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Hydrophobic Ion Hydration and the Magnitude of the Dipole Potential

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Hydrophobic Ion Hydration and the Magnitude of the Dipole Potential View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Biophysical Journal Volume 82 June 2002 3081–3088 3081 Hydrophobic Ion Hydration and the Magnitude of the Dipole Potential Jens Schamberger and Ronald J. Clarke School of Chemistry, University of Sydney, Sydney NSW 2006, Australia ABSTRACT The magnitude of the dipole potential of lipid membranes is often estimated from the difference in conductance between the hydrophobic ions, tetraphenylborate, and tetraphenylarsonium or tetraphenylphosphonium. The calculation is based on the tetraphenylarsonium-tetraphenylborate hypothesis that the magnitude of the hydration energies of the anions and cations are equal (i.e., charge independent), so that their different rates of transport across the membrane are solely due to differential interactions with the membrane phase. Here we investigate the validity of this assumption by quantum mechanical calculations of the hydration energies. Tetraphenylborate (⌬Ghydr ϭϪ168 kJ molϪ1) was found to have a significantly stronger interaction with water than either tetraphenylarsonium (⌬Ghydr ϭϪ145 kJ molϪ1) or tetraphenylphos- phonium (⌬Ghydr ϭϪ157 kJ molϪ1). Taking these differences into account, literature conductance data were recalculated to yield values of the dipole potential 57 to 119 mV more positive in the membrane interior than previous estimates. This may partly account for the discrepancy of at least 100 mV generally observed between dipole potential values calculated from lipid monolayers and those determined on bilayers. INTRODUCTION The extrathermodynamic TATB (tetraphenylarsonium tet- density, the solvation should closely resemble that of an raphenylborate) hypothesis, i.e., that the structurally very uncharged molecule of equal size and structure (e.g., tetra- similar hydrophobic ions tetraphenylarsonium (TPAϩ) and phenylmethane) and the sign of the charge should become tetraphenylborate (TPBϪ) (Fig. 1) have identical interaction irrelevant. According to Grunwald et al. (1960) this limiting energies with solvating water molecules, has found wide situation should already be reached by TPBϪ and TPPϩ application in physical chemistry and biophysics. In physi- with average ionic radii of 4.2 Å. cal chemistry it is often used as a basis for the calculation of A major reason for the importance of hydrophobic ions in thermodynamic properties of isolated ionic species, which membrane biophysics lies in the fact that the investigation are experimentally not directly accessible, e.g., free energies of their conductance across black lipid membranes led to the of hydration and free energies of transfer between different discovery of the membrane dipole potential (Liberman and solvents (Grunwald et al., 1960; Choux and Benoit, 1969; Topaly, 1969). The motive for their studies was to use Cox and Parker, 1973; Fawcett, 1993; Benko et al., 1996). hydrophobic ions as model systems for the carrier mecha- In membrane biophysics, the different degrees of interaction nism of ion transport. Surprisingly, however, they discov- of TPBϪ, TPAϩ, and TPPϩ with lipid membranes has been ered that the permeability of the membrane for TPBϪ was used to calculate the electrical dipole potential within the approximately 105 greater than that of TPPϩ. To explain membrane interface with the TATB hypothesis as an un- this difference in behavior they hypothesized that the inte- derlying assumption. rior of the membrane must initially be positively charged. A version of the TATB hypothesis was first proposed by Haydon and coworkers (Haydon and Myers, 1973; Hladky Grunwald et al. (1960), who used it to calculate the rate of and Haydon, 1973) later recognized that the positive charge change of the standard partial molar free energy with chang- within the membrane must arise from oriented molecular ing mole fraction of water for a variety of single anions and dipoles in the membrane surface and coined the term “di- cations. They reasoned that the symmetrically arranged pole potential.” phenyl residues around the central charged atom should act The absolute magnitude of the dipole potential has been as an insulating layer, protecting the charge from interaction estimated by a number of groups (Andersen and Fuchs, with surrounding solvent molecules. If the thickness of the 1975; Pickar and Benz, 1978; Flewelling and Hubbell, insulating layer were sufficiently large with the charge 1986; Gawrisch et al., 1992; Franklin and Cafiso, 1993) remaining buried at the center and very low surface charge Submitted November 8, 2001, and accepted for publication February 13, 2002. Jens Schamberger’s current address is Graffinity Pharmaceutical Design GmbH, Im Neuenheimer Feld 518-519, D-69120 Heidelberg, Germany. Address reprint requests to Dr. Ronald J. Clarke, School of Chemistry, University of Sydney, Sydney, NSW, 2006, Australia. Tel.: 61-2- 93514406; Fax: 61-2-93513329; E-mail: [email protected]. © 2002 by the Biophysical Society FIGURE 1 Structures of the hydrophobic ions, tetraphenylphosphonium 0006-3495/02/06/3081/08 $2.00 (TPPϩ), tetraphenylarsonium (TPAϩ), and tetraphenylborate (TPBϪ). 3082 Schamberger and Clarke from the magnitude of the relative conductivities of mem- surements of the dipole potential of lipid bilayers are TPBϪ branes for hydrophobic anions and cations as first observed and TPAϩ or TPPϩ. Rather than use rate constants as shown by Liberman and Topaly (1969). A high membrane conduc- in Eq. 3, it is, however, more usual to use the specific tance requires the hydrophobic ions to be able to move from conductances, g, in which case kϪ and kϩ must simply be one side of the membrane to the other. The membrane itself replaced in Eq. 3 by gϪ and gϩ. The application of Eq. 3 to can, therefore, be seen as an activation energy barrier for ion find an absolute value of the dipole potential requires that diffusion. Thus, we can define a rate constant for ion dif- ⌬ # Ϫ ϩ ϩ the values of Go for TPB and TPA or TPP are equal. fusion, k, which is related to the free energy of transfer of an As pointed out by several authors (Andersen and Fuchs, ⌬ # ion from the aqueous phase into the membrane, G , simply 1975; Pickar and Benz, 1978; Gawrisch et al., 1992), how- by the Arrhenius equation. The free energy of transfer of a ever, this assumption may be questionable. Even though the hydrophobic ion into the membrane is actually made up of hydrophobic anions, TPBϪ and TPAϩ, have almost identi- a number of individual free energy terms (Ketterer et al., # cal sizes, their values of ⌬G could differ, in particular, if 1971; Flewelling and Hubbell, 1986b; Benz, 1988): o their free energies of hydration are different, i.e., the TATB ⌬ # ϭ ⌬ # ϩ ⌬ # ϩ ⌬ # ϩ ⌬ # hypothesis is not valid. G GB GI GD GN (1) In fact, experimental evidence has been reported, which The individual contributions relate to the Born energy dif- suggests that the interactions of TPBϪ with water are sig- ⌬ # ϩ ϩ ference ( GB), due to the change in dielectric constant nificantly different from TPA and TPP . Different inter- between water and the membrane (Born, 1920), the image actions of solvent protons with the phenyl rings of TPBϪ ⌬ # ϩ ϩ energy contribution ( GI ), due to the polarization of water and both TPA and TPP have been reported by Coetzee molecules adjacent to the aqueous solution-membrane in- and Sharpe (1971). Differences in the interactions of water terface (Silver, 1985; Neumcke and La¨uger, 1969), the Ϫ ϩ ϩ molecules with TPB and either TPP or TPA have also dipole energy difference (⌬G# ), due to the interaction of the D been reported by Jo´zwiak and Taniewska-Osinska (1994), hydrophobic ion with the intrinsic dipole potential of the Stangret and Kamienska-Piotrowicz (1997), and Symons membrane (Flewelling and Hubbell, 1986), and the neutral ⌬ # (1999). From their measurements, Stangret and Kamienska- energy difference ( GN), which takes into account all in- teractions which a hypothetical neutral particle (generated Piotrowicz (1997) estimated that the interaction of water with TPBϪ could be up to 16 kJ molϪ1 stronger than that of by discharging the ion) would have with the aqueous phase ϩ and the membrane, e.g., van der Waals and steric interac- the interaction with TPP . tions. Now it is important to note that all of the energy terms Over the last decade major advances have been made except for the dipole energy contribution are independent of in the development of methods for quantum mechanical the sign of the charge of the ion. Eq. 1 can, therefore, be calculations on complex molecules (Frisch et al., 1998; simplified to: Barone and Cossi, 1998). The time is, therefore, ripe to carry out a theoretical analysis of the validity of the ⌬ # ϭ ⌬ # ϩ ⌿ G Go zF d (2) TATB hypothesis. The goals of the present paper are ⌬ # twofold: 1) calculate theoretically the free energies of in which Go includes all energy terms except for the Ϫ ϩ ϩ interaction of the hydrophobic ion with the dipole potential, hydration of TPB ,TPA , and TPP and 2) based on the ␺ calculated hydration energies, redetermine the magnitude d, in which z and F are the valence of the ion and Faraday’s constant, respectively. Now, if it is possible to find a hy- of the dipole potential. drophobic anion and a hydrophobic cation whose values of According to the quantum mechanical calculations it will ⌬ # be shown that previous estimates of the dipole potential of Go are identical, then the difference in their rate constants for ion diffusion would be solely due to the value of the lipid bilayers are likely to be significantly underestimated. dipole potential. Under these conditions, subtracting the relevant forms of the Arrhenius equation for an anion and a cation from one another and rearranging yields: THEORY RT kϪ If one does not accept the TATB hypothesis, one can write ⌿d ϭ ln (3) 2F kϩ a modified version of Eq. 2 for the free energy of transfer of a hydrophobic ion into the membrane: in which kϪ and kϩ are the rate constants for the transfer of the anion and the cation across the membrane, respec- ⌬ # ϭ ⌬ # Ϫ ⌬ ϩ ⌿ tively, R is the ideal gas constant, and T is the absolute G Go Ghyd zF d (4) temperature.
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