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      A note on the falsification of the ionic theory of hair cell transduction

      Communicative & Integrative Biology

      Taylor & Francis

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          Abstract

          A criticism of the paper, that I published in this journal, 1 which pointed out the contradiction between measured and theoretical hair reversal potential has validity and is addressed in this note. This paper, “Falsification of the ionic channel theory of hair cell transduction “applies the Nernst equation to hair cell measurements which deal with the movement of ions through the putative ‘transduction ion channel’. The Nernst equation applied to these measurements yielded a reversal potential that did not match the measured reversal potential. The criticism is that there is not only sodium on both sides of the cell membrane but there is also 140 mM of potassium inside the cell (Ki)while there is no potassium outside the cell (Ko). To take into account the presence more than one type of ion simultaneously traversing a ion channel the Nernst equation is not adequate. An expanded version of the Nernst equation the Goldman equation must be used. In the measurement by Corey and Hudspeth, 3 described above, the only ion available for transduction outside the cilia is 124 mM Na+. However inside the cell there is not only 12 mM Na+ but also 140 mM K+. In order to take into account the effect of both sodium and potassium ions passing in opposite directions through this proposed nonspecific ion channel we use an extension of the Nernst equation adapted for multiple ions which is the Goldman equation. A discussion of the Goldman equation can be found in Hill. 2 The Goldman equation gives us an expression for the reversal potential of a nonspecific ion channel. E r e v = R T Z F I n P N a N a o + P k K o P N a N a i + p k K i With only one permeable ion, E rev becomes the Nernst potential for that ion. With several permeable ions, E rev is a weighted mean of all the Nernst potentials.2 To solve this equation for zero reversal potential it is necessary to set the argument of the natural log function on the right side of the Goldman equation equal to 1. P N a N a o + P k K o P N a N a i + p k K i = 1 From Cory and Hudspeth 1 we get an estimate of the relative ion permeability of P Na = .9 and P k = 1 The ion concentrations: Nao = 129 mM; N ai = 12 mM; and k i = 140mM are known. The value of K 0 may therefore be solved for. The resulting value for the concentration of potassium outside the cell which is necessary to obtain a zero reversal potential is K 0 = 33 mM. But in this experiment there is no potassium in the external medium. This result reaffirms the “falsification of the ionic theory of hair cell transduction” that is developed in reference.1 Before embracing new satisfyingly simple theories, we would do well to keep in mind the observation made by Italio Calvino in 1943: “When a man cannot give clear form to his thinking, he expresses it in fables.”reference 4

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          The transduction channel of hair cells from the bull-frog characterized by noise analysis.

          Receptor currents in response to mechanical stimuli were recorded from hair cells in the excised epithelium of the bull-frog sacculus by the whole-cell, gigohm-seal voltage-clamp technique. The stimulus-dependent transduction current was separated from the cell's stimulus-independent K+ and Ca2+ currents; the K+ currents were blocked with an internal solution containing Cs+ while the Ca2+ current was reduced by holding the membrane potential below -70 mV. The temperature of the preparation was maintained at about 10 degrees C to slow the kinetics of the cells' transduction channels. Calibrated displacements of hair bundles of individual hair cells were made with a probe coupled by suction to the kinociliary bulb and moved with a piezoelectricbimorph stimulator. The root mean square noise of probe motion was less than 2 nm. The mean, I, and the variance, sigma 2, of the receptor current were measured from the response to saturating (+/- 0.5 micron) displacements of the hair bundle. I was corrected for current offsets and sigma 2 for the transduction-independent background variance. The relation between sigma 2 and I is consistent with the predictions of a two-conductance-state model of the transduction channel, a model having only one non-zero conductance state. The relation between sigma 2 and I was fitted by the equation sigma 2 = Ii-I2/N, where N is the number of transduction channels in the cell and i is the current through a single open channel. The conductance of the transduction channel is approximately ohmic with a reversal potential near 0 mV. The estimated conductance of a single transduction channel, gamma, is 12.7 +/- 2.7 pS (mean +/- S.D.; n = 18) at 10 degrees C. gamma is independent of the maximum transduction conductance of the cell, Gmax. The number of transduction channels, N, is proportional to Gmax. N ranges from 7 to 280 in cells with Gmax ranging from 0.08 to 2.48 nS. The largest values of N correspond to a few, perhaps four, active transduction channels per stereocilium. Control experiments show that transduction by the hair cell of two artifactual sources of hair-bundle stimulation, noisy or discontinuous motion of the probe, do not contribute substantially to the measured variance, sigma 2. Displacement-response curves are generally sigmoidal and symmetrical; they reasonably fit the predictions of a two-kinetic-state model, comprising one open state and one closed state. The estimated displacement-sensitive free energy, Z, is 5.7 +/- 1.1 kcal/mol micron (mean +/- S.D., n = 18).(ABSTRACT TRUNCATED AT 400 WORDS)
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            Falsification of the ionic channel theory of hair cell transduction

            The hair cell provides the transduction of mechanical vibrations in the balance and acoustic sense of all vertebrates that swim, walk, or fly. The current theory places hair cell transduction in a mechanically controlled ion channel. Although the theory of a mechanical input modulating the flow of ions through an ion pore has been a useful tool, it is falsified by experimental data in the literature and can be definitively falsified by a proposed experiment.
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              Author and article information

              Journal
              Commun Integr Biol
              Commun Integr Biol
              KCIB
              Communicative & Integrative Biology
              Taylor & Francis
              1942-0889
              Mar-Apr 2016
              15 December 2015
              15 December 2015
              : 9
              : 2
              Author notes
              CONTACT Michelangelo Rossetto marossetto@ 123456yahoo.com 125 W 86 Street, NY, New York, 10024, USA.
              Article
              1122144
              10.1080/19420889.2015.1122144
              4857787
              27195058
              © 2016 The Author(s). Published with license by Taylor & Francis Group, LLC

              This is an Open Access article distributed under the terms of the Creative Commons Attribution-Non-Commercial License http://creativecommons.org/licenses/by-nc/3.0/, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. The moral rights of the named author(s) have been asserted.

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              Molecular biology

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