Temperature-dependent regulation of electron transport and ATP synthesis in chloroplasts in vitro and in silico

Abstract

The significance of temperature-dependent regulation of photosynthetic apparatus (PSA) is determined by the fact that plant temperature changes with environmental temperature. In this work, we present a brief overview of temperature-dependent regulation of photosynthetic processes in class B chloroplasts (thylakoids) and analyze these processes using a computer model that takes into account the key stages of electron and proton transport coupled to ATP synthesis. The rate constants of partial reactions were parametrized on the basis of experimental temperature dependences of partial photosynthetic processes: (1) photosystem II (PSII) turnover and plastoquinone (PQ) reduction, (2) the plastoquinol (PQH₂) oxidation by the cytochrome (Cyt) b₆f complex, (3) the ATP synthase activity, and (4) the proton leak from the thylakoid lumen. We consider that PQH₂ oxidation is the rate-limiting step in the intersystem electron transport. The parametrization of the rate constants of these processes is based on earlier experimental data demonstrating strong correlations between the functional and structural properties of thylakoid membranes that were probed with the lipid-soluble spin labels embedded into the membranes. Within the framework of our model, we could adequately describe a number of experimental temperature dependences of photosynthetic reactions in thylakoids. Computer modeling of electron and proton transport coupled to ATP synthesis supports the notion that PQH₂ oxidation by the Cyt b₆f complex and proton pumping into the lumen are the basic temperature-dependent processes that determine the overall electron flux from PSII to molecular oxygen and the net ATP synthesis upon variations of temperature. The model describes two branches of the temperature dependence of the post-illumination reduction of ${\text{P}}_{700}^{ + }$ characterized by different activation energies (about 60 and ≤ 3.5 kJ mol⁻¹). The model predicts the bell-like temperature dependence of ATP formation, which arises from the balance of several factors: (1) the thermo-induced acceleration of electron transport through the Cyt b₆f complex, (2) deactivation of PSII photochemistry at sufficiently high temperatures, and (3) acceleration of the passive proton outflow from the thylakoid lumen bypassing the ATP synthase complex. The model describes the temperature dependence of experimentally measured parameter P/2e, determined as the ratio between the rates of ATP synthesis and pseudocyclic electron transport (H₂O → PSII → PSI → O₂).

Appendices

Appendix 1: equations and rate constants of the model

Equations (A1–A7) represent the system of ordinary differential equations (ODE), which describe the redox transitions of electron carriers (variables [Fd], [${\text{P}}_{ 7 0 0}^{ + }$], [${\text{P}}_{ 6 8 0}^{ + }$], [Pc], [PQ]), the acidification of the thylakoid lumen ([${\text{H}}_{\text{in}}^{ + }$]), and the yield of ATP (variable [ATP]).

$$ \frac{{d [ {\text{Fd]}}}}{d\tau } = \left\{ {k_{\text{Meh}} [ {\text{O}}_{ 2} ({T} ) ]} \right\} \cdot \left( { [ {\text{Fd]}}_{ 0} - [ {\text{Fd]}}} \right) - L_{1} \cdot k_{{{\text{P}}_{ 7 00} }}^{{}} \cdot [ {\text{Fd]}} \cdot \left( { [ {\text{P}}_{ 7 0 0} ]_{ 0} - [ {\text{P}}_{ 7 0 0}^{ + } ]} \right) $$

(A1)

$$ \frac{{d [ {\text{P}}_{ 7 0 0}^{ + } ]}}{d\tau } = L_{1} \cdot k_{{{\text{P}}_{ 7 0 0} }}^{{}} \cdot [ {\text{Fd]}} \cdot \left( { [ {\text{P}}_{ 7 0 0} ]_{ 0} - [ {\text{P}}_{ 7 0 0}^{ + } ]} \right) - k_{\text{Pc}} \cdot [ {\text{P}}_{ 7 0 0}^{ + } ]\cdot \left( { [ {\text{Pc]}}_{ 0} - [ {\text{Pc]}}} \right) $$

(A2)

$$ \frac{{d [ {\text{Pc]}}}}{d\tau } = k_{\text{Pc}} \cdot [ {\text{P}}_{ 7 0 0}^{ + } ]\cdot \left( { [ {\text{Pc]}}_{ 0} - [ {\text{Pc]}}} \right) - k_{\text{Q}} ( [ {\text{PQ],[Pc],[H}}_{\text{in}}^{ + } ] ,T ) $$

(A3)

$$ \frac{{d [ {\text{P}}_{ 6 8 0}^{ + } ]}}{d\tau }{ = }L_{ 2} \cdot \xi (T )\cdot {k}_{{{\text{P}}_{ 6 8 0} }} ({T} )\cdot [ {\text{PQ]}} \cdot \left( { [ {\text{P}}_{ 6 8 0} ]_{ 0} - {\text{ [P}}_{ 6 8 0}^{ + } ]} \right) \, - \, {k}_{{{\text{H}}_{ 2} {\text{O}}}} \cdot [ {\text{P}}_{ 6 8 0}^{ + } ] $$

(A4)

$$ \frac{{d [ {\text{PQ]}}}}{d\tau } = 0.5 \cdot k_{\text{Q}} ( [ {\text{PQ],[Pc],[H}}_{\text{in}}^{ + } ] ,T )- 0.5 \cdot L_{2}\cdot \xi(T)\cdot k_{{{\text{P}}_{ 6 8 0} }} (T )\cdot [ {\text{PQ]}} \cdot [ {\text{H}}_{\text{out}}^{ + } ]\cdot \left( { [ {\text{P}}_{ 6 8 0} ]_{ 0} - [ {\text{P}}_{ 6 8 0}^{ + } ]} \right) $$

(A5)

$$ \frac{{d[{\text{ATP}}]}}{d\tau } = \frac{{k_{\text{ATP}} (T)}}{m} \cdot \left( {[{\text{ADN}}]_{0} - [{\text{ATP}}]} \right) \cdot \frac{{[{\text{H}}_{\text{out}}^{ + } ] \cdot [1 0^{{\Delta {\text{pH}}}} - 1 ]}}{{\alpha + [{\text{H}}_{\text{out}}^{ + } ] \cdot [1 0^{{\Delta {\text{pH}}}} + \beta ]}} - k_{{{\text{AD}}P}} (T) \cdot [{\text{ATP}}] $$

(A6)

$$ \begin{aligned} \left[ { 1 { + }\frac{{K_{\text{M}} \cdot {\text{B}}_{\text{in}} }}{{ (K_{\text{M}} {\text{ + [H}}_{\text{in}}^{ + } ] )^{ 2} }}} \right]\frac{{d [ {\text{H}}_{\text{in}}^{ + } ]}}{d\tau } = k_{{{\text{H}}_{ 2} {\text{O}}}} \cdot [ {\text{P}}_{ 6 8 0}^{ + } ] { + 2} \cdot k_{\text{Q}} ( [ {\text{PQ],[Pc],[H}}_{\text{in}}^{ + } ] ,T )\hfill \\ - \, k_{{{\text{H}}^{ + } }} (T )\cdot ( [ {\text{H}}_{\text{in}}^{ + } ] { } - {\text{ [H}}_{\text{out}}^{ + } ] ) { } - k_{\text{ATP}} (T )\cdot \left( { [ {\text{ADN]}}_{ 0} - [ {\text{ATP]}}} \right) \cdot \frac{{ [ {\text{H}}_{\text{out}}^{ + } ]\cdot [ 1 0^{{\Delta {\text{pH}}}} \, - { 1]}}}{{\alpha {\text{ + [H}}_{\text{out}}^{ + } ]\cdot [ 1 0^{{\Delta {\text{pH}}}} { + }\beta ]}} \hfill \\ \end{aligned}. $$

(A7)

Here, the function $k_{\text{Q}} ( [ {\text{PQ],[Pc],[H}}_{\text{in}}^{ + } ] ,T )$ describes the electron transfer from PQH₂ to Pc via the Cyt b₆f complex [see above Eqs. (1) and (2)]. ΔpH is the trans-thylakoid pH difference, ΔpH = pH_out – pH_in. We assume that pH_out to be constant, pH_out = 8, due to sufficiently high buffer capacity of the outer medium. [ADN]₀ is the total concentration of ADP and ATP. The model parameters α and β in Eqs. (A6) and (A7) are determined by the rate constants of the proton exchange with the proton-accepting groups of the ATP synthase (see Fig. 3 and the explanations below). Formulating Eqs. (A1–A7), we assume the following stoichiometry between the electron transport and ATP synthase complexes: [PSI]/[PSII]/[b₆f]/[CF₀-CF₁] = 1/1/1/1. The relative capacity of the photo-reducible PQ pool, Fd, and Pc was taken as [PQ]₀/[PSI] = 10, [Fd]₀/[PSI] = 3, and [Pc]₀/[PSI] = 1.5, respectively.

The model parameters L₁ and L₂ describe the numbers of light quanta per unit time exciting P₇₀₀ and P₆₈₀, respectively. Parameter m expresses the stoichiometry of proton transfer through the ATP synthase, H⁺/ATP; m = n/3 = 14/3 is the stoichiometry ratio, the ratio between a number n = 14 of subunits c in the c_n-ring to three ATP molecules formed per one turn (360^o) of the membrane rotor c_n (Seelert et al. 2000; Vollmar et al. 2009). Constants marked with a subscript “0” are the maximal concentrations of the relevant variables. Constants $k_{{{\text{P}}_{ 6 8 0} }}^{{}}$, $k_{{{\text{P}}_{ 7 0 0} }}^{{}}$, k_Q, k_Pc, and k_Meh are the effective rate constants of the reactions shown in Fig. 1. Constant k_ADP governs the effective rate of ATP hydrolysis. The function k_Q, which characterizes the oxidation of PQH₂, depends on pH_in (for details see Eqs. 1 and 2; Dubinskii and Tikhonov 1997; Vershubskii et al. 2011). The model parameters K_M and B_in, characterize the buffer properties of the system. Here, K_M is the equilibrium constant for the reaction of proton binding by buffer groups inside of thylakoids; the model parameter B_in is the concentration of these buffer groups. In this work, we assume the stoichiometric ratio B_in/PSI = 100 (for details, see Vershubskii et al. 2011). Note that parameters K_M and B_in (the left side of Eq. A7) can influence the time-course of the system response to switching the actinic light on. The steady-state levels of all the variables of the model, however, are independent on the K_M and B_in values (Dubinskii and Tikhonov 1997).

The formulation of the system of differential equations and the choice of the apparent rate constants have been considered in details in our previous works (Vershubskii et al. 2011, 2018). The rate constants for key stages of electron flow and proton transport were determined by fitting the respective experimental and simulated kinetic curves. In particular, effective rate constant for PQH₂ oxidation by the Cyt b₆f complex was derived by comparing calculated and experimental plots for the rates of the post-illumination reduction of ${\text{P}}_{ 7 0 0}^{ + }$ at different pH_in ( “Appendix 3”, Fig. 13). Effective rate constants of the transmembrane proton transport coupled to ATP synthesis and passive leak of protons through the thylakoid membrane were determined by the comparison of calculated and experimental data on the light-induced acidification of the thylakoid lumen (for details, see “Appendix 2”; Dubinskii and Tikhonov 1995). The values of the rate constants, which characterize different stages of the electron transfer along the ETC, from the water-splitting complex of PSII to PSI acceptors, were chosen on the basis of the literature data on the kinetics of partial reactions of electron transport in different segments of the chloroplast ETC as described above. The characteristic times of electron transfer reactions are given in Table 1.

Table 1 Characteristic times of partial reactions of electron transfer considered within the framework of the model and their comparison with experimental data

Appendix 2: proton transport and ATP synthesis in the model

There are indications that the proton conductivity of a lipid bilayer is determined mainly by the presence of acidic groups in the membrane (Deamer 1987; Gutknecht 1987; Nagle 1987). In this work, the equations for the active (J_ATP) and passive (J_pass) fluxes of protons were derived from a simple model based on the assumption that the processes of the transmembrane transfer of protons occur through the acidic groups bound either to the ATP synthase or buried inside the thylakoid membrane, respectively (Dubinskii and Tikhonov 1995). According to the model considered in our work, the proton transfer through the CF_o segment of the ATP synthase includes stages of protonation and deprotonation of carboxyl groups of the c_m-ring: –COO^– + ${\text{H}}_{\text{in}}^{ + }$ → –COOH → –COO^– + ${\text{H}}_{\text{out}}^{ + }$. Concerning the passive trans-thylakoid transport of H⁺ ions, we assume that the proton first binds to the intramembrane proton-accepting group and then dissociates into the stroma. The efficient rate constants of the proton exchange with the proton-accepting group are indicated in Fig. 3b. The rate constants of the direct and reverse reactions are related by the ratio $k_{1}^{\text{in}} /k_{ - 1}^{\text{in}} = K_{\text{M1}}$ and $k_{2}^{\text{out}} /k_{ - 2}^{\text{out}} = K_{\text{M2}}$, where K_M1 and K_M2 are the effective constants of the proton equilibrium for the buffer group –COO⁻ and hydrogen ions inside and outside of the thylakoid, respectively. It is reasonable to assume that, for the proton-accepting groups –COO⁻ fixed in the membrane and involved in the passive transfer of protons across the membrane, the equality K_M1 = K_M2 ≡ K_M must be true. Fitting of the rate constant parameters related to proton transfer through the membrane acidic groups has been performed by means of the comparison of calculated and experimental data on the light-induced uptake of protons by the chloroplasts (Dubinskii and Tikhonov 1995). For the ΔpH-driven flux of protons through the ATP synthase, J_ATP, coupled to ATP synthesis, we used the following relationship:

$$ J_{\text{ATP}} = k_{\text{ATP}} (T )\cdot \left( { [ {\text{ADN]}}_{ 0} - [ {\text{ATP]}}} \right) \cdot \frac{{ [ {\text{H}}_{\text{out}}^{ + } ]\cdot [1 0^{{\Delta {\text{pH}}}} - 1 ]}}{{\alpha + [ {\text{H}}_{\text{out}}^{ + } ]\cdot [1 0^{{\Delta {\text{pH}}}} + \beta ]}}, $$

(A8)

where ΔpH = pH_out − pH_in is the driving force for the operation of the ATP synthase (for details, see Tikhonov and Vershubskii 2014). Coefficients α and β are the model parameters, the values of which are determined by pK_A of the acidic group –COO⁻ of the c_n-ring of the ATP synthase and the values of the efficient rate constants k₁ and k₂ characterizing proton transport to -COO⁻ from the lumen and stroma, respectively; $\alpha = 10^{ - \text{p}K_\text{A}} \left( {1 + \beta } \right)$, $\beta = k_{ 2}^{\text{out}} /k_{1}^{\text{in}}$. In our calculations we used the model parameters pK_A = 7.3 and β = 20, which values have been chosen on the basis of our previous works (Vershubskii et al. 2011, 2017, 2018; Vershubskii and Tikhonov 2020). Formula (A8) provides a sigmoid dependence of the ATP synthesis rate versus the proton-motive force ΔpH (Fig. 3c), which is typical of experimental force–flux relationships in chloroplasts (Turina et al. 2016). Note that variations of the model parameters α and β influence markedly a threshold ΔpH_th, above which value the ATP synthase efficiently produces ATP. Numerical values of the model parameters, related to the trans-thylakoid proton transfer, were determined by fitting theoretical curves to relevant experimental dependences of the light-induced acidification of the lumen at different values of external pH_out. Fitting of the rate constants $k_{ 1}^{\text{in}}$, $k_{ - 1}^{\text{in}}$, $k_{ 2}^{\text{in}}$, and $k_{ - 2}^{\text{in}}$ was performed earlier (Dubinskii and Tikhonov 1995).

The model parameter $k_{{{\text{H}}^{ + } }}$, which stands in the right side of Eq. A7, determines the passive efflux of protons (J_pass) from the lumen to the outer space: J_pass = $k_{{{\text{H}}^{ + } }} (T )\cdot ( [ {\text{H}}_{\text{in}}^{ + } ] { } - {\text{ [H}}_{\text{out}}^{ + } ] )$. The $k_{{{\text{H}}^{ + } }} (T )$ values were chosen by means of fitting calculated values of J_pass to experimentally measured proton fluxes determined for chloroplasts in the metabolic state 4 (compare experimental and theoretical data in Fig. 4c).

It is well-known fact that the ATP synthase activity is controlled by the redox status of chloroplasts. The light-induced activation of the ATP synthase is associated with the reduction of the thiol groups in the subunit γ, rotating together with the c_n-ring (Bakker-Grunwald and van Dam 1974; Bald et al. 2001). It is conceivable that the reduction of these groups may be mediated through the pigments found in the central cavity of the c₁₄-rotor (Varco-Merth et al. 2008; Vlasov et al. 2019). In the current work, however, we ignored this effect, because we compared experimental and theoretical data on the initial phase of the light-induced ATP synthesis (during 10-s illumination), when the linear growth of ATP concentration was not affected by the light-induced modulation of the chloroplast ATP synthase. According to our previous measurements, the light-induced activation of the ATP synthase was observed after 2 min of chloroplast illumination in the presence of methylviologen (data not shown).

Appendix 3: materials and experimental methods

Plant material and preparation of chloroplasts

Class B chloroplasts were isolated from greenhouse bean leaves (Vicia faba, 2–3 weak old) as described by Tikhonov et al. (1981). Chloroplasts were suspended at a final concentration of 2–3 mg chlorophyll/ml in the medium containing 0.2 M sucrose, 2 mM MgCI₂, and 10 mM Tricine-NaOH buffer (pH between 6.5 and 9.5) or Mes-HCl buffer (pH between 4.5 and 6.5). For measurements of chloroplast activity at different pH of the chloroplast suspension, we also used the medium which contained 0.2 M sucrose, 2 mM MgC1₂, 10 mM phosphate-citrate buffer, and 4 mM Mg-ADP. 20 μM methylviologen was used as a mediator of electron transfer from PSI to molecular oxygen. The pH value of the suspending medium was checked with a Radiometer glass electrode GK2321C.

In this work, we refer to experimental results described in earlier works of our group (Tikhonov et al. 1980, 1981, 1983, 1984; Timoshin et al. 1984; Kukushkin and Tikhonov 1988; Tikhonov and Subczynski 2005). The batches of chloroplasts used in these works were isolated from bean leaves of different harvests, including plants grown under variable experimental conditions (different seasons and concomitant changes in environmental conditions). In general, plants were cultivated at growth temperatures in the range 18–32 °C, depending on the season. We found that variability in the plant cultivation conditions could cause somewhat different temperature dependences of photosynthetic processes in isolated bean chloroplasts (compare, for example, panels c, d, and e in Fig. 9). Variability of this kind proved useful for analyzing the structure–function relationships in chloroplasts. In particular, statistically significant coincidence of the peculiar temperatures of the “structural” (membrane fluidity) and “functional” (ATP synthesis) characteristics was observed for each individual batch of chloroplasts (Fig. 9). Inflexion points in temperature dependences of the plots of “structural” and “functional” parameters coincided with a sufficiently high precision (±1 °C). In the meantime, the harvest-depending scattering of these peculiar points was more significant (for example, in the range 25–33 °C, Fig. 9). This observation allowed us to suggest that the temperature dependences of electron and proton transport processes were controlled by the physical state of thylakoid membranes.

EPR measurements of PSII activity and the intersystem electron transfer

The redox transients of P₇₀₀ were monitored by measuring the light-induced changes in the amplitude of the EPR signal from ${\text{P}}_{700}^{ + }$ (Tikhonov et al. 1980, 1981; Tikhonov 2015). The EPR measurements of ${\text{P}}_{700}^{ + }$ were performed with a Varian EPR spectrometer (model E-4) at 4 G modulation amplitude and 10 mW microwave power. Far-red background illumination (interference filter SIF707, Karl Zeiss Jena; λ_max = 707 nm, Δλ_l/2 = 5 nm) was applied to provide the re-oxidation of the ETC between PSII and PSI. The intensity of this light, provided by a 150 W incandescent lamp equipped with a water filter and focusing lens, was adjusted to reach maximal level of P₇₀₀ oxidation. A similar light source without the interference filter (white light) was used for efficient excitation of both photosystems. Two kinds of white light pulses of were used to test PSII activity: (i) short flashes (τ_l/2 = 7 μs) of saturating intensity, and (ii) long flashes (τ_l/2 = 750 μs) were applied for multiple operation of P₆₈₀. The energy released in the discharge circuit was 10 and 100 J, respectively (Tikhonov et al. 1980).

Figure 12a shows a simplified diagram illustrating electron transfer from PSII and O₂, the terminal acceptor of electrons donated by PSI. Illumination of chloroplasts by the far-red (or white) light induces generation of the EPR signal from ${\text{P}}_{700}^{ + }$ shown in Fig. 12b. After sudden shutdown of white light (WL), ${\text{P}}_{700}^{ + }$ rapidly reduces due to electrons donated by reduced PQH₂ molecules (Fig. 12c). The half-time of ${\text{P}}_{700}^{ + }$ decay (parameter τ_1/2) characterizes the rate of electron transfer from PQH₂ to ${\text{P}}_{700}^{ + }$.

Fig. 12

Modified figures adopted from (Tikhonov et al. 1984)

Simplified diagram illustrating electron transfer from PSII and O₂, the terminal acceptor of electrons donated by PSI (panel a); EPR signals of bean chloroplasts in the dark and during illumination with the far-red light, λ_max = 707 nm, as indicated (panel b); the post-illumination kinetics of ${\text{P}}_{700}^{ + }$ reduction in bean chloroplasts pre-illuminated by continuous white light (panel c)

Figure 13 shows experimental and theoretical dependencies of the half-time of ${\text{P}}_{700}^{ + }$ reduction after switching off the white light on the intra-thylakoid pH_in. Open symbols, experimental data; filled symbols, calculated data. Experimental points were obtained for the suspension of uncoupled chloroplasts (on the basis of results published by Tikhonov et al. (1980)).

Fig. 13

Experimental and theoretical dependencies of the half-time of ${\text{P}}_{700}^{ + }$ reduction after switching off the white light on the intra-thylakoid pH_in. Open symbols, experimental data; filled symbols, calculated data. Experimental points were obtained for the suspension of uncoupled chloroplasts (on the basis of results published in Tikhonov et al. 1984)

Figure 14a shows the time-course of P₇₀₀ redox changes in aerated suspension of bean chloroplasts. Illumination of chloroplasts by the far-red light (λ₇₀₇), absorbed predominantly by PSI, induced oxidation of P₇₀₀. Application of a short saturating pulse (τ_1/2 = 7 µs) induced the reduction of ${\text{P}}_{700}^{ + }$ due to the injection of electrons from PSII to the intersystem ETC. The reduction of ${\text{P}}_{700}^{ + }$ is followed by the re-oxidation of P₇₀₀ due to the action of the continuous far-red light. The area W₁ over the kinetic curve can serve as a measure of PSII photochemical activity: in response to a short flash, each PSII donates one electron (on an average). In this case, the Mn₄Ca cluster is oxidized by one electron and one electron is donated to the intersystem ETC (Cardona et al. 2012). After the action of a prolonged flash (τ_1/2 = 750 µs), the area over the kinetic curve (parameter W₂) increases. This occurs due to a multiple charge separations in PSII and donation of several electrons to the PQ pool (Tikhonov and Vershubskii 2017). Figure 14b shows the temperature dependences of parameters W₁ and W₂. The ratio f = W₂/W₁ is determined by the rate of electron transfer from PSII to the PQ pool (Fig. 14c). The temperature of a sample was regulated with the Varian temperature controller.

Fig. 14

a The light-induced redox transients of P₇₀₀ in bean chloroplasts induced by the far-red light (λ₇₀₇) and pulses of white light of different durations. Parameters W₁ and W₂ are proportional to the numbers of electrons injected into intersystem electron transport chain (for other details see text and Tikhonov et al. 1980). b Temperature dependences of parameters W₁ and W₂ shown in the panel a. c Temperature dependence of the ratio f = W₂(T)/W₁(T), which determines a number of electrons donated by PSII during the action of the long flash

Potentiometry methods of assaying the chloroplasts activity

The rate of pseudocyclic electron flow J_Fd–O2 (H₂O → PSII → PSI → MV → O₂; the so-called “water-water” cycle; Asada 1999) was determined by measuring the O₂ uptake (O₂ + e⁻ → O ^•−₂ ) in an aerated suspension of chloroplasts, using a laboratory-made Clark-type electrode. In this case, the superoxide and catalase activities of chloroplasts were inhibited by the addition of small amounts of NaN₃ as described earlier (Timoshin et al. 1984).

The rate of ATP formation (V_ATP) was routinely measured by the potentiometry method (Nishimura et al. 1962; Timoshin et al. 1984). All controls including that of adenylate kinase activity were properly made. Adequacy of potentiometric measurements of photophosphorylation (ADP + P_i → ATP + H₂O) was verified independently by the use of enzymatic (Malenkova et al. 1982) and modified luciferin-luciferase (Ataullakhanov and Pichugin 1981) methods. The rate of ATP hydrolysis was also determined by measuring changes in the ³¹P NMR spectra of ATP, ADP, and P_i in bean chloroplast suspension according to (Ogawa et al. 1980). Results of this study, performed together with professor E.K. Ruuge, will be published elsewhere.

Having measured, under the same experimental conditions, the rates of ATP synthesis (V_ATP) and electron transport (J_Fd–O2), we could determine the ratio V_ATP/J_Fd–O2, which characterizes the efficiency of coupling of electron transport and ATP synthesis (often termed as the so-called ratio “P/2e”; Ivanov 1993). Figure 15 reproduces the temperature dependence of the ratio P/2e that was determined earlier in our work (Timoshin et al. 1984). As one can see, the ratio P/2e increases with temperature, reaching a plateau at temperatures above 25 °C.

Fig. 15

Modified figures after (Timoshin et al. 1984)

Temperature dependences of parameter P/2e, which denotes the ratio between the rates of photophosphorylation (ADP + P_i → ATP) and pseudocyclic electron flow and ATPase activity of bean chloroplasts (closed and open symbols were obtained on different batches of chloroplasts)

Measurements of ΔpH generation

Transmembrane pH difference (ΔpH) across the thylakoid membrane was measured by three independent methods based on the use of the EPR technique: (1) the determination of the pH_in-dependent rate of the intersystem electron transfer from the kinetics of the post-illumination reduction of ${\text{P}}_{700}^{ + }$ (Tikhonov et al. 1981, 1984), (2) the use of pH-sensitive water-soluble spin probes located in the thylakoid lumen (Tikhonov et al. 2008; Tikhonov 2017; Vershubskii et al. 2017), and (3) the determination of ΔpH in chloroplasts from the partitioning of a water-soluble spin label tempamine (Trubitsin and Tikhonov 2003; Tikhonov 2017). We used experimental data on ΔpH measurements in bean chloroplasts in order to perform the final fitting of the model parameters (see, for example, Vershubskii and Tikhonov 2020).

Spin-labeling study of thermo-induced structural changes in thylakoid membranes

Thermo-induced changes in the lipid domains of the thylakoid membranes were studied with the lipid-soluble spin probes, paramagnetic derivatives of stearic acid, 5-SASL (Fig. 9b), as described in Tikhonov et al. (1980, 1983), Timoshin et al. (1984), Lutova and Tikhonov (1988), Ligeza et al. (1998), and Tikhonov and Subczynski (2005). A small aliquot (1% v/v) of 5-SASL dissolved in ethanol was added to chloroplast suspension. After 10-min incubation of thylakoids with the spin probe, the suspension of spin-labeled thylakoids was used for EPR measurements. The temperature of a sample placed into the cavity of a Varian (E-4) X-band EPR spectrometer was regulated with the Varian temperature controller, with precision up to ± 0.5 °C.