arXiv:1809.07662v1 [physics.bio-ph] 20 Sep 2018 fboebaefnto.Tems rmnn xml stet the is example prominent most The function. biomembrane of hreflwi h lcrclfil,adtedfuiecurrent diffusive ( the the differences concentration and of ion field, sum to electrical the due the as in current flow equati ion charge Nernst-Planck transmembrane The the sodium. selectivity considers display e.g., may ions, membrane different oth the for to of impermeable regions and Other potassium, ions. e.g., permeabl ion, only semi-permeable particular is regions a of some to in existence that the membrane a of i.e., walls, consequence the is tage ABSTRACT Blegdamsv Copenhagen, of University Institute, Bohr Niels Heimburg Thomas polarization? by caused potentials transmembrane Are Goldm the equation of Hodgkin-Katz reinterpretation Ikeda’s & Tamagawa on Comment eti h ogi-uly(H oe ( model (HH) Hodgkin-Huxley the cent in a rectification, ment are that for relations understanding current-voltage non-linear an i.e., provides equation GHK P rnmmrn otg n ebaepreblt.I rece a In permeability. membrane and voltage transmembrane it h ieto fcret,eg,atratmoayvol temporary a after e.g., currents, of direction the dicts t is ion single one just potential, for Nernst permeability of case simplest the permeability, membrane the h equation, Goldman-Hodgkin-Katz the concept, underlying urnsi eo o ntne ntepeec fpotassium of presence finds one the ions in chloride instance, and For sodium zero. is currents a ob anandb h ciiyo o up.I the If pumps. (e.g., ion ion single of one activity to potenti permeable resting the only the by is reason, membrane maintained this be For to zero. has is the currents but all where exist, of currents situation Individual non-equilibrium matter. a permeabilities describes equation This hr the where where rmteNrs-lnkeuto.I eemnsavoltage a determines It potential, resting the equation. called the derived Nernst-Planck by is the addressed which from is al equation, case of (GHK) This currents Goldman-Hodgkin-Katz simultaneously. the which zero for are exist ions will voltage no outside Typically, and permeability. inside the between on depend ratio not the does po- but of Nernst concentrations function The a zero. is is membrane tential the across balanc current are the forces and electric and diffusive where case librium and tions, Cl V R nteve feetohsooy h rnmmrn vol- transmembrane the , of view the In nabooia el ayin r rsn simultaneously. present are ions many , biological a In 0 = = [ C RT F n eoestersetv entptnil The potential. Nernst respective the recovers one ) in z P ] h aec ftersetv o.Ti steequi- the is This ion. respective the of valency the ln and i  r h emaiiisfrtedfeetions. different the for permeabilities the are P P [ C h mrec feetia ed cosbooia membra biological across fields electrical of emergence The K K out [ [ K V K ] ] ] out = in r nieadotieinconcentra- ion outside and inside are RT + zF + P V P P Na R ln Na h taysaeslto in solution state steady The . twihtesmo l ion all of sum the which at , [ [ [ [ Na C Na C ] ] out in ] ] in out 3 .I spootoa to proportional is It ). , + + P 1 P Cl .Frhr tpre- it Further, ). Cl [ Cl [ Cl ] out ] in  P j1,20 oehgnØ emr [email protected] - Denmark Ø, Copenhagen 2100 17, ej a ele- ral Na , sum tage ed, (2) (1) on he = er al e s l sbe hlegd( challenged been as , 1 essbnigstsfrin ihbnigconstant binding with pos- ions wall for impermeable sites the binding that sesses assume provide They Ikeda ions theory. and simple Tamagawa no a membrane. though the even across GHK-equation flow can the of follows dependence voltage concentration the measured author The the wall. that take impermeable could demonstrate an to them equivalent between is This ions AgCl place. of two diffusion and no wire two but a The electrodes, by KBr. coupled one electrically other were the containers and KCl containing one beakers, thermodynamics. i and rooted solidly concepts physical are Ling’s they because controversial, supporters While numerous found pumps. and channels ibr ig( Ling Gilbert o dopinmcaimrte hnapreto process an permeation a by than namely ( rather way, mechanism different adsorption completely ion can a GHK-equation in the interpreted that be suggested Ikeda equation: and GHK Tamagawa the of interpretation Another scale. molecular a on hard selectivity is and it flux However, ion detect binding. to specific by channels individual ahmtclyietclt h H-qain ntecs o case the equatio In resulting GHK-equation. the the to Surprisingly, identical mathematically potential. density well-known surface charge the surface to using relates by which theory, calculate Gouy-Chapman of authors side the potenti other transmembrane that a the emerges net different, on a is concentration wall acquires ion impermeable surface the the the depends If result, ions a density. adsorbed As charge action of mass concentration. amount the ion total to on according the bind Therefore, ions and law. ion), an of index rnmmrn urn a eatnae yteueo toxins of ( use tetrodotoxin as the t such by of attenuated be phases can different current i because transmembrane selective plausible of is notion proteins The channel ions. respective per- the membrane for macroscopic meability the to speci proportional the are of conductances channels the that voltage-g and by proteins, controlled channel ion are ions different for meabilities interpreta data. present electrophysiological the of tion for important very are underlyi GHK-equation concepts theoretical the Therefore, excitation. 2 .Te trbt hsie oteAeia elphysiologis cell American the to idea this attribute They ). tatceb aaaa&Iea( Ikeda & Tamagawa by article nt xbo oe o h cinptnil( potential action the for model extbook aaaaadIearpre xeiet ihtoglass two with experiments reported Ikeda and Tamagawa oa,i sgnrlyblee htseicmmrn per- membrane specific that believed generally is it Today, 5 , 6 e scnrlt u rsn understanding present our to central is nes 2 ,woi nopnn ftecneto ion of concept the of opponent an is who ), .Ti ilb icse below. discussed be will This ). 4 ,wihi trbtdt h lcigof blocking the to attributed is which ), → link 1 ,a important an ), htrle on relies that ) K Recently, i ( i gthe ng an- sthe is ated is n on fic he al n s f - t potassium, sodium and chloride ions, they would obtain (2)): References

RT KK [K]out + KNa[Na]out + KCl[Cl]in 1. Hodgkin, A. L., and A. F. Huxley. 1952. A quantitative descrip- VR = ln , (3) F  KK [K]in + KNa[Na]in + KCl[Cl]out  tion of membrane current and its application to conduction and excitation in nerve. J. Physiol. London 117:500–544. which is identical to eq. (2), but replaces permeabilities, Pi, by adsorption constants, Ki. The difference between the two 2. Tamagawa, H., and K. Ikeda. 2018. Another in- interpretations of this equation is that eq. (2) describes a terpretation of the Goldman-Hodgkin-Katz equation steady state situation that is not at equilibrium, while eq. (3) based on the ling’s adsorption theory. Eur. Biophys. J. refers to an equilibrium state where no ions flow and no ion https://doi.org/10.1007/s00249-018-1332-0. pumps are required. This is one of the elements of Ling’s 3. Goldman, D. E. 1943. Potential, impedance and rectification in association-induction hypothesis (5). membranes. J. Gen. Physiol. 27:37–60. Tamagawa and Ikeda conclude from this that the GHK- equation is no reliable tool to determine permeabilities. In 4. Moczydlowski, E. G. 2013. The molecular mystique of tetro- their view, the Pi in the GHK-equation are merely paramet- dotoxin. Toxicon 63:165–183. ers to fit the concentrationdependenceof the voltage, but they 5. Ling, G. N., 1962. A physical theory of the living state: the do not have to represent permeabilities. association-induction hypothesis. Blaisdell Publishing Com- pany, New York, London. Polarization: The differential adsorption of ions to the two sides of a membrane (described by Tamagawa and Ikeda) ef- 6. Ling, G. N., 2001. Life at the Cell and Below-Cell Level. The fectively creates a polarization in the absence of membrane Hidden History of a Fundamental Revolution in . Pacific Press. permeability. It has in fact been shown that sodium and chlor- ide ions can bind to lipid membranes (7). There are other 7. B¨ockmann, R. A., A. Hac, T. Heimburg, and H. Grubm¨uller. possible origins of polarization, e.g., an uneven distribution 2003. Effect of sodium chloride on a lipid bilayer. Biophys. J. of charged lipids in both monolayers, asymmetric membrane 858:1647–1655. proteins, or membrane curvature via the so-called flexoelec- 8. Petrov, A. G., 1999. The lyotropic state of matter. Molecular tric effect (8–10). Although these effects clearly exist, po- physics and living matter physics. Gordon and Breach Science larization effects are totally absent in conventional biomem- Publishers, Amsterdam. brane theories. When it comes to nerves, there exists an al- ternative approach to explain the nerve pulse, the so-called 9. Petrov, A. G. 2001. Flexoelectricity of model and living mem- soliton model, which considers the an elec- branes. Biochim. Biophys. Acta 1561:1–25. tromechanical pulse (11). Here, voltage changes are a con- 10. Mosgaard, L. D., K. A. Zecchi, and T. Heimburg. 2015. sequence of variations in capacitance and polarization, and Mechano-capacitive properties of polarized membranes. Soft no selective permeabilities for ions are required. Matter 11:7899–7910.

Conclusion: The paper by Tamagawa and Ikeda addresses 11. Heimburg, T., and A. D. Jackson. 2005. On soliton propaga- the contribution of binding-induced polarization to the elec- tion in biomembranes and nerves. Proc. Natl. Acad. Sci. USA trical properties of membranes. Adsorption of ions to bio- 102:9790–9795. membranes is practically unavoidable. Therefore, it seems obvious that existing electrophysiological models are at least incomplete. In the opinion of Tamagawa and Ikeda, they may even be wrong. Channels and pumps may not be needed to understand transmembrane potentials, as suggested by Ling’s association-induction hypothesis. Instead, Tamagawa and Ike- da provide a refreshing reinterpretation of the electrical be- havior of biomembranes, which is based on ion adsorption. I consider their remarkable results an important progress in the interpretation of electrical membrane phenomena from a physical-chemistry perspective.

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