Berg, Howard Curtis

Biophysical Journal

Molecular and Cellular BiologyVersion of Recor

Berg, Howard

Harvard University - DASH

 Membrane Dipole Potentials  (Article begins on next page)The Harvard community has made this article openly available.Please share how this access benefits you. Your story matters.Citation Berg, H.C. 1968. “Membrane Dipole Potentials.” BiophysicalJournal 8 (9) (September): 1051–1053.Published Version doi:10.1016/S0006-3495(68)86538-5Accessed February 19, 2015 4:05:37 PM ESTCitable Link http://nrs.harvard.edu/urn-3:HUL.InstRepos:12220686Terms of Use This article was downloaded from Harvard University's DASHrepository, and is made available under the terms and conditionsapplicable to Other Posted Material, as set forth athttp://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAALETTERS TO THE EDITORMembrane Dipole PotentialsDear Sir:It is commonly assumed that a biological membrane is a simple dielectric, i.e., that theelectrical potential difference across it, V, is proportional to the charge on its surfaces, 4Q:V = 47rLQ/eA = QIC, (1)where L is the membrane thickness, e the dielectric constant, A the area, and C _ eA/47rLthe capacitance.This is not true if molecules with permanent electric dipole moments are embedded in themembrane, for then part of the volume polarization is independent of the macroscopicelectric field.' If the component of this part of the polarization normal to the surface of themembrane is P (positive in the direction +Q to -Q), then2V = 4rLQ/eA - 47rLP/e = (Q - PA)/C. (2)In the usual case a membrane of high specific resistance separates two solutions of lowspecific resistance. The equilibrium or steady-state electrical potential difference, V., isdetermined solely by the chemical potentials of the ions in the solutions (those to which themembrane is permeable) and by their transport numbers (3, 4). Ifions are able to move fromone side of the membrane to the other through a resistive pathway of resistance R, the sys-tem is electrically equivalent to the following circuit:C I FVPAA zero-impedance voltage source PA/C appears in series with the capacitor. The ion fluxchanges the charge on the capacitor, Q, and the potential across it, Q/C, but it does notchange P.If P is constant, V approaches V. exponentially with the time constant RC, just as in thecase ofthe simple dielectric, but Q approaches CV. + PA rather than CV. (5).If P changes gradually, the membrane behaves like a wax electret (6). Adams (7) andSwann (2, 8) have discussed this casefor the exponential decay P = Po exp (-t/r), where Pois the initial polarization, t is the time, and r is a decay constant. In the limit T >> RC, thepotential changes exponentially with the time constant RC from its initial value (whatever it1See the discussion ofelectric fields in matter given byPurcell (1).2If there are n molecules per unit volume with surface-normal dipole moments p, P = np. If thepolarization is not uniform, Pis the value averaged over the thickness ofthe membrane (reference 2).1051may be) to the value V. + PoARIT, and then it decays back to V, with the time constant r.The voltage offset PoAR/r is large only if the membrane is thick and has a high specific re-sistance.Beament (9) has generated offsets as large as 4 v by using an external battery to polarize a0.25 Acoating ofgrease onthe cuticle ofthe cockroach Periplaneta (T = 1.2 x 108 sec, RC =102 sec). The results of these "over-charge" experiments are consistent with the electrettheory if P0 is oforder 20 statcoulomb/cm2, a value which is not unreasonable.If P changes rapidly, so rapidly that the transient is complete in a time short compared toRC, the membrane potential follows the change in polarization, since Q remains constantduring this period of time. High-frequency components of P appear at the output of theequivalent circuit without appreciable attenuation or change in phase. Therefore, if somemechanism exists for driving P, the membrane can generate signals at a frequency largecompared to 1/27rRC.8An example is the early receptor potential ofthe eye observed in intraretinal recordings byBrown and Murakami (11) and in the electroretinogram by Cone (12). Rhodopsin is knownto be a major component of the membranes of the outer segment of the photoreceptors, tobe packed in an ordered fashion, and to undergo rapid isomerizations triggered by the ab-sorption of light. If the isomerizations change the component of the electric dipole momentofthe rhodopsin molecule normal to the plane ofthe membrane, then potential changes willbe generated. If P changes suddenly by an amount 5P, the potential willjump by an amountV = -OPAIC, and then it wil decay back to its equilibrium or steady-state value exponen-tially with thetime constant RC. IfNphotons are absorbed by area A ofmembrane andeachchanges the surface-normal dipole moment of a rhodopsin molecule by an amount 8p,V = -8pN/LC. For 8p = 1 Debye, N = 1018, L = 10-6 cm, and C = 1 LF, the potentialjump is 3.3 mv. The experimental evidence for a mechanism of this kind is now substantial(13, 14). My purpose here is to point out how the problem can be stated in terms of ele-mentary electric theory and to show how early receptor potentials are related to potentialsgenerated by certain electrets.This work was supported in part by USPHS Grant GM1'4423. Discussions with Alec Bangham, J.W. L. Beament, and R. A. Cone are gratefully acknowledged.Receivedforpublication 15 March 1968 and in revisedform 4 June 1968.HOWARD C. BERGDepartment of Biochemistry andMolecular BiologyHarvard UniversityCambridge, Massachusetts 02138REFERENCES1. PURCELL, E. M. 1965. Electricity and Magnetism. McGraw-Hill Book Co., New York. Chapter 9.2. SwANN, W. F. G. 1950. J. Franklin Inst. 250:219.3. CRAxFoRD, S. R., 0. GATrY, and ROTHSCHILD. 1938. Nature. 141:1(d8.8The only other way this can be done is to modulate C, e.g., by stretching the membrane (changingL and A); see Katz (10).1052 BIOPHYSICAL JouRNAL VOLUME 8 19684. DEAN, R. B., 0. GATry, andE. K. RmIEAL. 1940. Trans. FaradaySoc. 36:161.5. HEAVisDE, 0. 1892. Electrical Papers. Macmillan and Co., London, England. Vol. 1, p. 493.6. EGUCHI, M. 1925. Phil. Mag. Sixth Ser. 49:178.7. ADAMS, E. P. 1927. J. Franklin Inst. 204:469.8. SWANN, W. F. G. 1953. J. Franklin Inst. 255:513; 256:167.9. BEAMwNT, J. W. L. 1961. Nature. 191:217.10. KATZ, B. 1950. J. Physiol. (London). 111:261.11. BROWN, K. T., and M. MuRAKAMI. 1964. Nature. 201:626.12. CoNE, R. A. 1964. Nature. 204:736.13. CoNE, R. A. 1967. Science. 155:1128.14. HAGINS, W. A., and R. E. MCGAUGHY. 1968. Science. 159:213.LFITERS TO THE EDIToR 1053

Membrane Dipole Potentials

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Membrane Dipole Potentials

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