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Time resolved measurements of a single proton diffusing in the Gramicidin A channel
SOLID STATE
loHlcs
Solid State lonics 77 ( 1995) 79-83 EISEVIER
Time resolved measurements of a single proton diffusing in the Gramicidin A channel E. Nachliel, M. Gutman, L. Even Zohar LaserLaboratoryfor Fast
Reactions in Biology. Department of Biochemistry,
Tel Aviv University, Tel Aviv 69978, Israel
Abstract The stochastic motion of a single proton in the Gramicidin channel was measured in the time resolved domain. The results indicate that the diffusional mobility within the 4A diameter channel is very close to that of bulk water. Icqvwords: Gramicidin; Fast electric transient; Lipid bilayer; Proton diffusion
1. Introduction Gramicidin is a short peptide made of 15 alternating D and L amino acids. This sequence allows it to fold into a helix where all hydrophobic side chains are facing out while the peptide chain carbonyls form a narrow channel, 4A in diameter. A dimer of two Gramicidin molecules is long enough to form a channel, 28A in length, which crosses the width of a phospholipid, or biological, membrane. This artificial pore breaches the continuity of the membrane and ions, mostly H+, Kf and Na+ leak across the membrane. The resulting ion flux collapses the electrochemical proton potential ( ApH+ ) leading to a bactericidal effect. For this reason Gramicidin falls into the general group of antibiotic compounds. The ease of having a ready-made pore, which can be plugged into a membrane, made Gramicidin a favored model for the study of ion flux through biomembranes. Biophysical studies of the channel employed a variety of methods. Equilibrium binding using NMR methodologies [ 11, steady-state kinetics [ 21, molecular dynamics [3], and electrostatic modeling [4]. For a comprehensive review see Busath [ 51. 0167-2738/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDlO167-2738(94)00260-6
The passage of ions through Gramicidin were monitored by steady-state conductance, single channel conductance and noise analysis of a single channel. The results were interpreted according to a model assuming that the channel offers to the moving ion a set of energy barrier and binding sites. The analysis of the results was attained by varying the rate of the reactions and the height of the barrier to fit the predicted rates with the measured ones. Ion flux experiments are usually carried out under the influence of external driving force, be it either concentration gradient of the diffusing cation or an electric field. Both parameters affect the flux in a non-linear mode. The binding of the cation to the channel corresponds with two sites, having high and low affinity, where sites on one face affect those on the opposite side of the membrane [ 61. In a similar way the dependence of flux on the electric field is not precisely linear [ 2,7] and is described by expansion of the appropriate equation of the potential field within the channel as perturbed by the external field [3]. Thus, in order to improve understanding of the mechanism of ion flux within the channel, it is of advantage to gain timeresolved measurements under vanishing external force,
E. Nachfief et af. /Solid State Ionics 77 (1995) 79-83
80
i.e. to follow the stochastic motion of a charge within the channel. The experiment described below demonstrates the feasibility of such measurements and provides a detailed analysis of a single proton diffusion within the channel under no external force. The technique used for this purpose is the laser-induced proton pulse as implemented for selective pulse acidification of one side of a phospholipid membrane [ 8,9]. A black lipid membrane, made of two monomolecular layers of phosphoiipids is built upon a small pore (1 mm in diameter) (see Scheme I) and pyranine (+GH, 8hydroxypyrene-1, 3, 6-trisulfonate) is added on the back compartment. A UV laser pulse is irradiating the unstirred layer, exciting the pyranine to its first electronic singlet state (@H*) . In the excited state pyranine is a strong acid (pK* = 1.4) and massive dissociation takes place, releasing some 10-30 PM H+ within few ns. The binding of protons to the membrane causes a capacitance current to flow within the measuring circuit, which is digitized, averaged and analyzed
f&9]. In the present study we impregnated the membrane with Gramicidin and looked for the electric signal corresponding with the transmembranal motion of the protonic charge. While, in principle, the experiment is a straightforward one, there are some inherent complications which must be stressed. Pyranine, inspite of its three sulfonoanions has an appreciable tendency to adsorb on uncharged phospholipid membrane, and ionization of membrane-bound dye drives large capacitance current which complicates the analysis of the results. For this reason we added negatively charged phospholipid (phosphatidyl serine) to the membrane, which repels
the dye. The abundant phosphatidyl serine affects also the proton distribution in the aqueous phase with subsequent stabilization of the proton binding to the Gramicidin’s cation binding site [ IO]. Thus, our boundary conditions consist of Gramicidin A channels, spanning a negatively charged membrane, where one side of the membrane is temporarily perturbed by a brief proton pulse. The selective acidification on one side causes some protons to diffuse, by random walk to the other face, and the experimental signal records both the forward passage of the proton and their subsequent back flux till the prepulse equilibrium is re-established. The rate constants of the proton flux are rigorously analyzed and its magnitude is discussed with respect to diffusion controlled reactions and the height of energy barriers.
2. Materials and methods The black lipid membrane was made of phosphatidyl cholin and phosphatidyl serine both obtained from Avanti polar lipid. Pyranine (%hydroxypyrene- 1,3,6trisulfonate) was by Eastman Kodak. Gramicidin A was obtained from Sigma. The observation cell, shown in Scheme I was filled with conducting electrolyte
*DO- t H+ o @OH *PS- + H+ c) PSH G + H+ c> GH
PSH-G
ts
GH+ +PS
‘PSH + U’O- c> PS- + @OH GH++@Ot> G + @OH
I
GH
=GH *PS-+H+oPSH G+H+ c, GH+ PSH+G o GH++PS-
Lipid bkoyer membrane Scheme I.
L
-
*known rateconstants Scheme II.
R
E. Nachliel et al. /Solid State Ionics 77 (1995) 79-83
(O.lM choline chloride) plus 50 PM MES buffer pH 5.3. The black lipid membrane was formed by application of 5 ~1 of 0.15% solution of the lipids dissolved in Decane. The electric signals were monitored by a current-voltage amplifier made at the electronic shop of the School of Chemistry, Tel Aviv University. The response time of the measuring circuit, determined by the resistance of the electrolyte, amplifier impedance and the membrane’s capacitance was 2 pus. For this reason we made no attempt to simulate the first 4 ps of the observed signals. The excitation of the dye was attained by a 337.4 nm pulse of a Nitrogen Laser operating at 0.2 Hz with output of 0.25 mJ/pulse. The beam was focused at the center of the membrane without irradiating the lipid torus around the membrane. The numeric simulation of the transients is based on a set of coupled non linear differential rate equations which correspond with a pulse perturbation of the equilibria detailed in Scheme II. The computer program upset the equilibrium of reaction 1 (see Scheme II) by
-0.15 0
81
a predetermined delta function, and propagated the effect to all other reactants according to the (adjustable) rate constant. The summation of charge-incremental rates (CQldt) between the two faces of the membrane corresponds with the measured current signal. The adjustable parameters are systematically varied to obtain an overlap of the theoretical curve on the experimental trace. The program and differential equations are available upon request.
3. Results and discussion 3.1. Experimental observation Pulse protonation of a black lipid membrane generates a transient capacitance current [ 81 as seen in curve A of Fig. 1. Addition of Gramicidin A, which lets some of the proton diffuse across the membrane, does not change much the shape of the current transient (curve B ), yet the amplitude is consistently smaller. The dif-
I
I
30.
60. IJS
Fig. 1. Time resolved capacitance current associated with selective protonation of one side of a black lipid membrane. The membrane was built over a 1 mm pore separating two compartments containing 0.1 M cholin chloride, 50 FM MES buffer pH = 5.3 (see Scheme I). The back side compartment was supplemented by 400 PM pyranine. The dye was excited by a series of laser pulses (337.4 nm 1 ns FWHM, 250 ~/pulse at 0.2 Hz) focused on the center of the membrane. The resulting capacitance current, flowing through the measuring circuit was picked by black Pt electrodes (shielded from light) and amplified by a current voltage converter (10’ V/A). The signals were averaged for 256 pulses. Curve A was measured in the absence of Gramicidin. Curve B was measured 20 min after addition of lo-* M Gramicidin A to each side of the membrane. Curve C is the difference between the two, i.e. B-A. The smooth line superpositioned over curve C is a theoretical fit of the signal using the procedure detailed in the text. The rate constants used for the tit am given in Table 1 and the reactions are detailed in Scheme II.
82
E. Nachtietet al. /Solid State Ionics 77 (1995) 79-83
ference between the two transients, curve C, is the signal emerging from the translocation of protons through the membrane via the Gramicidin channels. 3.2. Mode of analysis The signal, as measured, suggests a fast transient of protons yet its quantitation calls for a numerical reconstruction of the chemical reactions which proceed on both sides of the membrane plus the flux across it. These reactions are detailed in Scheme II. The scheme describes the chemical reactions proceeding on the pyranine containing face of the membrane (upper-left side reaction in the scheme), passage of proton across the membrane, and those taking place on the other face of the membrane (bottom-right side of the scheme). On each side we defined the reversible protonation of the phosphoserine head groups (PS) , the reversible protonation of Gramicidin (G) and proton exchange between PSH and Gramicidin. The passage of proton from one side to another is given by GH(,, +GH,,, reaction where, in the absence of external electric field, the forward and backward rates are identical. On the pyranine containing side of the membrane we also consider the reversible protonation of the dye as well as the reaction of @- with either PSH or GH. All these equilibria had been converted into a set of coupled non-linear differential rate equations which upon integration recreate the observed current transient [ 91. The simulated dynamics appears as the continuous smooth curve super-positioned over curve C in Fig. 1. The analysis, as demonstrated in Fig. 1, has been carried out for 15 independent experiments, using varying Gramicidin A concentrations. As seen in Table 1 all signals were reconstructed with a single set of rate constants. 3.3. Evaluation of rate constants The rate of proton binding to Gramicidin A, 1.5 X 10” M-l s-‘, is compatible with a diffusion controlled reaction. This value indicates that between the bulk and the proton binding site there is no appreciable energy barrier. The rate at which +O- abstructs proton from GH+ (1.75 X lo9 M-’ s-‘) also corroborate the exposed position of the proton binding site.
Table 1 The rate constants characterizing the proton passage across Gramacidin channels imbedded in phosphatidyl cholin/phosphatidyl serine black lipid membrane Reaction
Rate constant
+O- +H+ PS+H+ PSH+ 40G+H+ G+PSH GH’ t&OGH+ =GHa PK 9GH pK PSH pK GH+
M-1 s-I 5x101°a M-l s-I 1 x 10’0= 1x109= M-Is-’ M-I s-I 1.50*0.05x 10’0 M-I s-I 1.00+0.10x 10’0 M-l s-* 1.75f 0.05 x lo9 6.50*0.50x 10“ SK’ 7.50 = 4.60 ’ 5.35 * 0.05
a These values were determined independently. See Refs. [ 8,111.
The passage of protons across the channel, under no external field, corresponds with a first passage time of T= k - ’ = 1.5 ps. This time constant can be treated as a sum of two processes. One is the diffusional time (7d) while the other is the passage of the protonic charge over the energy barrier ( 7t)). r=Td+Tb. The potential energy barrier is basically the Born Energy associated with the propagation of the charge into the low dielectric medium, which is further attenuated by the dipole of the carbonyls in the channel 14,121. Assuming that the diffusivity of proton within the channel is similar to that in bulk water, than the diffusion time through the length (L) of the channel is given by 7d = L2/2D = 0.3 ns. Under these assumptions we estimate the energy barrier to be E= - kTln XI/ 7b= 6.5 Kcal/mol, which is in accord with values derived by theoretical considerations [ 3,4,13]. Consequently we conclude that the diffusivity of the proton within the channel is very close to that in bulk water and the main delay is due to the enhanced electrostatic potential built up as the proton penetrates the channel into the low dielectric matter of the membrane. Once we deduced that the diffusivity has a minor effect on the mobility of proton we can extrapolate the rate we measured at AV=O into higher potential gradient (k= b exp( QAVlkT)) [ 141 and project, for AV=2CQmV, apassagerateof 2X 10’s_‘. This value is comparable with that rep&ted by Heineman and Sigworth [ 71.
E. Nachliel et al. /Solid State lonics 77 (1995) 79-B
83
3.4. DifSusion of proton in a singlefile water molecule
References
The aqueous phase within Gramicidin channel constitutes a single file of water molecules protruding the low dielectric matter of the membrane which is surrounded by the carbonyls of the peptide backbone. Our data indicate that protons can diffuse in this special environment with a diffusion coefficient comparable to that of bulk water. Similar measurements of proton diffusion in microscopic space like the 10-20 A deep water layer between phospholipid membranes [ 151 or in the Heme binding site of apomyoglobin [ 161 yielded comparable diffusion coefficient. Thus we conclude that even under the restricted motion by the surrounding dipoles of the carbonyls a single file of water molecules still retains its liquid-like mobility and rotational freedom.
[ 1I J.F. Hinton, J.Q. Femandes, D.C. Shingu, W.L. Whaley, R.E. Koppe and F.S. Millet, Biophys. J. 54 ( 1988) 527. [2] M. Akeson and D.W. Deamer, Biophys. J. 60 ( 1991) 101. [ 3 I B. Roux and M. Karplus, Biophys. J. 59 ( 1991) 96 1. [41 M. Sancho and G. Martinez, Biophys. J. 60 (1991) 81. [5] D. Busath, Annu. Rev. Physiol. 55 (1993) 473. [6] D.W. Urry, K.U. Prasad and T.L. Trapon, Proc. Natl. Acad. Sci., USA. 79 ( 1982) 390. 171 S.H. Heineman andF.J. Sigworth,Biochim. Biophys. Acta (1989) 8. [8] M. Gutman, E. Nachliel, E. Bamberg and B. Christensen, Biochim. Biophys. Acta 905 ( 1987) 390. 191 M. Gutman and E. Nachliel, Electrochim. Acta 34 (1984) 1801. [ 101 H.J. Apel1.E. Bambergand P. Longer, B&him. Biophys. Acta 553 (1979) 369. [ 1I] M. Gutman and E. Nachliel, B&him. Biophys. Acta 1015 (1990) 391. [ 121 M.B. Pattenski and P.C. Jordan, J. Phys. Chem. 96 (1992) 3906. [ 131 J. Aquist and A. Warshel, Biophys. J. 56 (1989) 171. [ 141 A. Finkelstein and OS. Anderson, J. Membrane Biol. 59 (1981) 155. [ 151 M. Gutman, E. Nachliel and S. Kiryati, S. Biophys. J. 63 (1992) 281. [ 161 E. Shimoni, Y. Tsfadia, E. Nachliel and M. Gutman, Biophys. J. 64 (1993) 472.
Acknowledgement
This research is supported by the office of naval research NOOO14-940533 and the U.S.-Israel Binational Science Foundation 91/00226. The authors are grateful to Dr. P. Jordan for stimulating discussion.
loHlcs
Solid State lonics 77 ( 1995) 79-83 EISEVIER
Time resolved measurements of a single proton diffusing in the Gramicidin A channel E. Nachliel, M. Gutman, L. Even Zohar LaserLaboratoryfor Fast
Reactions in Biology. Department of Biochemistry,
Tel Aviv University, Tel Aviv 69978, Israel
Abstract The stochastic motion of a single proton in the Gramicidin channel was measured in the time resolved domain. The results indicate that the diffusional mobility within the 4A diameter channel is very close to that of bulk water. Icqvwords: Gramicidin; Fast electric transient; Lipid bilayer; Proton diffusion
1. Introduction Gramicidin is a short peptide made of 15 alternating D and L amino acids. This sequence allows it to fold into a helix where all hydrophobic side chains are facing out while the peptide chain carbonyls form a narrow channel, 4A in diameter. A dimer of two Gramicidin molecules is long enough to form a channel, 28A in length, which crosses the width of a phospholipid, or biological, membrane. This artificial pore breaches the continuity of the membrane and ions, mostly H+, Kf and Na+ leak across the membrane. The resulting ion flux collapses the electrochemical proton potential ( ApH+ ) leading to a bactericidal effect. For this reason Gramicidin falls into the general group of antibiotic compounds. The ease of having a ready-made pore, which can be plugged into a membrane, made Gramicidin a favored model for the study of ion flux through biomembranes. Biophysical studies of the channel employed a variety of methods. Equilibrium binding using NMR methodologies [ 11, steady-state kinetics [ 21, molecular dynamics [3], and electrostatic modeling [4]. For a comprehensive review see Busath [ 51. 0167-2738/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDlO167-2738(94)00260-6
The passage of ions through Gramicidin were monitored by steady-state conductance, single channel conductance and noise analysis of a single channel. The results were interpreted according to a model assuming that the channel offers to the moving ion a set of energy barrier and binding sites. The analysis of the results was attained by varying the rate of the reactions and the height of the barrier to fit the predicted rates with the measured ones. Ion flux experiments are usually carried out under the influence of external driving force, be it either concentration gradient of the diffusing cation or an electric field. Both parameters affect the flux in a non-linear mode. The binding of the cation to the channel corresponds with two sites, having high and low affinity, where sites on one face affect those on the opposite side of the membrane [ 61. In a similar way the dependence of flux on the electric field is not precisely linear [ 2,7] and is described by expansion of the appropriate equation of the potential field within the channel as perturbed by the external field [3]. Thus, in order to improve understanding of the mechanism of ion flux within the channel, it is of advantage to gain timeresolved measurements under vanishing external force,
E. Nachfief et af. /Solid State Ionics 77 (1995) 79-83
80
i.e. to follow the stochastic motion of a charge within the channel. The experiment described below demonstrates the feasibility of such measurements and provides a detailed analysis of a single proton diffusion within the channel under no external force. The technique used for this purpose is the laser-induced proton pulse as implemented for selective pulse acidification of one side of a phospholipid membrane [ 8,9]. A black lipid membrane, made of two monomolecular layers of phosphoiipids is built upon a small pore (1 mm in diameter) (see Scheme I) and pyranine (+GH, 8hydroxypyrene-1, 3, 6-trisulfonate) is added on the back compartment. A UV laser pulse is irradiating the unstirred layer, exciting the pyranine to its first electronic singlet state (@H*) . In the excited state pyranine is a strong acid (pK* = 1.4) and massive dissociation takes place, releasing some 10-30 PM H+ within few ns. The binding of protons to the membrane causes a capacitance current to flow within the measuring circuit, which is digitized, averaged and analyzed
f&9]. In the present study we impregnated the membrane with Gramicidin and looked for the electric signal corresponding with the transmembranal motion of the protonic charge. While, in principle, the experiment is a straightforward one, there are some inherent complications which must be stressed. Pyranine, inspite of its three sulfonoanions has an appreciable tendency to adsorb on uncharged phospholipid membrane, and ionization of membrane-bound dye drives large capacitance current which complicates the analysis of the results. For this reason we added negatively charged phospholipid (phosphatidyl serine) to the membrane, which repels
the dye. The abundant phosphatidyl serine affects also the proton distribution in the aqueous phase with subsequent stabilization of the proton binding to the Gramicidin’s cation binding site [ IO]. Thus, our boundary conditions consist of Gramicidin A channels, spanning a negatively charged membrane, where one side of the membrane is temporarily perturbed by a brief proton pulse. The selective acidification on one side causes some protons to diffuse, by random walk to the other face, and the experimental signal records both the forward passage of the proton and their subsequent back flux till the prepulse equilibrium is re-established. The rate constants of the proton flux are rigorously analyzed and its magnitude is discussed with respect to diffusion controlled reactions and the height of energy barriers.
2. Materials and methods The black lipid membrane was made of phosphatidyl cholin and phosphatidyl serine both obtained from Avanti polar lipid. Pyranine (%hydroxypyrene- 1,3,6trisulfonate) was by Eastman Kodak. Gramicidin A was obtained from Sigma. The observation cell, shown in Scheme I was filled with conducting electrolyte
*DO- t H+ o @OH *PS- + H+ c) PSH G + H+ c> GH
PSH-G
ts
GH+ +PS
‘PSH + U’O- c> PS- + @OH GH++@Ot> G + @OH
I
GH
=GH *PS-+H+oPSH G+H+ c, GH+ PSH+G o GH++PS-
Lipid bkoyer membrane Scheme I.
L
-
*known rateconstants Scheme II.
R
E. Nachliel et al. /Solid State Ionics 77 (1995) 79-83
(O.lM choline chloride) plus 50 PM MES buffer pH 5.3. The black lipid membrane was formed by application of 5 ~1 of 0.15% solution of the lipids dissolved in Decane. The electric signals were monitored by a current-voltage amplifier made at the electronic shop of the School of Chemistry, Tel Aviv University. The response time of the measuring circuit, determined by the resistance of the electrolyte, amplifier impedance and the membrane’s capacitance was 2 pus. For this reason we made no attempt to simulate the first 4 ps of the observed signals. The excitation of the dye was attained by a 337.4 nm pulse of a Nitrogen Laser operating at 0.2 Hz with output of 0.25 mJ/pulse. The beam was focused at the center of the membrane without irradiating the lipid torus around the membrane. The numeric simulation of the transients is based on a set of coupled non linear differential rate equations which correspond with a pulse perturbation of the equilibria detailed in Scheme II. The computer program upset the equilibrium of reaction 1 (see Scheme II) by
-0.15 0
81
a predetermined delta function, and propagated the effect to all other reactants according to the (adjustable) rate constant. The summation of charge-incremental rates (CQldt) between the two faces of the membrane corresponds with the measured current signal. The adjustable parameters are systematically varied to obtain an overlap of the theoretical curve on the experimental trace. The program and differential equations are available upon request.
3. Results and discussion 3.1. Experimental observation Pulse protonation of a black lipid membrane generates a transient capacitance current [ 81 as seen in curve A of Fig. 1. Addition of Gramicidin A, which lets some of the proton diffuse across the membrane, does not change much the shape of the current transient (curve B ), yet the amplitude is consistently smaller. The dif-
I
I
30.
60. IJS
Fig. 1. Time resolved capacitance current associated with selective protonation of one side of a black lipid membrane. The membrane was built over a 1 mm pore separating two compartments containing 0.1 M cholin chloride, 50 FM MES buffer pH = 5.3 (see Scheme I). The back side compartment was supplemented by 400 PM pyranine. The dye was excited by a series of laser pulses (337.4 nm 1 ns FWHM, 250 ~/pulse at 0.2 Hz) focused on the center of the membrane. The resulting capacitance current, flowing through the measuring circuit was picked by black Pt electrodes (shielded from light) and amplified by a current voltage converter (10’ V/A). The signals were averaged for 256 pulses. Curve A was measured in the absence of Gramicidin. Curve B was measured 20 min after addition of lo-* M Gramicidin A to each side of the membrane. Curve C is the difference between the two, i.e. B-A. The smooth line superpositioned over curve C is a theoretical fit of the signal using the procedure detailed in the text. The rate constants used for the tit am given in Table 1 and the reactions are detailed in Scheme II.
82
E. Nachtietet al. /Solid State Ionics 77 (1995) 79-83
ference between the two transients, curve C, is the signal emerging from the translocation of protons through the membrane via the Gramicidin channels. 3.2. Mode of analysis The signal, as measured, suggests a fast transient of protons yet its quantitation calls for a numerical reconstruction of the chemical reactions which proceed on both sides of the membrane plus the flux across it. These reactions are detailed in Scheme II. The scheme describes the chemical reactions proceeding on the pyranine containing face of the membrane (upper-left side reaction in the scheme), passage of proton across the membrane, and those taking place on the other face of the membrane (bottom-right side of the scheme). On each side we defined the reversible protonation of the phosphoserine head groups (PS) , the reversible protonation of Gramicidin (G) and proton exchange between PSH and Gramicidin. The passage of proton from one side to another is given by GH(,, +GH,,, reaction where, in the absence of external electric field, the forward and backward rates are identical. On the pyranine containing side of the membrane we also consider the reversible protonation of the dye as well as the reaction of @- with either PSH or GH. All these equilibria had been converted into a set of coupled non-linear differential rate equations which upon integration recreate the observed current transient [ 91. The simulated dynamics appears as the continuous smooth curve super-positioned over curve C in Fig. 1. The analysis, as demonstrated in Fig. 1, has been carried out for 15 independent experiments, using varying Gramicidin A concentrations. As seen in Table 1 all signals were reconstructed with a single set of rate constants. 3.3. Evaluation of rate constants The rate of proton binding to Gramicidin A, 1.5 X 10” M-l s-‘, is compatible with a diffusion controlled reaction. This value indicates that between the bulk and the proton binding site there is no appreciable energy barrier. The rate at which +O- abstructs proton from GH+ (1.75 X lo9 M-’ s-‘) also corroborate the exposed position of the proton binding site.
Table 1 The rate constants characterizing the proton passage across Gramacidin channels imbedded in phosphatidyl cholin/phosphatidyl serine black lipid membrane Reaction
Rate constant
+O- +H+ PS+H+ PSH+ 40G+H+ G+PSH GH’ t&OGH+ =GHa PK 9GH pK PSH pK GH+
M-1 s-I 5x101°a M-l s-I 1 x 10’0= 1x109= M-Is-’ M-I s-I 1.50*0.05x 10’0 M-I s-I 1.00+0.10x 10’0 M-l s-* 1.75f 0.05 x lo9 6.50*0.50x 10“ SK’ 7.50 = 4.60 ’ 5.35 * 0.05
a These values were determined independently. See Refs. [ 8,111.
The passage of protons across the channel, under no external field, corresponds with a first passage time of T= k - ’ = 1.5 ps. This time constant can be treated as a sum of two processes. One is the diffusional time (7d) while the other is the passage of the protonic charge over the energy barrier ( 7t)). r=Td+Tb. The potential energy barrier is basically the Born Energy associated with the propagation of the charge into the low dielectric medium, which is further attenuated by the dipole of the carbonyls in the channel 14,121. Assuming that the diffusivity of proton within the channel is similar to that in bulk water, than the diffusion time through the length (L) of the channel is given by 7d = L2/2D = 0.3 ns. Under these assumptions we estimate the energy barrier to be E= - kTln XI/ 7b= 6.5 Kcal/mol, which is in accord with values derived by theoretical considerations [ 3,4,13]. Consequently we conclude that the diffusivity of the proton within the channel is very close to that in bulk water and the main delay is due to the enhanced electrostatic potential built up as the proton penetrates the channel into the low dielectric matter of the membrane. Once we deduced that the diffusivity has a minor effect on the mobility of proton we can extrapolate the rate we measured at AV=O into higher potential gradient (k= b exp( QAVlkT)) [ 141 and project, for AV=2CQmV, apassagerateof 2X 10’s_‘. This value is comparable with that rep&ted by Heineman and Sigworth [ 71.
E. Nachliel et al. /Solid State lonics 77 (1995) 79-B
83
3.4. DifSusion of proton in a singlefile water molecule
References
The aqueous phase within Gramicidin channel constitutes a single file of water molecules protruding the low dielectric matter of the membrane which is surrounded by the carbonyls of the peptide backbone. Our data indicate that protons can diffuse in this special environment with a diffusion coefficient comparable to that of bulk water. Similar measurements of proton diffusion in microscopic space like the 10-20 A deep water layer between phospholipid membranes [ 151 or in the Heme binding site of apomyoglobin [ 161 yielded comparable diffusion coefficient. Thus we conclude that even under the restricted motion by the surrounding dipoles of the carbonyls a single file of water molecules still retains its liquid-like mobility and rotational freedom.
[ 1I J.F. Hinton, J.Q. Femandes, D.C. Shingu, W.L. Whaley, R.E. Koppe and F.S. Millet, Biophys. J. 54 ( 1988) 527. [2] M. Akeson and D.W. Deamer, Biophys. J. 60 ( 1991) 101. [ 3 I B. Roux and M. Karplus, Biophys. J. 59 ( 1991) 96 1. [41 M. Sancho and G. Martinez, Biophys. J. 60 (1991) 81. [5] D. Busath, Annu. Rev. Physiol. 55 (1993) 473. [6] D.W. Urry, K.U. Prasad and T.L. Trapon, Proc. Natl. Acad. Sci., USA. 79 ( 1982) 390. 171 S.H. Heineman andF.J. Sigworth,Biochim. Biophys. Acta (1989) 8. [8] M. Gutman, E. Nachliel, E. Bamberg and B. Christensen, Biochim. Biophys. Acta 905 ( 1987) 390. 191 M. Gutman and E. Nachliel, Electrochim. Acta 34 (1984) 1801. [ 101 H.J. Apel1.E. Bambergand P. Longer, B&him. Biophys. Acta 553 (1979) 369. [ 1I] M. Gutman and E. Nachliel, B&him. Biophys. Acta 1015 (1990) 391. [ 121 M.B. Pattenski and P.C. Jordan, J. Phys. Chem. 96 (1992) 3906. [ 131 J. Aquist and A. Warshel, Biophys. J. 56 (1989) 171. [ 141 A. Finkelstein and OS. Anderson, J. Membrane Biol. 59 (1981) 155. [ 151 M. Gutman, E. Nachliel and S. Kiryati, S. Biophys. J. 63 (1992) 281. [ 161 E. Shimoni, Y. Tsfadia, E. Nachliel and M. Gutman, Biophys. J. 64 (1993) 472.
Acknowledgement
This research is supported by the office of naval research NOOO14-940533 and the U.S.-Israel Binational Science Foundation 91/00226. The authors are grateful to Dr. P. Jordan for stimulating discussion.