. Box 158, H-8201 Veszprém, Hungary
| | - Tamás Kristóf
- Department of Physical Chemistry, University of Pannonia, P.O. Box 158, H-8201 Veszprém, Hungary
| | - Eszter Mádai
- Department of Physical Chemistry, University of Pannonia, P.O. Box 158, H-8201 Veszprém, Hungary
| | - Dávid Fertig
- Department of Physical Chemistry, University of Pannonia, P.O. Box 158, H-8201 Veszprém, Hungary
| | - Dirk Gillespie
- Department of Physiology and Biophysics, Rush University Medical Center, Chicago, Illinois 60612, USA
| | - Dezső Boda
- Department of Physical Chemistry, University of Pannonia, P.O. Box 158, H-8201 Veszprém, Hungary
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