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Transmembrane Transport[Version 2; Peer Review: 2 Approved] F1000Research 2018, 7:1468 Last updated: 19 MAY 2021 RESEARCH ARTICLE A thermodynamic description for physiological transmembrane transport [version 2; peer review: 2 approved] Marco Arieli Herrera-Valdez Department of Mathematics, Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, CDMX, 04510, Mexico v2 First published: 14 Sep 2018, 7:1468 Open Peer Review https://doi.org/10.12688/f1000research.16169.1 Second version: 21 Nov 2018, 7:1468 https://doi.org/10.12688/f1000research.16169.2 Reviewer Status Latest published: 19 May 2021, 7:1468 https://doi.org/10.12688/f1000research.16169.3 Invited Reviewers 1 2 Abstract A general formulation for both passive and active transmembrane version 3 transport is derived from basic thermodynamical principles. The (revision) derivation takes into account the energy required for the motion of 19 May 2021 molecules across membranes, and includes the possibility of modeling asymmetric flow. Transmembrane currents can then be version 2 described by the general model in the case of electrogenic flow. As it (revision) report is desirable in new models, it is possible to derive other well known 21 Nov 2018 expressions for transmembrane currents as particular cases of the general formulation. For instance, the conductance-based formulation version 1 for current turns out to be a linear approximation of the general 14 Sep 2018 report report formula for current. Also, under suitable assumptions, other formulas for current based on electrodiffusion, like the constant field approximation by Goldman, can also be recovered from the general 1. Kyle C.A. Wedgwood , University of formulation. The applicability of the general formulations is illustrated Exeter, Exeter, UK first with fits to existing data, and after, with models of transmembrane potential dynamics for pacemaking cardiocytes and 2. Moisés Santillán , Center for Research neurons. The general formulations presented here provide a common and Advanced Studies of the National ground for the biophysical study of physiological phenomena that depend on transmembrane transport. Polytechnic Institute (CINVESTAV), Monterrey, Mexico Keywords Transmembrane transport, ion channels, passive transport, active Any reports and responses or comments on the transport, rectification, bidirectional assymetric flow, AMPA-Kainate article can be found at the end of the article. receptor, excitable cell Page 1 of 30 F1000Research 2018, 7:1468 Last updated: 19 MAY 2021 Corresponding author: Marco Arieli Herrera-Valdez ([email protected]) Author roles: Herrera-Valdez MA: Conceptualization, Data Curation, Formal Analysis, Funding Acquisition, Investigation, Methodology, Project Administration, Resources, Software, Validation, Visualization, Writing – Original Draft Preparation, Writing – Review & Editing Competing interests: No competing interests were disclosed. Grant information: This work was supported by UNAM-PAPIIT IA208618. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Copyright: © 2018 Herrera-Valdez MA. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. How to cite this article: Herrera-Valdez MA. A thermodynamic description for physiological transmembrane transport [version 2; peer review: 2 approved] F1000Research 2018, 7:1468 https://doi.org/10.12688/f1000research.16169.2 First published: 14 Sep 2018, 7:1468 https://doi.org/10.12688/f1000research.16169.1 Page 2 of 30 F1000Research 2018, 7:1468 Last updated: 19 MAY 2021 Ussing, 1949c). The energy for primary active transport is usually REVISE D Amendments from Version 1 obtained from biochemical reactions (e.g. ATPases, light-driven The new version contains edits and comments that take into pumps). For instance, the energy to transport molecules against account the observations made by Reviewers 1 and 2, which their (electro)chemical gradient via ATPases is obtained from can be found in the open review section. The most important hydrolysis of ATP (Chapman, 1973). In secondary and tertiary changes include (i) expanded the Introduction section with details active transport, the electrochemical gradient of at least one about the transmembrane transport, (ii) precisions about, and notation additions to the formulas for the energy associated to the ion types provides the energy to transport other molecules ATP hydrolysis, (iii) an expansion of the Discussion section about against their (electro)chemical gradient (SKou, 1965). Two large the sharpness of the upstroke in the action potential in neurons. classes of non-primary active transport pumps are the symporters Header lines with physical units have been added to the data files and counterporters, carrying at least two types of molecules in for more clarity. Also, a JuPyTeR notebook has been included as Supplementary File 3. The notebook contains code to generate the same, or in opposite directions, respectively, with at least the figures for the paper. one type against its electrochemical gradient. For instance Na-H exchangers carry Na+ and H+ in opposite directions, typically See referee reports using the driving force from Na+. In contrast, K-Cl symporters carry K+ and Cl− in the same direction, which means that one of the two ion types is carried against its concentration gradient. Introduction This is because the K+ and Cl− concentration gradients are One of the most important physiological mechanisms underlying typically oriented in opposite directions. As a consequence, communication within and between cells is the transport of the movement of one of the two ions releases energy from its molecules across membranes. Molecules can cross membranes electrochemical gradient, enabling the transport of the other ion either passively (Stein & Litman, 2014), or via active transport against its gradient. (Bennett, 1956). Molecules are passively transported across a membrane when they move along their (electro)chemical gradient. Theoretical models of transmembrane transport play a critical In contrast, active transport involves transmembrane motion of role in developing our understanding of the function and mecha- molecules against their electrochemical gradients. One important nisms underlying electrical signaling and cellular excitability functional distinction between channels and pumps is that the (Barr, 1965; Cole, 1965; DiFrancesco & Noble, 1985; Endresen rate of transport for channels is generally several orders of et al., 2000; Gadsby, 2009; Goldman, 1943; Kell, 1979; Kimizuka magnitude faster than the rate for pump-mediated transport & Koketsu, 1964; Läuger, 1973; Stevens & Tsien, 1979; Wiggins, (Gadsby, 2009; Ussing, 1949a). Such differences are reflected 1985a; Wiggins, 1985b; Wiggins, 1985c), and some of its asso- in the sizes of different transmembrane fluxes typically observed ciated pathologies (Ashcroft, 2005; Marbán, 2002). The best in excitable cells (Herrera-Valdez & Lega, 2011). known transmembrane transport models include the widely used conductance-based formulation from the seminal work of Passive transport may occur through transmembrane proteins Hodgkin & Huxley (1952), the Goldman-Hodgkin-Katz equa- (Hille, 1992; Stein & Litman, 2014) that may be selective for tion (Goldman, 1943; Hodgkin & Katz, 1949; Pickard, 1976), molecules of specific types Almers( & McCleskey, 1984; and several other expressions for carrier and channel mediated Doyle et al., 1998; Favre et al., 1996), typically mediating transport with many different functional forms (DiFrancesco & (electro)diffusion through them. Sometimes these proteins are Noble, 1985; Rasmusson et al., 1990a; Rasmusson et al., 1990b; also gated by conformational changes triggered by different Rosenberg & Wilbrandt, 1955). Other formulations for ionic signlling mechanisms. Passive transport has also been observed transport across membranes derived from biophysical principles in pores spontaneously formed within synthetic lipid bilayers available in the literature include those in the work by Jacquez (Blicher & Heimburg, 2013), which could also occur in natural & Schultz (1974); Kimizuka & Koketsu (1964); Pickard, 1969; conditions (Gurtovenko & Anwar, 2007). One example of Pickard, 1976. See also Jacquez (1981) and similar work by importance in the context of energy homeostasis is the Endresen et al. (2000), and those in the excellent book by transport of monosaccharides and other similar molecules Johnston et al. (1995). Such formulations describe the relation- through GLUT transporters. GLUT transporters first bind to ship between the activity and permeability of ions across mem- their substrates, triggering a conformational change that allows branes, and the transmembrane potential. However general models the substrate to cross in the direction of its chemical gradient that describe physiological transport including passive and active (e.g. GLUT5 is highly specific to fructose, Mueckler & transport of charged or non-charged molecules, with bidirec- Thorens (2013)). Channels are another important class of trans- tional but possibly asymmetric flows, are still missing. The work membrane proteins that typically mediate fast passive transport, presented here builds upon the results previously mentioned often displaying selectivity for specific ion types, gated by by describing transport macroscopically in terms of the energy
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