Eur Biophys J (2014) 43:301–315 DOI 10.1007/s00249-014-0963-z
Original Paper
The binding of quinone to the photosynthetic reaction centers: kinetics and thermodynamics of reactions occurring at the QB‑site in zwitterionic and anionic liposomes Fabio Mavelli · Massimo Trotta · Fulvio Ciriaco · Angela Agostiano · Livia Giotta · Francesca Italiano · Francesco Milano
Received: 14 January 2014 / Revised: 7 April 2014 / Accepted: 25 April 2014 / Published online: 14 May 2014 © European Biophysical Societies’ Association 2014
Abstract Liposomes represent a versatile biomimetic environment for studying the interaction between integral membrane proteins and hydrophobic ligands. In this paper, the quinone binding to the QB-site of the photosynthetic reaction centers (RC) from Rhodobacter sphaeroides has been investigated in liposomes prepared with either the zwitterionic phosphatidylcholine (PC) or the negatively charged phosphatidylglycerol (PG) to highlight the role of the different phospholipid polar heads. Quinone binding (KQ) and interquinone electron transfer (LAB) equilibrium constants in the two type of liposomes were obtained by charge recombination reaction of QB-depleted RC in the presence of increasing amounts of ubiquinone-10 over the temperature interval 6–35 °C. The kinetic of the charge recombination reactions has been fitted by numerically solving the ordinary differential equations set associated with a detailed kinetic scheme involving electron transfer reactions coupled with quinone release and uptake. The Fabio Mavelli and Massimo Trotta contributed equally to this work. Electronic supplementary material The online version of this article (doi:10.1007/s00249-014-0963-z) contains supplementary material, which is available to authorized users. F. Mavelli · F. Ciriaco · A. Agostiano Department of Chemistry, University of Bari, 70126 Bari, Italy M. Trotta · A. Agostiano · F. Italiano · F. Milano (*) Italian National Research Council, Institute for Physical and Chemical Processes (CNR-IPCF), 70126 Bari, Italy e-mail: [email protected] L. Giotta Department of Biological and Environmental Sciences and Technologies (DiSTeBA), University of Salento, 73100 Lecce, Italy
entire set of traces at each temperature was accurately fitted using the sole quinone release constants (both in a neutral and a charge separated state) as adjustable parameters. The temperature dependence of the quinone exchange rate at the QB-site was, hence, obtained. It was found that the quinone exchange regime was always fast for PC while it switched from slow to fast in PG as the temperature rose above 20 °C. A new method was introduced in this paper for the evaluation of constant KQ using the area underneath the charge recombination traces as the indicator of the amount of quinone bound to the QB-site. Keywords Bacterial photosynthesis · Protein–lipid interaction · Ligand binding
Introduction The photosynthetic reaction center (RC) is the key protein in the conversion of solar light to chemical energy during the photosynthetic process (Allen and Williams 1998). The RC is a membrane protein that, in the purple bacterium Rhodobacter (Rb.) sphaeroides, is located in the intra-cytoplasmic membranes (Feher and Okamura 1978). The structure of the protein has been obtained at atomic resolution of 1.87 Å (Koepke et al. 2007). Its interaction with lipids (Jones 2007) is becoming of great interest both for basic research (Deshmukh et al. 2011a, b; De Leo et al. 2009; Wohri et al. 2009; Milano et al. 2007a) and for potential device assembly (Boghossian et al. 2011; Ham et al. 2010). The protein contains several cofactors arranged in two symmetrical branches, A and B, and, upon light absorption, a cascade of electron transfer reactions is promoted. An electron is released along the A branch from the primary donor (D) and reaches the primary quinone acceptor QA (Gunner 1991; Kleinfeld et al. 1984a).
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The electron is reversibly exchanged with the secondary quinone acceptor QB, most likely through an iron–histidine bridge (Di Donato et al. 2004; Burggraf and Koslowski 2011). In the presence of an exogenous electron donor, typically a cytochrome molecule, these electron transfer reactions occur twice, leading to the full reduction of QB to quinol, which leaves the protein and is replaced by a new quinone molecule uptake from the membrane pool (McPherson et al. 1990). Both quinone and quinol continuously bind and unbind to the QB site of the protein (Crofts et al. 1983). In isolated RC, in absence of an exogenous donor, the final charge-separated state decays in the dark via a charge recombination reaction (CRR), whose kinetics can be used to retrieve kinetic and thermodynamic information about the energetics of the electron acceptor complex and the quinone binding. The interquinone electron transfer equilibrium constant LAB and its temperature dependence in different environments is well-stated in the literature (Agostiano et al. 1998), while the quinone binding constant KQ is more difficult to assess since the native ubiquinone-10 (UQ10) is highly hydrophobic. In detergent micelles, only thermodynamic data of KQ for the water soluble ubiquinone-0 (UQ0) are available (McComb et al. 1990). This problem has been partially overcome studying the binding of UQ10 to RC in reverse micelles, where the quinone is dispersed in the bulk organic phase (Mallardi et al. 1997). In another paper (Palazzo et al. 2000), RCs are reconstituted in lecithin vesicles, and KQ is studied by exploiting the quinone concentration polydispersity between different liposomes at high Q/RC ratio. Compared to direct or reverse micelles, liposomes represent a solubilizing environment that better mimics the conditions in which RCs are found in the intracytoplasmic membranes. Furthermore, liposomes allow one to use the physiological UQ10 for the QB-site binding studies and to modulate the UQ10/RC ration over a wide range. The possibility of assembling liposomes from different phospholipids also enables revealing specific features of the lipid–protein interaction. In the present work, the RC was reconstituted in both PC and PG vesicles and the specific role of the lipid environment on the quinone binding reaction was studied by titrating the QB-site in the temperature interval 6–35 °C and recording the relevant CRR decays. In the investigated temperature range, the liposome bilayer is always in its fluid state, ensuring that the quinone mobility is modulated only by temperature. The binding constants at different temperatures were obtained by means of established methods in the literature (Shinkarev and Wraight 1993), fitting appropriate parameters, extracted from the CRR kinetics, versus the quinone concentration, under different quinone mobility regimes in the bilayer. Quinone mobility is heavily dependent on temperature; hence, none of the previously mentioned methods can be applied in the entire investigated temperature range. A method independent from the
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mobility regime, based on the area underneath the CRR curves is, hence, introduced, leading to an improved system description. The CRR data were also analyzed by means of numerical simulation, using all the kinetic constants involved in the process, evaluating their confidence intervals and their possible correlations. By this approach, reliable values for the quinone binding constants in both kinds of liposomes and information on the mobility of the quinone as a function of the temperature were obtained. This kind of study is gaining increasing relevance in System Biology; since mathematical models of biological systems have been recently successfully extended to the level of small cellular compartments (Geyer et al. 2007, 2010; Mavelli 2012; Mavelli and Ruiz-Mirazo 2010). It becomes crucially important to estimate the highest possible number of kinetic parameters with independent experiments to increase the robustness of theoretical models.
Materials Chemicals The phospholipids 1,2-diacyl-sn-glycerol-3-phosphocholine (99 %—phosphatidylcholine, PC), 1,2-diacyl-snglycerol-3-phosphoryl glycerol (98 %—phosphatidylglycerol, PG) and ubiquinone-10 (UQ10) were purchased from Sigma, stored at −70 °C and used without any further purification. Sodium cholate was also from Sigma. Lauryl dimethyl amino N-oxide (LDAO) was from Fluka. Terbutryne was obtained from Chem Service, USA. Sephadex G-50 was purchased from Pharmacia. Reaction centers Reaction centers were isolated from Rb. sphaeroides strain R26 following the procedure illustrated by Isaacson et al. (1995). Protein purity was checked using the ratio of the absorbance at 280 and 802 nm, which was kept below 1.3, and the ratio of the absorbance at 760 and 865 nm, which was kept equal to or lower than 1. The average quinone content was 1.8 per RC. QB site depletion was accomplished following the procedure outlined in (Okamura et al. 1975) yielding a depletion of about 95 %. Steady state and transient optical spectroscopy RC optical spectra were recorded using a Cary 5000 spectrophotometer (Varian Inc., Australia). CRR kinetics were recorded at the chosen wavelength using a kinetic spectrophotometer of local design (Milano et al. 2003) implemented with a Hamamatsu R928 photomultiplier
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and a Nd–Yag laser (Quanta System) used for saturating RC photoexcitation. The decay traces were recorded up to complete recovery (at least 4–5 times their decay times) and the samples were dark adapted for at least 5–6 times the time interval used for recording the signal. Three to six independent experiments were performed for each sample and each experiment was an average of at least four traces. No drift induced by the measuring beam was visible in any of the experiments. Liposomes preparation RC reconstitution in liposomes was accomplished by the micelle to vesicle transition (MVT) method using gel exclusion chromatography for detergent removal following the procedure outlined in Trotta et al. (2002), Venturoli et al. (1991) and Kutuzov (1990) and using a phospholipid to RC ratio of 1,000:1. The size of the vesicle was assessed from their hydrodynamic radius, obtained by dynamic light scattering (DLS) using the Horiba LB-550 nanoparticle size analyzer (Horiba Jobin Yvonne) as previously described (Milano et al. 2009). In the present work the hydrodynamic radius of liposomes was found to be 55 ± 6 nm. The RC and quinone concentrations used in the following discussion are always referred to the bilayer volume. The calculation was performed as previously described (Milano et al. 2009) using a value of [RC]bilayer = 1.2 ± 0.3 mM. The quinone concentration could not be evaluated directly; hence, it was assumed that the molar ratio realized in the mixed micelles before loading in the column is maintained in the final liposome preparation (Milano et al. 2009).
Mathematical background In this section, the kinetic mechanism used to describe the charge recombination will be described along with the numerical integration algorithm and the best-fitting procedure used to get the quinone binding constants. Kinetic mechanism and experimental decay curves The complete set of elementary events assumed to describe the time behavior of RC after a short flash of saturating excitation light is reported in Fig. 1 (Crofts et al. 1983) which is well accepted by researchers in the field (McComb et al. 1990; Shinkarev and Wraight 1997; Gunner 1991). This scheme allows one to rationalize the decay of the fraction of all species in a charge separated state χD+:
χD+ = χD+ Q− + χD+ Q− QB + χD+ QA Q− . A
A
B
In fact, the CRR reaction rate is strongly affected by the quinone exchange kinetics at the QB-site that also depends
Fig. 1 Proposed set of elementary reactions for flash excitation and ′ dark relaxation of isolated RC. kAD and kAD represent the kinetic − constant of the electron transfer from QA to D+ when the QB pocket is empty or occupied respectively; kBD is the kinetic constant of the + ∗ direct charge recombination from Q− B to D ; kin and kin represent the bimolecular kinetic constant of the quinone association to the QB site ∗ and k in the charge separated and neutral state respectively; kout out represent the kinetic constant of the quinone dissociation from the QB site in the charge separated and neutral state respectively; kAB is the kinetic constant for the electron transfer reaction from Q− A to QB, while kBA is the kinetic constant for the electron transfer in the opposite direction. A detailed description for all kinetic constants is given in supplementary material
on the RC environment, i.e., direct or reverse micelles or liposomes. For instance, if the QB pocket is empty, CRR occurs by direct tunneling from Q− A with a mono-exponential decay and a typical time constant τ which is quite independent of the RC surroundings: 1/τ = kAD ≈ 10 s−1. On the other hand, at saturating quinone concentrations, the decay is still mono-exponential but slower, with a time constant: τ∞ = (1 + LAB)/kAD dependent on LAB = kAB/kBA, whose actual value varies for different solubilizing environment of the protein (Kleinfeld et al. 1984b; Shinkarev and Wraight 1993). This retardation arises because the backreaction occurs mainly from the D+ Q− A state and electron transfer to QB diminishes the time averaged population of − + Q− A, while the direct route from D QA QB accounts for less than 5 % (Kleinfeld et al. 1984b). When the quinone concentration is in the sub-saturating range, the CRR becomes generally biphasic:
χD+ = AF exp(−kAD t) + AS exp(−t/τS ),
(1)
where the first exponential accounts for the direct charge recombination (fast decay with amplitude AF) and its time constant 1/kAD is independent from the occupancy of the QB-site. The time constant τS of the second exponential (slow decay with amplitude AS) results from a complex combination of electron transfers and quinone binding ∗ , k ) and unbinding (k ∗ , k ) from the Q -site (Shinka(kin in B out out rev and Wraight 1993). AS is roughly proportional to the fraction of QB-populated RCs and AS + AF = 1.0, since at time t = 0 all the reactions centers are present in the excited states: χD+ = 1.0.
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Furthermore, in this quinone concentration range, different CRR time behaviors can be also observed since the different solubilizing environment can affect the quinone release kinetic constant kout. Therefore, it is possible to define a slow (kout ≪ kAD) and a fast quinone exchange regime (kout ≫ kAD). In the slow exchange regime, like in the case of the detergent LDAO (Agostiano et al. 1999; Mezzetti et al. 2011), the CRR is still biphasic and τS is independent of the QB-site population. The contribution of slow decay AS to χD+ can be directly used for the quinone binding constant determination (KQ) by fitting AS vs. total quinone concentration with a quadratic function (Agostiano et al. 1999) (amplitude method or AM, see “Appendix 1”). When kout ≫ kAD, like in reverse micelles (Mallardi et al. 1997), and [Q] ≫ [RC] the CRR time course reduces to a single exponential decay, and τS can be proved to be a function of the free average quinone concentration 〈[Q]〉 and the light binding constant KQ∗ (Shinkarev and Wraight 1993): LAB KQ∗ �[Q]� 1 . τS = 1+ (2) kAD 1 + KQ∗ �[Q]� In fact, under these conditions a quasi-equilibrium − + + − state between D+ Q− A , D QA QB , and D QA QB can be assumed and the kinetics of χD+ reduction can be described by a single exponential if the direct charge recombination from D+ Q− A is negligible. At very high [Q]T, τS reaches the constant value τ∞ = (1 + LAB)/kAD. Therefore, Eq. (2) can be used to estimate the binding constant from τS plotted against [Q]T (time method or TM, see “Appendix 2”). Finally, when kout ≈ kAD the kinetics of CRR shows a simultaneous QB-site population dependence of both AS and τS, like in the case investigated in this work (Milano et al. 2003), and only numerical integrations can be in principle used to extract quantitative data from the mixedorder kinetics (Shinkarev and Wraight 1993). To avoid this mathematically cumbersome technique, we present an additional procedure of analysis of the quinone titration best-fit data that uses the amplitude of the slow phase weighted by its time constant ASτS/τ∞ plotted as a function of quinone concentration (weighted amplitude method or WAM, see “Appendix 3”). We will show that this method can be applied in all the spanned range of quinone concentration and without doing any assumption on the quinone exchange regime. The AM, TM and WAM methods will be compared using a training set of simulated data obtained by means of numerical integration with different sets of kinetic constants in order to simulate CRR occurring in the three different exchange regimes.
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Fig. 2 Comparison between charge recombination traces obtained by ODE set numerical solutions (thin crosses) and biexponential fitting curves (solid lines). Starting conditions and kinetic parameters are set as follows: [RC] = 1 µM, Q/RC variable in the interval 0.1–60, LAB = 20, KQ∗ = KQ = 1,000 M−1 and individual kinetic constants listed in the inset
Numerical integration Charge recombination reaction traces can be reproduced in silico by a deterministic kinetic approach setting the appropriate kinetic constants and the total RC and quinone concentrations. Accordingly to Fig. 1, the set of ordinary differential equations (ODE) can be then written down and the problem of initial values (i.e., initial concentrations) can be numerically solved by using an algorithm suitable for “stiff” systems (Magrab et al. 2010). Therefore, for a given set of kinetic constants, the algorithm calculates the temporal evolution of each species starting from a time instant immediately after + − the flash, when all RCs are present as D+ Q− A , or D QA QB , − − + + i.e. [RC]T = [D QA ]0 + [D QA QB ]0 . Thus, the initial concentrations are determined by the pre-flash equilibrium concentrations of the species DQA, DQAQB and Q according to the dark binding equilibrium constant KQ and assuming that the flash light produces the charge separated state, + − i.e., [D+ Q− A ]0 = [DQA ]Eq , and [D QA QB ]0 = [DQA QB ]Eq on a timescale much faster than CRR. Finally, the CRR curve is obtained from the ODE set solutions as the sum of all species in the charge separation state: − + − + χD+ = ([D+ Q− A ]t + [D QA QB ]t + [D QA QB ]t )/[RC]T . Figure 2 reports as an example the χD+ time course (thin crosses) obtained from the ODE set integration for different initial concentrations of quinone and using the set of kinetic constant displayed in the figure inset. Bi‑exponential function optimization procedure Solid lines reported in Fig. 2 have been fitted by means of the bi-exponential function shown in Eq. (1) in order to obtain
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the amplitude AS and the time constant τS of the slow phase as best fit parameters by minimizing the square root of displacements. The kAD has been instead fixed to 10.1 s−1 the estimated experimental value (see later in the text) also used for the ODE set integration, while AF = (1 − AS). This procedure has been then applied both to experimental and training data. The only difference found is a further best-fit parameter c needed to be introduced in the case of experimental curves to take into account the background noise. The c remains always very small, typically below 2 % of the overall signal in all the recorded real traces, and, therefore, the amplitude of the fast phase was expressed as follows: AF = (1 − c − AS). KQ evaluation method benchmark For the same initial concentration range: [RC] = 1 µM, 10−2 ≤ [Q]T/[RC]T ≤ 102, a training data set has been implemented as a collection of traces calculated fixing KQ = 1.0 × 103 M−1 and varying both kout and kin = KQ/ kout to simulate chemical systems in slow and fast quinone exchange regimes. A first set of traces has been calculated ∗ =k by assuming KQ∗ = KQ and consequently setting kout out 3 −1 ∗ and kin = kin . Then, keeping KQ = 1.0 × 10 M we investigated the cases (KQ∗ /KQ ) = 0.1, 5, 10, and 50, by chang3 −1 ∗ =k ing 10−1 s−1 ≤ kout out ≤ 10 s , kin = KQ kout and set∗ ∗ ting kin = kin (KQ /KQ ), in order to study how CRR traces can be affected by differences in the quinone exchange equilibrium among charged and uncharged states. It is worthwhile to remark that the two cases KQ∗ ≤ KQ are only hypothetical, since there are experimental indications that the light constant KQ∗ is likely to be larger than the dark one (McComb et al. 1990). In all the training data set, the calculated χD+ time courses were always well fitted by Eq. (1) (R2 > 0.994) and parameters τS and AS numerically obtained by means of an optimization procedure along with error estimates. All the results are reported in the supplementary materials. From the best-fit values, we estimate KQEV according to the three approximated methods previously introduced and (EV = AM, TM and WAM), and these value have been compared with KQ and KQ∗ constants used to produce the traces by the ODE set integration. In Tables 1 and 2, KQEV values obtained by means of each method are listed as function of log10(kout) in the two cases (KQ∗ /KQ ) = 1 and (KQ∗ /KQ ) = 10, respectively, while in Fig. 3 the three methods are compared for different quinone exchange regimes when ((KQ∗ /KQ ) = 5. Values reported in Tables 1 and 2 and Fig. 3 clearly show that, when 1 ≤ (KQ∗ /KQ ) ≤ 10, KQAM and KQTM are close to the correct ones only if applied in the slow (kout ≪ kAD = 10 s−1) and fast (kout ≫ kAD = 10 s−1) exchange regime, respectively, while KQWAM values remain between to the two true values KQ∗ and KQ when applied in
305 Table 1 Quinone binding equilibrium constants KQEV obtained with different approximated methods in different exchange regimes Log10(kout)
KQAM (103 M−1)
KQWAM (103 M−1)
KQTM (103 M−1)
−1.0 0.0 0.5 1.0 1.5 2.0 2.5
1.02 ± 0.01 1.23 ± 0.08 1.64 ± 0.15 2.73 ± 0.27 6.39 ± 0.60 11.92 ± 4.76 15.92 ± 11.91
1.02 ± 0.01 1.08 ± 0.03 1.10 ± 0.03 1.06 ± 0.05 0.96 ± 0.10 0.89 ± 0.13 0.86 ± 0.15
16.92 ± 14.12 11.28 ± 6.69 4.62 ± 2.09 1.78 ± 0.43 0.97 ± 0.04 0.74 ± 0.08 0.67 ± 0.11
3.0
16.92 ± 15.48
0.85 ± 0.15
0.65 ± 0.12
The parameters AS and τ were obtained by optimizing Eq. (1) on traces calculated by setting KQ = KQ∗ = 103 and all the kinetic ∗ =k constants as reported in Fig. 2 except for kout out that has been changed as reported in the first column Table 2 Quinone binding equilibrium constants KQEV obtained with different approximated methods in different exchange regimes Log10(kout)
KQAM (103 M−1)
KQWAM (103 M−1)
KQTM (103 M−1)
−1.0 0.0 0.5 1.0 1.5 2.0 2.5
1.22 ± 0.07 2.74 ± 0.26 6.28 ± 0.51 11.92 ± 3.79 16.92 ± 10.41 18.92 ± 15.03 18.92 ± 16.43
1.36 ± 0.10 3.58 ± 0.24 6.37 ± 0.23 7.28 ± 1.42 7.28 ± 2.37 7.28 ± 2.79 7.28 ± 2.94
22.92 ± 45.36 24.92 ± 67.81 16.92 ± 15.61 8.28 ± 1.10 5.64 ± 0.88 4.69 ± 0.96 4.43 ± 0.99
3.0
19.92 ± 17.69
7.47 ± 3.09
4.35 ± 1.00
The parameters AS and τ were obtained by optimizing Eq. (1) on traces calculated by setting KQ = KQ∗ /10 = 103 and all the kinetic ∗ and k ∗ constants as reported in Fig. 2 except for kout out = kout /10 that have been changed as reported in the first column
the all kout range (see Fig. 3 and supplementary materials). In particular, WAM appears to be the most robust method since for whatever ratio KQ∗ /KQ it returns KQ < KQWAM < KQ∗ with KQWAM more shifted towards KQ∗ as far as kout ≫ kAD and this behavior is also confirmed for the hypothetical case KQ∗ /KQ = 0.1 (see supplementary material). On the other hand, when 10 < (KQ∗ /KQ ) < 50, both AM and TM return KQEV between the real values but with a lower accuracy than WAM. Moreover, it is important to stress that TM can be correctly applied only for kout ≫ kAD and [Q]T/[RC]T > 0.9 and this last condition requires a precise determination of the fitting parameter τS and, therefore, a high experimental precision in recording the decay curves. ODE set optimization procedure At each different working temperature, LAB and KQ evaluation from experimental data is the first step for a full characterization of the CRR mechanism completed by the
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log10(KAM ) Q
6 4 2 0 -1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
1.5
2
2.5
3
3.5
1.5
2
2.5
3
3.5
log10(kout)
) log10(KTM Q
6 4 2 0 -1.5
-1
-0.5
0
0.5
1
log10(kout)
log10( KWAM ) Q
6 4 2 0 -1.5
-1
-0.5
0
0.5
1
log10(kout)
Fig. 3 Estimated KQ values with methods AM, TM and WAM as a function of imposed kout, for the case KQ = 103 M−1 and (KQ∗ /KQ ) = 5
theoretical values that these constants can attain (“Appen∗ and k dix 4”). As a consequence of this, the optimized kout out values are to be considered as upper limits. As an example of this approach, in Supplementary Materials, the start guess values for all kinetic constants for PC and PG liposomes at 25 °C are summarized in table S1 together with the figure of merit Δk/k (Δk is the 95 % confidence interval), the root mean squared displacements (RMSD) and the R2 values before optimization. The comparison between experimental data and optimized curves is reported in Fig. S1. It is worth to note the high R2 values indicating that the starting guess values already provide a good description of the system. ∗ and k After evaluating the kout out upper limits, we also tried to estimate the lower limits by determining the goodness of ∗ when this parameter is fixed and the fit as a function of kout ∗ instead kin and kin are optimized at different temperatures for both PC and PG (see section C in Supplementary Material). ∗ and k The real values kout out will fall within the interval so determined. By analyzing the results it has been possible to infer that a fast quinone exchange takes place at all temperatures for PC, while for PG the quinone exchange regime is likely to switch from slow to fast as the temperature raises, as discussed later in the “Experimental results”.
Experimental results estimation of the single kinetic constants governing the quinone binding. It is important to realize that among the nine kinetic constants involved in the charge recombination pro∗ , k ∗ , k and cess, those really unknown are only four: kin out in kout since the remaining constants can be assigned thanks to previous experimental observations or reasonable assumptions. For instance, kAB can be assessed for both PC and PG liposomes at all temperatures with separate experiments (Milano et al. 2007b) while kBA is obtained from kAB/LAB. kAD can be directly estimated by fitting QB depleted charge ′ recombination traces and kAD = kAD is assumed in first approximation; kBD is set equal to 0.06 s−1 (Kleinfeld et al. 1984b) at all temperatures. KQWAM can then be used for an initial guesses in order to get accurate best fit estimations of the searched constants. Therefore, the four unknown constants might be in principle derived by means of an optimization procedure that minimizes the mean squared displacements (MSD) between the ODE set solutions and the experimental decay curves obtained with a different [Q]T/ [RC]T ratio at a fixed working temperature ranging from 6.6 to 35.6 °C. Unfortunately, since these constants are strongly correlated, they cannot be optimized all together. ∗ and k ) canIn particular, the faster kinetic constants (kin in not be directly optimized, even though they affect the value of strongly correlated smaller kinetic constants (see section ∗ and k will be D Supplementary Material). Therefore, kin in fixed to educated guesses, which represent the maximum
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The previously described methods and mathematical procedure will now be applied to experimental data. QBdepleted RCs were reconstituted in both zwitterionic (PC) and negatively charged (PG) liposomes and the QB-site was titrated adding increasing amounts of UQ10 in the temperature range 6.5–35 °C. The charge recombination traces were recorded at 865 nm and the normalized absorbance decay has been fitted by using the bi-exponential function reported in Eq. (1) plus a constant term c introduced to take into account the background noise. The c remains always very small, typically below 2 % of the overall signal. For the case of PC at 25 °C, experimental CRR traces in the presence of increasing amounts of quinone are compared with fitting curves in Fig. 4. In Figure 5 (panels A, B and C) the best fit parameters τS, AS and ASτS/τ∞ are plotted against [Q]T for PC (on the left) and PG (on the right) liposomes, respectively, for three temperature values. In the presence of QB inhibitors, the decay of the charge separated state is mono-exponential with a rate constant kAD = 10.1 ± 0.2 s−1 both for PC and PG over the temperature range. In agreement with previous observations (Feher et al. 1987), the recombination from the state D+ Q− A is insensitive to temperature and to the external molecular environment. In contrast, τS increases when Q/RC rises indicating that the rate of quinone exchange between RCs and the membrane pool is at least comparable with or
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Fig. 4 Experimental charge recombination traces at 865 nm for PC at 25 °C fitted to Eq. (1) along with the relevant residuals plots. Q/RC ratios increases as follows: 0.1 (A), 0.5 (B), 0.8 (C) and 20 (D)
faster than the charge recombination from Q− A. This is in agreement with the analysis of our training data and with what was observed experimentally (Agostiano et al. 1995; Palazzo et al. 2000). AS also increases along with Q/RC, as expected in a system where the QB-site is titrated with quinone concentration comparable to that of the protein.
Fig. 5 QB-site titration curves for PC and PG liposomes at three selected temperatures: 6.6 °C (black circles), 20.0 °C (white squares) and 35.6 °C (black diamonds) using τS, AS and ASτS/τ∞ indicators (see text for details). Error bars are smaller than symbols. In panels A(1,2) the best fit lines to Eq. 13 are shown while in panels B(1,2) and C(1,2), the fitting function is Eq. 8, using light grey for 6.5 °C, black for 20 °C and dark grey for 35 °C. The same ordinate scale is maintained in corresponding panels for sake of clarity
LAB evaluation The time constant τ∞ obtained at saturating quinone concentration (i.e., Q/RC ≥ 10) can be combined with kAD to calculate LAB (Shinkarev and Wraight 1993):
LAB =
τ∞ kAD − 1 ≈ τ∞ kAD − 1. 1 − τ∞ kBD
(3)
At 25 °C LAB evaluated values are 18.0 for PC and 33.0 for PG, respectively, in agreement with previously published results (Nagy et al. 2004). Furthermore, for both PC and PG liposomes in the range 6.5–35 °C, LAB, decreases with temperature as shown by the van’t Hoff plot reported in Fig. 6. Since both curves ln(LAB) against 1/T exhibit a linear – and S O O – trend then HAB AB can be assumed constant in the given temperature range and derived as best fit linear parameters (Table 3).
Fig. 6 Van’t Hoff plot for the equilibrium constant LAB in PC (circles) and PG (squares) liposomes
Also this result is in agreement with what has been already observed in LDAO solutions with native ubiquinones (Mancino et al. 1984; McComb et al. 1990). The
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Table 3 Thermodynamic parameters for LAB in PC and PG liposomes
PC PG
−1 ∆G–O AB kJ mol
O – kJ mol−1 ∆HAB
O – JK−1mol−1 ∆SAB
R2
−6.97 ± 0.04
−16.2 ± 1.2
−30.9 ± 4.0
0.996
−8.90 ± 0.04
−13.3 ± 0.9
−15.1 ± 3.0
KQ evaluation Table 4 summarizes the binding constants obtained with the three methods TM, AM, and WAM. For both PC and PG, KQWAM is smaller than the corresponding KQAM and KQTM at all temperatures. This can be a first indication that the rate of the quinone exchange is in an intermediate/fast regime for the considered systems and that KQ∗ ≥ KQ. Therefore, since the quinone exchange regime is not well defined and, most importantly, it changes over the investigated temperature range, both AM and TM are not fully appropriate. Conversely, the homogeneous and good fitting accuracy of WAM with R2 is always greater than 0.980 at all temperatures (see Fig. 5, panels C1 and C2) confirming that this method is less influenced by the quinone exchange regime. Going into details, in the case of PC liposomes, Table 4 shows that KQAM regularly increases with temperature while the fitting accuracy (R2) worsens. In contrast, KQTM decreases while R2 values slightly improve though remaining quite high at all temperatures. This indicates that the quinone exchange regime becomes faster when temperature increases, and the fast quinone exchange is always a good description of the system. Indeed, at 35.6 °C the exchange rate is so fast that even at Q/RC = 0.1, AS accounts for almost 40 % of the overall signal, but with a small τS (Fig. 5B1). In the case of PG liposomes, the AM fitting worsens with increasing temperature, but shows a better accuracy R2 ≥ 0.990 and AS does not change so much with temperature (Fig. 5B2) indicating that the slow exchange approximation holds better. This result is also confirmed by TM that exhibits a fit accuracy generally worse: 0.713 (6.6 °C) ≤ R2 ≤ 0.970 (35.2 °C), with R2 increasing
0.996
difference between the PC and PG liposomes can be ascribed to the different stabilization exhibited by the two phospholipids on the charge-separated state (Nagy et al. 1999; Agostiano et al. 1995). A similar effect has been observed also in other systems of biotechnological interest (Magyar et al. 2011; Dorogi et al. 2006). The signs of – and S O O – HAB AB indicate a reaction driven by enthalpy with an unfavorable entropic contribution for both kind of liposomes at room temperature. The values obtained for PC are in agreement with those found in soybean PC vesicles (Palazzo et al. 2000), in reversed micelles (Mallardi et al. 1997) and in LDAO micelles (Mancino et al. 1984). – It is worthwhile to note that PG has a more negative GO AB , despite the smaller absolute value of the enthalpic term, arising from a much lower entropic contribution. A similar behavior was found also in liposomes made with other negatively charged phospholipids such as phosphatidylinositol and phosphatidic acid (data not shown), and it can be ascribed to a sort of solvent thermodynamic effect since negatively charged membrane seems to better stabilize the D+ QA Q− B species. This effect needs to be investigated in more details and it will be the topic of future work by our group and requires a more systematic analysis to discriminate a pure electrostatic contribute from other molecular interactions. Table 4 Binding constants KQ obtained by different methods for PC and PG liposomes. Errors are always within ±10 %
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t (°C)
KQAM (×103 M−1)
R2
KQTM (×103 M−1)
R2
PC 6.6 9.8 14.8 19.8 25.2 30.6 35.2
12.5 15.1 15.5 20.2 20.2 21.6 30.5
0.997 0.994 0.991 0.970 0.935 0.822 0.732
4.72 5.41 3.81 3.26 2.35 1.84 1.39
0.942 0.951 0.970 0.982 0.989 0.990 0.991
1.98 2.28 1.82 1.74 1.42 1.23 1.07
0.990 0.986 0.985 0.985 0.988 0.987 0.992
PG 6.6 10.3 15.2 20.1 25.2 30.6
29.6 42.1 40.2 41.3 30.5 40.4
0.994 0.994 0.997 0.998 0.996 0.993
626 150 45.3 21.7 12.6 8.18
0.713 0.884 0.954 0.976 0.984 0.977
15.7 13.0 9.29 7.37 4.93 4.13
0.988 0.987 0.987 0.984 0.989 0.992
35.1
27.2
0.990
5.04
0.966
2.36
0.986
KQWAM (×103 M−1)
R2
Eur Biophys J (2014) 43:301–315 Table 5 Optimized upper limits ∗ and k , and derived for kout out quantities KQ∗(ODE) and KQ(ODE) for PC and PG
309 t (°C) PC 6.6 9.8 14.8 19.8 25.2 30.6 35.2 PG 6.6 10.3 15.2 20.1 25.1 30.6 35.1
kout (s−1)
KQ∗(ODE) × 103 M−1
KQ(ODE) × 103 M−1
R2
34.8 ± 0.4 33.1 ± 0.5 53.2 ± 0.7 80.4 ± 1.2 146 ± 2 238 ± 4 450 ± 4
57 ± 3 37 ± 2 57 ± 3 109 ± 6 267 ± 18 589 ± 56 (1.4 ± 0.2) × 104
2.23 ± 0.02 2.86 ± 0.04 2.35 ± 0.03 2.04 ± 0.03 1.49 ± 0.02 1.17 ± 0.02 0.797 ± 0.008
1.23 ± 0.06 2.54 ± 0.13 2.18 ± 0.10 1.50 ± 0.08 0.82 ± 0.06 0.47 ± 0.05 0.026 ± 0.003
0.997 0.996 0.996 0.996 0.996 0.995 0.996
3.43 ± 0.09 4.36 ± 0.10 9.8 ± 0.3 14.6 ± 0.3 36.2 ± 0.7 71.6 ± 1.2
17.4 ± 1.4 9.4 ± 0.8 40 ± 4 45 ± 3 164 ± 12 (1.08 ± 0.15) × 103
22.9 ± 0.6 22.3 ± 0.5 13.1 ± 0.4 11.4 ± 0.3 5.93 ± 0.12 3.90 ± 0.07
4.5 ± 0.4 10.4 ± 0.9 3.2 ± 0.3 3.7 ± 0.2 1.27 ± 0.09 0.26 ± 0.04
0.994 0.993 0.996 0.996 0.996 0.996
(1.10 ± 0.10) × 104
2.37 ± 0.02
0.033 ± 0.003
0.994
∗ (s−1) kout
151.3 ± 1.5
significantly at high temperature indicating the exchange regime change from slow to fast above 20 °C. The fast exchange regime between the QB site and the immediate quinone pool is assumed to be fast both in micellar (Shinkarev and Wraight 1997) and liposomal (Palazzo et al. 2000) systems. The present analysis confirms this assumption, at least at temperatures higher than room temperature, and shows that the quinone exchange is modulated by the polar head of the phospholipid forming the liposomes. ∗ Optimization of kout and kout
The quinone binding process is completely described if the ∗ , k ∗ , k and k four relevant constants kin out are determined. out in As discussed in the “ODE set optimization procedure”, these constants could be in principle estimated as the best fit parameters, but since entrance and exit kinetic constants ∗ and k are highly correlated, kout out have been obtained by optimization as upper and lower limits in independent sets of optimization. We will start by discussing the upper limits ∗ ∗ and k of kout out obtained by fixing kin = kin at their maximum value limited by quinone diffusion in the bilayer. For both PC and PG, in the investigated temperature range, data ∗(ODE) (ODE) are summarized in Table 5 where KQ and KQ are ∗ ∗ obtained as kin /kout and kin/kout, respectively. Since the exchange quinone regime is mainly affected ∗ , values in Table 5 allows the inference that PG by kout liposomes show a regime transition passing from slow to ∗ becomes greater than k fast above 20 °C, where kout AD and ∗ that for PC the quinone exchange is always fast being kout at least three times larger than kAD. Both these observations are in agreement with the three methods for the evaluation
of KQEV and will be below confirmed by an evaluation of ∗ lower value. The numerical simulations allowed the kout us to separate the contributions of the light and dark qui∗ and k none binding constants by means of kout out that could otherwise not have been discriminated by means of a phenomenological description. In Fig. 7 for both PC and PG ∗(ODE) log(KQ ) is reported against 1/T, compared with KQWAM values. A linear trend is exhibited in the range 10–35 °C for PG and 10–30 °C for PC, respectively (open data). A similar (ODE) behavior has been also obtained for KQ although the data are more scattered, since the curves calculated by the numerical integration are less sensitive to kin and kout parameters (data not shown). By fitting the van’t Hoff equation in the temperature range where a linear behavior is shown, relevant thermodynamic parameters can be obtained and results are listed in Table 6 for both amphiphiles in dark and light conditions. – values for PC and PG do not differ too much, The GO Q indicating a similar affinity of UQ10 towards the QB-site in (ODE) the two systems. The smaller values of KQ compared ∗(ODE) to KQ are in agreement with the hypothesis of proximal (in the light) and distal (in the dark) binding site of QB (Stowell et al. 1997): in the D+ Q− A QB state QB is in the proximal state, more buried within the protein, and, hence, more tightly bound. The quinone binding constant and the relevant thermodynamic parameters have been previously determined in reverse micelles formed by a mixture of negatively charged and zwitterionic phospholipids using the τS dependence on quinone concentration. The – = −50.7 kJ/mol, − T �S O – values �HQO Q = 39 kJ/mol and 2 −1 KQ = 1.1 × 10 M at 298 K were found (Mallardi et al. 1997). The same authors also assessed the parameters in
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Fig. 7 Van’t Hoff plot for estimated KQ∗(ODE) for PG (open squares) and PC (open circles) compared with and KQWAM for PG (filled squares) and PC (filled circles) Table 6 Thermodynamic parameters for KQ∗(ODE) and KQ(ODE) obtained from simulations in PC and PG liposomes ∆G–O Q (kJ mol−1)
PC KQ∗(ODE) PC KQ(ODE) PG PG
KQ∗(ODE) KQ(ODE)
−18.10 ± 0.06
O ∆HQ– (kJ mol−1)
−31 ± 2
O – ∆SQ (J K−1 mol−1)
R2
−43 ± 6
0.999
−140 ± 20
0.996
−16.7 ± 0.7
−60 ± 20
−144 ± 77
0.958
−17 ± 2
−117 ± 70
−335 ± 230
0.901
−21.48 ± 0.17
−63 ± 5
PC liposomes exploiting the temperature dependence of the kS value and its polydispersity at Q to RC ratios of 10 and 25, finding similar values (Palazzo et al. 2000). All values were attributed to the binding to the QB-site when the protein is in the D+ Q− A state and, hence, correspond∗(ODE) ing to the KQ value of this work. The thermodynamic ∗(ODE) parameters of KQ listed in Table 6 for PC are somewhat different, however, in the previous papers a real titration of the QB-site was performed only in the case of the reverse micelles. The values found in this paper for PC and PG confirm that the quinone binding is substantially enthalpy-driven with an unfavorable entropic contribution, as expected for an association reaction, and indicate that the different polar head of the phospholipid has a great influence on the quinone binding reaction. Indeed a complete description requires the evaluation ∗ . A set of independent optimizaof lower limits for kout tions were, hence, performed using twenty values between ∗ . For each run, new 1 and 100 s−1 as fixed values for kout ∗ optimized values of kin and kin are obtained. The depend∗ is shown in figure S2 for PC ence of the R2 values on kout ∗ and PG. By varying kout in the above mentioned range, the
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exchange regime is forced to change from slow to fast and the simulated decays show correspondingly a different agreement with the experimental CRR traces. The value of ∗ at which the R2 value starts to decrease can be taken kout ∗ lower limit (see table S2 in Supplementary as the kout Material). For PC this value is around 20 s−1 at all temperatures confirming that the system is always in the fast quinone ∗ lower and upper limits listed exchange regime. For PG, kout in table S2 are consistent with a quinone exchange regime switch at 20 °C. The conclusions based on the numerical simulations are perfectly consistent with the findings of the phenomenological approach. A recent evaluation of the quinone unbinding constant found optimizing the parameters of the whole photosynthetic unit (Geyer et al. 2010) gave a value of 87 s−1, which falls in the range ∗
Original Paper
The binding of quinone to the photosynthetic reaction centers: kinetics and thermodynamics of reactions occurring at the QB‑site in zwitterionic and anionic liposomes Fabio Mavelli · Massimo Trotta · Fulvio Ciriaco · Angela Agostiano · Livia Giotta · Francesca Italiano · Francesco Milano
Received: 14 January 2014 / Revised: 7 April 2014 / Accepted: 25 April 2014 / Published online: 14 May 2014 © European Biophysical Societies’ Association 2014
Abstract Liposomes represent a versatile biomimetic environment for studying the interaction between integral membrane proteins and hydrophobic ligands. In this paper, the quinone binding to the QB-site of the photosynthetic reaction centers (RC) from Rhodobacter sphaeroides has been investigated in liposomes prepared with either the zwitterionic phosphatidylcholine (PC) or the negatively charged phosphatidylglycerol (PG) to highlight the role of the different phospholipid polar heads. Quinone binding (KQ) and interquinone electron transfer (LAB) equilibrium constants in the two type of liposomes were obtained by charge recombination reaction of QB-depleted RC in the presence of increasing amounts of ubiquinone-10 over the temperature interval 6–35 °C. The kinetic of the charge recombination reactions has been fitted by numerically solving the ordinary differential equations set associated with a detailed kinetic scheme involving electron transfer reactions coupled with quinone release and uptake. The Fabio Mavelli and Massimo Trotta contributed equally to this work. Electronic supplementary material The online version of this article (doi:10.1007/s00249-014-0963-z) contains supplementary material, which is available to authorized users. F. Mavelli · F. Ciriaco · A. Agostiano Department of Chemistry, University of Bari, 70126 Bari, Italy M. Trotta · A. Agostiano · F. Italiano · F. Milano (*) Italian National Research Council, Institute for Physical and Chemical Processes (CNR-IPCF), 70126 Bari, Italy e-mail: [email protected] L. Giotta Department of Biological and Environmental Sciences and Technologies (DiSTeBA), University of Salento, 73100 Lecce, Italy
entire set of traces at each temperature was accurately fitted using the sole quinone release constants (both in a neutral and a charge separated state) as adjustable parameters. The temperature dependence of the quinone exchange rate at the QB-site was, hence, obtained. It was found that the quinone exchange regime was always fast for PC while it switched from slow to fast in PG as the temperature rose above 20 °C. A new method was introduced in this paper for the evaluation of constant KQ using the area underneath the charge recombination traces as the indicator of the amount of quinone bound to the QB-site. Keywords Bacterial photosynthesis · Protein–lipid interaction · Ligand binding
Introduction The photosynthetic reaction center (RC) is the key protein in the conversion of solar light to chemical energy during the photosynthetic process (Allen and Williams 1998). The RC is a membrane protein that, in the purple bacterium Rhodobacter (Rb.) sphaeroides, is located in the intra-cytoplasmic membranes (Feher and Okamura 1978). The structure of the protein has been obtained at atomic resolution of 1.87 Å (Koepke et al. 2007). Its interaction with lipids (Jones 2007) is becoming of great interest both for basic research (Deshmukh et al. 2011a, b; De Leo et al. 2009; Wohri et al. 2009; Milano et al. 2007a) and for potential device assembly (Boghossian et al. 2011; Ham et al. 2010). The protein contains several cofactors arranged in two symmetrical branches, A and B, and, upon light absorption, a cascade of electron transfer reactions is promoted. An electron is released along the A branch from the primary donor (D) and reaches the primary quinone acceptor QA (Gunner 1991; Kleinfeld et al. 1984a).
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The electron is reversibly exchanged with the secondary quinone acceptor QB, most likely through an iron–histidine bridge (Di Donato et al. 2004; Burggraf and Koslowski 2011). In the presence of an exogenous electron donor, typically a cytochrome molecule, these electron transfer reactions occur twice, leading to the full reduction of QB to quinol, which leaves the protein and is replaced by a new quinone molecule uptake from the membrane pool (McPherson et al. 1990). Both quinone and quinol continuously bind and unbind to the QB site of the protein (Crofts et al. 1983). In isolated RC, in absence of an exogenous donor, the final charge-separated state decays in the dark via a charge recombination reaction (CRR), whose kinetics can be used to retrieve kinetic and thermodynamic information about the energetics of the electron acceptor complex and the quinone binding. The interquinone electron transfer equilibrium constant LAB and its temperature dependence in different environments is well-stated in the literature (Agostiano et al. 1998), while the quinone binding constant KQ is more difficult to assess since the native ubiquinone-10 (UQ10) is highly hydrophobic. In detergent micelles, only thermodynamic data of KQ for the water soluble ubiquinone-0 (UQ0) are available (McComb et al. 1990). This problem has been partially overcome studying the binding of UQ10 to RC in reverse micelles, where the quinone is dispersed in the bulk organic phase (Mallardi et al. 1997). In another paper (Palazzo et al. 2000), RCs are reconstituted in lecithin vesicles, and KQ is studied by exploiting the quinone concentration polydispersity between different liposomes at high Q/RC ratio. Compared to direct or reverse micelles, liposomes represent a solubilizing environment that better mimics the conditions in which RCs are found in the intracytoplasmic membranes. Furthermore, liposomes allow one to use the physiological UQ10 for the QB-site binding studies and to modulate the UQ10/RC ration over a wide range. The possibility of assembling liposomes from different phospholipids also enables revealing specific features of the lipid–protein interaction. In the present work, the RC was reconstituted in both PC and PG vesicles and the specific role of the lipid environment on the quinone binding reaction was studied by titrating the QB-site in the temperature interval 6–35 °C and recording the relevant CRR decays. In the investigated temperature range, the liposome bilayer is always in its fluid state, ensuring that the quinone mobility is modulated only by temperature. The binding constants at different temperatures were obtained by means of established methods in the literature (Shinkarev and Wraight 1993), fitting appropriate parameters, extracted from the CRR kinetics, versus the quinone concentration, under different quinone mobility regimes in the bilayer. Quinone mobility is heavily dependent on temperature; hence, none of the previously mentioned methods can be applied in the entire investigated temperature range. A method independent from the
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mobility regime, based on the area underneath the CRR curves is, hence, introduced, leading to an improved system description. The CRR data were also analyzed by means of numerical simulation, using all the kinetic constants involved in the process, evaluating their confidence intervals and their possible correlations. By this approach, reliable values for the quinone binding constants in both kinds of liposomes and information on the mobility of the quinone as a function of the temperature were obtained. This kind of study is gaining increasing relevance in System Biology; since mathematical models of biological systems have been recently successfully extended to the level of small cellular compartments (Geyer et al. 2007, 2010; Mavelli 2012; Mavelli and Ruiz-Mirazo 2010). It becomes crucially important to estimate the highest possible number of kinetic parameters with independent experiments to increase the robustness of theoretical models.
Materials Chemicals The phospholipids 1,2-diacyl-sn-glycerol-3-phosphocholine (99 %—phosphatidylcholine, PC), 1,2-diacyl-snglycerol-3-phosphoryl glycerol (98 %—phosphatidylglycerol, PG) and ubiquinone-10 (UQ10) were purchased from Sigma, stored at −70 °C and used without any further purification. Sodium cholate was also from Sigma. Lauryl dimethyl amino N-oxide (LDAO) was from Fluka. Terbutryne was obtained from Chem Service, USA. Sephadex G-50 was purchased from Pharmacia. Reaction centers Reaction centers were isolated from Rb. sphaeroides strain R26 following the procedure illustrated by Isaacson et al. (1995). Protein purity was checked using the ratio of the absorbance at 280 and 802 nm, which was kept below 1.3, and the ratio of the absorbance at 760 and 865 nm, which was kept equal to or lower than 1. The average quinone content was 1.8 per RC. QB site depletion was accomplished following the procedure outlined in (Okamura et al. 1975) yielding a depletion of about 95 %. Steady state and transient optical spectroscopy RC optical spectra were recorded using a Cary 5000 spectrophotometer (Varian Inc., Australia). CRR kinetics were recorded at the chosen wavelength using a kinetic spectrophotometer of local design (Milano et al. 2003) implemented with a Hamamatsu R928 photomultiplier
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and a Nd–Yag laser (Quanta System) used for saturating RC photoexcitation. The decay traces were recorded up to complete recovery (at least 4–5 times their decay times) and the samples were dark adapted for at least 5–6 times the time interval used for recording the signal. Three to six independent experiments were performed for each sample and each experiment was an average of at least four traces. No drift induced by the measuring beam was visible in any of the experiments. Liposomes preparation RC reconstitution in liposomes was accomplished by the micelle to vesicle transition (MVT) method using gel exclusion chromatography for detergent removal following the procedure outlined in Trotta et al. (2002), Venturoli et al. (1991) and Kutuzov (1990) and using a phospholipid to RC ratio of 1,000:1. The size of the vesicle was assessed from their hydrodynamic radius, obtained by dynamic light scattering (DLS) using the Horiba LB-550 nanoparticle size analyzer (Horiba Jobin Yvonne) as previously described (Milano et al. 2009). In the present work the hydrodynamic radius of liposomes was found to be 55 ± 6 nm. The RC and quinone concentrations used in the following discussion are always referred to the bilayer volume. The calculation was performed as previously described (Milano et al. 2009) using a value of [RC]bilayer = 1.2 ± 0.3 mM. The quinone concentration could not be evaluated directly; hence, it was assumed that the molar ratio realized in the mixed micelles before loading in the column is maintained in the final liposome preparation (Milano et al. 2009).
Mathematical background In this section, the kinetic mechanism used to describe the charge recombination will be described along with the numerical integration algorithm and the best-fitting procedure used to get the quinone binding constants. Kinetic mechanism and experimental decay curves The complete set of elementary events assumed to describe the time behavior of RC after a short flash of saturating excitation light is reported in Fig. 1 (Crofts et al. 1983) which is well accepted by researchers in the field (McComb et al. 1990; Shinkarev and Wraight 1997; Gunner 1991). This scheme allows one to rationalize the decay of the fraction of all species in a charge separated state χD+:
χD+ = χD+ Q− + χD+ Q− QB + χD+ QA Q− . A
A
B
In fact, the CRR reaction rate is strongly affected by the quinone exchange kinetics at the QB-site that also depends
Fig. 1 Proposed set of elementary reactions for flash excitation and ′ dark relaxation of isolated RC. kAD and kAD represent the kinetic − constant of the electron transfer from QA to D+ when the QB pocket is empty or occupied respectively; kBD is the kinetic constant of the + ∗ direct charge recombination from Q− B to D ; kin and kin represent the bimolecular kinetic constant of the quinone association to the QB site ∗ and k in the charge separated and neutral state respectively; kout out represent the kinetic constant of the quinone dissociation from the QB site in the charge separated and neutral state respectively; kAB is the kinetic constant for the electron transfer reaction from Q− A to QB, while kBA is the kinetic constant for the electron transfer in the opposite direction. A detailed description for all kinetic constants is given in supplementary material
on the RC environment, i.e., direct or reverse micelles or liposomes. For instance, if the QB pocket is empty, CRR occurs by direct tunneling from Q− A with a mono-exponential decay and a typical time constant τ which is quite independent of the RC surroundings: 1/τ = kAD ≈ 10 s−1. On the other hand, at saturating quinone concentrations, the decay is still mono-exponential but slower, with a time constant: τ∞ = (1 + LAB)/kAD dependent on LAB = kAB/kBA, whose actual value varies for different solubilizing environment of the protein (Kleinfeld et al. 1984b; Shinkarev and Wraight 1993). This retardation arises because the backreaction occurs mainly from the D+ Q− A state and electron transfer to QB diminishes the time averaged population of − + Q− A, while the direct route from D QA QB accounts for less than 5 % (Kleinfeld et al. 1984b). When the quinone concentration is in the sub-saturating range, the CRR becomes generally biphasic:
χD+ = AF exp(−kAD t) + AS exp(−t/τS ),
(1)
where the first exponential accounts for the direct charge recombination (fast decay with amplitude AF) and its time constant 1/kAD is independent from the occupancy of the QB-site. The time constant τS of the second exponential (slow decay with amplitude AS) results from a complex combination of electron transfers and quinone binding ∗ , k ) and unbinding (k ∗ , k ) from the Q -site (Shinka(kin in B out out rev and Wraight 1993). AS is roughly proportional to the fraction of QB-populated RCs and AS + AF = 1.0, since at time t = 0 all the reactions centers are present in the excited states: χD+ = 1.0.
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Furthermore, in this quinone concentration range, different CRR time behaviors can be also observed since the different solubilizing environment can affect the quinone release kinetic constant kout. Therefore, it is possible to define a slow (kout ≪ kAD) and a fast quinone exchange regime (kout ≫ kAD). In the slow exchange regime, like in the case of the detergent LDAO (Agostiano et al. 1999; Mezzetti et al. 2011), the CRR is still biphasic and τS is independent of the QB-site population. The contribution of slow decay AS to χD+ can be directly used for the quinone binding constant determination (KQ) by fitting AS vs. total quinone concentration with a quadratic function (Agostiano et al. 1999) (amplitude method or AM, see “Appendix 1”). When kout ≫ kAD, like in reverse micelles (Mallardi et al. 1997), and [Q] ≫ [RC] the CRR time course reduces to a single exponential decay, and τS can be proved to be a function of the free average quinone concentration 〈[Q]〉 and the light binding constant KQ∗ (Shinkarev and Wraight 1993): LAB KQ∗ �[Q]� 1 . τS = 1+ (2) kAD 1 + KQ∗ �[Q]� In fact, under these conditions a quasi-equilibrium − + + − state between D+ Q− A , D QA QB , and D QA QB can be assumed and the kinetics of χD+ reduction can be described by a single exponential if the direct charge recombination from D+ Q− A is negligible. At very high [Q]T, τS reaches the constant value τ∞ = (1 + LAB)/kAD. Therefore, Eq. (2) can be used to estimate the binding constant from τS plotted against [Q]T (time method or TM, see “Appendix 2”). Finally, when kout ≈ kAD the kinetics of CRR shows a simultaneous QB-site population dependence of both AS and τS, like in the case investigated in this work (Milano et al. 2003), and only numerical integrations can be in principle used to extract quantitative data from the mixedorder kinetics (Shinkarev and Wraight 1993). To avoid this mathematically cumbersome technique, we present an additional procedure of analysis of the quinone titration best-fit data that uses the amplitude of the slow phase weighted by its time constant ASτS/τ∞ plotted as a function of quinone concentration (weighted amplitude method or WAM, see “Appendix 3”). We will show that this method can be applied in all the spanned range of quinone concentration and without doing any assumption on the quinone exchange regime. The AM, TM and WAM methods will be compared using a training set of simulated data obtained by means of numerical integration with different sets of kinetic constants in order to simulate CRR occurring in the three different exchange regimes.
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Fig. 2 Comparison between charge recombination traces obtained by ODE set numerical solutions (thin crosses) and biexponential fitting curves (solid lines). Starting conditions and kinetic parameters are set as follows: [RC] = 1 µM, Q/RC variable in the interval 0.1–60, LAB = 20, KQ∗ = KQ = 1,000 M−1 and individual kinetic constants listed in the inset
Numerical integration Charge recombination reaction traces can be reproduced in silico by a deterministic kinetic approach setting the appropriate kinetic constants and the total RC and quinone concentrations. Accordingly to Fig. 1, the set of ordinary differential equations (ODE) can be then written down and the problem of initial values (i.e., initial concentrations) can be numerically solved by using an algorithm suitable for “stiff” systems (Magrab et al. 2010). Therefore, for a given set of kinetic constants, the algorithm calculates the temporal evolution of each species starting from a time instant immediately after + − the flash, when all RCs are present as D+ Q− A , or D QA QB , − − + + i.e. [RC]T = [D QA ]0 + [D QA QB ]0 . Thus, the initial concentrations are determined by the pre-flash equilibrium concentrations of the species DQA, DQAQB and Q according to the dark binding equilibrium constant KQ and assuming that the flash light produces the charge separated state, + − i.e., [D+ Q− A ]0 = [DQA ]Eq , and [D QA QB ]0 = [DQA QB ]Eq on a timescale much faster than CRR. Finally, the CRR curve is obtained from the ODE set solutions as the sum of all species in the charge separation state: − + − + χD+ = ([D+ Q− A ]t + [D QA QB ]t + [D QA QB ]t )/[RC]T . Figure 2 reports as an example the χD+ time course (thin crosses) obtained from the ODE set integration for different initial concentrations of quinone and using the set of kinetic constant displayed in the figure inset. Bi‑exponential function optimization procedure Solid lines reported in Fig. 2 have been fitted by means of the bi-exponential function shown in Eq. (1) in order to obtain
Eur Biophys J (2014) 43:301–315
the amplitude AS and the time constant τS of the slow phase as best fit parameters by minimizing the square root of displacements. The kAD has been instead fixed to 10.1 s−1 the estimated experimental value (see later in the text) also used for the ODE set integration, while AF = (1 − AS). This procedure has been then applied both to experimental and training data. The only difference found is a further best-fit parameter c needed to be introduced in the case of experimental curves to take into account the background noise. The c remains always very small, typically below 2 % of the overall signal in all the recorded real traces, and, therefore, the amplitude of the fast phase was expressed as follows: AF = (1 − c − AS). KQ evaluation method benchmark For the same initial concentration range: [RC] = 1 µM, 10−2 ≤ [Q]T/[RC]T ≤ 102, a training data set has been implemented as a collection of traces calculated fixing KQ = 1.0 × 103 M−1 and varying both kout and kin = KQ/ kout to simulate chemical systems in slow and fast quinone exchange regimes. A first set of traces has been calculated ∗ =k by assuming KQ∗ = KQ and consequently setting kout out 3 −1 ∗ and kin = kin . Then, keeping KQ = 1.0 × 10 M we investigated the cases (KQ∗ /KQ ) = 0.1, 5, 10, and 50, by chang3 −1 ∗ =k ing 10−1 s−1 ≤ kout out ≤ 10 s , kin = KQ kout and set∗ ∗ ting kin = kin (KQ /KQ ), in order to study how CRR traces can be affected by differences in the quinone exchange equilibrium among charged and uncharged states. It is worthwhile to remark that the two cases KQ∗ ≤ KQ are only hypothetical, since there are experimental indications that the light constant KQ∗ is likely to be larger than the dark one (McComb et al. 1990). In all the training data set, the calculated χD+ time courses were always well fitted by Eq. (1) (R2 > 0.994) and parameters τS and AS numerically obtained by means of an optimization procedure along with error estimates. All the results are reported in the supplementary materials. From the best-fit values, we estimate KQEV according to the three approximated methods previously introduced and (EV = AM, TM and WAM), and these value have been compared with KQ and KQ∗ constants used to produce the traces by the ODE set integration. In Tables 1 and 2, KQEV values obtained by means of each method are listed as function of log10(kout) in the two cases (KQ∗ /KQ ) = 1 and (KQ∗ /KQ ) = 10, respectively, while in Fig. 3 the three methods are compared for different quinone exchange regimes when ((KQ∗ /KQ ) = 5. Values reported in Tables 1 and 2 and Fig. 3 clearly show that, when 1 ≤ (KQ∗ /KQ ) ≤ 10, KQAM and KQTM are close to the correct ones only if applied in the slow (kout ≪ kAD = 10 s−1) and fast (kout ≫ kAD = 10 s−1) exchange regime, respectively, while KQWAM values remain between to the two true values KQ∗ and KQ when applied in
305 Table 1 Quinone binding equilibrium constants KQEV obtained with different approximated methods in different exchange regimes Log10(kout)
KQAM (103 M−1)
KQWAM (103 M−1)
KQTM (103 M−1)
−1.0 0.0 0.5 1.0 1.5 2.0 2.5
1.02 ± 0.01 1.23 ± 0.08 1.64 ± 0.15 2.73 ± 0.27 6.39 ± 0.60 11.92 ± 4.76 15.92 ± 11.91
1.02 ± 0.01 1.08 ± 0.03 1.10 ± 0.03 1.06 ± 0.05 0.96 ± 0.10 0.89 ± 0.13 0.86 ± 0.15
16.92 ± 14.12 11.28 ± 6.69 4.62 ± 2.09 1.78 ± 0.43 0.97 ± 0.04 0.74 ± 0.08 0.67 ± 0.11
3.0
16.92 ± 15.48
0.85 ± 0.15
0.65 ± 0.12
The parameters AS and τ were obtained by optimizing Eq. (1) on traces calculated by setting KQ = KQ∗ = 103 and all the kinetic ∗ =k constants as reported in Fig. 2 except for kout out that has been changed as reported in the first column Table 2 Quinone binding equilibrium constants KQEV obtained with different approximated methods in different exchange regimes Log10(kout)
KQAM (103 M−1)
KQWAM (103 M−1)
KQTM (103 M−1)
−1.0 0.0 0.5 1.0 1.5 2.0 2.5
1.22 ± 0.07 2.74 ± 0.26 6.28 ± 0.51 11.92 ± 3.79 16.92 ± 10.41 18.92 ± 15.03 18.92 ± 16.43
1.36 ± 0.10 3.58 ± 0.24 6.37 ± 0.23 7.28 ± 1.42 7.28 ± 2.37 7.28 ± 2.79 7.28 ± 2.94
22.92 ± 45.36 24.92 ± 67.81 16.92 ± 15.61 8.28 ± 1.10 5.64 ± 0.88 4.69 ± 0.96 4.43 ± 0.99
3.0
19.92 ± 17.69
7.47 ± 3.09
4.35 ± 1.00
The parameters AS and τ were obtained by optimizing Eq. (1) on traces calculated by setting KQ = KQ∗ /10 = 103 and all the kinetic ∗ and k ∗ constants as reported in Fig. 2 except for kout out = kout /10 that have been changed as reported in the first column
the all kout range (see Fig. 3 and supplementary materials). In particular, WAM appears to be the most robust method since for whatever ratio KQ∗ /KQ it returns KQ < KQWAM < KQ∗ with KQWAM more shifted towards KQ∗ as far as kout ≫ kAD and this behavior is also confirmed for the hypothetical case KQ∗ /KQ = 0.1 (see supplementary material). On the other hand, when 10 < (KQ∗ /KQ ) < 50, both AM and TM return KQEV between the real values but with a lower accuracy than WAM. Moreover, it is important to stress that TM can be correctly applied only for kout ≫ kAD and [Q]T/[RC]T > 0.9 and this last condition requires a precise determination of the fitting parameter τS and, therefore, a high experimental precision in recording the decay curves. ODE set optimization procedure At each different working temperature, LAB and KQ evaluation from experimental data is the first step for a full characterization of the CRR mechanism completed by the
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log10(KAM ) Q
6 4 2 0 -1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
1.5
2
2.5
3
3.5
1.5
2
2.5
3
3.5
log10(kout)
) log10(KTM Q
6 4 2 0 -1.5
-1
-0.5
0
0.5
1
log10(kout)
log10( KWAM ) Q
6 4 2 0 -1.5
-1
-0.5
0
0.5
1
log10(kout)
Fig. 3 Estimated KQ values with methods AM, TM and WAM as a function of imposed kout, for the case KQ = 103 M−1 and (KQ∗ /KQ ) = 5
theoretical values that these constants can attain (“Appen∗ and k dix 4”). As a consequence of this, the optimized kout out values are to be considered as upper limits. As an example of this approach, in Supplementary Materials, the start guess values for all kinetic constants for PC and PG liposomes at 25 °C are summarized in table S1 together with the figure of merit Δk/k (Δk is the 95 % confidence interval), the root mean squared displacements (RMSD) and the R2 values before optimization. The comparison between experimental data and optimized curves is reported in Fig. S1. It is worth to note the high R2 values indicating that the starting guess values already provide a good description of the system. ∗ and k After evaluating the kout out upper limits, we also tried to estimate the lower limits by determining the goodness of ∗ when this parameter is fixed and the fit as a function of kout ∗ instead kin and kin are optimized at different temperatures for both PC and PG (see section C in Supplementary Material). ∗ and k The real values kout out will fall within the interval so determined. By analyzing the results it has been possible to infer that a fast quinone exchange takes place at all temperatures for PC, while for PG the quinone exchange regime is likely to switch from slow to fast as the temperature raises, as discussed later in the “Experimental results”.
Experimental results estimation of the single kinetic constants governing the quinone binding. It is important to realize that among the nine kinetic constants involved in the charge recombination pro∗ , k ∗ , k and cess, those really unknown are only four: kin out in kout since the remaining constants can be assigned thanks to previous experimental observations or reasonable assumptions. For instance, kAB can be assessed for both PC and PG liposomes at all temperatures with separate experiments (Milano et al. 2007b) while kBA is obtained from kAB/LAB. kAD can be directly estimated by fitting QB depleted charge ′ recombination traces and kAD = kAD is assumed in first approximation; kBD is set equal to 0.06 s−1 (Kleinfeld et al. 1984b) at all temperatures. KQWAM can then be used for an initial guesses in order to get accurate best fit estimations of the searched constants. Therefore, the four unknown constants might be in principle derived by means of an optimization procedure that minimizes the mean squared displacements (MSD) between the ODE set solutions and the experimental decay curves obtained with a different [Q]T/ [RC]T ratio at a fixed working temperature ranging from 6.6 to 35.6 °C. Unfortunately, since these constants are strongly correlated, they cannot be optimized all together. ∗ and k ) canIn particular, the faster kinetic constants (kin in not be directly optimized, even though they affect the value of strongly correlated smaller kinetic constants (see section ∗ and k will be D Supplementary Material). Therefore, kin in fixed to educated guesses, which represent the maximum
13
The previously described methods and mathematical procedure will now be applied to experimental data. QBdepleted RCs were reconstituted in both zwitterionic (PC) and negatively charged (PG) liposomes and the QB-site was titrated adding increasing amounts of UQ10 in the temperature range 6.5–35 °C. The charge recombination traces were recorded at 865 nm and the normalized absorbance decay has been fitted by using the bi-exponential function reported in Eq. (1) plus a constant term c introduced to take into account the background noise. The c remains always very small, typically below 2 % of the overall signal. For the case of PC at 25 °C, experimental CRR traces in the presence of increasing amounts of quinone are compared with fitting curves in Fig. 4. In Figure 5 (panels A, B and C) the best fit parameters τS, AS and ASτS/τ∞ are plotted against [Q]T for PC (on the left) and PG (on the right) liposomes, respectively, for three temperature values. In the presence of QB inhibitors, the decay of the charge separated state is mono-exponential with a rate constant kAD = 10.1 ± 0.2 s−1 both for PC and PG over the temperature range. In agreement with previous observations (Feher et al. 1987), the recombination from the state D+ Q− A is insensitive to temperature and to the external molecular environment. In contrast, τS increases when Q/RC rises indicating that the rate of quinone exchange between RCs and the membrane pool is at least comparable with or
Eur Biophys J (2014) 43:301–315
307
Fig. 4 Experimental charge recombination traces at 865 nm for PC at 25 °C fitted to Eq. (1) along with the relevant residuals plots. Q/RC ratios increases as follows: 0.1 (A), 0.5 (B), 0.8 (C) and 20 (D)
faster than the charge recombination from Q− A. This is in agreement with the analysis of our training data and with what was observed experimentally (Agostiano et al. 1995; Palazzo et al. 2000). AS also increases along with Q/RC, as expected in a system where the QB-site is titrated with quinone concentration comparable to that of the protein.
Fig. 5 QB-site titration curves for PC and PG liposomes at three selected temperatures: 6.6 °C (black circles), 20.0 °C (white squares) and 35.6 °C (black diamonds) using τS, AS and ASτS/τ∞ indicators (see text for details). Error bars are smaller than symbols. In panels A(1,2) the best fit lines to Eq. 13 are shown while in panels B(1,2) and C(1,2), the fitting function is Eq. 8, using light grey for 6.5 °C, black for 20 °C and dark grey for 35 °C. The same ordinate scale is maintained in corresponding panels for sake of clarity
LAB evaluation The time constant τ∞ obtained at saturating quinone concentration (i.e., Q/RC ≥ 10) can be combined with kAD to calculate LAB (Shinkarev and Wraight 1993):
LAB =
τ∞ kAD − 1 ≈ τ∞ kAD − 1. 1 − τ∞ kBD
(3)
At 25 °C LAB evaluated values are 18.0 for PC and 33.0 for PG, respectively, in agreement with previously published results (Nagy et al. 2004). Furthermore, for both PC and PG liposomes in the range 6.5–35 °C, LAB, decreases with temperature as shown by the van’t Hoff plot reported in Fig. 6. Since both curves ln(LAB) against 1/T exhibit a linear – and S O O – trend then HAB AB can be assumed constant in the given temperature range and derived as best fit linear parameters (Table 3).
Fig. 6 Van’t Hoff plot for the equilibrium constant LAB in PC (circles) and PG (squares) liposomes
Also this result is in agreement with what has been already observed in LDAO solutions with native ubiquinones (Mancino et al. 1984; McComb et al. 1990). The
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Table 3 Thermodynamic parameters for LAB in PC and PG liposomes
PC PG
−1 ∆G–O AB kJ mol
O – kJ mol−1 ∆HAB
O – JK−1mol−1 ∆SAB
R2
−6.97 ± 0.04
−16.2 ± 1.2
−30.9 ± 4.0
0.996
−8.90 ± 0.04
−13.3 ± 0.9
−15.1 ± 3.0
KQ evaluation Table 4 summarizes the binding constants obtained with the three methods TM, AM, and WAM. For both PC and PG, KQWAM is smaller than the corresponding KQAM and KQTM at all temperatures. This can be a first indication that the rate of the quinone exchange is in an intermediate/fast regime for the considered systems and that KQ∗ ≥ KQ. Therefore, since the quinone exchange regime is not well defined and, most importantly, it changes over the investigated temperature range, both AM and TM are not fully appropriate. Conversely, the homogeneous and good fitting accuracy of WAM with R2 is always greater than 0.980 at all temperatures (see Fig. 5, panels C1 and C2) confirming that this method is less influenced by the quinone exchange regime. Going into details, in the case of PC liposomes, Table 4 shows that KQAM regularly increases with temperature while the fitting accuracy (R2) worsens. In contrast, KQTM decreases while R2 values slightly improve though remaining quite high at all temperatures. This indicates that the quinone exchange regime becomes faster when temperature increases, and the fast quinone exchange is always a good description of the system. Indeed, at 35.6 °C the exchange rate is so fast that even at Q/RC = 0.1, AS accounts for almost 40 % of the overall signal, but with a small τS (Fig. 5B1). In the case of PG liposomes, the AM fitting worsens with increasing temperature, but shows a better accuracy R2 ≥ 0.990 and AS does not change so much with temperature (Fig. 5B2) indicating that the slow exchange approximation holds better. This result is also confirmed by TM that exhibits a fit accuracy generally worse: 0.713 (6.6 °C) ≤ R2 ≤ 0.970 (35.2 °C), with R2 increasing
0.996
difference between the PC and PG liposomes can be ascribed to the different stabilization exhibited by the two phospholipids on the charge-separated state (Nagy et al. 1999; Agostiano et al. 1995). A similar effect has been observed also in other systems of biotechnological interest (Magyar et al. 2011; Dorogi et al. 2006). The signs of – and S O O – HAB AB indicate a reaction driven by enthalpy with an unfavorable entropic contribution for both kind of liposomes at room temperature. The values obtained for PC are in agreement with those found in soybean PC vesicles (Palazzo et al. 2000), in reversed micelles (Mallardi et al. 1997) and in LDAO micelles (Mancino et al. 1984). – It is worthwhile to note that PG has a more negative GO AB , despite the smaller absolute value of the enthalpic term, arising from a much lower entropic contribution. A similar behavior was found also in liposomes made with other negatively charged phospholipids such as phosphatidylinositol and phosphatidic acid (data not shown), and it can be ascribed to a sort of solvent thermodynamic effect since negatively charged membrane seems to better stabilize the D+ QA Q− B species. This effect needs to be investigated in more details and it will be the topic of future work by our group and requires a more systematic analysis to discriminate a pure electrostatic contribute from other molecular interactions. Table 4 Binding constants KQ obtained by different methods for PC and PG liposomes. Errors are always within ±10 %
13
t (°C)
KQAM (×103 M−1)
R2
KQTM (×103 M−1)
R2
PC 6.6 9.8 14.8 19.8 25.2 30.6 35.2
12.5 15.1 15.5 20.2 20.2 21.6 30.5
0.997 0.994 0.991 0.970 0.935 0.822 0.732
4.72 5.41 3.81 3.26 2.35 1.84 1.39
0.942 0.951 0.970 0.982 0.989 0.990 0.991
1.98 2.28 1.82 1.74 1.42 1.23 1.07
0.990 0.986 0.985 0.985 0.988 0.987 0.992
PG 6.6 10.3 15.2 20.1 25.2 30.6
29.6 42.1 40.2 41.3 30.5 40.4
0.994 0.994 0.997 0.998 0.996 0.993
626 150 45.3 21.7 12.6 8.18
0.713 0.884 0.954 0.976 0.984 0.977
15.7 13.0 9.29 7.37 4.93 4.13
0.988 0.987 0.987 0.984 0.989 0.992
35.1
27.2
0.990
5.04
0.966
2.36
0.986
KQWAM (×103 M−1)
R2
Eur Biophys J (2014) 43:301–315 Table 5 Optimized upper limits ∗ and k , and derived for kout out quantities KQ∗(ODE) and KQ(ODE) for PC and PG
309 t (°C) PC 6.6 9.8 14.8 19.8 25.2 30.6 35.2 PG 6.6 10.3 15.2 20.1 25.1 30.6 35.1
kout (s−1)
KQ∗(ODE) × 103 M−1
KQ(ODE) × 103 M−1
R2
34.8 ± 0.4 33.1 ± 0.5 53.2 ± 0.7 80.4 ± 1.2 146 ± 2 238 ± 4 450 ± 4
57 ± 3 37 ± 2 57 ± 3 109 ± 6 267 ± 18 589 ± 56 (1.4 ± 0.2) × 104
2.23 ± 0.02 2.86 ± 0.04 2.35 ± 0.03 2.04 ± 0.03 1.49 ± 0.02 1.17 ± 0.02 0.797 ± 0.008
1.23 ± 0.06 2.54 ± 0.13 2.18 ± 0.10 1.50 ± 0.08 0.82 ± 0.06 0.47 ± 0.05 0.026 ± 0.003
0.997 0.996 0.996 0.996 0.996 0.995 0.996
3.43 ± 0.09 4.36 ± 0.10 9.8 ± 0.3 14.6 ± 0.3 36.2 ± 0.7 71.6 ± 1.2
17.4 ± 1.4 9.4 ± 0.8 40 ± 4 45 ± 3 164 ± 12 (1.08 ± 0.15) × 103
22.9 ± 0.6 22.3 ± 0.5 13.1 ± 0.4 11.4 ± 0.3 5.93 ± 0.12 3.90 ± 0.07
4.5 ± 0.4 10.4 ± 0.9 3.2 ± 0.3 3.7 ± 0.2 1.27 ± 0.09 0.26 ± 0.04
0.994 0.993 0.996 0.996 0.996 0.996
(1.10 ± 0.10) × 104
2.37 ± 0.02
0.033 ± 0.003
0.994
∗ (s−1) kout
151.3 ± 1.5
significantly at high temperature indicating the exchange regime change from slow to fast above 20 °C. The fast exchange regime between the QB site and the immediate quinone pool is assumed to be fast both in micellar (Shinkarev and Wraight 1997) and liposomal (Palazzo et al. 2000) systems. The present analysis confirms this assumption, at least at temperatures higher than room temperature, and shows that the quinone exchange is modulated by the polar head of the phospholipid forming the liposomes. ∗ Optimization of kout and kout
The quinone binding process is completely described if the ∗ , k ∗ , k and k four relevant constants kin out are determined. out in As discussed in the “ODE set optimization procedure”, these constants could be in principle estimated as the best fit parameters, but since entrance and exit kinetic constants ∗ and k are highly correlated, kout out have been obtained by optimization as upper and lower limits in independent sets of optimization. We will start by discussing the upper limits ∗ ∗ and k of kout out obtained by fixing kin = kin at their maximum value limited by quinone diffusion in the bilayer. For both PC and PG, in the investigated temperature range, data ∗(ODE) (ODE) are summarized in Table 5 where KQ and KQ are ∗ ∗ obtained as kin /kout and kin/kout, respectively. Since the exchange quinone regime is mainly affected ∗ , values in Table 5 allows the inference that PG by kout liposomes show a regime transition passing from slow to ∗ becomes greater than k fast above 20 °C, where kout AD and ∗ that for PC the quinone exchange is always fast being kout at least three times larger than kAD. Both these observations are in agreement with the three methods for the evaluation
of KQEV and will be below confirmed by an evaluation of ∗ lower value. The numerical simulations allowed the kout us to separate the contributions of the light and dark qui∗ and k none binding constants by means of kout out that could otherwise not have been discriminated by means of a phenomenological description. In Fig. 7 for both PC and PG ∗(ODE) log(KQ ) is reported against 1/T, compared with KQWAM values. A linear trend is exhibited in the range 10–35 °C for PG and 10–30 °C for PC, respectively (open data). A similar (ODE) behavior has been also obtained for KQ although the data are more scattered, since the curves calculated by the numerical integration are less sensitive to kin and kout parameters (data not shown). By fitting the van’t Hoff equation in the temperature range where a linear behavior is shown, relevant thermodynamic parameters can be obtained and results are listed in Table 6 for both amphiphiles in dark and light conditions. – values for PC and PG do not differ too much, The GO Q indicating a similar affinity of UQ10 towards the QB-site in (ODE) the two systems. The smaller values of KQ compared ∗(ODE) to KQ are in agreement with the hypothesis of proximal (in the light) and distal (in the dark) binding site of QB (Stowell et al. 1997): in the D+ Q− A QB state QB is in the proximal state, more buried within the protein, and, hence, more tightly bound. The quinone binding constant and the relevant thermodynamic parameters have been previously determined in reverse micelles formed by a mixture of negatively charged and zwitterionic phospholipids using the τS dependence on quinone concentration. The – = −50.7 kJ/mol, − T �S O – values �HQO Q = 39 kJ/mol and 2 −1 KQ = 1.1 × 10 M at 298 K were found (Mallardi et al. 1997). The same authors also assessed the parameters in
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Fig. 7 Van’t Hoff plot for estimated KQ∗(ODE) for PG (open squares) and PC (open circles) compared with and KQWAM for PG (filled squares) and PC (filled circles) Table 6 Thermodynamic parameters for KQ∗(ODE) and KQ(ODE) obtained from simulations in PC and PG liposomes ∆G–O Q (kJ mol−1)
PC KQ∗(ODE) PC KQ(ODE) PG PG
KQ∗(ODE) KQ(ODE)
−18.10 ± 0.06
O ∆HQ– (kJ mol−1)
−31 ± 2
O – ∆SQ (J K−1 mol−1)
R2
−43 ± 6
0.999
−140 ± 20
0.996
−16.7 ± 0.7
−60 ± 20
−144 ± 77
0.958
−17 ± 2
−117 ± 70
−335 ± 230
0.901
−21.48 ± 0.17
−63 ± 5
PC liposomes exploiting the temperature dependence of the kS value and its polydispersity at Q to RC ratios of 10 and 25, finding similar values (Palazzo et al. 2000). All values were attributed to the binding to the QB-site when the protein is in the D+ Q− A state and, hence, correspond∗(ODE) ing to the KQ value of this work. The thermodynamic ∗(ODE) parameters of KQ listed in Table 6 for PC are somewhat different, however, in the previous papers a real titration of the QB-site was performed only in the case of the reverse micelles. The values found in this paper for PC and PG confirm that the quinone binding is substantially enthalpy-driven with an unfavorable entropic contribution, as expected for an association reaction, and indicate that the different polar head of the phospholipid has a great influence on the quinone binding reaction. Indeed a complete description requires the evaluation ∗ . A set of independent optimizaof lower limits for kout tions were, hence, performed using twenty values between ∗ . For each run, new 1 and 100 s−1 as fixed values for kout ∗ optimized values of kin and kin are obtained. The depend∗ is shown in figure S2 for PC ence of the R2 values on kout ∗ and PG. By varying kout in the above mentioned range, the
13
exchange regime is forced to change from slow to fast and the simulated decays show correspondingly a different agreement with the experimental CRR traces. The value of ∗ at which the R2 value starts to decrease can be taken kout ∗ lower limit (see table S2 in Supplementary as the kout Material). For PC this value is around 20 s−1 at all temperatures confirming that the system is always in the fast quinone ∗ lower and upper limits listed exchange regime. For PG, kout in table S2 are consistent with a quinone exchange regime switch at 20 °C. The conclusions based on the numerical simulations are perfectly consistent with the findings of the phenomenological approach. A recent evaluation of the quinone unbinding constant found optimizing the parameters of the whole photosynthetic unit (Geyer et al. 2010) gave a value of 87 s−1, which falls in the range ∗
