Energy transfer method in membrane studies: some theoretical and practical aspects

J. Biochem. Biophys. Methods 52 (2002) 45 – 58 www.elsevier.com/locate/jbbm

Energy transfer method in membrane studies: some theoretical and practical aspects Galina P. Gorbenko*, Yegor A. Domanov Department of Physics and Technology, V.N. Karazin Kharkov National University, 4 Svobody Sq., Kharkov, 61077, Ukraine Received 18 October 2001; received in revised form 29 April 2002; accepted 29 April 2002

Abstract Some applications of resonance energy transfer (RET) method to distance estimation in membrane systems are considered. The model of energy transfer between donors and acceptors randomly distributed over parallel planes localized at the outer and inner membrane leaflets is presented. It is demonstrated that RET method can provide evidence for specific orientation of the fluorophore relative to the lipid – water interface. An approach to estimating the depth of the protein penetration in lipid bilayer is suggested. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Resonance energy transfer method; Membrane systems; Orientational effects; Protein bilayer location

1. Introduction Resonance energy transfer (RET) is known to be a physical process characterized by an explicit dependence on the distance between chromophores acting as energy donor and acceptor [1]. Due to this feature, RET technique has proved to be highly informative in the structural characterization of a wide variety of macromolecular assemblies, particularly, biological membranes [2– 5]. The rate of energy transfer in membrane systems is governed by numerous factors including the curvature of membrane surface, spatial arrangement of donors and acceptors in the lipid bilayer, randomness of their lateral distribution, the effect of excluded area, relative orientation of donor and acceptor, etc. It is evident that the extent to which all the above factors are taken into account in

*

Corresponding author. 52-52 Tobolskaya Str. 61072, Kharkov, Ukraine.

0165-022X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 5 - 0 2 2 X ( 0 2 ) 0 0 0 3 1 - 3

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the theoretical model employed for quantitative interpretation of experimental data determines the validity of structural information derived from RET measurements. Theoretical background for description of energy transfer in membrane systems is provided by a number of models [6 –11]. These models treat the cases where donors and acceptors are randomly distributed over the infinite plane, parallel infinite planes [6– 8], surfaces of concentric spheres or two separated spheres [9] and exhibit good agreement with each other in the transfer efficiencies predicted for a given acceptor surface density. The approaches to analyzing the possibilities of acceptor exclusion from an area around donor and interplanar separation of the donor and acceptor arrays have been developed [11,12]. The formalism allowing to take into account orientational effects has been suggested [13]. As shown in our previous works, the main limitation of RET method originating from the unknown mutual orientation of donor and acceptor could be reduced to some degree by employing multiple donor – acceptor pairs [14,15]. Principal possibility of differentiating between random and specific chromophore orientations relative to the lipid – water interface has been demonstrated [15]. Given that most situations encountered in practice involve chromophore distribution between the bilayer leaflets, we have modified the model of energy transfer in two dimensions [8] by considering the case of several donor and acceptor planes. Further extension of this model has been aimed to evaluate the depth of the protein penetration in the membrane interior through analyzing the changes in the RET efficiency caused by the excluded area effect [16]. In the present paper, we treat the problem of energy transfer in the planar membrane systems making emphasis on the practical guides to planning the RET experiment. Our goals include: (i) to analyze how the distribution of donors or acceptors between the outer and inner bilayer leaflets affects the rate of energy transfer; (ii) to ascertain whether specific orientation of donor and acceptor (i.e. nonisotropic value of orientation factor) could manifest itself in the shape of the dependencies of donor fluorescence on the surface acceptor concentration; (iii) to evaluate the possibility of choosing the optimum set of the donor – acceptor pairs providing a minimum uncertainty in the distance determination for a given membrane system; and (iv) to predict the conditions under which the exclusion of acceptor from an area occupied by the protein molecule would influence the RET efficiency, thereby allowing to estimate the depth of the protein bilayer penetration. In approaching these goals, we use simulated and some experimental data described in more detail elsewhere [15].

2. Theory 2.1. General formalism As indicated in a number of works, in the cases where the diameter of bilayer membrane vesicles is more than twofold greater than Fo¨rster radius, the curvature effect is negligible, so that energy transfer can be considered as occurring in a plane. This is valid for a major part of membrane studies since the range of the possible Fo¨rster radii is 1– 10 nm [1], while the radius of vesicles formed by the model or isolated native membranes

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47

usually exceeds 20 nm. In terms of the formalism developed in the aforementioned models [8], the energy transfer between donors and acceptors randomly distributed in a plane can be described as follows. The rate constant of de-excitation of the donor fluorescence is represented as a function of the lifetime of excited donor in the absence of acceptors (sd), Fo¨rster radius (Ro), the distance between the donor and given acceptor (Ri) and the number of acceptors within the disc of radius (Rd), beyond which energy transfer is insignificant (N):

k¼

s1 da

¼

s1 d

1þ

N X

! ðRo =Ri Þ

6

ð1Þ

i¼1

The number of acceptor molecules involved in energy transfer is related to the concentration of acceptors per unit area (Cas) that, in turn, depends on the molar concentrations of lipids (L) and bound acceptor (B): N ¼ pR2d Cas ;

Cas ¼

NA B ; SL

SL ¼ NA L

X

f i Si

ð2Þ

where NA is Avogadro’s number, SL is the membrane surface area accessible to acceptors, fi and Si are mole fractions and mean areas per molecule of lipid species constituting the membrane. Since de-excitation of a donor fluorescence exhibits first-order kinetics, the following relationships hold: ! N X dPðtÞ 6 1 ¼ kPðtÞ ¼ sd 1 þ  ðRo =Ri Þ PðtÞ dt i¼1

PðtÞ ¼ expðt=sd Þ

N Y

h i exp ðt=sd ÞðRo =Ri Þ6

ð3Þ

ð4Þ

i¼1

where P(t) is the probability that an originally excited donor is still excited after time t. If a donor is surrounded by N acceptor molecules, the ensemble average decay function PN(t) is given by: PN ðtÞ ¼ expðt=sd Þ

N Z Y i¼1

Rd

h i exp ðt=sd ÞðRo =Ri Þ6 W ðRi ÞdRi

ð5Þ

Re

where W(Ri)dRi is the probability of finding ith acceptor in the annulus between radii Ri and Ri + dRi and Re being the distance of closest approach between donor and acceptor in a plane. Random distribution of donors is characterized by identical W(Ri) for all values of i,

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so that one can write W(Ri) = W(R). Finally, relative quantum yield of donor ( Qr) can be written as: Z l Z l PN ðtÞdt QDA 0 ¼Z l exp½kðIðtÞÞN dk; ¼ QD 0 expðt=sd Þdt 0 Z Rd h i IðtÞ ¼ exp  kðRo =RÞ6 W ðRÞdR ð6Þ Re

where QD and QDA are the donor quantum yields in the absence and presence of acceptors, respectively, k = t/sd. 2.2. Model of energy transfer between donors and acceptors located at different levels across the membrane Given that fluorescent probes employed as energy donors or acceptors can partition between outer and inner membrane leaflets, the above model was extended to the case where donors are localized at both membrane sides (Fig. 1) while acceptors are situated in the outer monolayer only and separated from a nearest donor plane by a distance da. For the outer monolayer, the probability of finding acceptor at a distance R from a donor can be written as: 2RdR W1 ðRÞdR ¼ 2 ð7Þ Rd  da2 Meantime, for the donors localized in the inner monolayer, two possibilities must be considered corresponding to the cases when donors are situated deeper than acceptors or

Fig. 1. Schematic representation of the localization of donor and acceptor planes in the lipid bilayer.

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49

vice versa, acceptors reside deeper than donors, where dt is the distance separating the donor planes: 2RdR

W2 ðRÞdR ¼

R2d  ðdt þ da Þ2

2RdR

W2 ðRÞdR ¼

R2d

 ðdt  da Þ2

ðDonors are deeper than acceptorsÞ

ð8Þ

ðAcceptors are deeper than donorsÞ

ð9Þ

Thus, relative quantum yield of a donor can be represented as a sum of two terms characterizing energy transfer from the outer and inner donor planes: Z l Z l N1 N2 exp½kðI1 ðkÞÞ dk þ exp½kðI2 ðkÞÞ dk ð10Þ Qr ¼ 0:5 0

I1 ðkÞ ¼

Z

Rd

0

"



exp k

da

I2 ðkÞ ¼

Z

Rd

dt Fda

"

Ro R



6 #

Ro exp k R

N1 ¼ pCas ðR2d  da2 Þ;

6 #

2R dR R2d  da2 2R

ð11Þ !

R2d  ðdt Fda Þ2



N2 ¼ pCas R2d  ðdt Fda Þ2

dR

ð12Þ

ð13Þ

In analogous manner, one can treat the case where acceptors are distributed between the two monolayers, while donors are localized at the outer or both membrane sides. The only difference consists in the calculation of the surface acceptor concentration. Before applying this model for analyzing the results of RET measurements, one should solve the following tasks: (1) to determine the donor quantum yield in the membrane environment and calculate Fo¨rster radius for the donor – acceptor pairs employed; (2) to evaluate the amount of membrane bound acceptors; (3) to obtain experimental dependencies of the relative quantum yield of a donor on the surface acceptor concentration; and (4) to define the most probable limits for varying distances separating donor and acceptor planes. Provided that these tasks are solved, the data treatment yields the sets of parameters Re, da and dt, giving the best fit of experimental results. The fitting procedure involves minimization of the following function:

f ¼

na 1X ðQer  Qtr Þ2 na i¼1

ð14Þ

where Qtr with the superscripts ‘e’ and ‘t’ denote the donor quantum yields determined experimentally and calculated by numerical integration of Eqs. (10) –(13), respectively; na is the number of acceptor concentrations employed in the RET experiments.

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In conclusion, it seems of significance to point out some factors that can complicate the data treatment within the framework of the aforementioned models, leading to unreasonable values of the fitting parameters. These factors include, in particular, the competition between the donor and acceptor for the membrane binding sites and formation of a complex between donor and acceptor. In this case, experimental dependencies of the donor quantum yield on the surface acceptor concentration appear to be more drastic than those predicted by the model, indicating that there exist another reason, besides energy transfer, for the decrease of a donor fluorescence. 2.3. Orientation factor problem It seems of importance to emphasize that all estimates derived from the energy transfer measurements are based on some assumptions, concerning, in particular, the vertical separation of donor and acceptor planar arrays and lateral distance of closest approach. It is evident that these distances depend on the membrane structural state that could change due to structural reorganization of lipid bilayer, conformational alterations in the proteins, etc. These factors cannot be strictly formalized thus introducing some uncertainty in the RETbased distance determination. However, much more serious problem encountered in analyzing the results of RET studies consists in correct choice of the orientation factor value (j2) that is used in calculating Fo¨rster radius [1]: Z

1=6 Q J ; Ro ¼ 979 j2 n4 D r

J¼

0

l

FD ðkÞeA ðkÞk4 dk Z

ð15Þ

l

FD ðkÞdk

0

where QD is the donor quantum yield, nr is the refractive index of the medium (nr = 1.37), j2 is an orientation factor, J is the overlap integral calculated by numerical integration, FD(k) is the donor fluorescence intensity and eA(k) is the acceptor molar absorbance at the wavelength k. Orientation factor, depending on the angle between the donor emission and acceptor absorption transition dipoles and the angles between these dipoles and a vector joining donor and acceptor, can vary from 0 to 4. The minimum value corresponds to perpendicularly oriented donor and acceptor dipoles, while the maximum one characterizes the case when these dipoles are parallel and identically directed. In a major part of works on energy transfer, orientation factor is taken to be equal to 0.67. This value is valid for the isotropic and dynamic averaging conditions, when donors and acceptors are rapidly tumbling and their transition dipoles can adopt all orientations in a short time compared with the transfer time. However, in highly anisotropic membrane environment, rotational mobility of donors and acceptors is usually restricted and the isotropic condition is hardly satisfied. Besides, if the donor and acceptor dipoles exhibit certain preferable orientations, for instance, when the formation of protein – lipid or other type of complexes is mediated by specific sites, the j2 value may differ substantially from the isotropic one. Such an

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uncertainty in the choice of orientation factor appears to be a major limitation of RET method. This problem has been addressed by a number of authors [17 –20]. In terms of the approach of Dale et al. [17], j2 limits can be narrowed using the depolarization factors related to the steady-state and fundamental anisotropies of donor and acceptor. Gryczynski et al. [18] have calculated such limits for some hemoproteins on the basis of crystallographic and linear dichroism data. Teissie [19] has introduced j2 as an optimizing parameter in the data fitting. Wu and Brand [20] have demonstrated that combination of steady-state and time-resolved RET measurements could be conducive to rather accurate distance estimation. Since anisotropy or time-resolved fluorescence measurements are frequently difficult to perform, we made an attempt to enhance the validity of the steadystate RET data using multiple donor –acceptor pairs and varying j2 value in the data fitting. Our approach to the data treatment is applicable to the case of one donor (or acceptor) plane confined to the outer membrane side and two acceptor (or donor) planes disposed symmetrically with respect to the bilayer midplane (Fig. 1). Let us consider energy transfer in the system containing one acceptor and two donor planes. In this case, data analysis should include two main steps. First step involves fitting of the experimental dependencies Qr(Cas) to those calculated within the framework of the above model (Eqs. (10) – (13)) with parameter da being optimized at the constant values of dt and j2. The value of dt can be slightly changed in the limits consistent with the putative location of donor planes in the outer and inner bilayer leaflets while j2 is allowed to vary in the widest possible range (0– 4). Second step of the data treatment consists in obtaining the relationships between orientation factor and acceptor distance from the bilayer midplane (dc) related to da and dt as dc = 0.5dt F da (where ‘‘ + ’’ stands for the location of the outer donor plane deeper than the acceptor plane, while ‘‘  ’’ corresponds to the opposite case). To illustrate what kind of information can be obtained with the help of the above approach, it seems reasonable to consider some real RET data. Presented in Fig. 2 are the typical dependencies dc(j2) derived for the donor – acceptor pairs containing lipid-bound fluorescent probes (3-methoxybenzanthrone (MBA), N,NV-bishexamethylenrhodamine (RH), rhodamine 6G (R6G) and 4(dimethylaminostyryl)-1-dodecylpiridine (DSP-12)) as the donors and heme group of cytochrome c as an acceptor. Several features of these dependencies are worthy of mention. As can be seen, for each of the donors employed there exists certain minimum j2 value characterizing the case where acceptors reside at the bilayer midplane (dc = 0), and maximum heme distance from the bilayer center (dcmax), estimated at j2 = 4. In the case of random reorientation of donors and acceptors, one should expect the intersection or closing of the plots (dc(j2)), obtained for different donors, in the point corresponding to the isotropic value of orientation factor (j2 = 0.67) and actual heme separation from the bilayer midplane. The absence of such an intersection can be considered as one of the arguments in favor of specific orientation of the heme group with respect to the membrane surface. Another evidence for this assumption comes from the finding that for such donors as MBA and RH, the minimum possible j2 values exceeds the isotropic one (Fig. 2). It should also be noted that the heme distance from the bilayer center appears to be invariant for a given kind of lipid vesicles over a series of donors, so one can assume that the most probable

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Fig. 2. Distance of heme group of cytochrome c from the center of model membranes composed of phosphatidylcholine and diphosphatidylglycerol (9:1, mol/mol). Donors: 1—MBA, 2—RH, 3—R6G, 4—DSP-12.

values of this parameter fall in the range, being common for all donors, and its actual maximum value dcmax equals the lowest of the estimates, derived for various donors. As follows from the above considerations, if the x-intercept of the plots dc(j2) is greater than 0.67, analysis of the dependencies dc(j2) provides evidence for specific orientation of the fluorophore with respect to the bilayer surface. Note that for the intrinsic protein fluorophores, such an evidence can be obtained only in the case where particular orientation of the lipid-bound protein relative to the lipid –water interface is combined with considerable restriction of the fluorophore rotational mobility within the protein molecule. It is important to emphasize that the proposed approach becomes untenable when applied to interpreting the data obtained with donors whose fluorescence is influenced by the factors differing in nature from energy transfer. In addition to the aforementioned competitive or complex-forming relationships between donor and acceptor, such factors may involve structural reorganization of a lipid bilayer caused by acceptor itself or acceptor-containing macromolecule. The latter capability is characteristic of a wide variety of the proteins, including cytochrome c. Numerous studies indicate that cytochrome c binding to a lipid bilayer can be conducive to the lipid redistribution [21], formation of nonlamellar structures [22], changes in the conformation of lipid molecules [23,24] and protein aggregation [25]. All these phenomena can affect the physical properties of donor microenvironment thus changing its quantum yield and distorting the quenching profiles observed in RET studies. For this reason, the acquisition of RET data is desirable to be performed under conditions minimizing lipid-mediated protein effect on the donor spectral characteristics. One of such condition is the low bound protein-to-lipid molar ratio (B/L). The results of RET measurements discussed above have been obtained with the surface concentrations of cytochrome c corresponding to one protein molecule per 50 –400 lipid molecules.

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Approximating cytochrome c by a prolate ellipsoid with the dimensions 3.0  3.4  3.4 and cross-sectional area ca. 9 nm2 one obtains that complete surface coverage by the protein is reached with one cytochrome c molecule per ca. 13 phospholipids (an average area per lipid headgroup for liposomes PC/DPG (9:1) is taken as 0.7 nm2). These estimates imply that within the range of B/L ratios used in RET experiments, the extent of surface occupancy by cytochrome c does not exceed 30%. Under such conditions, no pronounced changes in the maximum and half-width of MBA and RH emission spectra were observed, suggesting that the protein did not cause significant alterations in the polarity and relaxation characteristics of the donor microenvironment. This allowed us to consider energy transfer as the main factor contributing to the quenching of donor fluorescence on cytochrome c association with the lipid bilayer. All the above rationales indicate that the applicability of the formalism developed here is restricted to the donors characterized by rather low sensitivity to the acceptor-induced membrane perturbation. Interestingly, being applied to analyzing RET in another system containing tryptophan residue of Ac-18A-NH2 peptide as a donor and MBA or anthrylvinyl-labeled PC as acceptors our approach appeared to be suggestive of specific orientation of the tryptophan indole ring [26]. In this regard, it is noteworthy that preferential orientation of Ac-18A-NH2 in a membrane (parallel with the bilayer surface) has been evidenced by X-ray diffraction studies [27]. In the following, it seems of interest to assess whether experimental profiles for the quenching of donor fluorescence by acceptor could be indicative of the nonrandom fluorophore orientation. Presented in Fig. 3 are typical results of numerical simulation derived by varying j2 in the widest possible limits (from 0 to 4). Analysis of the simulated data indicates that initial slope of the curves Qr (B/L) (Sin = DQr/D(B/L)) decreases with increasing dt and dc values and lowering the Fo¨rster radius calculated at j2 = 0.67. This allows one to estimate limiting Sin values corresponding to j2 = 0.67, dc = 0 and dtmin (Table 1). The reasonable choice for dtmin seems to be ca. 1 nm since the lesser dt values are characteristic of the terminal methyl group region where fluorophores possess substantial freedom of motion and cannot be considered as distributing between the two planes. Thus, if for a given donor – acceptor pair, initial slope of the experimental curve Qr (B/L) exceeds the limits presented in Table 1, nonrandom fluorophore orientation is likely to occur, with actual j2 value being greater than 0.67. 2.4. Criteria for optimum choice of donor –acceptor pairs Another point of practical significance concerns the choice of the donor set providing a greatest accuracy of the distance estimation. In relation to the aforementioned fluorophore distribution (two donor planes and one acceptor plane), the task consists in the choice of a series of donors exhibiting minimum difference between the dc values recovered for a given acceptor. In an attempt to solve this task, we used the following reasoning. Each donor –acceptor pair can be fully characterized by the five parameters—QD, J, j2, dt and dc. The first three parameters contribute to Ro value, while dt and dc are determined by the bilayer location of donors (dt) and acceptors (dc). As indicated above, the treatment of

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Fig. 3. Quenching profiles derived from numerical integration of Eqs. (10) – (13) by varying distances of the acceptor plane from the bilayer center (a), orientation factor (b) and separation of the outer and inner donor planes (c).

RET data yields the relationships dc(j2) corresponding to certain experimental dependencies Qr(Cas). Allowing j2 to vary from 0 to 4 permits evaluating the widest dc limits— 0– dcmax. Further narrowing of these limits can be achieved by calculating minimum Table 1 Limiting values for initial slope of the plots Qr(B/L) derived for various Fo¨rster radii Ro (nm)

 Sin

2.0 2.5 3.0 3.5 4.0 4.5 5.0

19.7 29.1 38.7 47.7 55.5 61.7 65.9

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2 2 (jmin ) and maximum (jmax ) j2 values for each donor according to approach of Dale et al. [17]

j2min ¼ 2=3ð1  0:5ðdD þ dA ÞÞ

ð16Þ

j2max ¼ 2=3ð1 þ dD þ dA þ 3dD dA Þ

ð17Þ

where dD and dA are depolarization factors related to the steady-state (r) and fundamental (ro) anisotropies of the donor and acceptor:  dD ¼

rD roD

1=2

 ;

dA ¼

rA roA

1=2 ð18Þ

Using the plots dc(j2), one can derive dcmin and dcmax values for a particular donor. In simultaneously analyzing dcmin and dcmax estimates over a series of donors, the final lower dc limit (dcfmin) can be taken as maximum of all dcmin, while final upper dc limit (dcfmax ) would correspond to minimum of all dcmax. Hence, the uncertainty in dc estimation can be reduced by minimizing the difference D = dcfmax  dcmin. In the following, it seems of interest to assess whether there exist certain criteria for the choice of donor set giving minimum D value. The aforementioned rationales appeared to be indicative of at least two of such criteria. Firstly, for the donors markedly differing in their depolarization factors, one could expect the minimum overlap between j2 intervals. As a consequence, the overlap of dc intervals would exhibit narrowing. Secondly, decrease in D value could be attained by reducing the difference between the relationships dc(j2). One way to reduce such a difference is based on employing the donors with close Ro values, i.e. close product of the quantum yield ( QD) and overlap integral ( J) (Eq. (15)). In this case, distinctions between the plots Qr(Cas) (and hence, between the plots dc(j2)) are determined mainly by the differences in j2 and, to a lesser extent, in dt values (Fig. 2). The above two criteria (distinct dD and close Ro) could, in principle, be satisfied by the derivatives of a certain fluorophore varying in their hydrophobicity and residing at different levels within the bilayer. For such fluorescent probes, increase in the quantum yield resulting from the transfer to less polar environment could be compensated by the lowering overlap integral (due to blue shift of emission spectra), thereby providing similar Ro values for a series of donors. 2.5. RET technique in determining bilayer location of the proteins One of the widespread goals of energy transfer membrane studies consists in ascertaining the protein disposition relative to the lipid – water interface, which is characterized, in particular, by the depth of the protein penetration in the lipid bilayer. Within the framework of the above model, this goal can be achieved by two approaches. The first approach can be applied when both donor and acceptor are represented by the lipid-bound fluorescent probes, and the protein penetrates in the outer lipid monolayer

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deeper than acceptors, thereby excluding certain areas in the acceptor plane. In this case, Eqs. (7) – (9) can be rewritten as: W1 ðRÞ ¼

2ð1  fP ÞR ; R2d  da2  NP1 R2P

W2 ðRÞ ¼

2ð1  fP ÞR R2d

 ðdt Fda Þ2  NP2 R2P

;

ð19Þ

where fP = pCPsRP2 is the fraction of an area excluded by protein in the acceptor plane, RP is the radius of the protein cross-section in the acceptor plane, CPs is the surface concentration of bound protein, NP1 and NP2 stand for the number of the protein molecules within the distance Rd from the donor confined to the outer or inner bilayer leaflets, respectively:

NP1 ¼ p R2d  da2 CPs ; NP2 ¼ p R2d  ðdt Fda Þ2 CPs ð20Þ CPs ¼

NA CPb NA CPb P ¼ SL þ SP NA L fi Si þ NA pR2P CPb

ð21Þ

where CPb is the molar concentration of bound protein and SP is the protein contribution to the surface area of the outer acceptor plane. Eq. (13) can be rearranged to give:

N1 ¼ pCas ð1  fP Þ R2d  da2 ; N2 ¼ pCas ð1  fP Þ R2d  ðdt Fda Þ2 ; ð22Þ Parameter RP can be derived from the fitting of experimental data to Eqs. (10), (19) –(22) and then the depth of the protein bilayer penetration can be estimated as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð23Þ dP ¼ R*  R*2  R2P þ dal where R* is an average radius of the protein molecule and dal is the distance from the acceptor plane to lipid – water interface. Another approach to estimating the depth of the protein penetration into the membrane interior is applicable when a lipid-bound fluorescent probe is used as a donor, with the protein intrinsic chromophore (like heme group of cytochrome c) being the acceptor [15,16]. In this case, the lower and upper limits for the depth of the protein penetration in the membrane interior (dP) are given by:

dPmin ¼ 0:5dm  dcmax  rh ; dPmax ¼ 0:5dm  dcmin  rh ð24Þ where rh is the vertical distance from the center of protein-embedded acceptor moiety to the protein face, being in contact with lipids, dm is the membrane thickness. Application of this approach requires extracting the most probable rh value from the crystallographic or otherwise derived information on the protein structure. In practical aspect, it seems of importance to assess what fraction of the acceptor plane should be excluded by the protein to ensure reliable estimation of the parameter RP from the results of RET experiments. This requires the difference between the Qr values measured in the absence and presence of the protein to be markedly greater than experimental accuracy of fluorescence measurements taken as its upper limit of ca. 5%.

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Table 2 Excluded areas (%) corresponding to particular relative increases in Qr value (DP) on the protein addition Ro (nm)

fP (%) DP = 10%

DP = 15%

DP = 20%

2.0 3.0 4.0 5.0 6.0

60 22 11 7 6

89 33 17 11 9

– 45 23 15 12

The data presented in Table 2 are suggestive of the principal possibility for the effect of excluded area to manifest itself in the protein-induced changes of the RET efficiency. The most realistic fP values (less than 20%) that could be attained in experiment are derived with Ro of 4– 6 nm. Thus, donor – acceptor pairs whose Fo¨rster radius exceeds 4 nm seem to be most appropriate for estimating the radius of the protein cross-section in the acceptor plane. Based on these estimates, the depth at which a spherical protein molecule penetrates in the membrane interior can be determined from Eq. (21). Assuming irregular shape of the membrane-incorporated protein fragment, one can evaluate the size of this fragment by employing a set of acceptors located at different levels across the bilayer.

3. Conclusions By summarizing all the questions discussed above, it seems of importance to point out some principal aspects of the energy transfer studies on membrane systems. Experimental examination of such systems must include determination of the amount of membrane-bound acceptors and measurements of the donor quantum yield as a function of the surface acceptor concentration for multiple donor – acceptor pairs. Analyzing the relationships between acceptor distance from the bilayer midplane and orientation factor could be indicative of the specific fluorophore orientation with respect to the membrane surface. The uncertainty in determining the bilayer location of a particular acceptor appears to be minimal for a set of donors with close critical distances of energy transfer but different depolarization factors. In estimating the depth of the protein penetration within the membrane interior, it is desirable to employ a series of acceptors differing in their bilayer location.

Acknowledgements We are indebted to the referee for valuable remarks. References [1] Lakowicz JR. Principles of fluorescent spectroscopy. New York: Plenum; 1999. [2] Matko J, Edidin M. Energy transfer methods in detecting molecular clusters on cell surfaces. Methods Enzymol 1997;278:444 – 62.

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