Analysis of the Kinetics of P+HAâ Recombination in Membrane

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Analysis of the Kinetics of PH Recombination in MembraneEmbedded Wild-Type and Mutant Rhodobacter Sphaeroides Reaction Centers Between 298 and 77 K Indicates that the Adjacent Negatively Charged Q Ubiquinone Modulates the Free Energy of PH and May Influence the Rate of the Protein Dielectric Response A

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Krzysztof Gibasiewicz, Maria Pajzderska, Andrzej Tomasz Dobek, Klaus Brettel, and Michael R. Jones J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp4011235 • Publication Date (Web): 11 Mar 2013 Downloaded from http://pubs.acs.org on March 11, 2013

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The Journal of Physical Chemistry

Analysis of the Kinetics of P+HA- Recombination in Membrane-Embedded Wild-Type and Mutant Rhodobacter sphaeroides Reaction Centers Between 298 and 77 K Indicates that the Adjacent Negatively Charged QA Ubiquinone Modulates the Free Energy of P+HA- and May Influence the Rate of the Protein Dielectric Response.

Krzysztof Gibasiewicza,*, Maria Pajzderskaa, Andrzej Dobeka, Klaus Brettelb, and Michael R. Jonesc

a

Department of Physics, Adam Mickiewicz University, ul. Umultowska 85, 61-614 Poznań,

Poland b

Laboratoire Mécanismes Fondamentaux de la Bioénergétique, UMR 8221, CEA - iBiTec-S,

CNRS, Université Paris Sud, 91191 Gif-sur-Yvette, France. c

School of Biochemistry, Medical Sciences Building, University of Bristol, University Walk,

Bristol, BS8 1TD, United Kingdom

*Address for correspondence: Krzysztof Gibasiewicz, Department of Physics, Adam Mickiewicz University, ul. Umultowska 85, 61-614 Poznań, Poland, tel.: +48 61 8296370, email: [email protected]

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Abstract Time-resolved spectroscopic studies of recombination of the P+HA- radical pair in photosynthetic reaction centers (RCs) from Rhodobacter. sphaeroides give an opportunity to study protein dynamics triggered by light and occurring over the lifetime of P+HA-. The state P+HA- is formed after the ultrafast light-induced electron transfer from the primary donor pair of bacteriochlorophylls (P) to the acceptor bacteriopheophytin (HA). In order to increase the lifetime of this state, and thus increase the temporal window for the examination of protein dynamics, it is possible to block forward electron transfer from HA- to the secondary electron acceptor QA. In this contribution the dynamics of P+HA- recombination were compared at a range of temperatures from 77 K to room temperature, electron transfer from HA- to QA being blocked either by pre-reduction of QA or by genetic removal of QA.

The observed

P+HA- charge recombination was significantly slower in the QA-deficient RCs, and in both types of complex lowering the temperature from RT to 77 K led to a slowing of charge recombination. The effects are explained in the frame of a model in which charge recombination occurs via competing pathways, one of which is thermally activated and includes transient formation of a higher-energy state, P+BA-. An internal electrostatic field supplied by the negative charge on QA increases the free energy levels of the state P+HA-, thus decreasing its energetic distance to the state P+BA-. In addition, the dielectric response of the protein environment to the appearance of the state P+HA- is accelerated from ~50-100 ns in the QA-deficient mutant RCs to ~1-16 ns in WT RCs with a negatively charged QA-. In both cases, the temperature dependence of the protein dynamics is weak.

Keywords: transient absorption spectroscopy, purple bacteria, photosynthetic reaction center, electron transfer, charge recombination, protein dynamics.


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Introduction Electron transfer (ET) in biological systems often occurs between redox centers embedded within a complex protein matrix comprising main chain groups, twenty varieties of amino acid side chain of different characters, and embedded water molecules and other bound small molecules or ions. The change in charge distribution upon transfer of an electron induces a dynamic response of the surrounding protein/solvent scaffold, and in turn this ET process itself may be affected by protein dynamics.1-6 At the atomic level the dielectric properties of proteins are complex, and the spontaneous internal dynamics of the component groups are known to cover time scales from picoseconds to seconds.7,8 Insertion of a permanent point charge (such as by formation of QA– in purple bacterial reaction centers; see below), is expected to interact with and modify the dynamic properties of the surrounding protein scaffold and may, as a consequence, affect ET reactions in the protein. Photosynthetic reaction centers (RCs) are particularly convenient model systems for study of the influence of protein dynamics on the intraprotein charge transfer. They contain several discrete electron transfer (ET) cofactors – chlorophylls, pheophytins and quinones – embedded in an intramembrane protein scaffold, and the structural and functional properties of some RCs are known in great detail.9,10 Time-resolved spectroscopic studies of RCs give an opportunity to observe ET inside the protein by recording transient absorption signals originating from changes in the energetic or redox states of particular ET cofactors as they form an excited electronic configuration, or donate or accept electrons. The time constants of particular ET steps in RCs range from subpicoseconds to seconds, with the fastest reactions occurring during the initial steps of the charge separation process. These time constants correspond to those characteristic for protein dynamics and so each ET step could be expected to occur in parallel with specific structural rearrangements of the protein environment. This gives rise to the possibility that the measured rate constant(s) of a particular ET reaction are



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governed both by the intrinsic properties of the ET cofactors, tuned to some degree by static properties of the surrounding protein-solvent matrix, and by the dynamic properties of that protein-solvent matrix. A nanosecond time scale ET reaction that occurs in purple bacterial reaction centers under certain conditions is recombination of the radical pair P+HA-,1,11-19 where P is the primary electron donor dimer of bacteriochlorophylls and HA is a bacteriopheophytin electron acceptor located approximately half-way across the membrane. These two species participate in the initial picosecond time scale charge separation, an electron passing from the singlet excited state of P (P*) to HA in ~3-6 ps via an intervening monomeric bacteriochlorophyll, labeled BA.10,20-27 P is separated from BA, and BA from HA by a similar edge-to-edge distance of ~5 Å, whereas the direct edge-to-edge distance from P to HA is ~10 Å (shown for the RC from Rhodobacter (Rba.) sphaeroides in Figure 1A).28-30 From HA- the electron is transferred across the remainder of the membrane in around 200 ps to quinone QA, unless this step is blocked by pre-reduction of QA or its removal by biochemical or genetic means. In the latter case the electron returns from HA- to P+, forming mostly the ground singlet state of P or, in a minority of RCs, the triplet excited state denoted 3P.11,16,18,19 This recombination of the P+HA- radical pair occurs on a subnanosecond to few tens of nanoseconds time scale with multiexponential kinetics,1,5,16,17,31 and in recent publications it has been argued that it occurs preferentially via a thermally activated intermediate P+BA- state, 5,16,17,31,32

with a relatively small admixture of a temperature-independent single step ET in

which BA serves only as a virtual intermediate.32 The multiexponential character of P+HArecombination has been attributed to the dielectric response of the protein environment to the initial appearance of this radical pair leading to gradual decrease of the free energy of this state relative to that of the state P+BA-. Studies of the temperature dependence of the charge recombination reaction in isolated Rba. sphaeroides RCs with pre-reduced quinone QA (QA-)


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allowed an estimation of the rates of protein relaxation, and in the frame of a model describing a two-step relaxation process, gave values of ~(0.6 ns)-1 and ~(11 ns)-1 that were essentially independent of temperature.32 According to the model applied in that paper the nanosecond lifetimes associated with P+HA- recombination appeared to be mostly the result of energetic stabilization of P+HA- due to the response of the protein dielectric, with recombination predicted to be much faster (~0.7 ns) in the absence of protein relaxation. Such a fast charge recombination was indeed observed for a series of mutants with decreased free energy gaps between P+HA- and P+BA-, in which protein relaxation was apparently less competitive with rapid charge recombination than was the case for WT RCs.31 This model for P+HA- charge recombination, including competition between a thermally activated pathway via the state P+BA- and protein relaxation, is now well supported by the experimental observations.5,16,17,31,32 In the present contribution the model is used to extract a protein relaxation rate constant for a site-directed mutant RC from Rba. sphaeroides which lacks the QA ubiquinone due to structural change in the QA binding pocket,33-35 and compare it to the equivalent parameter for the wild-type (WT) Rba. sphaeroides RC with QA pre-reduced. The QA-deficient RC has an alanine at the 260 position of the M-polypeptide changed to tryptophan – denoted AM260W) In previous publications it was reported that overall P+HA- recombination was significantly slower for RCs missing quinone QA either due to chemical treatment11-15 or due to genetic removal through the AM260W mutation33,34 than for RCs with QA pre-reduced. In this report we examine the temperature-dependence of the kinetics of P+HA- recombination in AM260W and WT RCs between 77 K and room temperature (RT). It is concluded that the protein dynamics appear to be much faster for QAreduced RCs than for QA-removed RCs.

Materials and methods



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Biological material Alanine 260 of the M-polypeptide of the Rba. sphaeroides RC was changed to tryptophan (AM260W) as described previously,33-35 by mutation of the relevant codon of the pufM gene. The altered pufM gene in expression vector pRKEH10D36 was expressed in Rba. sphaeroides deletion strain DD13.37 This produced transconjugant strains that had mutant RCs but lacked both types of Rba. sphaeroides light-harvesting complex.37 Antenna-deficient strains of Rba. sphaeroides assembling WT or mutant AM260W RCs were grown under dark/semi-aerobic conditions as described elsewhere,37 and intracytoplasmic membranes were isolated by breakage of harvested cells in a French pressure cell, followed by purification on 15 %/40 % (w/v) sucrose density step gradients.38 Isolated RCs were purified as described previously.39

Transient absorption measurements For nanosecond transient absorption experiments, concentrated isolated WT RCs were diluted in 1.5 mM Tris buffer (pH 8.2), containing 0.05% β-dodecyl maltoside (β-DM), 0.1 mM EDTA and 60% glycerol (v/v). Membrane-bound RCs (WT and AM260W mutant) were diluted in a similar buffer but with lower amount of β-DM (~0.0001%). To WT RCs, 20 mM sodium ascorbate and 12 mM o-phenanthroline16,17,40,41 were added, and these samples were constantly illuminated during the experiments with a background white light (~1 mW/cm2). It was shown that under these conditions the RCs are permanently in a state with QA reduced.11,12,16,17,31 The same amount of sodium ascorbate was added and the same background illumination was applied to AM260W RCs in order to ensure similar experimental conditions for all samples. RCs were placed in a cuvette formed by two round plastic windows separated with a 1.5-mm thick o-ring. The cuvette was set at a 45 degree angle relative to the direction of the excitation, probe, and background beams. The excitation


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and background beams entered the samples from two opposite sides, and the probe beam entered the sample at a right angle to the excitation beam. The typical optical density of the samples was OD800nm, 1.5mm = 0.53. The cuvette was placed in cryostat (Janis VPF-100) cooled with liquid nitrogen. For each sample, a transient absorption decay curve was measured only once at each temperature, as an average of the signals induced by 1024 laser shots. The transient absorption instrument was described previously.31,42 Vertically polarized saturating excitation flashes of ~2 mJ energy and of 100 ps duration at 532 nm were provided by a Nd:YAG laser (Continuum Leopard SS-10) at a repetition rate of ~2 Hz. A diode laser system (EOSI 2010) was used as a probe light source at 690 nm. The monitoring light was chopped in order to minimize its excitation effect. The probe beam was detected by a fast photodiode (rise time 200 ps; model UPD-200-UP from Alphalas) plugged into a digitizing oscilloscope (Agilent Infinium 81004B; 10 GHz; sampling rate, 40 Gsamples/s) yielding a time resolution of about 300 ps. The experiments were made in a 6 µs temporal window. Transient absorption kinetic traces were fitted with the sum of two or three exponential functions plus a constant using the program Origin. The fitting was performed in a 100, 200, and/or 500 ns window. The starting point of the fits was at the maximum of the experimental kinetics.

Results and discussion Comparison of P+HA- recombination in isolated and membrane-bound RCs. The transient absorption measurements presented in this paper were performed both on isolated RCs and on RCs embedded in the native membrane, using strains of Rba. sphaeroides lacking the LH1 and LH2 antenna proteins.36,37 The natural lipid bilayer environment of RCs may in principle exert somewhat different effects on ET reactions than the artificial environment of the detergent micelle required for isolation of RCs, and small



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differences in the primary ET reactions between isolated and membrane-bound RCs have been reported.36,43 In order to properly refer the results of the present work on membraneembedded RCs to a previous study of the temperature dependence of P+HA- recombination performed on isolated RCs,32 Fig. 2A compares transient absorption kinetics at 690 nm recorded over 100 ns for either isolated or membrane-bound WT RCs in which QA had been pre-reduced. As explained in previous reports,17,31 P+HA- recombination is observed at this wavelength, the decay of the initial absorption increase being mostly due to the decay of ∆A(HA- – HA) transient absorption signal, with a possible small admixture of the ∆A(P+ – P) signal. The residual signal that does not decay on the ~100-ns time scale is attributable to the transient absorption of the

3

P triplet state.31 On the basis of information from the

literature,12,44,45 it was estimated that at 690 nm the amplitude of the signal arising from the triplet state underestimates about five-fold the efficiency of triplet formation, due to different differential extinction coefficients for the triplet state, ∆ε(3P – P), and for the charge separated state, ∆ε(P+HA- – PHA).32 As shown in Fig. 2A, charge recombination at RT was slightly faster for isolated WT RCs than for WT RCs embedded in the membrane, but at later times both traces reached similar amplitudes indicating similar efficiencies of triplet formation (assuming the same values of ∆ε(3P – P) for both samples relative to those of ∆ε(P+HA- – PHA)). For both types of sample lowering the temperature caused a systematic slowing of the overall decay. At 78 K the two traces were similar over the first 30 ns of the decay, but at later times the amplitude of the signal for isolated RCs was bigger, suggesting a higher yield of triplet formation than for membrane-embedded RCs. All four decays shown in Figure 2A were fitted with a two- or three-exponential function, yielding the lifetimes and amplitudes shown in Table 1. Overall, it was concluded that the temperature dependence of the recombination kinetics was slightly stronger for isolated WT RCs than for membrane-bound WT RCs.


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Comparison of P+HA- recombination in WT and AM260W membrane-bound RCs. At all temperatures between 77 K and RT, charge recombination was much slower in membrane-bound QA-deficient AM260W RCs than in membrane-bound WT RCs with QA pre-reduced (Fig. 2B). In both cases, lowering the temperature caused a systematic slowing of the overall decay (kinetics for intermediate temperatures are not shown for clarity). Unlike in WT RCs, in the AM260W RC there was no clear ~1 ns decay component either at RT or 77 K (see the inset to Fig. 2B). Due to the relatively large noise and narrow ~100-ns temporal window (Fig. 2B) it is not immediately obvious how much triplet state is generated in the two types of RC (i.e. the amplitude of the non-decaying component). This could be resolved only on a longer time-scale (data not shown). The main differences between the kinetics of recombination in the WT and AM260W membrane-embedded RCs are quantified in Table 1. For WT membrane-embedded RCs, two sets of fits were performed using either twoor three-exponential functions. Two-exponential fits were satisfactory when fitting the experimental traces recorded over a 100 ns period, the advantage of this approach being that the amplitudes of the two components behaved more regularly as a function of temperature than was the case for a three-exponential fit (compare Figs. 3C and 4C). However, for data recorded over a 200 ns time scale a third exponential component clearly improved the fits, yielding a better description of the fastest (subnanosecond) and slowest processes as well as of the constant signal (A3 or A4; Table 1). A disadvantage of the three-exponential fit was more irregular behavior of the amplitudes as a function of temperature (especially amplitudes A3 and A4 – see Fig. 4C) resulting, in all likelihood, from the relatively high level of noise in the raw experimental data.

Temperature dependence of lifetimes and amplitudes 9 ACS Paragon Plus Environment


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As mentioned above, all experimental traces measured at temperatures ranging from 77 K to RT were fitted by a sum of up to three exponential functions and a constant: ∆A = ΣAiexp(-t/τi) + A4, where i = 1, 2, 3,

(1)

where ΣAi = 1, i = 1, 2, 3, 4. Both lifetimes (τi) and amplitudes (Ai) showed a more or less regular behavior as a function of temperature. The temperature dependence of the lifetimes for the WT (in the cases of two- and three-exponential fits) and AM260W RCs are shown in Figs. 3A, 4A and 5A, respectively. The temperature dependence of the respective amplitudes are shown in Figs. 3C, 4C and 5C. In the case of the two-exponential fit of decays recorded for WT RCs (Fig. 3A) the faster lifetime, τ1, ranged from 2.4 to 3.8 ns and showed a general tendency to increase weakly with decreasing temperature. In contrast the second lifetime, τ2, increased strongly from ~13 ns at RT to ~26 ns at 78 K. The amplitudes of the two phases, A1 and A2, did not show a clear dependence on temperature (Fig. 3C). On the other hand, the amplitude of the non-decaying component, A3, systematically grew with decreasing temperature from ~0.05 at RT to ~0.10 at 78 K. As might be expected, adding a third exponential component in the analysis of transient absorption signal from WT RCs accelerated the fastest component, decelerated the slowest component, introduced an intermediate lifetime and slightly decreased the amplitude of the non-decaying component (Figs. 4A and 4C). Due to the difficulty of precisely resolving the fastest component of the decay, the lifetime of which was close to the temporal resolution of the system, this parameter was fixed at a value of τ1 = 0.7 ns for all temperatures, in a similar fashion to that employed for isolated RCs analyzed previously.32 Introducing this fixed lifetime allowed resolution of two other clearly temperature-dependent lifetimes, τ2 which


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increased from ~6 to ~11 ns as the temperature decreased from RT to 78 K, and τ3 which increased from ~17 to ~38 ns over the same temperature range (Fig. 4A). The temperature dependence of the amplitudes A1-A3 in the three-exponential fits of data for WT RCs was not very regular (Fig. 4C), due to an insufficient signal to noise ratio in the experiments. On the other hand the amplitude of the non-decaying component, A4, clearly grew with decreasing temperature from ~0.04 at RT to ~0.08 at 78 K, showing a similar behavior to that of the A3 constant component in the two-exponential fit described above. In contrast to WT RCs, two exponential phases were clearly sufficient to describe the kinetics of recombination in AM260W RCs, with the faster lifetime, τ1, increasing quite systematically but rather weakly from ~18 ns at RT to ~23 ns at the lowest temperatures (Fig. 5A). The value of the second lifetime, τ2, was fixed at 80 ns. Leaving τ2 as a free parameter resulted in a range of values for this lifetime distributed around 80 ns, with no clear tendency to increase or decrease with temperature. The amplitudes of both of these components, A1 and A2, and of the non-decaying component, A3, behaved very systematically as a function of temperature: as the temperature decreased from RT to 78 K A1 decreased from ~0.86 to ~0.72, A2 increased from ~0.07 to ~0.21, and A3 increased from ~0.062 to ~0.075 (Fig. 5C, Table 1).

Fitting the temperature dependence of the experimentally extracted lifetimes. The temperature dependence of the experimentally extracted lifetimes could be fitted using a relatively simple model employed previously32 in which the charge separated state P+HA- decays through three competing pathways. One of these pathways is temperaturedependent and the two other are assumed in the first approximation to be temperatureindependent. As described in Fig. 6B, decay of the initially-formed P+HA- state (denoted (P+HA-)1) by the temperature-dependent pathway involves formation a thermally activated



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P+BA- state, the rate of decay via this pathway being dependent on temperature, the free energy gap between P+BA- and P+HA-, and the rate of P+BA- charge recombination, kPB. The second pathway is direct charge recombination of (P+HA-)1 to the ground singlet state with a rate kdir1. The third pathway is relaxation of (P+HA-)1 to a lower-energy form, represented in Figure 6B by (P+HA-)2. When P+HA- is already in the lowest relaxation state, this third pathway is replaced by charge recombination to the triplet state 3PHA. In the case of the AM260W RCs an optional charge recombination to the triplet state from the unrelaxed (P+HA-)1 state was also considered (scheme C in Fig. 6; see below). In this modeling the multiexponential decay of the transient absorption signals was a simple consequence of consecutive appearance of two or three relaxation states of P+HA- of increasing energy gap, ∆G, to P+BA- (Fig. 6A-B). These relaxation states were characterized by decreasing rates, kT1, kT2, kT3 (see Eqs. A6-A8 in the Appendix) of the thermally activated charge recombination as the corresponding energy gap to P+BA-, ∆G1-∆G3, became larger. The formulas for the rate constants, kPH1-kPH2 (or kPH1-kPH3 for a three-component fit), summing the rates of the three competing P+HA- charge recombination pathways and approximating the reciprocals of experimentally measured lifetimes, are shown in the Appendix (Eqs. A1-A5). In carrying out the modeling it was convenient to move from the lifetime domain to the inverted lifetime or rate constant domain. Therefore, instead of fitting directly the temperature dependence of lifetimes, the temperature dependences of inverted lifetimes, τi-1, were fitted with rates kPHi (i = 1, 2, (3); Eqs. A2-A5). Figs. 3B, 4B, and 5B show the experimental data and fits for two- or three-exponential models for the WT RC and twoexponential models for the AM260W RCs, respectively. In all these cases the fitting curves were calculated assuming, as in previous work,32 that for each exponential component the increase of kPHi with increasing temperature is caused exclusively by increasing values of the


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respective rate kTi. At the low temperature limit (77 K), for a ∆Gi of the order of a few tens of meV or more, the rate kTi approached zero (Eqs. A6-A8) and kPHi approached asymptotically a value which was the sum of the rate constants characterizing the remaining pathways (Eqs. A2-A5). Thus, the parameters of the fitting curves were kPB (assumed in this paper to equal (0.2 ns)-1),17,46,47 ∆Gi, and the sum of the rates of direct charge recombination (kdiri) and relaxation and/or triplet formation (k12, k23, kt) (Eqs. A2-A5). For modeling of data for the WT RC using two exponentials (Fig. 3B), the resulting free energy gaps for the two resolved relaxation states of P+HA-, (P+HA-)1 and (P+HA-)2, were 90 and 128 meV, respectively (Table 2). For modeling of the same data using three exponentials (Fig. 4B), the temperature independence of the lifetime τ1 = 0.7 ns (Tab. 1, Fig. 4A) indicated that the states (P+HA-)1 and P+BA- are roughly isoenergetic, as was also concluded for isolated WT RCs.32 The free energy levels of the next two relaxation states, (P+HA-)2 and (P+HA-)3, were calculated to be 110 and 135 meV below that of P+BA-, respectively (Tab. 2, Fig. 6A). This was similar to values estimated from the two-exponential fit and also similar to values reported previously for isolated WT RCs (102±10 and 142±10 meV).32 Modeling of data for the AM260W RC employing two exponentials (Fig. 5B) yielded larger energy gaps (∆G1 = 150 meV, ∆G2 = 250 meV) than was the case for WT RCs (Table 2, Fig. 6B). It is worth noting that the temperature-independence of τ2 = 80 ns may have resulted from the relatively large energy gap ∆G2 between (P+HA-)2 and P+BA-, which even at RT makes the thermally-activated pathway very ineffective (∆G2 is about 10-fold larger than the thermal energy factor kT at RT).

Calculation of corrected amplitudes D1-D4.



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In the model described in Fig. 6 the values of the amplitudes Ai result from competition between recombination of P+HA- to the ground state (either direct or thermally activated) and relaxation of P+HA- to a lower energy state(s) or charge recombination to the triplet state.18 So, for example, the faster is the relaxation from state “i” to state “i+1”, the smaller is amplitude Ai. The values of the amplitudes are therefore determined both by the relative concentrations of particular relaxation forms of P+HA- and of the triplet state 3P, and by the differential extinction coefficients ∆ε(P+HA- – PHA) and ∆ε(3P – P). For further modeling it was convenient to remove the dependence of these amplitudes on the differential extinction coefficients, and replace them with corrected amplitudes, Di, that depend exclusively on the relative concentrations of 3P and the different forms of P+HA-. The formulas for calculating Di can be found in the Appendix (Eqs. A9-A10). A large increase in the corrected amplitudes of the nondecaying component, D3 (Fig. 3D and 5D) or D4 (Figs. 4D), compared to the respective uncorrected amplitudes (Figs. 3C, 4C and 5C), caused compensatory changes in the remaining corrected amplitudes. In the case of the two-exponential fits performed for WT RCs, correction of amplitudes A1 and A2 that were rather temperature-independent (Fig. 3C) resulted in amplitudes D1 and D2 both generally decreasing with decreasing temperature (Fig. 3D). In the case of the threeexponential fits performed for WT RCs, the situation was less clear due to limitations related to the signal to noise ratio (see above). However, both D2 and D3 showed again a slight tendency to decrease with decreasing temperature (Fig. 4D). For the AM260W RC the behavior of corrected amplitudes D1-D3 as a function of temperature (Fig. 5D) was qualitatively the same as that of the amplitudes A1-A3 (Fig. 5C). However amplitude D3 was bigger than amplitude A3 at the expense of the amplitudes D1 and D2.


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Fitting the temperature dependence of the corrected amplitudes D1-D4. In the frame of a model in which P+HA- charge recombination to the ground state (direct or thermally activated) competes with relaxation of P+HA- or charge recombination to the triplet state (Fig. 6), the temperature dependence of the corrected amplitudes Di, may be fitted with model curves that are a function exclusively of the rates kPHi and the rate constants for relaxation (k12, k23) and triplet formation (kt, kt1). The exact formulas for these curves depend on the model, and for the three models presented in Fig. 6 the respective formulas can be found in the Appendix (Eqs. A11-A17). These formulas have been derived from sets of differential equations different for each model. As an example, the full set of differential equations for the model shown in Fig. 6A may be found in a previous report.32 The formulas A11-A17 were used to fit the temperature dependence of the corrected amplitudes Di either assuming that the relaxation and triplet formation rates are temperatureindependent (Figs. 3D, 4D, 5D) or allowing these rates to be temperature-dependent (Figs. 3E, 4E, 5E). In the former case, and for two-exponential fits, it can be seen from Eqs. A11-13 that optimization of only two free parameters, k12 and kt, has to be sufficient to approximate as many as three experimentally obtained curves D1-D3 (Figs. 3D and 5D). The fact that the two free parameters gave a good approximation to these curves (see below) is a strong argument for the correctness of the model used (Fig. 6). On the other hand, iterative optimization of these two parameters demonstrated that significant deviations from the optimized k12 and kt values (above ±10%) resulted in complete mis-fit for at least one curve. A similar discussion applies for three-exponential fits, for which three free parameters, k12, k23, and kt, were used to fit four curves (Eqs. A14-17, Fig. 4D). Introducing the temperature dependence of the rates k12, k23, and kt created a possibility of “manual” improvement of each particular temperature point of model curves (Eqs. A11-17) so that in principle they could almost exactly fit the experimental points. However, the experimental amplitudes were noisy 15 ACS Paragon Plus Environment


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whereas the fits were decided to be smooth curves (Figs. 3D, 4D, 5D). The smooth character of the fitting curves was ensured by an arbitrary constraint that the rate constants are a monotonic function of temperature. In the case of the data for the WT RC fitted with two exponentials, and with optimized but temperature-independent values of rate constants for relaxation (k12) and triplet formation (kt), the theoretical curves denoted D (i = 1, 2, 3;Eqs. A11-A13) properly reflect the general temperature dependence of the corrected amplitudes, Di (Fig. 3D). However, the fits were not very good and could be improved by introducing a weak dependence of the rates k12 and kt on temperature (Fig. 3E). As shown in Fig. 3D (and Table 2), the optimized temperatureindependent rates were k12 = (3.8 ns)-1 and kt = (38 ns)-1. Better fits (Fig. 3E) were obtained when both these rates decreased slightly with decreasing temperature from (3.3 ns)-1 to (4.1 ns)-1 and from (33 ns)-1 to (38 ns)-1, respectively (see also Fig. 7A and Table 2). A similar approach was employed to analyze data for the WT RC using the threeexponential model (Figs. 4D and 4E). Again, under the constraint that values of the rates k12, k23, and kt are temperature-independent, acceptable fits were obtained for k12 = (0.41 ns)-1, k23 = (15 ns)-1, and kt = (50 ns)-1 (Fig. 4D). Improvement of the fits, especially for D4, was reached when the rates k23 and kt could vary with the temperature (Fig. 4E). Since the rate k12 was estimated on the somewhat arbitrary fixing of the value of τ1 = 0.7 ns and ∆G1 = 0 meV (see above) further optimization of the D curve was not reasonable. Interestingly, the optimal fits were obtained again for k23 and kt decreasing slightly with decreasing temperature from (13.5 ns)-1 to (15.9 ns)-1 and from (40 ns)-1 to (56 ns)-1, respectively (Fig. 4E, Tab. 2. and Fig. 7B). The single calculated relaxation time in the two-exponential model of ~3.8 ns compared reasonably well to the two relaxation lifetimes of 0.41 ns and ~15 ns obtained using the three-exponential model. Also the rate of triplet formation obtained in these two models,


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~(38 ns)-1 and ~(50 ns)-1 respectively, compared well to each other. On the other hand, the values for the three rates obtained for the membrane-bound RCs, k12 = (0.41 ns)-1, k23 = (15 ns)-1, and kt = (50 ns)-1, compared well with those reported previously for isolated RCs: (0.6 ns)-1, (10-11 ns)-1 and (29-38 ns)-1, respectively.32 As mentioned above, fitting with two exponentials was clearly sufficient in the case of the kinetics measured for the AM260W RC. Figs. 5D and 5E present the results of fitting the corrected amplitudes calculated for this mutant performed according the same approach as that described above for WT RCs and using the model in Fig. 6B (the same model, but with different ∆Gi values, was used for the two-exponential analysis of the WT RCs data described above). Again, single temperature-independent rates, k12 = 50 ns and kt = 95 ns, approximated roughly properly a general temperature dependence of the amplitudes Di. However, the resulting temperature dependence of the model curve, D , was too weak to give a good fit. The situation was again improved by allowing a temperature-dependence of the rates. Interestingly however, unlike for the WT RC the relaxation rate for the mutant RC slightly increased with decreasing temperature (Fig. 7C, Tab. 2) from (52 ns)-1 to (48 ns)-1. This small increase contradicts an intuitive expectation that lowering the temperature should slow down, or at least not influence at all, the protein dynamics. On the other hand, the rate of triplet formation kt decreased with decreasing temperature, from (89 ns)-1 to (95 ns)-1, qualitatively in line with the results obtained for WT RCs (Figs. 7A-C, Tab. 2). Additionally, a modified model for the AM260W RC was considered in which triplet formation from the non-relaxed (P+HA-)1 state was possible (model C in Fig. 6). This model was applied to the mutant RCs because of the relatively long lifetime of its (P+HA-)1 state. It was assumed that the rate of triplet formation from the unrelaxed state, kt1 (Fig. 6C, Eq. A4), is the same as that from the relaxed state: kt1 = kt. Under this constraint it might be expected that a significant portion of the state (P+HA-)1 will recombine to the triplet state before it can



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relax to the state (P+HA-)2. As the calculations showed, introducing the new triplet pathway results in about a two-fold decrease of the calculated relaxation rate k12, from ~(50 ns)-1 to ~(91 ns)-1, and affects the rate kt to a much smaller extent – decreasing it from ~(95 ns)-1 to ~(112 ns)-1 (Fig. 7D, Table 2).

Comparison of the rates of relaxation and triplet formation in the WT and mutant RCs. Comparison of the relaxation rates calculated for the WT RC (k12 = (3.8 ns)-1 in the two-exponential model and k12 = (0.41 ns)-1, k23 = (15 ns) in the three-expoenential model) and the AM260W RC (k12 = (50 ns)-1 for kt1 = 0 ns-1, and k12 = (95 ns)-1 for kt1 = kt) demonstrates that in the frame of the model used, the relaxation was much slower in the RCs lacking QA because of a genetic change. This suggests that the charge on QA- present only in the pre-reduced WT RCs not only shifts the free energy levels of the states (P+HA-)i up relative to their values in the QA-deficient mutant (Table 2) but additionally accelerates the protein dynamics that underlie the rate(s) of P+HA- relaxation. Apparently, the amino acid residues and bound solvent molecules that participate in the dielectric response of the protein to the appearance of the P+HA- charge separated state are accelerated in their structural rearrangement by the additional negative charge located on the adjacent QA quinone. Alternatively, it is possible that a small structural change in the RC caused by the AM260W point mutation slowed protein dynamics compared to those in the WT (X-ray crystallography of the AM260W RC has shown that structural changes in this RC are limited to an interhelical loop that forms part of the QA binding pocket).34 Triplet formation rate was accelerated by a factor of around two, from (89-120 ns)-1 to (33-56 ns)-1, by the presence of QA– in WT RCs as compared to the QA-deficient mutant. As triplet formation occurs by charge recombination after singlet-to-triplet spin-conversion in the


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radical pair P+HA-, it is conceivable that spin-spin interactions with QA– accelerated the rate or the efficiency of spin-conversion in P+HA-. In all our analysis, somewhat better fits were obtained when the relaxation and triplet formation rates were allowed to vary with temperature. Yet, the obtained temperature dependencies were very weak.

Calculation of the direct charge recombination rate constants, kdiri. Having calculated rate constants for relaxation and triplet formation and knowing the values of ∆Gi and kPB it is straightforward to calculate the rate constants for direct recombination, kdiri (Eqs. A1-A8, Table 2). A general observation is that the more relaxed is the state P+HA- the slower is this direct recombination pathway (Table 2: data for the AM260W mutant and the three-exponential fit of data on WT RCs). In particular, direct recombination from the more relaxed P+HA- state(s) takes typically more than 100 ns, whereas direct recombination from the less relaxed P+HA- state(s) takes about 40 ns, both for the WT and mutant RC (an exception being for the two-exponential analysis of data on the WT RC). These values are in agreement with the respective numbers reported for isolated RCs.32

Acknowledgements MRJ acknowledges support from the Biotechnology and Biological Sciences Research Council of the United Kingdom. K.G. acknowledges financial support from the Polish government (project entitled “Electrostatic control of electron transfer in purple bacteria reaction center” no N N202 127 437).



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Appendix For three-exponential fits used in the case of WT RCs, the temperature dependence of the experimental lifetimes’ reciprocals, (τ1)-1 - (τ3)-1, can be fitted respectively with rates kPH1kPH3 given by the formulas:32 kPH1 = kT1 + [kdir1 + k12][1 + exp(-∆G1/kT)]-1,

(A1)

kPH2 = kT2 + kdir2 + k23,

(A2)

kPH3 = kT3 + kdir3 + kt,

(A3)

where k is a Boltzann constant, T is temperature and for explanation of the remaning symbols - see below and Fig. 6. The term [1 + exp(-∆G1/kT)]-1 is significantly different from 1 only if free energy gap between the states P+BA- and (P+HA-)1, ∆G1, is small (relative to kT) For two-exponential fits used both in the case of WT and AM260W mutant RCs the above formulas were replaced by: kPH1 = kT1 + kdir1 + k12 + kt1,

(A4)

kPH2 = kT2 + kdir2 + kt

(A5)

kT1 = kPB[1 + exp(∆G1/kT)]-1,

(A6)

kT2 = kPB[1 + exp(∆G2/kT)]-1,

(A7)

kT3 = kPB[1 + exp(∆G3/kT)]-1,

(A8)

where

and kt1 was set to zero in scheme B (Fig. 6; also in two-exponential fitting of WT RCs kinetics) and non-zero in scheme C (Fig. 6). Naturally, the rate kT3 applies only to threeexponential model and ∆G3 is free energy gap between the states P+BA- and (P+HA-)3. Corrected amplitudes were calculated from the following equations:32 Dj = fAj,

(A9)


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where f = 5 (f is a factor resulting from different differential extinction coefficients, ∆ε(P+HA– PHA) and ∆ε(3P – P), at 690 nm32) and j = 3 for two-exponential fitting and j = 4 for threeexponential fitting, and Di = Ai(1 – Dj) / (ΣAi),

(A10)

where i = 1, 2 for two-exponential fitting and i = 1, 2, 3 for three-exponential fitting. In the frame of the two-exponential model, the temperature dependence of the corrected amplitudes Di may be fitted with the model amplitudes D derived from the proper set of the differential equations (not shown):

D 1

D

D

1

k

1

,

(A11)

,

(A12)

,

(A13)

where all rate constants are explained in Fig. 6. In the scheme B (Fig. 6), kt1 = 0. Similarly, for the three-exponential model, the temperature dependence of the corrected amplitudes Di may be fitted with the model amplitudes D : D 1

D

D

1

1

D

1

1

,

(A14)

,

(A15)

1

,

(A16)


.

(A17)


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(24) Kirmaier, C.; Holten, D. An Assessment of the Mechanism of Initial Electron Transfer in Bacterial Reaction Centers. Biochemistry 1991, 30, 609-613. (25) Lockhart, D. J.; Kirmaier, C.; Holten, D.; Boxer, S. G. Electric Field Effects on the Initial Electron Transfer Kinetics in Bacterial Photosynthetic Reaction Centers. J. Phys. Chem. 1990, 94, 6987-6995. (26) Rodriguez, J.; Kirmaier, C.; Johnson, M. R.; Friesner, R. A.; Holten, D.; Sessler, J. L. Picosecond Studies of Electron Transfer in Quinone Substituted Monometalated Porphyrin Dimers: Evidence for Superexchange Mediated Electron Transfer in a Photosynthetic Model System. J. Am. Chem. Soc. 1991, 113, 1652-1659. (27) Chan, C. K.; DiMagno, T. J.; Chen, L. X.; Norris, J. R.; Fleming, G. R. Mechanism of the initial charge separation in bacterial photosynthetic reaction centers. Proc. Natl. Acad. Sci. USA 1991, 88, 11202-11206. (28) Deisenhofer, J.; Epp, O.; Miki, K.; Huber R.; Michel, H. X-ray Structure Analysis of a Membrane Protein Complex. Electron Density Map at 3 A Resolution and a Model of the Chromophores of the Photosynthetic Reaction Center from Rhodopseudomonas viridis. J. Mol. Biol. 1984, 180, 385-398. (29) Allen, J. P.; Feher, G.; Yeates, T. O.; Komiya, H.; Rees, D. C. Structure of the reaction center from Rhodobacter sphaeroides R-26: The cofactors. Proc. Natl. Acad. Sci. USA, 1987, 84, 5730-5734. (30) Warren J. J.; Winkler, J. R.; Gray, H. B. Hopping Maps for Photosynthetic Reaction Centers. Coordination Chemistry Reviews 2013, 257, 165–170. (31) Gibasiewicz, K.; Pajzderska, M.; Potter, J. A., Fyfe, P. K.; Dobek, A.; Brettel, K.; M. R. Jones, M. R. Mechanism of Recombination of the P+HA- Radical Pair in Mutant Rhodobacter sphaeroides Reaction Centers with Modified Free Energy Gaps Between P+BA- and P+HA-. J. Phys. Chem. B 2011, 115, 13037.



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(32) Gibasiewicz, K.; Pajzderska, M.; Dobek, A.; Karolczak, J.; Burdziński, G.; Brettel, K.; Jones, M. R. submitted (33) Ridge, J. P.; van Brederode, M.E.; Goodwin, M. G.; van Grondelle, R.; Jones, M. R. Mutations that Modify or Exclude Binding of the Q(A) Ubiquinone and Carotenoid in the Reaction Center from Rhodobacter sphaeroides. Photosynth. Res. 1999, 59, 9–26. (34) McAuley, K. E.; Fyfe, P. K.; Ridge, J. P.; Cogdell R. J.; Isaacs, N. W.; Jones, M. R. Ubiquinone Binding, Ubiquinone Exclusion, and Detailed Cofactor Conformation in a Mutant Bacterial Reaction Center. Biochemistry 2000, 39, 15032-15043. (35) Pawlowicz, N. P.; van Grondelle, R.; van Stokkum, I. H. M.; Jones, M. R.; Breton, J.; Groot, M. L. Identification of the First Steps in Charge Separation in Bacterial Photosynthetic Reaction Centers of Rhodobacter sphaeroides by Ultrafast Mid-Infrared Spectroscopy: Electron Transfer and Protein Dynamics. Biophysical Journal 2008, 95, 1268-1284. (36) Jones, M. R.; Visschers, R. W.; van Grondelle, R.; Hunter, C. N. Construction and Characterization of a Mutant of Rhodobacter Sphaeroides with the Reaction Center as the Sole Pigment-Protein Complex. Biochemistry 1992, 31, 4458-4465. (37) Jones, M. R.; Fowler, G. J. S.; Gibson, L. C. D.; Grief, G. G.; Olsen, J. D.; Crielaard, W.; Hunter, C. N. Mutants of Rhodobacter Sphaeroides Lacking one or More PigmentProtein Complexes and Complementation with Reaction-Centre, LH1, and LH2 Genes. Mol. Microbiol. 1992, 6, 1173-1184. (38) Jones, M. R.; Heer-Dawson, M.; Mattioli, T. A.; Hunter, C. N.; Robert, B. Site-Specific Mutagenesis of the Reaction Centre from Rhodobacter Sphaeroides Studied by Fourier Transform Raman Spectroscopy: Mutations at Tyrosine M210 do not Affect the Electronic Structure of the Primary Donor. FEBS Lett. 1994, 339, 18-24.


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(39) McAuley-Hecht, K. E.; Fyfe, P. K.; Ridge, J. P.; Prince, S. M.; Hunter, C. N.; Isaacs, N. W.; Cogdell, R. J.; Jones, M. R. Structural Studies of Wild-Type and Mutant Reaction Centers from an Antenna-Deficient Strain of Rhodobacter Sphaeroides: Monitoring the Optical Properties of the Complex from Bacterial Cell to Crystal. Biochemistry 1998, 37, 4740-4750. (40) Okamura, M. Y.; Isaacson, R. A.; Feher, G. Primary Acceptor in Bacterial Photosynthesis: Obligatory Role of Ubiquinone in Photoactive Reaction Centers of Rhodopseudomonas Spheroides. Proc. Natl. Acad. Sci. U.S.A., 1975, 79, 3491-3495. (41) Michel, H.; Epp, O.; Deisenhofer, J. Pigment-Protein Interactions in the Photosynthetic Reaction Centre from Rhodopseudomonas Viridis. EMBO J., 1986, 5, 2445-2451. (42) Byrdin, M.; Thiagarajan, V.; Villette, S.; Espagne, A. ; Brettel, K. Use of Ruthenium Dyes for Subnanosecond Detector Fidelity Testing in Real Time Transient Absorption. Rev. of scientific instruments 2009, 80, 043102. (43) Gibasiewicz, K.; Pajzderska, M.; Karolczak, J.; Burdziński, G.; Dobek, A.; Jones, M.R. Primary Electron Transfer Reactions in Membrane-Bound Open and Closed Reaction Centers from Purple Bacterium Rb. Sphaeroides. Acta Phys. Pol. A 2012, 122, 263-268. (44) Parson, W. W.; Clayton, R. K.; Cogdell, R. J. Excited States of Photosynthetic Reaction Centers at Low Redox Potentials. Biochim. Biophys. Acta, 1975, 387, 265-278. (45) Michel-Beyerle, M. E.; Scheer, H.; Seidlitz, H.; Tempus, D. Magnetic Field Effect on Triplets and Radical Ions in Reaction Centers of Photosynthetic Bacteria. FEBS Lett., 1980, 110, 129-132. (46) Heller, B. A.; Holten, D.; Kirmaier, C. Effects of Asp Residues near the L-side Pigments in Bacterial Reaction Centers. Biochemistry, 1996, 35, 15418-15427. (47) Katilius, E.; Turanchik, T.; Lin, S.; Taguchi, A. K. W.; Woodbury N. W. B-Side Electron Transfer in a Rhodobacter Sphaeroides Reaction Center Mutant in which the



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B-Side Monomer Bacteriochlorophyll is Replaced with Bacteriopheophytin. J. Phys. Chem. B 1999, 103, 7386-7389.


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Figure legends Figure 1. Structures of the WT and AM260W Rba. sphaeroides RCs. (A) In the WT RC residue Ala M260 (orange carbons) is located close to the QA ubiquinone (cyan carbons), prereduction of which blocks forward electron transfer and leads to recombination of P+HA-. (B) In the AM260W mutant RC Trp M260 (orange carbons) sterically excludes assembly of the QA quinone into the RC, also blocking electron transfer beyond P+HA-. In both panels the P BChls are shown with yellow carbons, BA BChl with green carbons and HA BPhe with pink carbons. For other atoms, red = oxygen, blue = nitrogen and magenta sphere = magnesium.

Figure 2. Comparison of transient absorption signals at 690 nm for (A) - purified WT RCs (denoted WT RC) and WT RCs embedded in the native membrane (denoted WT membr), and (B) membrane-bound WT and QA-deficient AM260W RCs.

Both panels show signals

recorded at RT (296-298 K) and 78 K. Insets show the first 5 ns of the traces in the main panels.

Figure 3. Temperature dependences of the parameters from two-exponential fits of charge recombination kinetics recorded for membrane bound WT RCs. Filled symbols represent fits to the data, whereas the open symbols depend on the model. (A) temperature dependences of lifetimes τ1 and τ2; (B) temperature dependences of inverted lifetimes, 1/τ1 and 1/τ2, and the fits of these dependences performed according to Eqs. A4-A7 from the Appendix (energetic parameters of these fits are shown; kPB = (0.2 ns)-1; kt1 = (0 ns)-1; (C) temperature dependences of amplitudes; (D) temperature dependences of corrected amplitudes and the fits of these dependences performed according to Eqs. A11-A13 from the Appendix, assuming temperature-independent values of the protein relaxation rate, k12, and the triplet formation



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

rate, kt; (E) the same analysis as in panel D but with parameters k12 and kt allowed to vary with temperature. The parameters of the fits shown in panels B, D, E are collected in Table 2.

Figure 4. Temperature dependences of the parameters from three-exponential fits of charge recombination kinetics recorded for membrane-bound WT RCs. Filled symbols represent fits to the data, whereas the open symbols depend on the model. (A) temperature dependences of lifetimes τ2 and τ3; (B) temperature dependences of inverted lifetimes, 1/τ2 and 1/τ3, respectively, and the fits of these dependences performed according to Eqs. A2-A3 from the Appendix (energetic parameters of these fits are shown; kPB = (0.2 ns)-1; (C) temperature dependence of amplitudes; D – temperature dependences of the corrected amplitudes and the fits of these dependences performed according to Eqs. A14-A17 from the Appendix, assuming temperature-independent values of the protein relaxation rates, k12, k23, and the triplet formation rate, kt; (E) the same analysis as in panel D but with parameters k23 and kt allowed to vary with temperature. The parameters of the fits shown in panels B, D, E are collected in Table 2.

Figure 5. Temperature dependences of the parameters from two-exponential fits of charge recombination kinetics recorded for membrane-bound AM260W RCs. Filled symbols represent fits to the data, whereas the open symbols depend on the model. (A) temperature dependences of lifetimes τ1 and τ2; (B) temperature dependences of inverted lifetimes, 1/τ1 and 1/τ2, and the fits of these dependences performed according to Eqs. A4-A7 from the Appendix (energetic parameters of these fits are shown; kPB = (0.2 ns)-1; kt1 = (0 ns)-1; (C) temperature dependences of amplitudes; (D) temperature dependences of corrected amplitudes and the fits of these dependences performed according to Eqs. A11-A13 from the Appendix, assuming temperature-independent values of the protein relaxation rate, k12, and


Page 30 of 42

Page 31 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the triplet formation rate, kt, for all temperatures; (E) the same analysis as in panel D but with parameters k12 and kt allowed to vary with temperature. The parameters of the fits shown in panels B, D, E are collected in Table 2.

Figure 6. Diagrammatic representation of the free energy levels of ground, charge separated and triplet states in (A) WT and (B, C) AM260W membrane-bound RCs. The distances between the levels of the states (P+HA-)i and P+BA- are drawn proportional to the calculated free energy gaps between these states (see Table 2) in order to demonstrate the effect of the mutation on these levels. In the modeling, all the (P+HA-)i states were assumed to be in equilibrium with the state P+BA-. This equilibrium is illustrated in (B) by the double opposing vertical arrows. For clarity, these double arrows were omitted in (A) and (C). In (C), direct triplet formation from the unrelaxed state (P+HA-)1 is included. In all panels the free energy level of the state P+BA- was arbitrarily set to zero. Rate constants shown in the diagrams depict: P+BA- charge recombination (kPB); direct P+HA- charge recombination from different relaxation forms of P+HA- to the ground singlet state (kdir1 - kdir3); P+HA- relaxation (k12, k23); P+HA- charge recombination the triplet state (kt, kt1). ∆Gi denotes the free energy gap between P+BA- and (P+HA-)i.

Figure 7. Temperature dependence of rate constants for relaxation (k12, k23) and triplet formation (kt) for (A, B) WT and (C, D) AM260W membrane-bound RCs. In panels A, C, and D, the rate constants were calculated from the two-exponential model, whereas in panel B they were calculated from the three-exponential model. Note that in panel B, relaxation rate k23 and not k12 is plotted.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 42

Tables

Table 1. Parameters from two- or three-exponential fits of charge recombination kinetics recorded for isolated or membrane-bound RCs at 78 K or RT.

WT isol. RCsa WT membr.RCs

3-exp

3-exp

2-exp AM260W membr.RCs

2-exp

T [K]

τ1 [ns]

τ2 [ns]

τ3 [ns]

A1

A2

A3

constd

78

0.7b

8.9

32.7

0.182

0.345

0.351

0.122

296

0.7b

5.4

21.2

0.270

0.490

0.192

0.049

78

0.7b

11.2

38.0

0.167

0.407

0.351

0.075

298

0.7b

6.2

17.4

0.189

0.417

0.353

0.041

78

3.8

26

0.290

0.620

0.093

298

2.4

13

0.340

0.610

0.048

78

22.3

80c

0.719

0.206

0.075

296

17.5

80c

0.864

0.074

0.062

Fitting was performed in a 100, 200 or 500 ns temporal window, for the two-exponential fit of membrane-bound WT RCs, for the three-exponential fit of both isolated and membranebound WT RCs, and for the two-exponential fit of membrane-bound AM260W RCs, respectively. a

b

Data taken from the previous work.32 The values of τ1 were fixed in the three-exponential fits because of temporal resolution

limitations (see text for details). c

This value was fixed. Completely free fits gave variety of τ2 values without significant

improvement of the fits and complicating the overall picture emerging from otherwise regular behavior of the amplitude values A1-A4 as a function of temperature. d

“const” denotes A3 in two-exponential fits and A4 in three-exponential fits.


Page 33 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2. Parameters of the models presented in Fig. 6. T [K]

∆G1 [meV]

∆G2 [meV]

∆G3 [meV]

k12 [ns-1] (τ12)

k23 [ns-1] (τ23)

kt [ns-1] (τt)

kdir1 [ns-1] (τdir1)

k dir2 [ns-1] (τ dir2)

k dir3 [ns-1] (τdir3)

WT 2-exp T-ind.

all

T-dep.

78

90

128

0

110

0.265 (3.8 ns) 0.245 (4.1 ns) 0.249 0.265 0.290 0.300 0.300 0.300 (3.3 ns)

150 200 250 275 294 298

0.026 0.038 0.014 (38 ns) (27 ns) (71 ns) 0.026 0.058 0.014 (38 ns) (17 ns) (71 ns) 0.026 0.054 0.014 0.0275 0.038 0.0125 0.029 0.013 0.011 0.030 0.003 0.01 0.030 0.003 0.01 0.030 0.003 0.01 (33 ns) (333 ns) (100 ns)

WT 3-exp T-ind.

all

T-dep.

78 150 200 250 275 294 298

135

2.4 0.067 (0.41 ns) (15.0 ns) 0.063 (15.9 ns) 0.063 0.066 0.072 0.074 0.074 0.074 (13.5 ns)

all

T-dep.

78

150

250

150 200 225 250 275 294 296

0.02 (50 ns) 0.0206 (48 ns) 0.0206 0.0194 0.0194 0.0194 0.0194 0.0194 0.0194 (52 ns)

AM260W T-ind.

all

T-dep.

78 150 200 225 250 275 294

150

250

0.028 0.0063 (35 ns) (158 ns) 0.032 0.0083 (31 ns) (120 ns) 0.032 0.0083 0.029 0.0073 0.023 0.0023 0.021 0.0013 0.021 0.0013 0.021 0.0013 (47 ns) (760 ns)

2-exp kt1 = 0 ns-1

AM260W T-ind.

0.020 (50 ns) 0.018 (56 ns) 0.018 0.019 0.024 0.025 0.025 0.025 (40 ns) 0.0105 (95 ns) 0.0099 (101 ns) 0.01033 0.011 0.0112 0.0112 0.0112 0.0112 0.0112 (89 ns)

0.0235 (43 ns) 0.0229 (44 ns) 0.0229 0.0241 0.0241 0.0241 0.0241 0.0241 0.0241 (42 ns)

0.002 (500 ns) 0.0026 (380 ns) 0.00217 0.0015 0.0013 0.0013 0.0013 0.0013 00013 (770 ns)

2-exp kt1 = kt

0.011 (91 ns) 0.0125 (80 ns) 0.0116 0.01 0.01 0.01 0.01 0.01

0.0089 (112 ns) 0.0083 (120 ns) 0.0087 0.0093 0.0095 0.0095 0.0095 0.0095


0.0325 0.0015 (31 ns) (670 ns) 0.0310 0 (32 ns) (∞) 0.0319 0.0009 0.0335 0,0025 0.0335 0,0025 0.0335 0,0025 0.0335 0,0025 0.0335 0,0025


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

296

0.01 (100 ns)

0.0095 (105 ns)

Page 34 of 42

0.0335 0,0025 (30 ns) (400 ns)

For WT RCs an additional two-exponential fitting was performed using the model shown in Fig. 6B, but yielding ∆Gi gaps different from those shown in Fig. 6B. The estimated errors for ∆Gi, k12, k23, and kt do not exceed ±10%. Parameters kdiri are much more uncertain. Their uncertainities may be judged from the distribution of their values when allowing temperature dependence of parameters k12, k23, and kt.


Page 35 of 42

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Figures

Figure 1.



time [ns] 0 1,0

40

60

80

1,0 ∆Anorm

∆Anorm

20

A

0,8

0,5

0,6

WT RC

78 K RT 78 K RT

WT membr

0,0 -1

0,4

0

1

2 3 time [ns]

4

0,2 0,0 1,0

1,0 ∆Anorm

0,8 0,6

∆Anorm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0,5

AM260W WT membr

0,0

0,4

0

1

0,2

2

78 K RT 78 K RT

3 4 time [ns]

0,0 0

20

40

60

80

time [ns]

Figure 2.


Page 36 of 42

Page 37 of 42

100

150

200

250

100

150

200

250

300

AB

25

lifetimes [ns]

300

0,4

20

τ1

0,3

15

τ2

∆G1 = 90 meV

10

1/τ1

1/τ2

5

kPH1

kPH2

0,2

∆G2 = 128 meV 0,1

-1

inverted lifetimes & fits [ns ]

0

0,0

C

τt = 38 ns

0,6

amplitudes [a.u.]

D1 2 D1

τ12=3.8 ns

A1

A2

D2 2 D2

D3 2 D3

τ12 = (3.3-4.1) ns τt = (33-38) ns

0,6

A3

0,4

0,4

0,2

0,2

D

0,0 100

150

200

T [K]

250

300

100

150

200

250

300

E 100

T [K]

Figure 3.


150

200

T [K]

250

300

0,0

corrected amplitudes and fits [a.u.]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



100

150

200

250

300

100

150

200

250

300

40

AB

lifetimes [ns]

35 30

τ1

25

τ2

20

1/τ2

1/τ3

kPH2

kPH3

τ3

0,15

∆G2 = 110 meV

15

0,10

∆G3 = 135 meV

10

0,05

5

-1


0

amplitudes [a.u.]

0,5

τ12=0.41 ns

C

τ23=15 ns τt = 50 ns

0,4

0,00

D1 3 D1

D2 3 D2

D3 3 D3

D4 3 D4

0,6

τ23 = (13.5-15.9) ns τt = (40-56) ns 0,4

0,3

0,2

A1

A2

A3

A4 0,2

0,1

E

D

0,0 100

150

200

T [K]

250

300

100

150

200

250

300

100

T [K]

Figure 4.


150

200

T [K]

250

300

0,0


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 42

Page 39 of 42

100

150

200

250

100

150

200

250

300

AB

80

lifetimes [ns]

300

60

0,05 0,04

τ1 τ2

40

1/τ1

1/τ2

∆G1 = 150 meV

kPH1

kPH2

∆G2 = 250 meV

0,03 0,02

20 0,01

-1


0 0,8

0,00

C

τt = 95 ns

0,7

amplitudes [a.u.]

D1 2 D1

τ12=50 ns

0,6

A1

A2

D2 2 D2

D3 2 D3

τ12 = (48-52) ns τt = (89-101) ns

A3

0,8

0,6

0,5 0,4

0,4

0,3 0,2

D

0,1

E

0,0

0,2

0,0 100

150

200

T [K]

250

300

100

150

200

250

300

100

T [K]

Figure 5.


150

200

T [K]

250

300


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



AM260W

WT +

free energy [meV]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0

PB

A

+

Page 40 of 42

-

(P HA )1

A

+

P BA

-

B

+

P BA

-

C

k12 (P+HA-)2

-100

∆G1 k23

+

kPB

kPB -200 kdir2

k12 +

kt1

k12

A 2

(P+HA-)2

(P H ) kdir1 kdir2

kdir3 3

PHA

PHA

-

(P HA )1 kPB

kt kdir1

+

∆G2

-

(P HA )1

(P+HA-)3

kt

kdir1 kdir2 3

3

PHA

PHA

PHA

Figure 6.


kt PHA

Page 41 of 42

100

rate constants [ns-1]

0,30 0,25

150

200

250

300

100

150

200

250

300

A

B

0,30 0,25

0,20

WT 2-exp k12

WT 3-exp k23

0,20

0,15

kt

kt

0,15

0,10

0,10

0,05

0,05

0,00

0,00

AMW 2-exp kt1= kt

0,020

rate constants [ns-1]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


k12

0,015

0,005

0,015

kt

0,010

0,010

AMW 2-exp kt1= 0 k12

C

0,020

D

kt

0,005

0,000

0,000 100

150

200

250

300

100

T [K]

200

T [K]

Figure 7.


300


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

TOC graphic


Page 42 of 42

Analysis of the Kinetics of P+HAâ Recombination in Membrane

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