8
Corrections BIOPHYSICS AND COMPUTATIONAL BIOLOGY, CHEMISTRY Correction for Protons migrate along interfacial water without signicant contributions from jumps between ionizable groups on the membrane surface,by Andreas Springer, Volker Hagen, Dmitry A. Cherepanov, Yuri N. Antonenko, and Peter Pohl, which appeared in issue 35, August 30, 2011, of Proc Natl Acad Sci USA (108:1446114466; rst published August 22, 2011; 10.1073/ pnas.1107476108). The authors note that Fig. 2 appeared incorrectly. The cor- rected gure and its legend appear below. This error does not affect the conclusions of the article. www.pnas.org/cgi/doi/10.1073/pnas.1115664108 GENETICS Correction for The naïve airway hyperresponsiveness of the A/J mouse is Kit-mediated,by Emily Cozzi, Kate G. Ackerman, Anders Lundequist, Jeffrey M. Drazen, Joshua A. Boyce, and David R. Beier, which appeared in issue 31, August 2, 2011, of Proc Natl Acad Sci USA (108:1278712792; rst published July 18, 2011; 10.1073/pnas.1106582108). The authors note that Fig. 1 appeared incorrectly. The cor- rected gure and its corresponding legend appear below. This error does not affect the conclusions of the article. www.pnas.org/cgi/doi/10.1073/pnas.1115306108 time (s) 1 2 3 F ( %) 70 80 90 100 PC PE GMO Fig. 2. Kinetics of uorescence changes on top of three different lipid bi- layers due to lateral proton migration. The observation area was located at a distance of 70 μm from the area of proton release. Because all FPE molecules are surrounded by DPhPC or DPhPE molecules, they are anticipated to accept protons, which are released from these molecules. GMO does not possess ionizable moieties so that in case of two-dimensional diffusion, proton re- lease from one FPE molecule seems to be required before the next FPE molecule may pick up the proton. Despite the huge differences in proton release rates from the different lipids, τ max for all three lipid bilayers was similar. That is, lateral proton diffusivity is independent of the choice of the lipid. The buffer contained 0.1 mM Capso (pH 9.0) and 100 mM NaCl. Fig. 1. Genetic depletion of tissue MC in congenic A/J × B6 F1 Wv/Wv mice abrogates AHR. B6 Wv/+ were crossed with A/J mice to create F1 Wv/+ progeny. The F1 Wv/+ mice were then backcrossed to A/J mice for 10 generations, cre- ating A/J N10 Wv/+ mice. These were then crossed to B6 Wv/+ mice to create F1 wildtype and F1 Wv/Wv mice for study. A/J mice had an increased airway re- sistance compared to B6 mice, and F1 mice had a naïve AHR phenotype equivalent to their parental A/J strain. F1 Wv/Wv mice displayed an airway resistance similar to normoresponsive B6 mice. Values represent mean ± SE, n = at least 10 in each group. www.pnas.org PNAS | November 1, 2011 | vol. 108 | no. 44 | 1818518186 CORRECTIONS Downloaded by guest on September 26, 2020 Downloaded by guest on September 26, 2020 Downloaded by guest on September 26, 2020 Downloaded by guest on September 26, 2020 Downloaded by guest on September 26, 2020 Downloaded by guest on September 26, 2020 Downloaded by guest on September 26, 2020 Downloaded by guest on September 26, 2020

Protons migrate along interfacial water without ... · Physical Chemistry and Electrochemistry, Moscow, Russia; and dBelozersky Institute of Physico-Chemical Biology, Moscow, Russia

  • Upload
    others

  • View
    9

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Protons migrate along interfacial water without ... · Physical Chemistry and Electrochemistry, Moscow, Russia; and dBelozersky Institute of Physico-Chemical Biology, Moscow, Russia

Corrections

BIOPHYSICS AND COMPUTATIONAL BIOLOGY, CHEMISTRYCorrection for “Protons migrate along interfacial water withoutsignificant contributions from jumps between ionizable groupson the membrane surface,” by Andreas Springer, Volker Hagen,Dmitry A. Cherepanov, Yuri N. Antonenko, and Peter Pohl,which appeared in issue 35, August 30, 2011, of Proc Natl Acad SciUSA (108:14461–14466; first published August 22, 2011; 10.1073/pnas.1107476108).The authors note that Fig. 2 appeared incorrectly. The cor-

rected figure and its legend appear below. This error does notaffect the conclusions of the article.

www.pnas.org/cgi/doi/10.1073/pnas.1115664108

GENETICSCorrection for “The naïve airway hyperresponsiveness of the A/Jmouse is Kit-mediated,” by Emily Cozzi, Kate G. Ackerman,Anders Lundequist, Jeffrey M. Drazen, Joshua A. Boyce, andDavid R. Beier, which appeared in issue 31, August 2, 2011, ofProc Natl Acad Sci USA (108:12787–12792; first published July18, 2011; 10.1073/pnas.1106582108).The authors note that Fig. 1 appeared incorrectly. The cor-

rected figure and its corresponding legend appear below. Thiserror does not affect the conclusions of the article.

www.pnas.org/cgi/doi/10.1073/pnas.1115306108

time (s)

1 2 3

F ( %

)

70

80

90

100

PCPEGMO

Fig. 2. Kinetics of fluorescence changes on top of three different lipid bi-layers due to lateral proton migration. The observation area was located at adistance of 70 μm from the area of proton release. Because all FPE moleculesare surrounded by DPhPC or DPhPE molecules, they are anticipated to acceptprotons, which are released from these molecules. GMO does not possessionizable moieties so that in case of two-dimensional diffusion, proton re-lease from one FPE molecule seems to be required before the next FPEmolecule may pick up the proton. Despite the huge differences in protonrelease rates from the different lipids, τmax for all three lipid bilayers wassimilar. That is, lateral proton diffusivity is independent of the choice of thelipid. The buffer contained 0.1 mM Capso (pH 9.0) and 100 mM NaCl.

Fig. 1. Genetic depletion of tissue MC in congenic A/J × B6 F1Wv/Wv miceabrogates AHR. B6Wv/+ were crossed with A/J mice to create F1Wv/+ progeny.The F1Wv/+ mice were then backcrossed to A/J mice for 10 generations, cre-ating A/J N10Wv/+ mice. These were then crossed to B6Wv/+ mice to create F1wildtype and F1Wv/Wv mice for study. A/J mice had an increased airway re-sistance compared to B6 mice, and F1 mice had a naïve AHR phenotypeequivalent to their parental A/J strain. F1Wv/Wv mice displayed an airwayresistance similar to normoresponsive B6 mice. Values represent mean ± SE,n = at least 10 in each group.

www.pnas.org PNAS | November 1, 2011 | vol. 108 | no. 44 | 18185–18186

CORR

ECTIONS

Dow

nloa

ded

by g

uest

on

Sep

tem

ber

26, 2

020

Dow

nloa

ded

by g

uest

on

Sep

tem

ber

26, 2

020

Dow

nloa

ded

by g

uest

on

Sep

tem

ber

26, 2

020

Dow

nloa

ded

by g

uest

on

Sep

tem

ber

26, 2

020

Dow

nloa

ded

by g

uest

on

Sep

tem

ber

26, 2

020

Dow

nloa

ded

by g

uest

on

Sep

tem

ber

26, 2

020

Dow

nloa

ded

by g

uest

on

Sep

tem

ber

26, 2

020

Dow

nloa

ded

by g

uest

on

Sep

tem

ber

26, 2

020

Page 2: Protons migrate along interfacial water without ... · Physical Chemistry and Electrochemistry, Moscow, Russia; and dBelozersky Institute of Physico-Chemical Biology, Moscow, Russia

IMMUNOLOGYCorrection for “Squalamine as a broad-spectrum systemic anti-viral agent with therapeutic potential,” by Michael Zasloff, A.Paige Adams, Bernard Beckerman, Ann Campbell, Ziying Han,Erik Luijten, Isaura Meza, Justin Julander, Abhijit Mishra, WeiQu, John M. Taylor, Scott C. Weaver, and Gerard C. L. Wong,which appeared in issue 38, September 20, 2011, of Proc NatlAcad Sci USA (108:15978–15983; first published September 20,2011; 10.1073/pnas.1108558108).The authors note that the affiliation for John M. Taylor should

instead appear as Fox Chase Cancer Center, Philadelphia, PA19111. The corrected author and affiliation lines appear below.The online version has been corrected.

Michael Zasloffa,1, A. Paige Adamsb, Bernard Beckermanc,Ann Campbelld, Ziying Hane, Erik Luijtenc,f, Isaura Mezag,Justin Julanderh, Abhijit Mishrai, Wei Quc, John M. Taylore,Scott C. Weaverb, and Gerard C. L. Wongi

aTransplant Institute, Departments of Surgery and Biochemistry andMolecular and Cell Biology, Georgetown University Medical Center,Washington, DC 20007; bInstitute for Human Infections and Immunity andDepartment of Pathology, University of Texas Medical Branch, Galveston,TX 77555-0609; cDepartment of Materials Science and Engineering,Northwestern University, Evanston, IL 60208-3108; dDepartment ofMicrobiology and Molecular Cell Biology, Eastern Virginia Medical School,Norfolk, VA 23507; eFox Chase Cancer Center, Philadelphia, PA 19111;fDepartment of Engineering Sciences and Applied Mathematics,Northwestern University, Evanston, IL 60208-3125; gDepartamento deBiomedicina Molecular, Research and Advanced Studies Center of theNational Polytechnic Institute of Mexico, 07360 Mexico D.F., Mexico;hInstitute for Antiviral Research, Utah State University, Logan, UT 84322-5600; and iBioengineering Department, Chemistry and BiochemistryDepartment, California Nano Systems Institute, University of California,Los Angeles, CA 90095-1600

www.pnas.org/cgi/doi/10.1073/pnas.1115667108

PLANT BIOLOGYCorrection for “Comparative transcriptome and metaboliteanalysis of oil palm and date palm mesocarp that differ dra-matically in carbon partitioning,” by Fabienne Bourgis, ArunaKilaru, Xia Cao, Georges-Frank Ngando-Ebongue, NoureddineDrira, John B. Ohlrogge, and Vincent Arondel, which appearedin issue 30, July 26, 2011, of Proc Natl Acad Sci USA (108:12527–12532; first published June 27, 2011; 10.1073/pnas.1106502108).The authors note the following: “A relevant reference by

Tranbarger et al. that describes the regulation of oil palm fruitripening should be added to the list of references in our article.In addition to providing data that complement our study,Tranbarger et al. reached similar conclusions with regard to theimportance of palm orthologs of the Arabidopsis WRINKLED1transcription factor.”

35. Tranbarger TJ, et al. (2011) Regulatory mechanisms underlying oil palm fruitmesocarp maturation, ripening, and functional specialization in lipid and carotenoidmetabolism. Plant Physiol 156:564–584.

www.pnas.org/cgi/doi/10.1073/pnas.1115243108

18186 | www.pnas.org

Dow

nloa

ded

by g

uest

on

Sep

tem

ber

26, 2

020

Page 3: Protons migrate along interfacial water without ... · Physical Chemistry and Electrochemistry, Moscow, Russia; and dBelozersky Institute of Physico-Chemical Biology, Moscow, Russia

Protons migrate along interfacial water withoutsignificant contributions from jumps betweenionizable groups on the membrane surfaceAndreas Springera, Volker Hagenb, Dmitry A. Cherepanovc, Yuri N. Antonenkod, and Peter Pohla,1

aInstitut für Biophysik, Johannes Kepler Universität, Linz, Austria; bLeibniz-Institut für Molekulare Pharmakologie, Berlin, Germany; cFrumkin Institute ofPhysical Chemistry and Electrochemistry, Moscow, Russia; and dBelozersky Institute of Physico-Chemical Biology, Moscow, Russia

Edited by Arieh Warshel, University of Southern California, Los Angeles, CA, and approved July 25, 2011 (received for review May 11, 2011)

Proton diffusion along membrane surfaces is thought to be essen-tial for many cellular processes such as energy transduction. Com-monly, it is treated as a succession of jumps between membrane-anchored proton-binding sites. Our experiments provide evidencefor an alternative model. We released membrane-bound cagedprotons by UV flashes and monitored their arrival at distantsites by fluorescence measurements. The kinetics of the arrival isprobed as a function of distance for different membranes andfor different water isotopes. We found that proton diffusionalong themembrane is fast even in the absence of ionizable groupsin the membrane, and it decreases strongly in D2O as comparedto H2O. We conclude that the fast proton transport along themembrane is dominated by diffusion via interfacial water, and notvia ionizable lipid moieties.

chemiosmotic theory ∣ fluorimetry ∣ planar bilayer ∣ proton-collectingantenna

Proton diffusion along membrane surfaces is thought to pro-vide an efficient link between sites of proton release and

proton consumption (1). Membrane surfaces seem to interactwith membrane-bound protein to increase proton-delivery rates toburied intraprotein sites. For example, wiring of the membrane-bound proton pump cytochrome c oxidase via specific amino acidresidues to the membrane surface enables fast proton transfer tothe catalytic site (2). Similarly, proton shuttling along the mem-brane from the mouth of the monocarboxylate transporter toneighboring carbonic anhydrase molecules was reported to be es-sential for an efficient lactate import via the cotransporter (3, 4).

The mechanism that is responsible for the two-dimensionalconfinement of protons to the membrane surface is unclear.According to molecular dynamics simulations, phosphate andcarbonyl groups stabilize the hydrated excess proton. However,proton release from these groups was so slow that the hydratedproton essentially followed the lipid motion (5).

This observation agrees well with theoretical predictions ofthe lateral proton (or hydroxyl ion) diffusion constant DB. Com-monly the lateral proton movement along the membrane surfaceis treated as a succession of multiple binding events, each fol-lowed by proton release. Because of the short distances betweenthe ionizable membrane-anchored groups B, DB is entirely deter-mined by the reaction constants of B. The protonation of mostionizable groups is diffusion limited, so that kon is in the rangeof 2 × 1010 s−1 M−1 (6). Consequently, the equilibrium constantdetermines the dissociation rate koff . For example, thepK ∼ 9.6 (7) of phosphatidylethanolamine (PE) corresponds toa koff ¼ 2 × 10ð10−pKÞ s−1 ≈ 5 s−1. Because koff sets the upper limitto the number of jumps v per unit time, DB is equal to (8)

DB ¼ 1

4vl2 ¼ 1

4koff l2: [1]

Assuming that the average length l of a hop is equal to the dis-tance between two PE molecules (approximately 10 �Å), we arrive

at DB ∼ 10−14 cm2 s−1. Because the diffusion constant of a lipidmolecule is orders of magnitude larger (9), excess proton andlipid move together.

pK ∼ 2.2 of phosphatidylcholine (PC) (6) corresponds tokoff ≈ 2 × 10ð10−2.2Þ s−1 ≈ 1.3 × 108 s−1. Accordingly, Eq. 1 pre-dicts that substitution of membrane PE by PC speeds up diffusionby seven orders of magnitude. But with DB ∼ 10−7 cm2 s−1, thetime interval τb ∼ δ2∕4DB, which the surface proton requires tocross the distance δ between two spots on the membrane isat least an order of magnitude larger than the respective timeinterval τc ∼ δ2∕6DC of a bulk proton. Assuming that the diffusioncoefficient DC of the proton carrier in the bulk is approximately5 × 10−6 cm2 s−1 or higher, we arrive at a ratio τb∕τc > 75. That is,the surface proton would be unable to compete with the fasterbulk protons, and the contribution of the surface proton toprocesses such as energy consumption would be physiologicallyirrelevant.

We conclude that there is a discrepancy between the biologicalsignificance attributed to the surface proton and the current con-cept of its movement along the membrane. In addition, we foundthat DB on PC membranes is orders of magnitude larger (10–12)than suggested by the “jump” model (Eq. 1). The goal of thepresent work was to solve the conundrum. Therefore, we testedthe jump model of lateral proton diffusion by changing the lipidcomposition of freestanding planar membranes. The observedindependence of DB on proton release rates from ionizable lipidsindicated that the jump model is invalid. A lateral proton trans-port mechanism must exist, which is independent from jumpsbetween ionizable membrane moieties.

Theoretical ModelThe immobile buffer molecules B imbedded in the membranecompete with mobile buffer molecules C in the aqueous solutionsfor the proton:

BHþOH− ⇆k2B

k1B− þH2O; [2]

CHþOH− ⇆k2c

k1C− þH2O: [3]

In addition, transfer reactions between the mobile and immobilebuffer molecules should be considered:

Author contributions: P.P. designed research; A.S. and Y.N.A. performed research; V.H.provided new analytical tools; A.S., D.A.C., Y.N.A., and P.P. analyzed data; and P.P. wrotethe paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed at: Altenberger Strasse 69, Institut fürBiophysik, Johannes Kepler Universität, 4040 Linz, Germany. E-mail: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1107476108/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1107476108 PNAS ∣ August 30, 2011 ∣ vol. 108 ∣ no. 35 ∣ 14461–14466

CHEM

ISTR

YBIOPH

YSICSAND

COMPU

TATIONALBIOLO

GY

Page 4: Protons migrate along interfacial water without ... · Physical Chemistry and Electrochemistry, Moscow, Russia; and dBelozersky Institute of Physico-Chemical Biology, Moscow, Russia

B− þ CH⇆k4

k3BHþ C−: [4]

The differential equations for the combined processes of diffu-sion and chemical reactions (formulas 2–4) adopt the followingform (13):

∂U1

∂t¼ DB

∂2U1

∂x2þQ1

∂Ui

∂t¼ Di

�∂2Ui

∂x2þ ∂2Ui

∂y2

�þQi; [5]

where U is the concentration of the ith species. i ¼ 1, 2, 3, and 4denotes the protonated fixed buffer BH, the protonated solublepH buffer, CH; the hydroxyl anion, OH−; and the deprotonatedsoluble pH buffer, C−, respectively. Proton movement along thesurface is characterized by the diffusion coefficient DB. It is de-scribed as a one-dimensional process because Hþ release from along stripe allowed reduction of system dimensionality (Fig. 1).The rates of expenditure Qi of the ith species were calculatedfrom formulas 2–4:

Q1 ¼ ½ð−k1UBHUOHÞ þ k2BðB0 − UBHÞþ ðk3ðB0 − UBHÞUCH − k4UBHUCÞ�BXC

Q2 ¼ −k1UCHUOH þ k2CUC

Q3 ¼ −k1UCHUOH þ k2CUC

Q4 ¼ k1UCHUOH − k2CUC; [6]

where B0 ¼ UB− þ UBH is the total concentration of the immo-bile buffer. Because mobile buffer molecules outnumber B0

by orders of magnitude, Eq. 4 may be neglected in Q2 and Q4.All rate constants are known (compare Table S1). Thus, themodel contained only two variable (unknown) parameters, thesurface diffusion coefficientDB and the probability BXC of proton

release from the surface into the bulk, which were both variedto fit the model to the experimental results. According toBXC ¼ expð−ΔG∕RTÞ, BXC may serve as a rough measure of theenergy barrier ΔG to proton surface to bulk release. A solutionfor the system of partial differential equations (PDEs) (Eqs. 5and 6) as obtained via an adaptive-grid finite-difference solverfor time-dependent parabolic two-dimensional PDEs (14).

ResultsFirst we tested whether lateral proton diffusivity between the siteof release and the site of measurement (Fig. 1) depended on thechoice of the lipid. We used glycerolmonoleate (GMO), diphyta-noyl phosphatidylcholine (DPhPC), or diphytanoyl phosphatidy-lethanolamine (DPhPE). AUV flash released the protons in lessthan 2 ns from membrane-bound (6,7-dimethoxycoumarin-4-yl)methyl (DMCM) caged diethyl phosphate (11), which was ad-sorbed to freestanding horizontal planar lipid bilayers. The re-sulting decrease of membrane surface pH was indicated by thedecrease of FPE fluorescence (Fig. 1). For all three lipids thetime τmax (compare Fig. 1 Inset) between the flash and the sub-sequent appearance of the maximum of the pH shift was equal toroughly 0.24 s (Fig. 2). Assuming a point-like Hþ source and adimensionless measurement spot, τmax, of approximately 0.24 sallows calculation of an apparent diffusion coefficient Dapp ≈ s2∕4τmax ∼ 5 × 10−5 cm2 s−1 for all three lipid membranes, wheres ¼ 70 μm is the distance between the site of release and themeasurement spot.

For a more sophisticated analysis, we fitted the PDE system(Eqs. 5 and 6) to the experimental traces (Fig. 2). The effectivesurface area per proton-binding site S0 and the thicknessY 0 ¼ 20 Å of the layer containing the proton acceptor moleculesenabled calculation of B0: B0 ¼ ðNAY 0S0Þ−1. We assumed surfaceareas per GMO, DPhPE, or DPhPC molecule of 38 Å2, 67 Å2,and 71 Å2, respectively. Because GMO itself does not contain

Fig. 1. Scheme of the experiments carried out on a planar bilayer lipidmembrane. A UV flash releases protons from (6,7-dimethoxycoumarin-4-yl)methyl (DMCM) caged diethyl phosphate in the rectangular area (red stripe).A photodiode detects the arrival of the protons in the blue square. Therefore,a pH probe [fluorescein phosphatidylethanolamine (FPE)] is exited in thegreen square. An example of the time course of fluorescence changes is given(Inset). τmax is the time interval between proton release and appearance offluorescence minimum in the observation area.

time (s)1 2 3

F (

%)

70

80

90

100

GMOPEPC

Fig. 2. Kinetics of proton release from ionizable groups of three differentlipids (Top) and kinetics of fluorescence changes on top of three differentlipid bilayers due to lateral proton migration (Bottom). The observation areawas located at a distance of 70 μm from the area of proton release. Becauseall FPE molecules are surrounded by DPhPC or DPhPE molecules, they areanticipated to accept protons, which are released from these molecules.GMO does not possess ionizable moieties so that in the case of two-dimen-sional diffusion, proton release from one FPE molecule seems to be requiredbefore the next FPE molecule may pick up the proton. Despite the huge dif-ferences in proton release rates from the different lipids, τmax for all threelipid bilayers was similar. That is, lateral proton diffusivity is independentof the choice of the lipid. The buffer contained 0.1 mM Capso (pH 9.0)and 100 mM NaCl.

14462 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1107476108 Springer et al.

Page 5: Protons migrate along interfacial water without ... · Physical Chemistry and Electrochemistry, Moscow, Russia; and dBelozersky Institute of Physico-Chemical Biology, Moscow, Russia

ionizable moieties, S0 ∼ 4;000 Å2 was derived from the relativeFPE concentration.

For GMOmembranes, BXC ∼ 3 × 10−6 resulted in a reasonablefit for times t ∼ τmax. Such BXC corresponds to an energy barrierof approximately 13 RT (where R is the gas constant and T is thetemperature). In case of smaller barriers, the protons were all lostinto the bulk before arriving at the measurement site. For DPhPCand for DPhPE membranes, BXC was even smaller (Fig. 2). Theincreased barrier for proton surface to bulk release reflects theavailability of membrane-anchored buffer molecules. Mostimportantly, Fig. 2 also shows that the jump model is invalid.In contrast to the seven orders of magnitude difference predictedfor proton diffusion along the three lipids, a single DB value ofabout ð5� 1Þ × 10−5 cm2 s−1 allowed fitting of all experimentaltraces for t ≤ τmax. For t > τmax the theoretical Hþ concentrationsdecayed back to baseline faster than the experimental traces.Most conceivably, the discrepancy was due to the fact that themodel did not take into account the minor fraction of protons,which was released from caged compounds dissolved in the bulk.Their presence cannot be completely avoided even by focusingthe UV flash onto a small membrane spot and using hydrophobiccaged protons. These “bulk” protons did not confound our the-oretical analysis because (i) they were outnumbered by “mem-brane” protons and (ii) they arrived at the measurement siteafter the membrane protons due to the larger travel distance.

Proton diffusion through the bulk is not compatible with theobserved τmax of approximately 0.24 s because (i) the mobilebuffer Capso (3-(cyclohexylamino)-2-hydroxy-1-propanesulfonicacid) would have carried approximately 2∕3 of the bulk protonsand because the characteristic time of Capso’s diffusion over adistance of 70 μm would have been ≈s2∕6D2 ∼ 1.2 s. To arrive atthese numbers, we first estimated buffer capacity β:

β ¼ 2.3�

C0Ka½Hþ�ðKa þ ½Hþ�Þ2

¼ 2.3 × 1 mM × 10−9.6 × 10−7.5

ð10−9.6 þ 10−7.5Þ2 ≈ 20 μM;

where C0 ¼ UC− þ UCH was the total Capso concentration. Therespective diffusion coefficients D2 and D4 were both equal toabout 7 × 10−6 cm2 s−1. We assumed that a spatially invariant βmay be used, which was calculated for an average pH of 7.5,although pH increased from 7.0 in the area where the protonis uncaged (index u) to pH 8.0 in the observation area (indexo). The superposition of Hþ, of OH−, and of buffer fluxes resultin the total flux J:

J ¼ JHþ þ JOH− þ JCapso

¼ ðð½Hþ�u − ½Hþ�oÞDH þ ðUOH;oÞ − UOH;uÞD3

þ ðpHu − pHoÞβD2Þ∕d¼ ≈1.3 × 10−12 þ 7 × 10−12 þ 2 × 10−11Þ mol cm−2 s−1 ≈ 3

× 10−11 mol cm−2 s−1:

Because Hþ and OH− diffusion contributed less than 30% to J,τmax of approximately 0.24 s (Fig. 2) must be the result of protonmigration along the membrane surface.

We figured that an increase in mobile buffer concentrationeventually leads to a situation where all excess protons are cap-tured by buffer molecules and thus reach the measurement spotby bulk diffusion. Indeed at 1.2 mM Capso τmax was equal to1.02 s on a GMO membrane (Fig. 3). This observation indicatedthat in case of large β-surface proton diffusion was negligible.Vice versa, it confirmed that in case of small β (Fig. 2), the protondiffused laterally along the membrane.

To increase the accuracy of Dapp and DB determination, werecorded families of traces where all conditions but s were kept

constant. Making a global fit of the PDEs to such complete setsof experimental traces revealed DB ≈ 3.5 × 10−5 cm2 s−1 andBXC ≈ 3 × 10−6 for GMOmembranes (Fig. 4). Using these modelparameters, we calculated a time series of signal amplitudes asa function of the distance the area of proton release (Fig. S1).For the reasons outlined above, the model described the experi-ment satisfactorily only for t ≤ τmax. Plotting τmax versus s2 (Fig. 4Inset) returned Dapp ≈ 4 × 10−5 cm2 s−1. Thus, Dapp and DB are inreasonable agreement with each other (Table S2).

To confirm that BXC is a meaningful quantity, we carried outa model independent analysis. We estimated that surface pHincreased from 7.3 at time point τmax ;o1 at the first site(so1 ¼ 45 μm) to 8.1 at τmax ;o2 at the second site (so2 ¼ 55 μm).Assuming (i) that all protons arrived exclusively due to surfacediffusion at both the first and at the second sites and (ii) that thisdiffusion is due to hops of a unitary length of approximately0.25 nm allowed calculation of the apparent probability Bappof proton surface to bulk release during a single hop:

time (s)0,01 0,1 1

I (%

)

80

85

90

95

100

0.10.40.81.2

Fig. 3. The increase in mobile buffer concentration shifts the proton path-way from surface to bulk diffusion. Shown are representative time tracesobtained for proton migration between two spots on a GMO bilayer thatare 70 μm apart. The buffer concentration increased from 0.1 mM Capsoto 1.2 mM Capso as indicated. All other conditions were as in Fig. 2. The cor-responding τmax increased from 0.24 to 1.02 s. The former value is incompa-tible with charge transport through the bulk. In contrast, the latter valuemeets the theoretical expectation for a mix of charge transport by Capsoand OH− diffusion (see text).

time (s)0 2 4 6

F (

%)

70

80

90

100

4555708295120

τmax (s)0 1

s2 (µm

2 )

5,000

10,000

15,000GMO

DPhPC

Fig. 4. Kinetics of proton diffusion over different distances s (45, 55, 70, 82,95, and 120 μm) along a GMO membrane. The buffer contained 0.1 mMCapso (pH 9.0) and 100 mM NaCl. The black lines show a fit of the set of dif-ferential equations for diffusion and chemical reactions to the experimentalprofiles with DB ¼ 3 × 10−5 cm2 s−1 and BXC ¼ 3 × 10−6. (Inset) The depen-dence of τmax on s2 for GMO (green line) and DPhPC (black line) membranes.The data for proton diffusion along a DPhPC membrane were taken from aprevious publication (10).

Springer et al. PNAS ∣ August 30, 2011 ∣ vol. 108 ∣ no. 35 ∣ 14463

CHEM

ISTR

YBIOPH

YSICSAND

COMPU

TATIONALBIOLO

GY

Page 6: Protons migrate along interfacial water without ... · Physical Chemistry and Electrochemistry, Moscow, Russia; and dBelozersky Institute of Physico-Chemical Biology, Moscow, Russia

Bapp ¼ ½Hþ�o1 − ½Hþ�o2nð½Hþ�o1 − ½Hþ�bÞ

¼ 2.1 × 10−5

where n and ½Hþ�b denote the number of proton hops and theproton bulk concentration, respectively. Because Bapp ignores thefinite sizes of release and of measurement areas as well as protonbulk diffusion, it may be considered to be in reasonable agree-ment with BXC. BXC and Bapp suggest that the energy barrier toproton release from a GMO membrane amounts to about11–13 RT.

Carrying out the same analysis for proton diffusion alongDPhPC membranes revealed BXC ≈ 5.5 × 10−7 and a DB of 2.5 ×10−5 cm2 s−1 (data were taken from ref. 10). Calculation of thetime series of the signal amplitudes as a function of the distancevisualizes that (i) the excess proton stays longer at the surface(Fig. S1) and that lateral migration is slower than on a GMOmembrane (Fig. S2). Recalculation of Dapp (with s taken asthe distance between the midpoints of uncaging and measure-ment areas) led to 2.5 × 10−5 cm2 s−1. Because pH at the corre-sponding τmax decreased from 8.4 to 8.2 for so1 ¼ 57 μm andso2 ¼ 76 μm, respectively, we arrive at Bapp ≈ 5.5 × 10−6. Accord-ingly, the barrier responsible for retarded proton release from aDPhPC membrane is in the range of 12–16 RT.

From the pK of FPE, which is equal to approximately 8.5,follows that koff ¼ 2 × 10ð10−8.5Þ s−1 ≈ 63 s−1; i.e., it takes FPE16 ms to receive a proton from another FPE molecule. BecauseFPE is the sole proton-binding moiety in our GMO membranes,Eq. 1 predicts DB ∼ of 10−13 cm2 s−1. That is, if proton surfacediffusion was due to jumps between binding sites, the protonshould travel six orders of magnitude faster along the PC mem-brane as compared to GMO membranes. In contrast, the differ-ence between the DB (Dapp) values obtained for GMO andDPhPC was equal or smaller than two.

We varied the surface density of ionizable residues to probethe relative contributions of diffusion via lipids and via water.For each concentration of PE and lipid bound dye molecules inGMO bilayers we carried out experiments similar to the one inFig. 4. Instead of observing a 3.2-fold difference in proton diffu-sivity due to the decrease in l, Dapp decreased only 2-fold upon a10-fold increase of immobile buffer concentration (Fig. S3).Moreover, the effects observed upon introducing PE or FPEmolecules were similar, despite their different pK values of 8.4and 9.6. It is worth noting that even at the lowest UB0 value,the time required to cross the distance between fixed buffer sitesby diffusion is orders of magnitude smaller than the time requiredto release the proton from any of these sites. That is, accordingto Eq. 1 release times >0.1 s have to be compared withτD ≈ s2∕4Dapp ≤ ð3 nmÞ2∕4 × 2 × 10−9 m2 s−1 ∼ 1 ns.

If the residence time of a proton on the immobile buffer doesnot correlate with its mobility on the membrane surface, a me-chanism that is different from the jump model should exist.We substituted H2O for D2O and measured DB again to testwhether the proton (i) migrates along the surface by a mechanismsimilar to the one in bulk water, in which the rate-determiningstep is hydrogen-bond cleavage or (ii) moves along hydrogen-bonded chains where the fast proton displacement within anindividual H bond from the donor to the acceptor is rate limiting.In the latter case, we expected an isotope effect ranging from 2.5to 7 (15). In the former case, the kinetic isotope effect shouldbe approximately

ffiffiffi2

p(16). To account for the effect that the read-

ing taken from a glass pH electrode deviates from the true pDof D2O solutions by 0.4 units (17), we carried out our D2O ex-periments at pD 9.4. Because deuterons generally are held moretightly than protons, we solved our system of PDEs assumingthat pK of all fixed and mobile buffers increased by 0.5 unitsin D2O (17).

We obtained Dapp ∼ 10−5 cm2 s−1 for both GMO and DPhPCmembranes in heavy water (Fig. 5). Most notably, the barrier

for proton surface to bulk release decreased. Fitting the PDEsto the time traces with DPhPC was possible with rather small DB

(approximately 4 × 10−6 cm2 s−1). This result suggests that sur-face diffusion did not make a significant contribution to the over-all proton transport in D2O.

If the vast majority of protons reach the measurement spotvia bulk diffusion, an increase in mobile buffer concentrationshould have only a small effect on τmax. In line with these con-siderations, running the experiment of Fig. 3 in D2O revealeda 10% increase of τmax (from 1.13 to 1.24 s) upon a 12-fold in-crease of β (Fig. 6). The contrast to the 5-fold increase of τmax

95

100

time (s)

0 2 4 6

I (%

)

95

100

557095110

τmax (s)

0 1 2

s2 (µm

2 )

4,000

8,000

12,000

16,000

DPhPCGMO

H2O

D2O

GMO

DPhPC

Fig. 5. Kinetics of charge diffusion in heavy water over different distancess (55, 70, 95, and 110 μm) along a GMO membrane (Upper) and a DPhPCmembrane (Lower). Apparently, the kinetics of Dþ diffusion is similar forboth membranes. The buffer contained 0.1 mM Capso (pH 9.4) and 100 mMNaCl. The black lines show a fit of the set of differential equations for diffu-sion and chemical reactions to the experimental profiles. Fitting was possiblewith DB ranging from 3 × 10−2 cm2 s−1 to 1 × 10−5 cm2 s−1 and BXC valuesbetween 4 × 10−3 and 10−5, indicating that the contribution of surface diffu-sion to the overall transport rate was rather small. In view of the large errorfor DB, the isotope effect was determined from Dapp. The two- or fourfoldsteeper slope for experiments carried out in H2O as compared to D2O indi-cates that proton surface migration is subject to a large isotope effect.

time (s)0,1 1

I (%

)

85

90

95

100

0.80.10.41.2

Fig. 6. The increase in mobile buffer concentration has little effect on thepathway of charge transport in heavy water. Shown are representative timetraces obtained for Dþ migration between two spots on a GMO bilayer thatwere 70 μm apart. The buffer concentration increased from 0.1 mM Capso to1.2 mM Capso. All other conditions were as in Fig. 2. The corresponding τmax

increased from 1.13 to 1.24 s. Both values are compatible with charge trans-port via bulk. A small contribution of surface diffusion in the former case mayexplain the difference in kinetics.

14464 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1107476108 Springer et al.

Page 7: Protons migrate along interfacial water without ... · Physical Chemistry and Electrochemistry, Moscow, Russia; and dBelozersky Institute of Physico-Chemical Biology, Moscow, Russia

in normal water confirms that the pathways of a proton and adeuterion are very different: While the former moves preferen-tially along the membrane surface, the latter is transported viathe bulk solution.

The lack of surface diffusion hampered the calculation of Bappin D2O. Judging from Dapp, the isotope effect varies between twoand four for DPhPC membranes and GMO membranes, respec-tively. The “true” isotope effect may be much larger. Its calcula-tion would require the exact value of DB to be known. However,under conditions where surface diffusion is not the rate limitingstep, determination of DB is subject to extremely large errors.

DiscussionOur experiments have shown that proton movement along thesurface of planar membranes does not involve jumps betweenmembrane-anchored proton-binding sites. We obtained four linesof evidence:

1. With approximately 4 × 10−5 cm2 s−1 the experimentally ob-served proton diffusivity is orders of magnitude faster thenexpected (compare Eq. 2) from any of the proton release con-stants from PE or PC headgroups or from the lipid anchoredfluorescent dye (Fig. 2).

2. If proton release (i.e., breakage of hydrogen bonds) was therate limiting step, interfacial diffusion in D2O was expectedto be

ffiffiffi2

pslower than in H2O. However, the observed isotope

effect is at least twice as large.3. Except the rare FPE molecules, GMO does not offer proton-

binding sites, yet long-range lateral proton migration occurs.4. If fixed membrane buffers were involved in lateral proton

migration, the difference in proton release rates would requirethat interfacial proton diffusion along PC membranes(approximately 10−7 cm2 s−1) is seven orders of magnitudefaster than diffusion along PE membranes (approximately10−14 cm2 s−1). In contrast, we did not detect a significantdifference between the interfacial proton mobilities for thetwo lipids. The same holds if OH− (instead of Hþ) accom-plishes charge transport. Although the equation for koff ¼ 2 ×10ð10−ð14−pKÞÞ s−1 is different, Eq. 1 would still predict DBvalues that are seven orders apart for PE and PC.

Calculation of koff from lipid pK and the diffusion-controlledon rate is valid for a group in equilibrium with the solution. Atclose distance, i.e., in the case of neighboring lipids with just oneor two intervening water molecules, proton transfer may occuralong preexisting hydrogen bonds. In contrast to the equilibriumsituation, the time constant for (PC)PE-hydroxide-PE(PC) or(PC)PE-hydronium-PE(PC) proton transfer does not dependon pKa. Calculation according to Marcus theory reveals thatthe apparent intrinsic barrier ΔG≠ for the bimolecular protontransfer with one intervening water molecule is typically about5 kcal∕mol (18). In case of two intervening water molecules itincreases to 7–12 kcal∕mol. Interestingly, Marcus theory also re-veals that the intrinsic barrierΔG≠ for this kind of proton transferreactions is approximately 1 kcal∕mol (18). This value is wellcompatible with (i) the observed DB on both PE and PC mem-branes. However, on a GMO membrane proton acceptor andproton donor are separated by approximately 14 water molecules.Bimolecular proton transfer with 14 intervening water moleculesseems to be unrealistic, because it would require extremely highvalues of ΔG0. Thus, the nonequilibrium approach reveals thesame result as the equilibrium assumption: The proton migrationalong the surface does not involve jumps between membrane-anchored proton-binding sites.

If proton-binding sites are not a prerequisite for proton move-ment along the membrane surface, the origin of the energeticbarrier for proton surface to bulk release is unclear. Accordingto molecular dynamics simulations, phosphate groups may stabi-lize the hydrated excess proton (19). However, proton release

was so slow that the hydrated proton essentially followed the lipidmotion (5). Because such a slow lateral migration is in contrastto our experimental results, phosphate groups cannot hold to beresponsible for the retarded surface to bulk transfer. Moreover,GMO does not contain phosphate moieties and yet lateral diffu-sion occurs.

Alternatively, computer simulations suggest that the barrier isdue to the structure of the excess proton. It donates three hydro-gen bonds to water molecules, but accepts none. As it strains thehydrogen-bond pattern of the surrounding liquid, this configura-tion is less stable in the bulk liquid (20). The resulting barrier wasdetermined to be approximately 6 RT adjacent to membranesmade of carbon nanotubes (20). This observation does not ex-plain why the barrier adjacent to GMO membranes (8.8–10 RT)is smaller than that in the vicinity of DPhPC membranes(12–16 RT).

However, in the basic pH experimental environment chargetransport is likely to be accomplished by the hydroxyl ion. In con-trast to the Eigen cation, the “active” OH− adopts a tetrahedralOH−ðH2OÞ3 configuration closely resembling that of a bulk watermolecule (21). That is, OH−ðH2OÞ3 does not strain bulk waterstructure as does the Eigen cation H9O4

þ, and therefore struc-tural considerations do not suggest a surface location. Rather,electrostatic attraction keeps OH− close to the surface. The mostlikely source of this attraction is the membrane dipole potentialφD. For GMO membranes φD is about 100 mV (22–24) with anorientation such that the membrane interior is positive. For thehydroxyl anion, φD corresponds to an energy barrier of ΔGD ¼zFφD ≈ 4 RT. Besides, the presence of carbonyl groups inDPhPC augments φD to about 220 mV (24, 25), so that ΔGDwould be equal to 8.8 RT. That is, the higher φD of phospholipidmembranes could explain the increased energy barrier to hydro-xyl anion release, which we observed close to PE and PC bilayers.However, so far experimental proof for φD’s contribution to theenergy barrier is missing.

Both hydroxyl ion mobility and proton diffusivity are domi-nated by second-shell hydrogen-bond cleavage, and the isotopeeffect in the two cases is limited to 1.4–1.7 (26). The larger iso-tope effect observed in our experiment would be in line with theidea that proton transfer within the H bond is rate limiting, i.e.,it is compatible with the view that lateral transport along themembrane water interface occurs along extended hydrogenbonded chains. These chains do not necessarily include ionizablegroups on the membrane surface. Rather water structuring at theinterface seems to be mandatory for both providing the pathwayand for generating the energy barrier opposing hydroxyl anionsurface to bulk release.

Materials and MethodsPlanar Membranes. Horizontal planar bilayer lipid membranes were formedfrom DPhPC (Avanti Polar Lipids), DPhPE (Avanti Polar Lipids) and GMO (Sig-ma-Aldrich) dissolved at 20 mg∕mL or alternatively at 100 mg∕mL for GMOin n-decane (Merck). The membrane-forming solution additionally containedfrom 0.5 to 3.5 mol % of FPE (Molecular Probes). The formation of the mem-brane was performed by spreading this solution across a circular aperture0.2–0.3 mm in diameter in a diaphragm separating two aqueous phasesof Teflon chamber. Top and lower aqueous phases had volumes of 0.5 mLand 2 mL, respectively.

The aqueous phase located directly under the membrane was about100 μm in height and confined by a lucent basement (Seal View, Roth).The aqueous salt solution (100 mM NaCl) inside the chamber was bufferedat pH 9 with 0.1 mM Capso (Sigma-Aldrich) if not stated otherwise.

Kinetic Measurements. The hydrophobic caged proton, (6,7-dimethoxycou-marin-4-yl)methyl diethyl phosphate (11) released protons, 6,7-dimethoxy-4-(hydroxymethyl)coumarin, and a diethyl phosphate anion in a region ofinterest when exposed to UV light emitted by a xenon flash lamp (Rapp OptoElectronics). For fluorescent excitation of the pH indicator FPE in a secondregion of interest, we used a 150-W xenon lamp, connected via a monochro-mator to an inverse microscope (20× objective). A photodiode collected the

Springer et al. PNAS ∣ August 30, 2011 ∣ vol. 108 ∣ no. 35 ∣ 14465

CHEM

ISTR

YBIOPH

YSICSAND

COMPU

TATIONALBIOLO

GY

Page 8: Protons migrate along interfacial water without ... · Physical Chemistry and Electrochemistry, Moscow, Russia; and dBelozersky Institute of Physico-Chemical Biology, Moscow, Russia

fluorescent light that went backward into the objective. After being passedto a current amplifier (Heka, EPC9) the signal was digitized and stored in apersonal computer for further analysis. Three sets of diaphragms were used(compare Fig. 1) to define the rectangular-shaped stripe for proton release,the quadratic area of fluorescence excitation, and quadratic area of emission

measurements (10). The distance between the areas of release and measure-ment varied between about 45 μm and 130 μm, respectively.

ACKNOWLEDGMENTS. Financial support by the Deutsche Forschungsge-meinschaft (Po 533/5 to P.P.) is gratefully acknowledged.

1. Williams RJP (1988) Proton circuits in biological energy interconversions. Annu RevBiophys Biophys Chem 17:71–97.

2. Ojemyr LN, Lee HJ, Gennis RB, Brzezinski P (2010) Functional interactions betweenmembrane-bound transporters and membranes. Proc Natl Acad Sci USA107:15763–15767.

3. Becker HM, Deitmer JW (2008) Nonenzymatic proton handling by carbonic anhydraseII during Hþ-lactate cotransport via monocarboxylate transporter 1. J Biol Chem283:21655–21667.

4. Becker HM, Klier M, Schüler C, McKenna R, Deitmer JW (2011) Intramolecular protonshuttle supports not only catalytic but also noncatalytic function of carbonic anhy-drase II. Proc Natl Acad Sci USA 108:3071–3076.

5. Yamashita T, Voth GA (2010) Properties of hydrated excess protons near phospholipidbilayers. J Phys Chem B 114:592–603.

6. Gutman M, Nachliel E (1990) The dynamic aspects of proton transfer processes.Biochim Biophys Acta 1015:391–414.

7. Tsui FC, Ojcius DM, Hubbell WL (1986) The intrinsic pKa values for phosphatidylserineand phosphatidylethanolamine in phosphatidylcholine host bilayers. Biophys J49:459–468.

8. Branden M, Sanden T, Brzezinski P, Widengren J (2006) Localized proton microcircuitsat the biological membrane-water interface. Proc Natl Acad Sci USA 103:19766–19770.

9. Horner A, Antonenko YN, Pohl P (2009) Coupled diffusion of peripherally boundpeptides along the outer and inner membrane leaflets. Biophys J 96:2689–2695.

10. Serowy S, et al. (2003) Structural proton diffusion along lipid bilayers. Biophys J84:1031–1037.

11. Geissler D, et al. (2005) (Coumarin-4-yl)methyl esters as highly efficient, ultrafastphototriggers for protons and their application to acidifying membrane surfaces.Angew Chem Int Ed Engl 44:1195–1198.

12. Antonenko YN, Pohl P (2008) Microinjection in combination with microfluorimetry tostudy proton diffusion along phospholipid membranes. Eur Biophys J 37:865–870.

13. Cherepanov DA, Junge W, Mulkidjanian AY (2004) Proton transfer dynamics at themembrane/water interface: Dependence on the fixed and mobile pH buffers, on

the size and form of membrane particles, and on the interfacial potential barrier.Biophys J 86:665–680.

14. Blom JG, Trompert RA, Vewer JG (1996) Algorithm 758: VLUGR2: A vectorizable adap-tive-grid solver for PDEs in 2D. ACM Trans Math Softw 22:302–328.

15. Karpefors M, Adelroth P, Brzezinski P (2000) The onset of the deuterium isotope effectin cytochrome c oxidase. Biochemistry 39:5045–5050.

16. le Coutre J, Gerwert K (1996) Kinetic isotope effects reveal an ice-like and aliquid-phase-type intramolecular proton transfer in bacteriorhodopsin. FEBS Lett398:333–336.

17. DeCoursey TE, Cherny VV (1997) Deuterium isotope effects on permeation and gatingof proton channels in rat alveolar epithelium. J Gen Physiol 109:415–434.

18. Guthrie JP (1996) Intrinsic barriers for proton transfer reactions involving electrone-gative atoms, and the water mediated proton switch: An analysis in terms of Marcustheory. J Am Chem Soc 118:12886–12890.

19. Smondyrev AM, Voth GA (2002) Molecular dynamics simulation of proton transportnear the surface of a phospholipid membrane. Biophys J 82:1460–1468.

20. Dellago C, Hummer G (2006) Kinetics and mechanism of proton transport across mem-brane nanopores. Phys Rev Lett 97:245901.

21. Tuckerman ME, Marx D, Parrinello M (2002) The nature and transport mechanism ofhydrated hydroxide ions in aqueous solution. Nature 417:925–929.

22. Pickar AD, Benz R (1978) Transport of oppositely charged lipophylic probes in lipidbilayer membranes having various structures. J Membr Biol 44:353–376.

23. Gawrisch K, et al. (1992) Membrane dipole potentials, hydration forces, and theordering of water at membrane surfaces. Biophys J 61:1213–1223.

24. Peterson U, et al. (2002) Origin of membrane dipole potential: Contribution of thephospholipid fatty acid chains. Chem Phys Lipids 117:19–27.

25. Pohl P, Rokitskaya TI, Pohl EE, Saparov SM (1997) Permeation of phloretin across bi-layer lipid membranes monitored by dipole potential and microelectrode measure-ments. Biochim Biophys Acta 1323:163–172.

26. Agmon N (2000) Mechanism of hydroxide mobility. Chem Phys Lett 319:247–252.

14466 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1107476108 Springer et al.