INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION REFERENCES

In bacterial photosynthesis the primary events of energy transduction are accomplished by the reaction center (RC), an integral pigment-protein complex spanning the intracytoplasmic membrane and promoting light-induced charge separation across the membrane dielectric (Gunner, 1991). In the RC of the purple bacterium Rhodobacter sphaeroides, photon energy promotes the primary electron donor, a bacteriochlorophyll dimer (P), to the first excited singlet state (P*). An electron is consequently transferred (via bacteriopheophytin) from P* to a first ubiquinone-10 (UQ₁₀) electron acceptor (Q_A), generating the primary charge separated state P⁺Q_A. The electron present on Q_A is then delivered to a secondary quinone acceptor, Q_B. In the absence of an electron donor to P⁺ the electron on Q_B recombines with the hole on P⁺ (Feher et al., 1989).

In the presence of electron donors to P⁺, a second photoactivation of the RC leads to the double reduction and protonation of Q_B, which leaves the RC in its quinol state, UQH₂ (Wraight, 1981; McPherson et al., 1990). In vivo, the function of the acceptor quinone complex is to deliver reducing equivalents to a pool of ubiquinone molecules present in the native membrane in stoichiometric excess over the RC (Crofts and Wraight, 1983). This occurs through the free exchange of UQH₂, at the Q_B site of the RC, with oxidized quinone from the pool. In view of the detailed functional and structural information gained in the last decades, the quinone acceptor system of bacterial RCs has become a reference model in the study of the diverse interactions of quinones with electron transfer complexes (Cramer and Knaff, 1990).

A very convenient way of studying the functional properties of the acceptor quinone complex is through the kinetics of charge recombination from either the P⁺Q_B state or the P⁺Q_A state, when in the presence of inhibitors of the Q_A to Q_B electron transfer. These reactions have been extensively studied, yielding to a wealth of information on the energetics of the electron transfer and protonation events involving the quinone acceptor complex (Mancino et al., 1984; Kleinfeld et al., 1984a; Kleinfeld et al., 1985; Gao et al., 1991). Moreover, with the availability of the X-ray diffraction structures of RCs from R. sphaeroides (Allen et al., 1987a, 1987b; Ermler et al., 1994) and Rhodopseudomonas viridis (Deisenhofer et al., 1984, 1985), the analysis of charge recombination kinetics within these RCs has been a valuable tool in testing electron transfer theories and in investigating the protein dynamics associated with charge transfer events (Gunner et al., 1986, 1996; Feher et al., 1988; Labahn et al., 1995; Ortega et al., 1996; McMahon et al., 1998).

These studies have been mainly performed in detergent RC micelles; only in a few cases charge recombination has been examined in RCs reincorporated into artificial phospholipid vesicles more closely mimicking their native environment (Wraight, 1981; Baciou et al., 1990; Agostiano et al., 1995; Nagy et al., 1999). When RCs are inserted into UQ-enriched liposomes, the kinetics of P⁺Q_B recombination is expected to carry information on the exchange interactions of ubiquinone between the RC and the membrane pool (Shinkarev and Wraight, 1993). In spite of this possibility, no systematic study has been carried out in proteoliposomes on the effect of quinone concentration in the lipid phase.

In the present paper the kinetics of P⁺Q_B charge recombination have been studied in RCs from R. sphaeroides reconstituted into lecithin vesicles in the presence of large UQ₁₀ pools and over a range of temperatures. We show that the observed non-exponential kinetics of P⁺ relaxation following a short flash of light can be satisfactorily described by assuming a fast exchange of quinone at the Q_B site of the RC and by considering a rate distribution function arising from an heterogeneity in UQ₁₀ concentration within the vesicle population.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION REFERENCES

Except where otherwise stated, all chemicals were from Sigma Chemical Co. (Darmstadt, Germany), of the highest purity and used without further purification.

The RCs were isolated and purified from R. sphaeroides R-26 according to Gray et al. (1990). The RC containing vesicles were prepared as follows. Soybean phosphatidylcholine (PC) (Epikuron 200, generous gift of Lukas Meyer, Germany) and the proper amount of ubiquinone-10 were dissolved in chloroform, dried under N₂ and resuspended in 10 mM imidazole/100 mM KCl/3% Na cholate (pH 7) buffer. RCs (in 10 mM Tris-HCl, 0.025% lauryldimethylamine N-oxide (LDAO), 1 mM EDTA, pH 7) were added to this suspension, previously sonicated until clarity. Detergent removal was obtained by eluting this suspension through a Sephadex G-50 (Pharmacia, Sweden) column with 10 mM imidazole/100 mM KCl (pH 7) buffer. Detergent removal results in RC-containing small unilamellar vesicles (SUVs) (Venturoli et al., 1993). The mole ratio PC/RC was fixed at 1000 and the RC concentration was about 5 µM.

The kinetics of charge recombination were measured spectrophotometrically by following the re-reduction of P⁺ generated by a short (3 µs half-duration) xenon flash at 540 nm and at 605 nm (Feher and Okamura, 1978). Flash-induced absorption changes (Abs) were recorded also at 450 nm, a wavelength which includes contributions from both P⁺ and semiquinone formation on the acceptor complex (Feher and Okamura, 1978). Flash-kinetic spectrophotometry was performed by using an apparatus of local design (Mallardi et al., 1997).

Sizing of the SUVs was performed by means of quasi-elastic light scattering (QELS) with the instrumental setup described in Berti et al. (1999). Basically the normalized temporal autocorrelation function g₂(q, ) of the intensity of the light scattered by the sample at an angle  with respect to the incident beam has been obtained. This quantity is related to the intensity of the scattered electric field g₁(q, ) through g₂(q, ) = 1 + |g₁(q, )|², where q = (4n/)sin(/2) ( being the wavelength of the beam and n the refractive index of the medium) and  is an instrumental parameter connected to the signal-to-noise ratio (Corti, 1985; Chu, 1991). In a solution of monodisperse spherical vesicles, when q¹ is much larger than the mean intraparticle distance, the autocorrelation function of the scattered electric field decays through a diffusive mechanism and g₂(q, ) = 1 +  exp(2D_Cq²), where D_C is the collective diffusion coefficient of the particles. In the infinite dilution limit, the radius R of the particle can be evaluated from D_C by means of the Stokes-Einstein relationship, D_C = k_BT/6₀R, where ₀ is the solvent viscosity (Corti, 1985).

All the numerical fitting procedures were performed running the STEFIT software (STELAR, Italy) and using routinely three different algorithms (simplex, Powell, quadric) in order to avoid local minima in ² minimization. Unless otherwise stated, confidence limits (67%) were evaluated as linear joint confidence intervals.

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION REFERENCES

Kinetics of P⁺ dark relaxation and quinone binding equilibria

In R. sphaeroides RCs, electron transfer reactions following absorption of a photon can be conveniently described by the following scheme (Shinkarev and Wraight, 1993):

(1)

where k_QB (k^*_QB) and k_BQ (k^*_BQ) are the second-order and first-order rate constants for UQ₁₀ binding and release, respectively, after (before) the light absorption and L_AB is the constant for Q_AQ_B  Q_AQ_B equilibrium, which is much faster than P⁺Q_A  P Q_A recombination (k_AP¹  0.1 s) (Vermeglio and Clayton, 1977; Kleinfeld et al., 1984a). Ubiquinone is tightly bound to the protein at the Q_A site, acting as a prosthetic group, while Q_B, in the oxidized form, can freely exchange with a UQ₁₀ pool present in the membrane bilayer. At room temperature, following photoactivation, the electron returns from Q_B to P⁺ via the primary quinone acceptor Q_A, the contribution of direct tunneling being negligible (Kleinfeld et al., 1984a).

Under pseudo-first-order conditions, i.e., in the presence of a stoichiometric excess of UQ₁₀ over the RC, Scheme 1 can be analytically solved (Shinkarev and Wraight, 1993). On this basis, the decay of P⁺ following a flash is described by a biexponential function, i.e.:

(2)

where k_F and k_S are given by:

(3)

(4)

In Eqs. 2-4, Q is the quinone concentration in the membrane pool, F and S = 1  F are the fraction of the fast and slow components which depend in general upon Q.

When the exchange of quinone between the RC and the exogenous pool is slower than P⁺Q_A recombination, k_F = k_AP and F is simply the fraction of RCs without Q_B at the time of the flash. If, on the contrary, quinone exchange at Q_B is faster than the return of the electron from Q_A to P⁺, as discussed in detail by Shinkarev and Wraight (1993), the expected kinetics of P⁺ re-reduction are well approximated by a monoexponential decay, characterized by a rate constant (k_P) that decreases as Q is increased, according to:

(5)

where K_bind = k_QB/k_BQ represents the equilibrium constant for UQ₁₀ binding after the light absorption.

We have analyzed the kinetics of charge recombination in R. sphaeroides RCs reconstituted into liposomes in the presence of a large UQ₁₀ pool, at two UQ/RC stoichiometric ratios, over the temperature range 275 K  T  307 K. Examples of the kinetics of the absorbance change (Abs) recorded at 450, 540, and 605 nm following a flash are shown in Fig. 1 for UQ₁₀/RC = 10 at T = 304 K. As is evident in Fig. 1, and under all conditions tested, the experimental P⁺ decay following a flash does not fit monoexponential kinetics; in a first attempt, therefore, the experimental kinetics, l(t) = Abs(t)/Abs(0), have been fitted to a double exponential function (Eq. 2). Since at each temperature and UQ₁₀/RC ratios tested the decay kinetics recorded at the three different wavelengths were found in excellent agreement when properly normalized, a procedure of global analysis was adopted (Becheem, 1992) in order to increase the confidence in the fitting parameters. Nonlinear ² minimization performed simultaneously on the kinetics recorded at 450, 540, and 605 nm yields the parameters listed in Table 1. A deconvolution of the P⁺Q_B charge recombination kinetics in two exponential components characterized by rate constants compatible with the results of Table 1 has been reported for RCs reconstituted into liposomes in the presence of excess quinone (Agostiano et al., 1995).

View larger version (17K): [in this window] [in a new window]   FIGURE 1   Kinetics of charge recombination following a flash of light measured at 450, 540, and 605 nm in R. sphaeroides RC incorporated into lecithin vesicles containing a pool of ubiquinone ([Q]/[RC] = 10). Proteoliposomes corresponding to a final RC concentration of 5 µM were suspended in 10 mM imidazole/100 mM KCl (pH 7) buffer. Each trace is the average of 4 measurements performed at 304 K. To increase figure readability only 10% of the experimental values digitized during the dark relaxation following the flash are plotted as open squares. All information has been used in numerical fitting. Continuous lines show the best fit to Eq. 6 obtained by numerical 2 minimization performed simultaneously over traces recorded at the three wavelengths.

Although a satisfactory fit could be obtained for each experimental condition, the corresponding values of k_F and k_S appear to be physically incompatible with the expectations of Scheme 1, as shown by the following argument.

Scheme 1 predicts a biexponential decay of P⁺ when quinone exchange between the pool and the Q_B site is slower than or comparable in rate with P⁺Q_A recombination. The possibility that the parameters of Table 1 reflect a slow exchange can be immediately rejected, since in this case k_F should coincide with k_AP, which is approx. 10 s¹ and is characterized by a slight inverse temperature dependence on the temperature range investigated (Feher et al., 1987). The k_F values obtained from a biexponential deconvolution of P⁺ decays are at least one order of magnitude smaller and they clearly increase when the temperature increases. On the other hand, when assuming that quinone exchange share the same time scale of P⁺Q_A recombination, Eqs. 3 and 4 fix a lower limit for the rate constants k_F and k_S, given by k_F + k_S > k_AP and k_Fk_S  k_AP²/(1 + L_AB). Fig. 2 shows that the data of Table 1 are in sharp conflict with the first inequality. The data are also in conflict with the second inequality by more than one order of magnitude (Fig. 2), when L_AB is calculated from the enthalpy (H_AB^o = 13.5 kJ mol¹) and entropy (S_AB^o = 19.3 J mol¹ K¹) changes for Q_AQ_B  Q_AQ_B electron transfer determined in reverse micelles of phospholipids in N-hexane (Mallardi et al., 1997). In detergent RC dispersions, very similar H_AB^o and S_AB^o values have been obtained (Mancino et al., 1984), which are expected to hold also in SUVs. We conclude that the non-exponential character of charge recombination kinetics systematically observed in liposomes cannot be accounted for by Eqs. 2-4.

View larger version (18K): [in this window] [in a new window]   FIGURE 2   Sum (triangles) and product (circles) of the rate constants obtained from biexponential deconvolution of P+ decay in proteoliposomes with [Q]/[RC] = 25 (filled symbols) and [Q]/[RC] = 10 (open symbols), as a function of temperature. Data are from Table 1. kAP has been set equal to 10 s1 (Kleinfeld et al., 1984a) and the equilibrium constant LAB has been evaluated according to LAB = exp(HABo/RT + SABo/R), assuming for the enthalpy (HABo) and entropy (SABo) changes the values (Table 2) determined in reverse micelles (Mallardi et al., 1997). The arrows indicate the appropriate ordinate scale for the different lines in the figure. Note that theory predicts kF + kS > kAP and kFkS > kAP/(1 + LAB). See text for further details.

Cumulant analysis

As pointed out by Shinkarev and Wraight (1993) various estimates of the rate of quinone exchange between RC and the UQ pool in the native membrane indicate that it is much faster than P⁺Q_A recombination and suggest that also in artificial phospholipid vesicles containing R. sphaeroides RCs and UQ₁₀, fast quinone exchange occurs. Under these conditions a monophasic kinetics of P⁺Q_B recombination is expected, characterized by a single (Q dependent) rate constant k_P (Eq. 5). However, this prediction of Scheme 1 assumes implicitly that the quinone pool is homogeneously available to all the RCs in the lipid phase. Such an assumption is expected to be seriously inappropriate in vesicles, where the size polydispersity could determine a broad quinone concentration distribution which would result in turn, according to Eq. 5, in a k_P distribution. Therefore, we describe the kinetics of P⁺Q_B recombination with a rate constant distribution function, P(k_P), according to l(t) = Abs(t)/Abs(0) = P(k_P)e^k_Ptdk_P. A similar approach has been adopted to account for the nonexponential kinetics of P⁺Q_A recombination in RCs cooled at cryogenic temperatures in the light (Kleinfeld et al., 1984b; McMahon et al., 1998).

In order to analyze accordingly the kinetics of charge recombination, a method based on the statistical cumulant generating function formalism is proposed, which has been successfully used in the analysis of QELS data in the last two decades. Since l(t) can be thought as a sum of exponential decays, exactly as the intensity autocorrelation function measured in QELS experiments (Koppel, 1972), we describe the charge recombination kinetics with a truncated cumulant expansion:
where K_i are the cumulants. K₁ = k_P gives the first moment of P(k_P) and K₂ = _k² gives the second moment around the mean (Koppel, 1972). The third and fourth cumulants can be related to higher moments of P(k_P), but in the case of our kinetics they have been found so close to zero that a truncation to the second term is appropriate to satisfactorily describe the charge recombination kinetics, l(t), according to:

(6)

Experimental decays have been fitted to Eq. 6, again performing a global analysis in which chi-square has been minimized simultaneously on the kinetic traces acquired at the three wavelengths for each condition (T, [Q]). An example of the best fitting decays obtained by this procedure is shown in Fig. 1. Under all conditions tested, deconvolution according to Eq. 6 yields accurate descriptions of the experimental kinetics, characterized by the parameters listed in Table 1. Qualitatively, as expected from Eq. 5 and from the thermodynamic parameters governing quinone binding and Q_AQ_B  Q_AQ_B electron transfer (Mallardi et al., 1997), k_P increases with T and decreases with [Q] (Fig. 3).

View larger version (23K): [in this window] [in a new window]   FIGURE 3   Mean rate constant, kP, obtained by fitting P+ decays to Eq. 6 as a function of temperature at two different [Q]/[RC] ratios (Table 1). Dotted curves represent the predictions of Eq. 5 with kAP = 10 s1 and LAB and Kbind calculated from the corresponding enthalpy and entropy changes determined in reverse micelles (Table 2). The prediction of Eq. 5 at saturating quinone concentrations is also shown (see text). Solid curves are the best fit to Eq. 5 obtained by considering simultaneously the [Q] and T dependence, with the enthalpy and entropy changes for the binding (Hbindo and Sbindo) and for the QAQB  QAQB (HABo and SABo) equilibria as adjustable parameters. The best fitting values of these parameters are listed in Table 2.

Origin of k_P polydispersity

In principle, the spread in k_p values implicitly assumed in the cumulant analysis could be explained in terms of different conformations of the guest protein or as due to an heterogeneity in the quinone concentration within the liposome population. The first hypothesis is related to the existence of several protein conformational substates, each of them having different intramolecular distances and relative orientations of the cofactors. Although several indications can be found in the literature supporting the existence of different RC substates (Kleinfeld et al., 1984b; McMahon et al., 1998; Graige et al., 1998), all the experimental evidence points to extremely short characteristic times (from 1 ps to 1 ms) (McMahon et al., 1998) for conformational interconversion at room temperature. Thus, in a time scale of seconds, the single turnover flash experiments should probe only an average protein conformation. As to the second hypothesis, from a kinetic point of view, a heterogeneity in the local UQ₁₀ concentration (Q) within the liposome population should be effective on a very long time scale (hours if not days). In fact, both ubiquinone and phospholipids are practically water-insoluble species (in both cases the monomer concentration in water is beyond the detection limit of current analytical techniques); moreover, on the time scale of interest, spontaneous fusion of vesicles is extremely unlikely to occur, requiring weeks in the absence of any fusogenic agent (Sackmann, 1995).

The spread in Q, in turn, can arise from two factors, namely, the random distribution of UQ₁₀ molecules among vesicles and the size polydispersity of the vesicles themselves. Information on this last point has been gained by QELS analysis of the same proteoliposome preparations in which charge recombination kinetics were examined. As pointed out in Materials and Methods, if non-interacting vesicles of different size are present, each population will contribute to the decay of the autocorrelation function with a term exp[D(R)q²], being D(R) the diffusion coefficient of the population of radius R. The field autocorrelation function will be given by

(7)

where P() is the appropriate normalized distribution of decay rates (R) = D(R)q², which, for spherical particles, is related to the size distribution P(R) through the Stokes-Einstein equation. The g₂(q, ) of the samples used in charge recombination measurements were analyzed for the vesicles' mean radius and size standard deviation, using both the classical cumulant analysis (above described) and the numerical inversion of the Laplace transform represented in Eq. 7, by means of the CONTIN routine implemented by Provencher (1982). These two approaches give consistent results (Fig. 4) and show that vesicle preparations are characterized by a mean radius, R, of 50 nm and a size standard deviation, _R, of about 15 nm. On this basis, the mean number of UQ₁₀ molecules per vesicle can be easily evaluated once the overall quinone and lecithin number density ([Q] and [PC], respectively) are known. The total interfacial surface for unitary volume is [PC], where  is the polar headgroup area of a lecithin molecule in a bilayer (0.7 nm²) (Angelico et al., 2000). Let P(R)dR be the probability of finding vesicles with radii bracketed by R and R + dR. Neglecting the bilayer thickness, the number density of liposomes with radii lying between R and R + dR is 1/2[PC] (R²P(R)dR)/(R²P(R)dR) · 1/4R² where the term 1/2 comes from the presence of two interfacial phospholipid layers per vesicle. Therefore, the total number of vesicle per unit volume, n_lip, is

(8)

where µ_R,2 = _R² + R² is the second moment of the size distribution. Thus the mean number of UQ₁₀ per liposome, N, is [Q]/n_lip.

View larger version (20K): [in this window] [in a new window]   FIGURE 4   Determination of the size distribution of proteoliposomes by QELS. Log-log plot of g2(q, )  1, determined in SUVs (dots) and best-fit obtained by cumulants analysis (solid line). The fit corresponding to the numerical inversion of the Laplace transform (CONTIN) is not shown for the sake of clarity. Experimental conditions: [Q]/[RC] = 25; T = 298 K;  = 90°;  = 532 nm. The sample was diluted in order to minimize the intervesicle interaction. For the refractive index n and the viscosity of the solvent 0 values of pure water have been assumed. The inset shows the size distribution obtained by CONTIN analysis (histogram) and the log-normal size distribution (solid line) characterized by the R and R values determined by cumulant analysis of QELS data (in this case only the moments of the distribution are accessible).

The distribution of guest molecules among colloidal hosts has been the subject of several studies which point to a Poisson distribution (Zana, 1987). Since N is quite high (of the order of thousands), the probability of quinone occupancy P(N) can be well approximated by a Gaussian distribution function centered at N and with a variance _N² = N. The local UQ₁₀ concentration (number of molecules per unit volume of lipidic phase) into a vesicle of radius R will be Q = N/(4R²v_lip), where the hydrophobic volume domain is calculated as the aggregation number (4R²/) times the molecular volume of the lecithin hydrophobic tails (v_lip = 1.053 nm³) (Angelico et al., 2000). Q is a function of N and R and can be expanded in Taylor series obtaining, at least in a first approximation, the mean value of quinone concentration Q. This, using Eq. 8, can be written as:

(9)

and the variance of P(Q) by means of the relationship:

(10)

where the partial derivatives are evaluated at N and R.

Eq. 10 deserves some comments: even in the case of monodispersed vesicles (_R = 0) a spread of Q with a variance _Q² = Q²/N is expected. On the other hand, for large N, _Q/Q = 2_R/R, which means that the degree of Q polydispersity will only depend on the vesicle size distribution and therefore any attempt to eliminate Q heterogeneity in polydispersed liposomes by increasing UQ₁₀ concentration, is useless.

By means of Eqs. 9 and 10 it is thus possible to evaluate with a sufficient accuracy the first and second moments of the UQ₁₀ distribution function, P(Q).

P(k_P), can be defined in terms of P(Q) as:

(11)

By considering that the rate constant describing the charge recombination kinetics, k_P, depends on Q according to Eq. 5, we have

(12)

and, combining Eqs. 11 and 12, the rate distribution function, P(k_P), can now be brought back to P(Q), obtaining:

(13)

Since both L_AB and K_bind are function of T, also P(k_P) will be temperature dependent.

Rate distribution functions, P(k_P), calculated over the T range investigated and for [Q]/[RC] = 25, are shown in Fig. 5. P(k_P) has been evaluated assuming both a Gaussian (with a cutoff at Q = 0) and a log-normal distribution, P(Q), of Q among vesicles. Eqs. 9 and 10 have been used to determine Q and _Q² from the lipid and quinone composition of the samples and from the R and _R values obtained by QELS analysis of proteoliposomes. Starting from P(Q) (Fig. 5, inset), Eqs. 5 and 13 allow the evaluation of P(k_P) at different temperatures. In these equations, L_AB and K_bind have been calculated at the appropriate temperature from the values of H^o and S^o for Q_AQ_B  Q_AQ_B electron transfer and quinone binding previously determined in reverse micelles (Mallardi et al., 1997; Table 2). The resulting P(k_P) distributions, shown in Fig. 5, are compatible with the corresponding values of k_P determined by cumulant analysis of experimental P⁺ decays (Table 1). Increasing T, k_P values increase and the P(k_P) distribution function becomes progressively broader. Analogous simulations, in good agreement with experimental k_P values, have been obtained at [Q]/[RC] = 10 (not shown). The predictions of Fig. 5 are relatively insensitive to the choice of the Q distribution. This last point lead us to use the first term of a Taylor expansions of k_P(Q) around Q to evaluate k_P from Eq. 5 simply by posing Q = Q. This theoretical prediction is shown in Fig. 3 (dotted line) for two values of [Q] as a function of T and is compared with the values of k_P coming from the cumulant analysis of the charge recombination kinetics. In Fig. 3 the T dependence expected at saturating Q, when k_P = k_AP/(1 + L_AB), is also presented. This prediction deviates appreciably from the theoretical behavior expected at [Q]/[RC] = 25 when the temperature increases, clearly indicating that the binding equilibrium is an important factor in determining the kinetics of charge recombination.

View larger version (26K): [in this window] [in a new window]   FIGURE 5   Rate distribution functions, P(kP), calculated according to Eq. 13 at different temperatures for [Q]/[RC] = 25, assuming Gaussian (dotted) and log-normal (solid) P(Q) distributions (inset). Values of Q and Q2 have been determined by means of Eqs. 9 and 10 from the lipid and quinone composition and from QELS analysis of proteoliposomes. In Eqs. 13 and 5, LAB and Kbind have been calculated at the appropriate temperature from the corresponding enthalpy and entropy changes determined in reverse micelles (Table 2). The arrows indicate the values of kP obtained from cumulant analysis of the experimental charge recombination kinetics (Table 1).

View this table: [in this window] [in a new window]   TABLE 2   Enthalpy, entropy, and free energy changes of quinone binding and QAQB  QAQB electron transfer as determined from the analysis of charge recombination kinetics in reverse micelles, phospholipid vesicles, and LDAO micelles

A comparison between simulation and experiment in the presence of 10 and 25 UQ₁₀ molecules per RC molecule reveals a remarkable agreement. Indeed, the absence of any adjustable parameter in the simulations of Figs. 3 and 5 has to be emphasized: experimental points come from the cumulant analysis of the kinetic traces, while predictions were done on the basis of chemical composition of the samples, of R and _R measured by QELS, and of the thermodynamic parameter and k_AP values previously determined in reverse micelles. This agreement suggests that the thermodynamic parameters ruling the charge recombination kinetics are very close in SUVs and in reverse micelles. A fit of Eq. 5 performed simultaneously to the data collected at the two [Q]/[RC] ratios, under the condition Q  Q and with the enthalpy and entropy changes for the binding (H_bind^o and S_bind^o) and for the Q_AQ_B  Q_AQ_B (H_AB^o and S_AB^o) equilibria as adjustable parameters results in a quite satisfactory description, shown in Fig. 3 by the solid lines, and yields the parameters listed in Table 2. Enthalpy and entropy changes obtained for quinone binding in reverse micelles and vesicles (Table 2) coincide within the experimental error, indicating the same quinone affinity for the Q_B binding site in SUVs and in reverse micelles. An analogous agreement is obtained between the thermodynamical parameters of Q_AQ_B  Q_AQ_B electron transfer in the two systems.

Comparison with the charge recombination kinetics in detergent RC suspensions

As mentioned in the Introduction, charge recombination kinetics has been studied extensively in detergent suspensions of purple bacteria RCs. Recently, Shinkarev and Wraight (1997) have analyzed the interaction of quinone and detergent with R. sphaeroides RCs developing a model which allows a deep understanding of charge recombination kinetics and providing a means of determining both L_AB and the equilibrium constant of quinone binding at the Q_B site. In view of a comparison with the results obtained by us in phospholipid vesicles, some differences and common features which characterize the two systems investigated and the models correspondingly proposed are summarized in the following: 1) both LDAO micelles and phospholipid vesicles are disconnected lipophilic domains, but only one RC is present in each detergent micelle, together with few or none quinone molecules, whereas several RCs are inserted in the same vesicle; 2) in the detergent micelles examined by Shinkarev and Wraight (1997) the ratio [Q]/[RC] is quite low (2) while in our experiments [Q]/[RC]  10); 3) as in vesicles, in detergent suspensions the exchange between the Q_B site and the immediate quinone pool (i.e., quinone within the same RC micelle) is assumed to be fast, while the exchange of quinone between different micelles occurs much more slowly than charge recombination. Thus (in LDAO micelles) the real physical system, established by the quinone distribution, is discrete (Shinkarev and Wraight, 1997), and the kinetics of P⁺ dark relaxation is described by the sum of exponential decays (actually the deconvolution of the experimental curves was limited to two exponential components).

From a physical point of view, our approach to the vesicle system is quite similar, the main difference being due to the presence of several RC which share the same quinone-pool, i.e., our system is continuous. When this feature is coupled with the size polydispersity (high in vesicles but extremely low in RC-containing detergent micelles) and with the high [Q]/[RC] ratio allowed by vesicles, different kinetics of charge recombination naturally emerge.

Since in detergent dispersions the kinetically relevant unit is the single RC micelle containing a number n of secondary/pool quinone molecules, quinone binding affinity at the Q_B site is determined by a (dimensionless) intramicellar association constant, K_Q⁺ (Shinkarev and Wraight, 1997). A comparison between the binding processes described in terms of concentrations (in vesicles and reverse micelles) and in terms of number of quinones per RC micelle (in LDAO) gives: K_Q⁺n = K_bind[Q]. We can evaluate the free energy change of quinone binding, G_bind,LDAO^o, in LDAO micelles by using the value K_Q⁺ = 0.6 ± 0.2 (Shinkarev and Wraight, 1997) and the relationship G_bind,LDAO^o = RTln(K_Q⁺ N_ag V_LDAO) where N_ag = 250 ± 50 is the number of detergent molecules in the RC "belt" (Feher and Okamura, 1978; Gast et al., 1994) and V_LDAO = 0.2557 L mol¹ is the LDAO molar volume (Milioto et al., 1987). This procedure yields G_bind,LDAO^o = 9.0 ± 1.3 kJ/mol, a value relatively close to that determined by us in phospholipid vesicles. As shown in Table 2 the free energy change of Q_AQ_B  Q_AQ_B electron transfer obtained from cumulant analysis in proteoliposomes coincides within the experimental error with that measured in LDAO RC micelles. It appears therefore that the qualitatively different kinetics of P⁺Q_B recombination observable in reverse micelles, vesicles, and LDAO direct micelles can all be brought back to the same process (governed by very similar thermodynamical parameters in the different environments), i.e., the fast exchange of quinone molecules between the protein binding site and a quinone pool. The hosting systems only defines the boundary conditions: number of RC sharing the same pool, size of the pool, heterogeneity of the lipophilic domain size, and rate of exchange between quinone pools in different domains.

	CONCLUSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION REFERENCES

A new approach, based on the formalism of the statistical cumulant generating function, has been developed to analyze the kinetics of charge recombination in RCs incorporated into small unilamellar phospholipid vesicles containing a large ubiquinone pool. This analysis, when considering the distribution of UQ₁₀ molecules in the vesicle population and the size polydispersity of proteoliposomes probed by QELS measurements, accounts satisfactorily for the non-exponential kinetics of P⁺Q_B recombination observed over a range of temperatures at different [Q]/[RC] ratios. The model provides a means of determining the equilibrium constant of quinone binding at the Q_B site and of electron transfer between Q_A and Q_B in a lipid environment mimicking the native membrane. The proposed approach provides a starting point in the analysis of the interaction between small lipophilic cofactors and membrane enzymes directly into the lipid matrix.