Analyzing the effect of ion binding to the membrane-surface on regulating the light-induced transthylakoid electric potential (ΔΨm)

The transthylakoid membrane potential (ΔΨ_m) is essential because it can drive the ATP synthesis through the CF₀–CF₁ type of ATP-synthase in chloroplasts as an energetic equivalent similar to ΔpH. In addition, a high fraction of proton motive force (PMF) stored as the ΔΨ_m component is physiologically important in the acclimation of photosynthesis to environmental stresses. It has been shown that ΔΨ_m is the sum of the Donnan potential difference (ΔΨ_dn) and the diffusion potential difference (ΔΨ_d). Specifically, ΔΨ_dn, ΔΨ_d, and ΔΨ_m are strongly associated with the ionic activities near the membrane surface, particularly, the extent of ion binding to the charged/neutral sites adjacent to the membrane surface. However, an in-depth analysis of the effect of altered cationic binding to the membrane surface on adjusting the transthylakoid electric potentials (ΔΨ_dn, ΔΨ_d, and ΔΨ_m) is still missing. This lack of a mechanistic understanding is due to the experimental difficulty of closely observing cations binding to the membrane surface in vivo. In this work, a computer model was proposed to investigate the transthylakoid electric phenomena in the chloroplast focusing on the interaction between cations and the negative charges close to the membrane surface. By employing the model, we simulated the membrane potential and consequently, the measured ECS traces, proxing the ΔΨ_m, were well described by the computing results on continuous illumination followed by a dark-adapted period. Moreover, the computing data clarified the components of transthylakoid membrane potential, unraveled the functional consequences of altered cationic attachment to the membrane surface on adjusting the transthylakoid electric potential, and further revealed the key role played by Donnan potential in regulating the energization of the thylakoid membrane. The current model for calculating electric potentials can function as a preliminary network for the further development into a more detailed theoretical model by which multiple important variables involved in photosynthesis can be explored.

Introduction

Light-driven electron transport triggers the proton translocation across thylakoid membranes, because of which, a transmembrane proton motive force (PMF) is established. Transmembrane proton motive force consists of two components, i.e., a chemical (expressed as ΔpH) and an electrical component (expressed as ΔΨ_m), which is defined by:

$$\text{PMF}=\mathrm{\Delta }{\mathrm{\Psi }}_{\mathrm{m},\mathrm{i}-\mathrm{o}}\left(\frac{2.3\text{RT}}{\text{F}}\right)\mathrm{\Delta }{\text{pH}}_{\text{o-i}}(1)$$

where ΔΨ_m,i–o and ΔpH_o–i represent the electric potential difference and the pH difference across thylakoid membranes, respectively. They are calculated as outside (stroma) minus inside (lumen) for ΔpH and inside (lumen) minus outside (stroma) for ΔΨ_m. The variables R, T, and F are the universal gas constant, the absolute temperature, and the Faraday constant, respectively. The PMF is the driving force for ATP synthesis facilitated by the CF₀–CF₁ type of ATP-synthase in chloroplasts. The two components of PMF are thermodynamically equivalent to drive ATP formation according to the chemiosmotic hypothesis (Mitchell, 1961, 1966, 2011). The ratio of PMF parsing into ΔΨ_m and ΔpH is a crucial quantity for reconciling the light use efficiency under rapid changes in environmental conditions (Davis et al., 2016, 2017; Li et al., 2021). More importantly, strong lumen acidification can initiate the process of non-photochemical quenching (NPQ) to protect photosystem II (PSII) from over-excitation by converting the excess light energy into heat (Li et al., 2009; Pinnola and Bassi, 2018). On the other hand, ΔΨ_m is physiologically essential because it not only functions to promote the ATP yield but also serves to regulate the electron transport reaction by affecting the midpoint redox potentials of electron acceptors and electron donors (Bulychev, 1984; Vredenberg and Bulychev, 2003; Davis et al., 2016). In addition, a high fraction of PMF stored as the ΔΨ_m component is particularly important during transitions from high to low light (Wang and Shikanai, 2019; Basso et al., 2020; Correa Galvis et al., 2020).

Moreover, ΔΨ_m is responsive to many factors including the composition of the bathing solution, the activity of proton pumping, the state of ion channels/transporters, and ionic activities near the membrane surface, which are themselves responsive to ΔΨ_m (Kinraide et al., 1998). It has been shown that ΔΨ_m is the sum of the Donnan potential difference (ΔΨ_dn) and the diffusion potential difference (ΔΨ_d) (Ohshima and Ohki, 1985; Ohshima and Kondo, 1987, 1988a,b, 1990). Specifically, Ψ_dn is the consequence of the interaction between solute ions in the contacting bulk-phase and the fixed charges arising from the protein ligands, since the thylakoid membrane is the lipo-protein system which carries the negative charges mainly due to carboxyl groups (probably glutamic and aspartic acid residues) of exposed segments of integral membrane protein constitutes (Barber, 1980b,1982). The specific value of the negative charges may be determined based on the microelectrophoresis studies and varies in terms of the plant species and physiological conditions within the same breed (Nakatani et al., 1978). The electrostatic ΔΨ_dn is often sufficiently negative to attract mobile divalent cations (e.g., Mg²⁺) more than mobile monovalent cations (e.g., K⁺, H⁺) and repel the mobile anions (e.g., Cl^–, OH^–). Previously, Siggel proposed a preliminary model to probe the role played by ΔΨ_dn during photosynthesis in a series of works (Siggel, 1981a,b,c). To date, the common neglect of ΔΨ_dn in a range of photosynthetic simulations probably reflects the computational complexity when all heterogeneous ions in situ together with the cations binding to the membrane surface are taken into account. Nevertheless, the existence of ΔΨ_dn-induced electrical phenomena near the thylakoid membrane should be considered for an improved understanding of many aspects of the photosynthetic events in and around the thylakoid membrane (Barber, 1980b,1982; Kaña and Govindjee, 2016). An alternative approach to theoretically analyze the ion charge interaction adjacent to the membrane surface, termed the Gouy–Chapman double-layer potential, assumes that the thickness of membrane surface charge layer (d_s) is zero and all membrane fixed charges are only located within the membrane surface (Barber, 1980a; Ohshima and Ohki, 1985; Ohshima and Kondo, 1990). This hypothesis may be unjustified because for a usual biological membrane, the d_s is commonly non-zero (Levine et al., 1983). Under this circumstance, the electrical potential in the region far inside the charge layer is practically equal to the Donnan potential (Ohshima and Kondo, 1988b).

The diffusion potential difference (ΔΨ_d) is initiated by the light-induced electron-coupled proton translocation which causes the luminal acidification. This eventually triggers the proton efflux through the ATP-synthase and the transthylakoid ion movement via ion channels/transporters. Early electrophysiological experiments showed that thylakoid-harbored cation pores are permeable to K⁺ and Mg²⁺ (Pottosin and Schönknecht, 1996), while anion pores are permeable to Cl^– (Schönknecht et al., 1988). The recent molecular biological assays confirmed the existence of K⁺/H⁺ antiporter KEA3 (Kunz et al., 2014; Basso et al., 2020), the voltage-gated Cl^– channel VCCN1 (Herdean et al., 2016b), and the Cl^– channel CLCe (Herdean et al., 2016a). The co-function of the proton translocation and the channel/transporter mediated ion movement ultimately determine the ΔΨ_d which itself conversely impact the redistribution of ions and homeostasis of the stacked membranous system.

Numerous studies have concentrated majorly on the interrelationship between the chemical component of PMF (ΔpH) and its impact on photosynthetic processes. However, less effort was put on explorations of the electric component of PMF. Here, we proposed a photosynthetic model, which is an extension of a previously published version (Lyu and Lazar, 2017a,b), to determine the effect of ion attached to the thylakoid membrane surface on regulating ΔΨ_dn, ΔΨ_d, and ΔΨ_m. Toward this end, the extension of model includes the determination of Ψ_dn and the corresponding change of quantities induced by Ψ_dn. Taken together, our goal was to gain a mechanistic insight into these variations in the highly complex and dynamic network of photosynthetic processes.

Materials and methods

Measurements were conducted with 10-day tobacco leaves (Nicotiana tabacum), grown in a growth chamber at 20°C on artificial soil composed of Perlit and Knop’s solution. The light regime was 8 h dark/16 h light (continuous white irradiation of 90 μmol photons m^–2 s^–1). Measured P515 signal was used as a proxy for ΔΨ_m (Klughammer et al., 2013). The P515 (ΔA515–550 nm) signal reflects the electrochromic shift (ECS) of absorption maximum of pigments (chlorophylls and carotenoids), which is proportional to ΔΨ_m across the thylakoid membrane (Witt, 1979; Vredenberg, 1981; Joliot and Joliot, 1989). ECS and P515 are used as synonyms in the text. The P515 signal measurements were done using Dual-PAM-100 system (Heinz Walz GmbH, Effeltrich, Germany) equipped with the P515/535 module. The system measures transmittance at 515 and 550 nm, and then their difference is assessed. The P515 signal was detected during continuous illumination of adaxial leaf side by white light of high intensity (1,024 μmol photons m^–2 s^–1). The measurements have been accomplished with seven different leaves and the typical curves are shown in Figure 1A and its inset. All samples were dark-adapted for 10 min before measurements.

FIGURE 1

Figure 1. Time courses of electrochromic shift (ECS) spectra and simulated electric potentials. (A) Comparison of the simulated response of ΔΨ_m to the measured ΔA515–560-nm signal upon continuous illumination for 60 s followed by the dark adaptation for another 120 s. The insert depicts the comparison of the measured ΔA515–560-nm signal with the simulated response of ΔΨ_m upon continuous illumination for ∼1 s followed by the dark treatment for ∼0.5 s. (B) Simulated responses of ΔΨ_dn, ΔΨ_d, and ΔΨ_m upon continuous illumination for 60 s followed by the dark adaptation for another 120 s. (C) Simulated responses of Ψ_dnl, Ψ_dns, and ΔΨ_dn upon continuous illumination for 60 s followed by the dark adaptation for another 120 s. (D) Simulated responses of ΔΨ_d, ΔΨ_h, ΔΨ_k, and ΔΨ_cl upon continuous illumination for 60 s followed by the dark adaptation for another 120 s. The insert depicts the simulated responses of ΔΨ_h and ΔΨ_k. Light intensity for continuous light (duration 1 or 60 s) was 1,024 μmol photons m^{– 2} s^–1.

Description of the model

A comprehensive model of proton-coupled electron transport in and around photosynthetic thylakoid membranes has been proposed in our previous studies (Lyu and Lazar, 2017a,b). The model was made up of several modules including the linear and cyclic electron transport, the proton outflow through ATP-synthase, Calvin-Benson cycle and regulatory pathways. Moreover, the ion fluxes were calculated based on the modified Goldman–Hodgkin–Katz (GHK) equation (Van Kooten et al., 1986) and/or the transition state rate theory (TSRT) (Lyu and Lazar, 2017b). All quantitative values for model parameters are taken from literature and details of the model are given in our previous studies (Lyu and Lazar, 2017a,b). In the previous model, the ion–charge interaction was roughly speculated based on a preliminary calculation for the surface potential. In this work, we introduce the Donnan equilibrium potential to elaborate on the electrical phenomena adjacent to the thylakoid membrane-surface. Overall, Ψ_dn can regulate the distribution of ions close to the membrane surface causing the enrichment of cations and repulsion of anions; hence, adjusting the dynamics of channels/antiporters mediated ion fluxes and the proton efflux through ATP-synthase.

To clarify, the overall concept of the model is presented in Scheme 1. The onset of the electron transport is coupled to the proton translocation from the stroma into the lumen. The PMF is thus established and then consumed to drive the ATP synthesis through the CF₀–CF₁ type of ATP-synthase in chloroplasts. The early electrophoresis findings show that the negative charge density (∼−0.035 C/m²) on the luminal side is higher than on the stromal side (∼−0.025 C/m²) (Barber, 1982). Nonetheless, to equilibrate the initial transthylakoid Donnan potential in darkness, the fixed negative charge on either membrane surface is evenly assigned the value of −0.035 C/m² (Barber, 1982). Several early physiological measurements also showed a rise, upon illumination, of Mg²⁺ concentration in the stroma by 1–5 mM (Krause, 1977; Portis, 1981) and it was speculated that the change of stromal Mg²⁺ concentration may affect the thylakoid stacking and hence the efficiency of energy transfer between photosystems I and II (Barber et al., 1977), but the relative contribution of Mg²⁺ ions remains a matter of discussion because Tester and Blatt (1989) also reported that there was no Mg²⁺ current in a direct measurement of ion movement by fusing spinach thylakoid vesicles into planar lipid bilayers (Tester and Blatt, 1989). It seems that the Mg²⁺ flux presented in the literature vary greatly and is highly impacted by assay conditions. Therefore, it has been suggested that the Mg²⁺ flux may only play a small part in balancing the light-driven H⁺ movements (Tester and Blatt, 1989) and it has also been suggested that under physiological conditions the current through the cation selective channel is mainly carried by K⁺ ions (Pottosin and Schönknecht, 1996). Furthermore, the Mg²⁺ related channels/antiporters in thylakoid membranes have not been identified so far by modern molecular studies. Therefore, it would be reasonable to only consider K⁺ and Cl^– as the main ions penetrating the membrane to modify the electric potentials, which has been suggested as well in a recently published model to in silico study the partitioning of PMF upon various light conditions (Li et al., 2021). To follow up, ions of K⁺ and Cl^– are redistributed to partition ΔΨ_m into ΔΨ_d and ΔΨ_dn via ion channels/antiporters, namely, the voltage-gated K⁺ channel V–K⁺, the K⁺/H⁺ antiporter KEA3, the voltage-gated Cl^– channel VCCN1, and the Cl^– channel CLCe. The resultant effect of ion redistribution causes the formation of the diffusion potential difference (ΔΨ_d) which consists of three components, i.e., ΔΨ_h, ΔΨ_k, and ΔΨ_cl. The concepts and terms necessary for the understanding of the results and discussion are described below and detailed description of all computational segments of the model is provided in Supplementary Material.

SCHEME 1

Scheme 1. Schematic diagram of establishment and classification of transthylakoid electric potential. The upper panel presents the establishment of ΔΨ_m and its components. The onset of electron transport as illumination commences is coupled to the proton translocation from the stroma into the lumen. The proton motive force is thus established due to the acidification of the lumen and the alkalization of the stroma, which is ultimately used to drive the ATP synthesis through the CF₀–CF₁ type of ATP-synthase in chloroplasts. In response to the environmental conditions, the proton motive force is partitioned into its two components (ΔpH and ΔΨ_m) via ion channels/antiporters, i.e., the voltage-gated K⁺ channel V–K⁺, the K⁺/H⁺ antiporter KEA3, the voltage-gated Cl^– channel VCCN1, and the Cl^– channel CLCe. The resultant effect of ion redistribution causes the formation of the diffusion potential difference (ΔΨ_d) which includes three components, i.e., ΔΨ_h, ΔΨ_k, and ΔΨ_cl. It can be observed that both surfaces of the thylakoid membrane carry fixed negative charges whilst the negative charge density on the luminal side is more significant than the stromal side. To equilibrate the initial transthylakoid Donnan potential in darkness, the fixed negative charge on either membrane-surface is equally assigned the value of −0.035 C m^–2. Besides, Donnan potential difference (ΔΨ_dn) is established between the membrane-surface and the electrolyte solution. The electrostatic ΔΨ_dn is often sufficiently negative to attract mobile divalent cations (e.g., Mg²⁺) more than mobile monovalent cations (e.g., K⁺, H⁺) and repel mobile anions (e.g., Cl^–, OH^–). The enriched cations (Mg²⁺, K⁺, and H⁺) can also bind to negative charge sites and/or neutral sites, ultimately altering the membrane-surface negativity. In the lower panel, the calculating equation for ΔΨ_m and the definition for all components of ΔΨ_m are clarified.

The calculation of electrical potential difference

As presented above, ΔΨ_m is responsive to the composition of the contacting solution, the activity of proton pumping, the state of ion channels/antiporters, and electrical characteristics near the membrane surface. In brief, ΔΨ_m and ΔΨ_d can be calculated by (see Scheme 1):

$$\mathrm{\Delta }{\mathrm{\Psi }}_{\text{m}}=\mathrm{\Delta }{\mathrm{\Psi }}_{\text{d}}+\mathrm{\Delta }{\mathrm{\Psi }}_{\text{dn}}(2)$$

$$\mathrm{\Delta }{\mathrm{\Psi }}_{\text{d}}=\mathrm{\Delta }{\mathrm{\Psi }}_{\text{h}}+\mathrm{\Delta }{\mathrm{\Psi }}_{\text{k}}+\mathrm{\Delta }{\mathrm{\Psi }}_{\text{cl}}(3)$$

Where ΔΨ_m equals to the sum of ΔΨ_d and ΔΨ_dn; ΔΨ_h, ΔΨ_k, and ΔΨ_cl sum up to form ΔΨ_d; ΔΨ_d, ΔΨ_dn, ΔΨ_h, ΔΨ_k, and ΔΨ_cl are caused, respectively, by the light-induced transmembrane redistribution of bulk electrolytes, by the interplay of negative thylakoid-membrane surface charges and the bathing solute ions, by the transmembrane H⁺ movement and H⁺ released from oxygen evolving complex (OEC), by the transmembrane K⁺ movement, and by the transmembrane Cl^– movement. More information on calculation of ΔΨ_d can be obtained in our previous works (Lyu and Lazar, 2017a,b).

The Donnan potential determination involving the ion attachment to the membrane surface

The Donnan potential is the electrical potential at which the electroneutrality of the entire system is reached (Ohshima and Kondo, 1990). It occurs due to the excess of impermeant anions (e.g., charged macromolecules and/or organic acids) sequestered in a living cell. This nonzero potential changes the concentrations of solute ions near the membrane away from their values in the bulk solution (Gillespie and Eisenberg, 2001), which can be determined from:

$$\sum _{\text{i}=1}^{\text{N}}{\text{z}}_{\text{i}}{\text{C}}_{\text{i}}^{\mathrm{\infty }}\text{exp}\left(-\frac{{\text{z}}_{\text{i}}\text{F}{\mathrm{\Psi }}_{\text{dn}}}{\text{RT}}\right)+\frac{\rho }{\text{F}}\times \text{ro}=0(4)$$

where z_i is the valence of the ith ion (i = 1, 2, …, N), C_i^∞ is the bulk concentration of the ith ion, F is the Faraday constant, R is the universal gas constant, T is the absolute temperature, ρ is the density of the non-neutralized membrane-fixed negative charges, and ro is the ratio of surface-area to volume, which is assigned the value of 10⁶ cm^–1 for thylakoid (Van Kooten et al., 1986).

Ions binding to the membrane-surface are incorporated by altering ρ in Eq. (4). Here, ρ depends in part on intrinsic surface charge density and also includes those solute ions that bind to the membrane surface. In this study, the model takes into account 1:1 binding of cations to a negatively charged site ([R^–]) and a neutral site ([P⁰]) as described in the following reactions:

$$R^{-}+I_i^{z_i}\to {\left(R{I}_i\right)}^{z_i-1}(5)$$

$$R^{-}\times I_i^{z_i}\times K_{ci}={\left(R{I}_i\right)}^{z_i-1}(6)$$

and

$${\text{P}}^0+{\text{I}}_{\text{i}}^{{\text{z}}_{\text{i}}}\to {\left({\text{PI}}_{\text{i}}\right)}^{{\text{z}}_{\text{i}}}(7)$$

$${\text{P}}^0\times {\text{I}}_{\text{i}}^{{\text{z}}_{\text{i}}}\times {\text{K}}_{\text{pi}}={\left({\text{PI}}_{\text{i}}\right)}^{{\text{z}}_{\text{i}}}(8)$$

and

$${\text{I}}_{\text{i}}^{{\text{z}}_{\text{i}}}={\text{C}}_{\text{i}}\times \text{exp}\left(-\frac{{\text{z}}_{\text{i}}\text{F}{\mathrm{\Psi }}_{\text{dn}}}{\text{RT}}\right)(9)$$

Thus, ρ can be computed from Eqs (4) to (8) as follows:

$$\frac{\rho }{\text{F}}\times \text{ro}=-\left[{\text{R}}^{-}\right]+\sum _{\text{i}=1}^{\text{N}}\left({\text{z}}_{\text{i}}-1\right)+\left[{\left({\text{RI}}_{\text{i}}\right)}^{{\text{z}}_{\text{i}}-1}\right]+\sum _{\text{i}=1}^{\text{N}}{\text{z}}_{\text{i}}\left[{\left({\text{PI}}_{\text{i}}\right)}^{{\text{z}}_{\text{i}}}\right](10)$$

where z_i is the valence of the ith ion (i = 1, 2, …, N), I_i^zi is the Ψ_dn-induced concentration of the ith ion close to the membrane surface, [R^–] and [P⁰] denote concentrations of the negatively charged sites and the neutral sites ([R^–] equals to 3.63 × 10^–5 mol/cm³ reflects [SC] which was set at −0.035 C/m²; P⁰ reflects [SP] and was assigned 8-fold of [R^–]), [(RI_i)^zi–1] and [(PI_i)^zi] denote product concentrations of the ith ion binding to the negatively charged site and the neutral site. For cations binding to the negative charge sites, both divalent (Mg²⁺) and monovalent species (K⁺ and H⁺) are considered in simulations. However, it can be observed from Eq. (10) that the concentration of negative charges remains unaffected provided a neutralized pair is randomly created for the monovalent cations binding to the negative charges. These formulas were initially proposed to investigate the rhizotoxicity of heavy metals binding to the root cell membrane (Kinraide et al., 1998). Unless stated otherwise, all theoretical details and parameter values involved in the formulations are presented in Supplementary Material.

Results

Following continuous illumination for 60 s and the ensuing 120 s in darkness, the ECS kinetics is in accordance with the previously reported measurements (Kramer and Sacksteder, 1998; Johnson and Ruban, 2014). Specifically, upon switching on the light, the ECS kinetics shows a sharp rise before decaying to ∼30% of its initial amplitude and then rising again till saturating within ∼20 s. When the light is switched off, the ECS signal shows a sharp fall before returning to the steady-state a bit higher above the dark baseline (Figure 1A). Overall, the ECS kinetics was well described by the modeled ΔΨ_m whereas the simulation lacks the shallow dip positioned during ∼10 to ∼30 s, and the ECS kinetics as illumination ceases appears to relax a bit faster than the modeled curve. According to Johnson and Ruban (2014), the transient dip and the following changes leading to the steady-state before illumination ceases is the slow phase of ECS, which is not caused by ΔΨ_m but the formation of qE-related absorption change. However, Kramer et al. suggested that a significant fraction of PMF in chloroplasts can be stored as ΔΨ_m under the steady-state conditions (Kramer and Sacksteder, 1998; Kramer et al., 1999; Cruz et al., 2001, 2005; Davis et al., 2017; Kanazawa et al., 2017). Our simulations show that the lasting ECS trace is partly contributed by ΔΨ_dn (see Figure 1B), and the dip may be related to K⁺ redistribution induced by the alteration of abundance of membrane surface charges on luminal surface or both surfaces ([SC]_l or [SC]_l and [SC]_s) (see Figures 2E,F). The insert of Figure 1A shows the comparison between the modeled ΔΨ_m and the ECS signal upon illumination for ∼1 s followed by a 0.5-s period of darkness. The measured ECS curve shows a bimodal pattern as illumination commences before decaying to a plateau. Upon switching off the light, the curve shows an exponential decay till reaching a steady-level largely below the dark baseline, in line with the measurements previously reported in the literature (Bulychev, 1984; Vredenberg, 1997; Bulychev and Vredenberg, 1999). The modeled ΔΨ_m can reproduce several features of the measured curve, e.g., the bimodal pattern, the timing of the first peak and the transient dip after the first peak, and the decaying kinetics in the darkness. However, the second peak of simulation appears to be less prominent than in the ECS signal, which may be related to the proton translocation induced by the alteration of abundance of membrane-surface charges on both membrane sides ([SC]_l and [SC]_s) (see Figure 2C). Figure 1B shows that ΔΨ_dn and ΔΨ_d sum up to form ΔΨ_m in which ∼40% amplitude of the steady-state ΔΨ_m is contributed by the formation of ΔΨ_dn (∼5 mV). The simulated ΔΨ_dn, which is the difference of Ψ_dns minus Ψ_dnl, is shown in Figure 1C. The negativity of Ψ_dnl is increased because of the light-driven cation efflux into the stroma (K⁺ out and H⁺ out) and anion influx into the lumen (Cl^– in). The Donnan equilibrium potential in either compartment is usually less than ∼−20 mV (Sperelakis, 2012) and apparently our results are approaching to this value.

FIGURE 2

Figure 2. Simulated responses of ΔΨ_h, ΔΨ_k, and ΔΨ_cl on assigning different values for adjustable parameters. (A) Simulated responses of ΔΨ_h by adjusting K_cmgl 1- and 10-fold of the controlled value. (B) Simulated responses of ΔΨ_h by adjusting [SC]_l 1- and 10-fold of the controlled value. (C) Simulated responses of ΔΨ_h by adjusting [SC]_l and [SC]_s 1- and 10-fold of the controlled value. (D) Simulated responses of ΔΨ_k by adjusting K_cmgl 1- and 10-fold of the controlled value. (E) Simulated responses of ΔΨ_k by adjusting [SC]_l 1- and 10-fold of the controlled value. (F) Simulated responses of ΔΨ_k by adjusting [SC]_l and [SC]_s 1- and 10-fold of the controlled value. (G) Simulated responses of ΔΨ_cl by adjusting K_cmgl 1- and 10-fold of the controlled value. (H) Simulated responses of ΔΨ_cl by adjusting [SC]_l 1- and 10-fold of the controlled value. (I) Simulated responses of ΔΨ_cl by adjusting [SC]_l and [SC]_s 1- and 10-fold of the controlled value.

The separation of the simulated ΔΨ_d into three components, namely, the electric potential difference caused by H⁺ translocation (ΔΨ_h), by K⁺ translocation (ΔΨ_k), and by Cl^– translocation (ΔΨ_cl) is shown in Figure 1D. As the light is switched on, the ΔΨ_h trace shows a sharp rise followed by a dip before rising again till reaching a steady-state. In contrast, ΔΨ_k and ΔΨ_cl, as the counterpart of ΔΨ_h, both decreased although ΔΨ_k decreased initially faster than ΔΨ_cl till reaching a negative steady-level (Figure 1D). As the light is switched off, the ΔΨ_h trace contains a sharp fall till the inverted ΔΨ_h attains the negative maximum and then followed by a slow relaxation returning to the dark baseline which is attributable to the leaky proton influx into the lumen (Supplementary Figures 3A,B). The inverted ΔΨ_h would suddenly force Cl^– back into the stroma till ΔΨ_cl is inverted to the positive maximum before relaxing to the dark baseline (Figure 1D). Simultaneously, the K⁺ flux out of the lumen will be decelerated due to the inverted ΔΨ_h till ΔΨ_k converges to the dark baseline. Notably, the ΔΨ_k relaxing trace during the dark phase is overlapped by the ΔΨ_h trace (insert of Figure 1D). This is understandable since the K⁺ efflux is mediated by the V–K⁺ channel which is strictly voltage dependent.

To investigate the effect of ion attached to the membrane surface on regulating ΔΨ_dn, ΔΨ_d, and ΔΨ_m, the controlling parameters that affect electric characteristics close to the membrane surface are adjusted including the binding constant of Mg²⁺ attached to the negative charge sites on both surfaces (K_cmgl and K_cmgs), the binding constants of Mg²⁺, K⁺, and H⁺ attached to the neutral sites on both surfaces (K_pmgl, K_pmgs, K_pkl, K_pks, K_phl, and K_phs), the density of the negative charge site on both surfaces ([SC]_l and [SC]_s), and the density of the neutral site on both surfaces ([SP]_l and [SP]_s). The change of these parameters or their compositions can take place near the luminal surface or the stromal surface or both. Since the variation of parameters near the stromal surface leads to the kinetics, which is sorted in a reverse order in comparison to the variation on single luminal surface (e.g., see insert of Figure 3A). Here, we consider the change of parameters occurring only on luminal surface or both surfaces. On luminal side, we have conducted simulations for 36 times by adjusting [SC]_l (control, 5-, and 10-fold), [SP]_l (0-fold, control, 10-, and 100-fold, the same change for the parameter composition followed), K_cmgl, K_pmgl, K_pkl, K_phl, [K_pmglK_pkl], [K_pmglK_phl], [K_pklK_phl], and [K_pmglK_pklK_phl], respectively. Similarly, a total of 37 simulations have been conducted by simultaneously adjusting parameters on both surfaces to the same extend as presented above except for the condition of [SC]_l and [SC]_s, which adds one more trial (0-fold). Simply diminishing [SC]_l to zero only on luminal face will cause the significant deviation of initial quantitative values for key variables from the equilibrium which ultimately cause the breakdown of the model operation, we thus explore the impact of negative surface charges by concurrently increasing [SC]_l and [SC]_s on both sides. For all of the 0-fold changes related to [SP]_l/[SP]_s, K_cmgl/K_cmgs, K_pmgl/K_pmgs, K_pkl/K_pks, and K_phl/K_phs, the modeled traces rarely show the difference to the standard curves. Therefore, only the controlled traces will be presented in figures. In brief, all simulations (73 trials) that show the obvious alteration compared to the controlled simulation are shown in Figure 3. These alterations can basically be summarized into the following three types: (i), the ΔΨ_m curve induced by the increased K_cmgl was characterized as a more negative starting point, a higher peak, a faster decay till reaching the steady-state during the light phase as well as a more rapid fall followed by an accelerated relaxation in the darkness (Figure 3A). This pattern was also reproduced in Figures 3D,E via 100-fold increasing K_cmgl or [SP]_l whereas the variation appears to be less prominent for the change of 10-fold of the controlled value (Figures 3D,E). The variation for the ΔΨ_m curve was due to an upleveled ΔΨ_d (Figure 4A) and a crossover of ΔΨ_dn from the positive to the negative (Figure 5A) which is mainly contributed by a less negative Ψ_dnl (Figure 5G) whereas Ψ_dns is slightly affected (Figure 5D). (ii), the ΔΨ_m curve for the increased [SC]_l (Figure 3B) contains the kinetic behavior antiparallel to the curve caused by the increased K_cmgl. This was due to a significantly decreased ΔΨ_d (Figure 4B) and a more positive ΔΨ_dn (Figure 5B) majorly contributed by an enormously negative Ψ_dnl (Figure 5H); (iii), the ΔΨ_m kinetics shows a different pattern induced by concurrently increasing [SC]_l and [SC]_s (Figure 3C), which shows a sharp rise as the light is switched on before experiencing a biphasic decay (a rapid decay followed by a slower decay) till reaching a steady-level. When the light is switched off, the ΔΨ_m kinetics shows a sharp fall below the dark baseline before returning to the steady-state much faster than in the controlled trace, whereas a much slower relaxation is visible for 0-fold of the controlled values (Figure 3C).

FIGURE 3

Figure 3. Simulated responses of ΔΨ_m on assigning different values for adjustable parameters. (A) Simulated responses of ΔΨ_m by adjusting K_cmgl 1-, 5-, and 10-fold of the controlled value. The insert illustrates simulated responses of ΔΨ_m by adjusting K_cmgs 1-, 5-, and 10-fold of the controlled value. (B) Simulated responses of ΔΨ_m by adjusting [SC]_l 1-, 5-, and 10-fold of the controlled value. (C) Simulated responses of ΔΨ_m by adjusting [SC]_l and [SC]_s 0-, 1-, 5-, and 10-fold of the controlled value. (D) Simulated responses of ΔΨ_m by adjusting K_pmgl 1-, 10-, and 100-fold of the controlled value. (E) Simulated responses of ΔΨ_m by adjusting [SP]_l 1-, 10-, and 100-fold of the controlled value.

FIGURE 4

Figure 4. Simulated responses of ΔΨ_d on assigning different values for adjustable parameters. (A) Simulated responses of ΔΨ_d by adjusting K_cmgl 1- and 10-fold of the controlled value. (B) Simulated responses of ΔΨ_d by adjusting [SC]_l 1- and 10-fold of the controlled value. (C) Simulated responses of ΔΨ_d by adjusting [SC]_l and [SC]_s 1- and 10-fold of the controlled value.

FIGURE 5

Figure 5. Simulated responses of Ψ_dnl, Ψ_dns, and ΔΨ_dn on assigning different values for adjustable parameters. (A) Simulated responses of ΔΨ_dn by adjusting K_cmgl 1- and 10-fold of the controlled value. (B) Simulated responses of ΔΨ_dn by adjusting [SC]_l 1- and 10-fold of the controlled value. (C) Simulated responses of ΔΨ_dn by adjusting [SC]_l and [SC]_s 1- and 10-fold of the controlled value. (D) Simulated responses of Ψ_dns by adjusting K_cmgl 1- and 10-fold of the controlled value. (E) Simulated responses of Ψ_dns by adjusting [SC]_l 1- and 10-fold of the controlled value. (F) Simulated responses of Ψ_dns by adjusting [SC]_l and [SC]_s 1- and 10-fold of the controlled value. (G) Simulated responses of Ψ_dnl by adjusting K_cmgl 1- and 10-fold of the controlled value. (H) Simulated responses of Ψ_dnl by adjusting [SC]_l 1- and 10-fold of the controlled value. (I) Simulated responses of Ψ_dnl by adjusting [SC]_l and [SC]_s 1- and 10-fold of the controlled value.

Overall, ΔΨ_dn and Ψ_dns progress in the same trend, i.e., the curve shows a rapid rise as illumination commences before attaining the steady-level followed by an exponential decay till the steady-state is reached as the light is switched off (Figures 5A–F). In contrast, the Ψ_dnl trace exhibits an opposite behavior which shows a rapid fall before attaining the steady-level followed by a slower rise till relaxing to the steady-state as the light is switched off (Figures 5G–I). The ΔΨ_dn curve was transferred to a more negative level by increasing K_cmgl (Figure 5A). This was majorly contributed by a smaller Ψ_dnl produced (less negative, Figure 5G). Intriguingly, increasing K_cmgl will cause a slight decrease of Ψ_dns (Figure 5D) which may be associated with the ion redistribution caused by various ionic fluxes. When increasing [SC]_l, the ΔΨ_dn trace was transferred to a more positive level (Figure 5B) due to a much larger Ψ_dnl (more negative, Figure 5H) together with a slight increase of Ψ_dns produced (Figure 5E). When concurrently increasing [SC]_l and [SC]_s, the ΔΨ_dn trace was transferred to a much smaller positive level (Figure 5C) due to a much larger Ψ_dnl (more negative as shown in Figure 5I similar as induced by individually increasing [SC]_l in Figure 5I) together with a significant upregulation of Ψ_dns produced (more negative as shown in Figure 5F for Ψ_dnl).

When K_cmgl or [SC]_l is increased, the ΔΨ_d curve is as a whole upshifted to a more positive level (Figure 4A) or downshifted to a more negative level (Figure 4B) with an extent for the latter is a bit larger than the former. When concurrently increasing [SC]_l and [SC]_s, the ΔΨ_d curve (Figure 4C) decays in a biphasic pattern till saturating in the light phase and shows an accelerated rise returning to the steady-state in the darkness.

When increasing K_cmgl 10-fold of the controlled value, the ΔΨ_h curve reaches a higher peak (∼70 mV) followed by a more prominent dip as the light is switched on till saturating to a larger steady-level (∼75 mV) (Figure 2A). As shutting off the light, the ΔΨ_h curve shows a rapid fall followed by an accelerated rise till reaching the steady-state slightly above the dark baseline (Figure 2A). The steady-state value of the ΔΨ_k curve for 10-fold condition is smaller (less negative) than the standard curve during the light phase (Figure 2D) and a more speeded relaxation occurs until reaching the steady-state significantly above the dark baseline as shutting off the light (Figure 2D). The steady-state value of the ΔΨ_cl curve for 10-fold condition is a bit smaller (less negative) than the standard trace during the light phase (Figure 2G). As switching off the light, the ΔΨ_cl curve shows a sharp rise followed by a decelerated exponential decay till reaching a steady-state moderately above the dark baseline than the controlled curve (Figure 2G).

When increasing [SC]_l 10-fold of the controlled value, the ΔΨ_h curve peaks at a lower level followed by a nearly diminished dip as switching on the light till saturating to a much smaller steady-level (∼58 mV) (Figure 2B). As shutting off the light, the ΔΨ_h curve shows a rapid fall followed by a faster rise till reaching the steady-state enormously below the dark baseline (Figure 2B). Upon the 10-fold increase of [SC]_l, the ΔΨ_k curve shows a sharp fall followed by an acute dip till attaining the steady-level much higher (more negative) than the standard trace during the light phase (Figure 2E). As shutting off the light, an accelerated relaxation occurs until reaching the steady-state ∼10 mV below the dark baseline (Figure 2E). Similarly, upon the 10-fold increase of [SC]_l, the ΔΨ_cl curve shows a slower exponential decay till attaining the steady-level much higher (more negative) than the controlled trace during the light phase (more negative, Figure 2H). As shutting off the light, the ΔΨ_cl curve shows a sharp rise reaching a smaller peak level (∼20 mV) followed by a much faster decay till reaching the steady-state ∼10 mV below the dark baseline (Figure 2H).

When concurrently increasing [SC]_l and [SC]_s 10-fold of the controlled value, the ΔΨ_h curve reaches the peak followed by a fast rise to a maximum at ∼25 s before decaying to a slightly smaller steady-level (∼62 mV) than the standard curve (Figure 2C). As switching off the light, the ΔΨ_h curve shows a sharp fall followed by a faster rise till reaching the dark baseline (Figure 2C). The ΔΨ_k curve upon the 10-fold increase of [SC]_l and [SC]_s shows a sharp fall to about ∼35 mV followed by a fast rise till leveling toward a smaller steady-level (∼25 mV) (Figure 2F). As switching off the light, a faster relaxation occurs until converging to the dark baseline as the controlled trace (Figure 2F). Upon concurrently increasing [SC]_l and [SC]_s 10-fold of the controlled value, the ΔΨ_cl curve shows a slower exponential decay till attaining the steady-level smaller (less negative) than the controlled curve in the light phase (Figure 2I). As switching off the light, the ΔΨ_cl curve shows a sharp rise peaking at a smaller level (∼25 mV) followed by an accelerated decay till converging to the dark baseline concomitant with the standard trace (Figure 2I).

Discussion

Specific roles of ion binding to the membrane-surface on regulating ΔΨ_dn, ΔΨ_d, and ΔΨ_m

To investigate specific roles of ion binding to the membrane-surface on regulating ΔΨ_dn, ΔΨ_d, and ΔΨ_m, controlling parameters which affect the electric characteristics adjacent to the membrane surface (i.e., K_cmgl, K_cmgs, K_pmgl, K_pmgs, K_pkl, K_pks, K_phl, K_chs, [SC]_l, [SC]_s, [SP]_l, and [SP]_s) were adjusted under various scenarios to conduct in silico experiments. Computing findings reveal that approximate three types of variations induced by the adjustable parameters may be derived as follows: (i) The K_cmgl-induced type, (ii) the [SC]_l-induced type, and (iii) the [SC]_l and [SC]_s-induced type. For the K_cmgl-induced type, high binding constant for Mg²⁺ reduces the negativity of Ψ_dnl (Figure 5G), which increases the concentration of Cl^– while decreases the concentration of cations (K⁺ and H⁺) close to the membrane-surface. This causes a larger Cl^– flux penetrating the membrane (Supplementary Figure 2B) and a larger concentration of H⁺ kept in the bulk phase (Supplementary Figure 3B). However, a more significant K⁺ flux cannot be notably observed (Supplementary Figure 1B). The K_cmgl-induced ion flux mediated by the KEA3 is slightly smaller than the controlled (Supplementary Figure 1D). The KEA3 functions to maintain the level of ΔΨ_m while decreasing the pH in lumen through the exchange of cations between K⁺ (in) and H⁺ (out) (Kunz et al., 2014; Armbruster et al., 2016; Wang et al., 2017; Wang and Shikanai, 2019). Additionally, the effect of ion flux mediated by the Cl^– channel CLCe is trivial (∼10^–4 mM/s) (Supplementary Figure 2D). This result was also visible in the computing data from Li et al. (2021). Conceivably, more Cl^– traveling to the stroma will increase the negativity of Ψ_dns (Figure 5D), in addition to the less negative Ψ_dnl, which ultimately converts the total Donnan potential (ΔΨ_dn) to negative values (Figure 5A). This, in turn, keeps the steady-level of ΔΨ_m only marginally altered by playing an essential counterpart against the highly increased ΔΨ_d (Figure 4A) due to the co-function of ΔΨ_h (Figure 2A), ΔΨ_k (Figure 2D), and ΔΨ_cl (Figure 2G). It should also be noted that the kinetics of ΔΨ_dn, ΔΨ_d, and ΔΨ_m as the light is switched off relaxes in the same pattern as described above. This holds in all simulations for three patterns.

For the [SC]_l-induced type, the consequence is, in fact, antiparallel to those induced by the high binding constant for Mg²⁺, since high abundance of negative charge sites increases the negativity of Ψ_dnl (Figure 5H), which in turn increases the concentration of cations (K⁺ and H⁺) while decreasing the concentration of Cl^– close to the membrane-surface. This causes a larger transmembrane K⁺ flux (Supplementary Figure 1B) and a smaller concentration of H⁺ stored in the bulk-phase (Supplementary Figure 3B) whereas a significantly reduced Cl^– flux cannot be notably observed (Supplementary Figure 2B). This might imply that the Cl^– enrichment close to the membrane-surface is likely to be more affected by the “screening” effect caused by cations binding to the surface charges nor the abundance of negative charge sites themselves. Understandably, more K⁺ traveling to the stroma will decreases the negativity of Ψ_dns (Figure 5E), in addition to the more negative Ψ_dnl, which ultimately produce a more positive value for the Donnan potential (ΔΨ_dn) (Figure 5B). However, under this condition, the co-function of ΔΨ_h (Figure 2B), ΔΨ_k (Figure 2E), and ΔΨ_cl (Figure 2H) makes ΔΨ_d a value being enormously negative (Figure 4B), which eventually decreases the steady-level of ΔΨ_m (Figure 3B) with an extent a bit larger than in the K_cmgl-induced type (Figure 3A). This might demonstrate that, by identically enlarging K_cmgl or [SC]_l 10-fold of the controlled, the abundance of the negative charge sites will cause more pronounced effects on regulating ΔΨ_dn, ΔΨ_d, and ΔΨ_m than the K_cmgl-induced type.

When concurrently increasing [SC]_l and [SC]_s, i.e., for the [SC]_l and [SC]_s-induced type, the high abundance of negative charge sites on both surfaces can concomitantly reduce both the negativity of Ψ_dnl and Ψ_dns (Figures 5F,I). This triggers the kinetic behavior a complexity compared to the K_cmgl-induced or the [SC]_l-induced type. With the negativity decrease for Ψ_dnl and Ψ_dns, the Cl^– flux density is largely reduced (Supplementary Figure 2B) but the enormously increased H⁺ (out)/K⁺ (in) flux conducted by the KEA3 (Supplementary Figure 1D) is observed following a complex dynamic pattern (a sharp rise followed by a deep well till leveling off) as the light is switched on. Intriguingly, the K⁺ flux nearly remains unaffected (Supplementary Figure 1B). The resultant effect of all ion fluxes causes a positive ΔΨ_dn with a small amplitude (Figure 5C) and makes the steady-state ΔΨ_d reach a value being more positive (Figure 4C). However, it is unparallel to the standard curve but softly decaying till saturating. Similarly, the ΔΨ_m bears a resemblance to ΔΨ_d but being more positive because it is apparent that the addition of ΔΨ_d and ΔΨ_dn (being positive) produces the ΔΨ_m. Taken together, our simulations show that Ψ_dn can affect the concentration of ions close to the membrane-surface and thus the diffuse potential (ΔΨ_d) and consequently the total membrane potential (ΔΨ_m). Therefore, Ψ_dn plays a key role on regulating the thylakoid-membrane energization during photosynthesis and should be considered in future studies, which are related to the transthylakoid electrical potential.

Role of a Mg²⁺ flux through the thylakoid membrane

As noted, thylakoid-harbored non-selective cation pores are not only permeable to K⁺ but also to Mg²⁺ (Enz et al., 1993; Pottosin and Schönknecht, 1996), causing a rise, upon illumination, of Mg²⁺ concentration in the stroma by 1–5 mM (Krause, 1977; Portis, 1981). To check the role of Mg²⁺ on regulating ΔΨ_m, we additionally merged a Mg²⁺ flux calculated by the GHK equation similar to K⁺ flux into our model and the value of permeability for Mg²⁺ was set at one-third of that for K⁺ based on the measuring data from Pottosin and Schönknecht (1996), i.e., the single channel conductance is 60 pS for K⁺ and 19 pS for Mg²⁺. It turns out that, although several local features of the ΔΨ_m (the total membrane potential) trace were altered (data not shown), the general kinetic trend keeps unaffected, which also shows a sharp rise upon illumination before decaying to certain extent of its initial amplitude and then rising again till reaching a steady-state. When the light is switched off, the ΔΨ_m curve also shows a sharp fall before returning to the dark baseline. The unaffected kinetic trend might be explained by the fact that more cationic effluxes into stroma would cause a raised dissipation for the diffusion potential difference (ΔΨ_d). On the other hand, more cations entry into stroma would cause an increase for the negativity of Ψ_dnl but a concomitant decrease for the negativity of Ψ_dns, ultimately triggering a rise of the Donnan potential difference (ΔΨ_dn), which compensates the loss of ΔΨ_d. Furthermore, we also conducted the simulations under which principles for regulations by the altered parameters on ΔΨ_m remain unchanged as those shown in Figure 3. For instance, the ΔΨ_m curve induced by the increased K_cmgl (control, ×5, and ×10) was also characterized as a more negative starting point, a higher peak, a faster decay till reaching the steady-state during the light phase as well as a more rapid fall followed by an accelerated relaxation returning to the baseline in the darkness. In essence, the adjustment of ΔΨ_m by the Mg²⁺ efflux manifests an “identical” effect as by the K⁺ efflux because they both are cations and merely differ in their valences.

Donnan potential or surface potential at the thylakoid membrane?

It has been shown that both surfaces of the thylakoid membrane carry fixed negative charges (Barber, 1980b,1982). An electrical potential difference is thus established between the membrane surface and the electrolyte solution, which is sufficiently negative to enrich the concentration of cations or to deplete the concentration of anions close to the thylakoid membrane surface. This electric potential has been mathematically computed by two different approaches, i.e., the Donnan equilibrium potential or the Gouy–Chapman double-layer potential (the surface potential is termed as a synonym). As noted above, the surface potential assumes that the thickness of membrane surface charge layer (d_s) is zero and all membrane fixed charges are only located within the membrane surface. Theoretically, provided d_s ≥ 1/κ (κ being the Debye–Hückel parameter), the electric potential in the region far inside the charge layer is practically equal to the Donnan potential (Ohshima and Ohki, 1985; Ohshima and Kondo, 1988b,1990). Provided d_s ≤ 1/κ, the electric potential at the membrane surface is practically equal to the surface potential. The Donnan potential (d_s → ∞) can be converted to the surface potential (d_s → 0) undergoing a smooth transition (Ohshima and Kondo, 1990). In essence, the surface potential is a transformer of the Donnan potential as d_s is approaching zero (Ohshima and Kondo, 1990). Up to the present, all attempts to estimate d_s have been subject to artifacts (Levine et al., 1983). Additionally, using the initial values of our model for all solute species, 1/κ for the thylakoid membrane is calculated as 61.5 nm (see Supplementary Material). Although the characterization of electric potential is dependent on d_s, it is still adequate to assume the inner space of the chloroplast as a Donnan system because the Gouy–Chapman potential is essentially an alternative “Donnan potential” at the extrema. Additionally, the Donnan potential has particularly been appropriate for studies of ion transport processes through membrane (Ohshima and Ohki, 1985). In our study, at the standard state, the Donnan potential is computed as within ∼−12.5 to ∼−10 mV for the luminal compartment (Ψ_dnl) (Figure 1C) and ∼−15 to ∼−12.5 mV for the stromal compartment (Ψ_dns) (Figure 1C), both of which agree with the literature data (Sperelakis, 2012; Qasem et al., 2018).

Conclusion

By employing an extended photosynthetic model, we investigated the effect of altered cationic binding to the negatively charged thylakoid membrane surface on adjusting the transthylakoid electric potential focusing on a cycle of illumination followed by a dark-adapted period. Consequently, the measured ECS traces were well described by the computing results by assigning the model parameters with the quantitative values taken from the literature. Moreover, the computing data clarified the components of transthylakoid membrane potential, unraveled the functional consequences of altered cationic attachment to the membrane surface on adjusting the transthylakoid electric potential, and revealed the key role played by the Donnan potential in bridging the diffusion potential with the total membrane potential. Ultimately, the compatibility of Donnan theory employed in the chloroplast in conjunction with the interrelationship between the Donnan potential and the Gouy–Chapman potential were discussed. The current model presented in this work can serve as a basis for further extension into a more detailed theoretical model by which multiple variables involved in photosynthesis can be explored.

Data availability statement

The original contributions presented in this study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding authors.

Author contributions

HL conceived the study, performed the experiments, constructed the model, performed the simulations, and wrote parts of the manuscript. DL analyzed the experimental data, constructed the model, wrote parts of the manuscript, and supervised the referencing. Both authors contributed to the article and approved the submitted version.

Funding

HL was supported from the National Natural Science Foundation of China (31960055 and 31960605), the Natural Science Foundation of Guizhou Province of China (qiankehejichu[2020]1Y068), and the Science and Technology Plan Project of Guizhou Province of China (qiankehepingtairen[2020]QNSYXM01). DL was supported from ERDF project “Plants as a tool for sustainable global development” (no. CZ.02.1.01/0.0/0.0/16_019/0000827).

Acknowledgments

We acknowledge Hiroyuki Ohshima for his useful comments on membrane potential.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fpls.2022.945675/full#supplementary-material

Supplementary Figure 1 | Simulated responses of the K⁺ flux and the H⁺/K⁺ flux on assigning different values for adjustable parameters. (A) 3D view of the K⁺-flux kinetics simulated under control and by 10-fold increasing K_cmgl, [SC]_l, and [SC]_l and [SC]_s, respectively; (B) 2D view of the K⁺-flux kinetics simulated under control and by 10-fold increasing K_cmgl, [SC]_l, and [SC]_l and [SC]_s, respectively; (C) 3D view of the H⁺/K⁺-flux kinetics simulated under control and by 10-fold increasing K_cmgl, [SC]_l, and [SC]_l and [SC]_s, respectively; (D) 2D view of the H⁺/K⁺-flux kinetics simulated under control and by 10-fold increasing K_cmgl, [SC]_l, and [SC]_l and [SC]_s, respectively.

Supplementary Figure 2 | Simulated responses of the Cl^– flux and the H⁺/Cl^– flux on assigning different values for adjustable parameters. (A) 3D view of the Cl^–-flux kinetics simulated under control and by 10-fold increasing K_cmgl, [SC]_l, and [SC]_l and [SC]_s, respectively; (B) 2D view of the Cl^–-flux kinetics simulated under control and by 10-fold increasing K_cmgl, [SC]_l, and [SC]_l and [SC]_s, respectively; (C) 3D view of the H⁺/Cl^–-flux kinetics simulated under control and by 10-fold increasing K_cmgl, [SC]_l, and [SC]_l and [SC]_s, respectively; (D) 2D view of the H⁺/Cl^–-flux kinetics simulated under control and by 10-fold increasing K_cmgl, [SC]_l, and [SC]_l and [SC]_s, respectively.

Supplementary Figure 3 | Simulated responses of [H⁺]_l and [H⁺]_s on assigning different values for adjustable parameters. (A) 3D view of [H⁺]_l responses simulated under control and by 10-fold increasing K_cmgl, [SC]_l, and [SC]_l and [SC]_s, respectively; (B) 2D view of the [H⁺]_l responses simulated under control and by 10-fold increasing K_cmgl, [SC]_l, and [SC]_l and [SC]_s, respectively; (C) 3D view of the [H⁺]_s responses simulated under control and by 10-fold increasing K_cmgl, [SC]_l, and [SC]_l and [SC]_s, respectively; (D) 2D view of the [H⁺]_s responses simulated under control and by 10-fold increasing K_cmgl, [SC]_l, and [SC]_l and [SC]_s, respectively.

Abbreviations

ATP, adenosine triphosphate; PMF, proton motive force; NPQ, non-photochemical quenching; PSII, photosystem II; Δ pH, transthylakoid pH difference; ΔΨ_m, membrane potential difference; ΔΨ_dn, Donnan potential difference; Ψ_dn, Donnan potential; Ψ_dnl, luminal Donnan potential; Ψ_dns, stromal Donnan potential; ΔΨ_d, diffusion potential difference; ΔΨ_h, electric potential difference caused by H⁺ translocation; ΔΨ_k, electric potential difference caused by K⁺ translocation; ΔΨ_cl, electric potential difference caused by Cl^– translocation; K_cmgl/K_cmgs, binding constant of Mg²⁺ attached to negative charge site on luminal/stromal membrane surface; K_pmgl/K_pmgs, binding constant of Mg²⁺ attached to neutral site on luminal/stromal membrane surface; K_pkl/K_pks, binding constant of K⁺ attached to neutral site on luminal/stromal membrane surface; K_phl/K_phs, binding constant of H⁺ attached to neutral site on luminal/stromal membrane-surface; [SC]_l ([SC]_s), density of negative charge site on luminal (stromal) membrane surface; [SP]_l ([SP]_s), density of neutral site on luminal (stromal) membrane surface; d_s, thickness of membrane surface charge layer; κ, Debye–Hückel parameter; ECS, electrochromic shift; GHK, Goldman–Hodgkin–Katz; TSRT, transition state rate theory; ρ, density of non-neutralized membrane-fixed negative charge; qE, energy-dependent NPQ of chlorophyll fluorescence; OEC, oxygen evolving complex.

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