Hacking the thylakoid proton motive force for improved photosynthesis: modulating ion flux rates that control proton motive force partitioning into Δψ and ΔpH

Abstract

There is considerable interest in improving plant productivity by altering the dynamic responses of photosynthesis in tune with natural conditions. This is exemplified by the ‘energy-dependent' form of non-photochemical quenching (q_E), the formation and decay of which can be considerably slower than natural light fluctuations, limiting photochemical yield. In addition, we recently reported that rapidly fluctuating light can produce field recombination-induced photodamage (FRIP), where large spikes in electric field across the thylakoid membrane (Δψ) induce photosystem II recombination reactions that produce damaging singlet oxygen (¹O₂). Both q_E and FRIP are directly linked to the thylakoid proton motive force (pmf), and in particular, the slow kinetics of partitioning pmf into its ΔpH and Δψ components. Using a series of computational simulations, we explored the possibility of ‘hacking' pmf partitioning as a target for improving photosynthesis. Under a range of illumination conditions, increasing the rate of counter-ion fluxes across the thylakoid membrane should lead to more rapid dissipation of Δψ and formation of ΔpH. This would result in increased rates for the formation and decay of q_E while resulting in a more rapid decline in the amplitudes of Δψ-spikes and decreasing ¹O₂ production. These results suggest that ion fluxes may be a viable target for plant breeding or engineering. However, these changes also induce transient, but substantial mismatches in the ATP : NADPH output ratio as well as in the osmotic balance between the lumen and stroma, either of which may explain why evolution has not already accelerated thylakoid ion fluxes. Overall, though the model is simplified, it recapitulates many of the responses seen in vivo, while spotlighting critical aspects of the complex interactions between pmf components and photosynthetic processes. By making the programme available, we hope to enable the community of photosynthesis researchers to further explore and test specific hypotheses.

This article is part of the themed issue ‘Enhancing photosynthesis in crop plants: targets for improvement’.

1. Introduction

This opinion/hypothesis paper was inspired by the recent Royal Society symposium on ‘Enhancing photosynthesis in crop plants: targets for improvement' (http://www.rsc.org/events/download/Document/cee7d4f2-9ff1-477b-b155-3e2492577d77) that brought together experts in a range of photosynthetic processes. A prominent theme of several of the presentations was the sensitivity of photosynthesis to rapid, rather than gradual, changes in environmental conditions. Of particular interest was the kinetic mismatch between fluctuations in photosynthetically active radiation (PAR), which can change by orders of magnitude within a second, and the relatively slow onset of photoprotective mechanisms [1,2]. Indeed, there is growing evidence that this mismatch can sensitize both photosystem I (PSI) and photosystem II (PSII) to oxidative photodamage [3,4]. The focus of the present paper is the irreversible damage to PSII (to D1 and other subunits) due to singlet oxygen (¹O₂) generated by PSII charge recombination. It has also been proposed that the slow reversal of photoprotection mechanisms can lead to loss of photochemical productivity when light levels are suddenly decreased [5,6]. Thus, such kinetic mismatches appear to be good engineering targets for increasing the efficiency and resilience of photosynthesis. Here, we present an extended re-examination of one of the key processes that controls and regulates photosynthesis, the thylakoid proton motive force (pmf), its components, and some emerging effects on photosynthetic reaction centres.

The energy-storing processes of photosynthesis start with the capture of PAR by photoactive pigments, transfer of the energy to specialized chlorophyll molecules in PSI and PSII, inducing the transfer of electrons through a series of redox intermediates to ultimately generate NADPH from NADP⁺ [7]. The electron transfer steps are tightly coupled to proton transfer reactions into the thylakoid lumen, storing potential energy in the pmf to drive the synthesis of ATP [8,9]. Both NADPH and ATP, in the correct ratios, are required for driving the assimilation of CO₂ and other cellular processes [10]. The electron and proton transfer processes can be highly efficient, but when energy capture outpaces the capacity of photosynthesis—a situation that can occur at high light and/or under adverse environmental conditions—reactive intermediates can accumulate in the photosynthetic apparatus, leading to generation of reactive oxygen species (ROS), mainly in PSI and mainly ¹O₂ in PSII, and these are responsible for oxidative photodamage. A range of photoprotective mechanisms have evolved to ameliorate photodamage and its effects, including non-photochemical quenching (NPQ) processes such as the q_E response [11], a complex cycle to repair damaged PSII [12], chloroplast movements [13], cyclic electron flow [14,15], redox tuning to redirect back-reactions to non-ROS producing pathways [16,17] and alternative electron acceptor systems [18,19]. Despite the diversity and complexity of these processes, in general, they result in the loss of light energy, for example, the decreased efficiency of light capture incurred by activation of NPQ [20], charge recombination [16] or the dissipation of redox energy when electrons are passed to the flavodiiron O₂ reductases [1]. Consequently, photosynthetic organisms appear to be constantly balancing the trade-offs between efficient photochemistry and the avoidance of toxic side reactions.

In higher plants and green algae, the pmf plays a central role in regulating key photoprotective mechanisms, by responding to changes in both energy input and the physiological status of the chloroplast [9]. It is, therefore, worthwhile to review the biophysical properties of the photosynthetic machinery that controls the partitioning of pmf into Δψ and ΔpH over different time-scales. In thermodynamic terms, the pmf can be described as the sum of two driving forces:

1.1

where Δψ and ΔpH represent the differences in electric field, expression difference in volts, and pH, respectively, between the lumenal and stromal faces of the thylakoid membrane, R is the universal gas constant and F is Faraday's constant. Over a broad range of physiological conditions, Δψ and ΔpH appear to be thermodynamically and kinetically equivalent drivers of the ATP synthase [21,22]. On the other hand, storing pmf in Δψ and ΔpH has distinct impacts on cellular processes. Most notably, storing energy in ΔpH imposes a substantial change in pH in one or more cellular compartments. In mitochondria, pmf is held mainly as Δψ, allowing enzymes to operate at optimal pH ranges. In chloroplasts, the build-up of ΔpH results in acidification of the thylakoid lumen, which acts to feedback regulate (or control) critical steps in the light reactions (reviewed in [19]), including (i) the activation of the photoprotective q_E response (through activation of violaxanthin deepoxidase and protonation of PsbS [11]); and (ii) ‘photosynthetic control' of electron flow at the cytochrome b₆f complex (reviewed in [23]), preventing the accumulation of electrons on PSI that would otherwise lead to severe PSI photodamage [1,2,19,24]. There have also been proposals that PSII can be regulated or inhibited [23,25] at low lumen pH, for example, by acid-induced release of Ca²⁺ from the oxygen-evolving complex (OEC), or by limiting electron flow by slowing of the OEC S-state transitions [25,26].

Early work on isolated thylakoids suggested that pmf was stored mainly as ΔpH, but more recent work suggests that a pure ΔpH pmf is incompatible with the known pH dependencies of photosynthetic processes [23,27]. A range of in vivo studies [4,19,24,28–32] support the view that the pmf is actively partitioned into Δψ and ΔpH components to avoid severe restrictions on b₆f activity or acid-induced damage to lumenal components, while balancing the needs for efficient energy storage and activation of lumen pH-responsive photoprotective processes [27]. These arguments are supported by our simulations (below) and straightforward thermodynamic considerations, which indicate that: with ΔG_ATP (the free energy of hydrolysis of ATP) between 40 and 45 kJ mol⁻¹, a stromal pH of 7.8, and the coupling stoichiometry for protons/ATP, n, of 4.67, the maximal lumen pH (even before illumination) should range between 6 and 6.5 units, near or below the pK_a values that govern the activation of q_E and the control of cytochrome b₆f activity. In short, with 100% ΔpH, the photosynthetic electron transport chain should be strongly downregulated even at low light. Nevertheless, there are opposing views that maintain pmf is stored almost exclusively in ΔpH under steady-state conditions [33]. It is worthwhile to note, however, that the phenomena discussed in this review are associated more with the dynamics of Δψ and ΔpH rather than their steady-state values.

In any case, the balancing of Δψ/ΔpH, and its kinetics, are dependent on the regulation of counter-ion homeostasis in the chloroplast [34], and recent work from several laboratories has identified putative components of these ion homeostatic machineries, including a thylakoid potassium channel [35], a K⁺/H⁺ antiporter [36], as well as transporters for other charged species [37–41]. There are also indications that the Δψ/ΔpH balance is controlled by the synthesis of membrane-permeable weak bases, such as putrescene, that effectively increase the proton buffering capacity of the lumen [42].

2. Interactions of the pmf with PSII: importance for energy storage and photodamage

The photosystems can be viewed as ‘energy traps' that capture energy from sunlight in the form of quasi-stable charge-separated states. To achieve this role, evolution has tuned the redox properties of reaction centre cofactors so that each progressive electron transfer reaction occurs more rapidly than the decay by other routes (e.g. back-reactions or charge recombination), successively stabilizing the resulting charge-separated states and minimizing the losses to back-reactions or recombination to the point where quantum efficiency is near unity but at the cost of free energy losses at each step [16]. Despite the high quantum yield of formation of stable charge-separated states, electron transfer back-reactions and charge recombination can occur, the rates of which depend on the energetics of the free energy gap, reorganizational energies and donor–acceptor distances between the oxidized and reduced components in the reaction centres [16,43,44]. For PSII, the most important recombination reaction (both in terms of rates and consequences for photodamage) occurs from the radical pair state (with P₆₈₀ oxidized and pheophytin reduced), which can be formed via both initial forward electron transfer, or by back-reactions via thermal activation of ‘stable’ intermediates in the PSII photocycle, e.g. , the state formed when dark-adapted PSII undergoes a single photochemical reaction. Further thermal activation of can repopulate the state, leading to essentially the full reversal of the initial light reactions, resulting in the emission of ‘delayed fluorescence' [45], though owing to the high energy of activation this process has a low quantum efficiency [45]. The intensity and temperature dependence of delayed fluorescence have been extensively used to estimate the energetics of reaction centres, and are potentially important probes for the more deleterious processes discussed below. More importantly for this discussion, the state can also decay non-radiatively, either directly to ground state, or via the triplet state of P₆₈₀ (³P₆₈₀) [46]. In turn, ³P₆₈₀ can interact with molecular O₂ to form singlet O₂ (¹O₂), a highly ROS that can damage both PSII and other cellular components [47].

The rates and yield of back-reactions leading to recombination should be accelerated under any conditions that make the energy gaps between and the subsequent radical pairs (e.g. ) shallower. For example, it is well known that when plants are treated with herbicides that are Q_B site inhibitors, such as 3-(3,4-dichlorophenyl)-1,1-dimethylurea (DCMU) or atrazine, which block electron transfer from to Q_B, the recombination reactions speed up by about 10- to 20-fold [48,49], and the enhanced formation of ¹O₂ triggers processes that can damage the cell. Our recent work describes a more physiological process that we term field recombination-induced photodamage (FRIP) in which large spikes in the photosynthetic Δψ, such as those caused by rapid fluctuations in light intensity, destabilize the PSII photochemically generated charge pairs, accelerating PSII back-reactions, charge recombination and ¹O₂ production [4]. Our results suggest that FRIP represents both a limitation for energy storage as well as a limitation to productivity from losses due to photodamage, especially under rapidly fluctuating conditions found in nature.

3. Computational exploration of the effects of altering pmf storage kinetics on q_E and field recombination-induced photodamage

NPQ and FRIP should both be sensitive to kinetic mismatches between the generation of Δψ and ΔpH and subsequent regulatory responses, and it is conceivable that engineering these processes could lead to improved photosynthesis. To test this possibility, we updated a previously published computational model for pmf [34,50] that describes how the intrinsic biophysical properties of the thylakoid system impact the extent and kinetics of pmf storage in Δψ and ΔpH, and how these properties may affect the susceptibility of photosynthesis to photodamage under rapidly fluctuating conditions. While simplified, our model recapitulates many key features of the pmf. The biophysical bases of the current model are similar to those presented in other models [51], and thus using our parameters, one would expect similar results. The updated model includes the effects of Δψ, ΔpH and Q_A redox state on FRIP. The code was written in Python 3.5 using open source modules and is presented in the form of a detailed Jupyter (www.jupyter.org) notebook, which is included in the electronic supplementary material and freely available online at Github (www.github.com/protonzilla/Delta_Psi_Py), allowing the reader to download, modify, extend and explore variations of the simulations presented here. The details of the code and references to the parameter set are presented in the extensive annotation in the code and accompanying explanatory notes in the electronic supplementary material and on the Github site.

4. The effects of ΔpH and Δψ on PSII recombination and ¹O₂ production in vivo

As illustrated in figure 1a, the cofactors in PSII are situated such that charge separation reactions occur across the low dielectric of the thylakoid membrane, and thus the movement of electrons from P₆₈₀ (near the luminal face), through pheophytin (Pheo) and to Q_A (near the stromal face) directly contribute to thylakoid Δψ. In addition, the oxidation of water at the OEC deposits protons into the lumen, while the reduction of plastoquinone (PQ) at the Q_B site takes up protons from the stroma, contributing to ΔpH. It follows that ‘backpressure' from either of the pmf components could accelerate recombination reactions, as has been amply demonstrated in past work [52,53]. However, Δψ and ΔpH should have differential effects on recombination depending on the properties of the charge pair involved. The Δψ component will primarily affect the energetics of ‘electrogenic' electron transfer reactions, i.e. those that occur vectorially across the thylakoid membrane, by shifting the equilibrium constant for these reactions towards the electron carrier closer to the lumenal side of the membrane (i.e. the positively charged side; figure 1b,c). The effect of Δψ on charge-separated states is dependent upon the physical distance between the redox cofactors and the perpendicular distance from the membrane edge, i.e. electron transfer between cofactors within the thylakoid membrane becomes progressively more destabilized by Δψ as the distance between charge-stable states spans larger distances across the membrane. For example, electron transfer from Pheo⁻ to Q_A moves a charge about halfway across the thylakoid dielectric, so that adding a Δψ of 120 mV should shift the free energy drop for this this reaction by about 60 meV, and alter the equilibrium constant for sharing the electron by a factor of about 10.

Figure 1.

Photosynthetic electron transfer energetics are influenced by membrane orientation and membrane potential. (a) PSII cofactors are oriented within the complex so that light-driven forward electron transfer induces the formation of a trans-thylakoid Δψ. Subsequent proton uptake (red arrows) at Q_B and release at the oxygen-evolving complex will contribute to the ΔpH. During linear electron flow, additional Δψ (blue arrows) is generated by light-induced charge separation in photosystem I, while both Δψ and ΔpH are generated by the Q-cycle at the cytochrome b₆f complex. (b) The loss of free energy during PSII forward electron transfer energetically stabilizes (thick lines) the charge-separated state, impeding (thin lines) recombination. (c) Imposing either Δψ or ΔpH decreases this stabilization energy, increasing the rate of recombination, leading to the generation of ³P680, which can interact with O₂ to form the toxic ¹O₂ species.

The ΔpH component, on the other hand, should primarily affect recombination reactions that involve the uptake or deposition of protons into the aqueous compartments. The pH of the stroma is thought to be relatively constant in the light, ranging between 7.0 in the dark to 8.0 in the light [54,55]. This pH change has a differential effect on versus , which are both located on the stromal side of the protein, during the initial dark–light transition in stromal pH. is unaffected by the light-induced alkalization of the stroma because no protonation reactions are involved in its redox chemistry. For , however, a proton is taken up when it is formed, and so a proton must be released when it is oxidized, thus favouring re-oxidation of with increasing stromal pH and destabilization of the semiquinone [56]. This affect, however, is likely to remain constant during the course of the day in chloroplasts, as the stromal pH appears relatively stable. On the luminal side, a decreased lumen pH via proton transfer reactions will destabilize the OEC S-states if the redox transition involves proton release. Past work [57] suggests that, over the relevant lumenal pH range (approx. from 5.5 to 7.5), the proton release pattern is 1, 0, 1, 2 for transitions S₀ → S₁, S₁ → S₂, S₂ → S₃ and S₃ → S₄ → S₀. The respective back-reactions should involve proton uptake by the OEC, and thus will be destabilized by low lumen pH. The S₀ → S₁ and S₃ → S₄ → S₀ transitions are considered to be irreversible, so once formed should not be prone to recombination. S₂ and S₃ recombine with and (with the back-reaction via as the dominant pathway); however, because the S₂ → S₁ back-reaction does not involve a proton transfer its rate should be unaffected by lowering the lumen pH. Therefore, only PSII centres in the S₃ state should display pH-dependent increases in recombination rates due to lowering the lumen pH (by 10-fold for a decrease of 1 pH unit). By contrast, Δψ should affect recombination for both S₂ and S₃ states. Under continuous light, the S-states are likely to be evenly distributed, so that Δψ should have about twice the effect of an energetically equivalent ΔpH on PSII recombination as it would affect approximately twice as many PSII centres.

The rate of recombination will also be affected by the redox state of the PSII electron acceptor Q_A, which is also influenced by the pmf. The reduced form, , accumulates when the rate of its photoreduction exceeds that of re-oxidation by downstream electron carriers, feeding electrons into the recombination pathways. Activation of q_E upon lowering the lumen pH as ΔpH builds up, results in decreases in the PSII excitation rate and thus the fraction of centres with . Antagonistically, pH-mediated downregulation of cytochrome b₆f turnover will slow the oxidation of PQH₂, increasing the fraction of centres with reduced as electron acceptors become limited.

5. Control of the extent and kinetics of pmf partitioning

At the first level, the partitioning of pmf into Δψ and ΔpH is controlled by the biophysical properties of the chloroplast compartments. The electrical capacitance of the thylakoid membrane is small (approx. 0.6 µF cm⁻²) [58] so that trans-thylakoid transfer of a single electron for each PSII centre can generate a rather large Δψ of about 30 mV, which is equivalent to an electric field across the membrane of about 50 000 V cm⁻¹ [59] as seen in the simulations of pmf after a single turnover excitation of PSI and PSII (see electronic supplementary material, Jupyter notebook, electronic supplementary material, figure S1a). On the other hand, the proton buffering capacity (β) of the lumenal compartment is quite high (β ∼ 0.03 M per pH) [60], so that the same single turnover flash should produce a very small change in lumen pH (approx. 0.001 units; electronic supplementary material, figure S1a). Changing the pH from 7 to 6 would require the deposition of 0.03 M of protons into the lumen (compared with approx. 10⁻⁶ M in the absence of lumen buffering groups).

These basic biophysical properties explain, in large part, why in early times (typically tens of seconds [4,34]) after illumination, pmf is predominantly composed of Δψ. As illustrated in figure 2a, and in the simulations in figure 3a.1–a.5, in a simple thylakoid membrane with no counter-ion channels, pmf remains predominantly as Δψ indefinitely, because Δψ by itself is sufficient to force protons deposited in the lumen back out through the ATP synthase, resulting in only small net changes in lumen pH. This situation is the predominant mode of action for mitochondrial and plasma membrane ATP synthase activity (reviewed in [61]) and likely allows pH-sensitive biochemical processes occurring in the internal spaces to proceed unhampered by large changes in proton concentrations. As shown in the simulation, the continuous presence of high Δψ (figure 3a.1) leads to destabilization of the PSII charge pairs, while the lack of ΔpH (figure 3a.2) prevents the formation of q_E (figure 3a.3), resulting in accumulation of reduced (figure 3a.4). The combination of these factors favours PSII back-reactions leading to recombination, producing large amounts of ¹O₂ (figures 3a.4 and a.5).

Figure 2.

Illustration of the factors contributing to the balancing of pmf into Δψ and ΔpH during different phases of illumination. The blue arrows on the upper thylakoid membrane show the directions of transmembrane electron flow that generates Δψ, while the red arrows show the uptake and deposition of protons that generates ΔpH. The semi-transparent arrows passing over the ATP synthase indicate the relative contributions of Δψ (blue) and ΔpH (red) to the ATP synthase reaction. (a) At early times after illumination, pmf is stored predominantly in Δψ, owing to the low electrical capacitance of the thylakoid membrane and the large proton buffering capacity of the lumen. The high Δψ effectively drives the efflux of protons from the lumen through the ATP synthase, maintaining a low ΔpH. (b) Activating counter-ion fluxes dissipates a fraction of Δψ, allowing additional proton influx and less efflux, which gradually protonates lumenal buffering groups, forming a ΔpH. (c) Counter-ion fluxes establish ion gradients that eventually reach a local equilibrium with Δψ, leading to a steady-state ratio of Δψ : ΔpH. The generation of ΔpH is then capable of downregulating cytochrome b₆f turnover (triangle) as well as activating q_E (dark blue circle).

Figure 3.

Simulated responses of thylakoid pmf components, linear electron flow, ion fluxes and ¹O₂ production during a 5-min light pulse. The simulations were performed using the DeltaPsi.py programme and initial values described in electronic supplementary material, Appendix S1. The timing and amplitude (maximum of 300 µmol photons m⁻² s⁻¹) of the excitation light are indicated by the light red coloured blocks. Simulations were repeated with the thylakoid permeability to counter-ions set at 0 (a.1–a.5), ‘normal' to approximately simulate the kinetics seen in leaves (b.1–b.5), and ‘fast' (10-fold faster than normal, c.1–c.5). (1) Light-induced changes in pmf (green dashed curves), Δψ (blue solid curves) and ΔpH (red dashed curves), all expressed in units of volts, so that a ΔpH of one is equivalent to 0.06 V. (2) The lumen pH (red, solid curves) and the relative rate constant for oxidation of PQH₂ at the cytochrome b₆f complex (blue dashed curves). (3) The responses of q_E (NPQ, green dashed curves) together with the concentration of counter-ions in the lumen, [K⁺] (black solid curves). (4) The fraction of Q_A in its reduced form (, green dashed curves) and the rate of ¹O₂ production (red solid curves) due to FRIP (s⁻¹ PSII⁻¹). (5) The cumulative LEF (green dashed curves) and ¹O₂ production (solid red curves). Note that the pmf parameters are shown as light-induced changes, relative to dark values. A version of this figure without this offset is included in the Jupyter notebook in electronic supplementary material, figure S2 and shows that pmf in the dark is preferentially stored in ΔpH, but as pmf increases, it progressively favours Δψ. LEF, linear electron flow.

As illustrated in figure 2b, adding an ion channel to the thylakoid membrane allows counter-ions to move across the membrane, down the Δψ gradient. For example, the simulation in figure 3b.1–b.5 shows the movement of K⁺ (figure 3b.3) in response to Δψ, from the lumen to the stroma, progressively dissipating Δψ (figure 3b.1), while depleting the lumen of K⁺. Anions, such as Cl⁻, will also dissipate Δψ, but in this case, they tend to accumulate in the lumen [62]. In either case, the resulting loss of Δψ slows the efflux of protons through the ATP synthase, allowing additional protons to be transferred to the lumen. Over time, the accumulation of protons overcomes the lumen buffering capacity, increasing ΔpH (figure 3b.1–b.2) at the expense of Δψ (see discussion in [8,34]). As illustrated in figure 2c and simulated in figure 3b.1, ion fluxes cannot completely dissipate Δψ because the resulting counter-ion gradient will eventually prevent further movements, and the extent to which Δψ is dissipated will thus depend, in part, on the starting concentrations of these ions in the stroma and lumen as well as the presence of other ion transporters and proton buffers (see discussion in [34,50]). The simulation in figure 3b.1–b.5 began with stromal and lumenal K⁺ concentration of 40 mM, and resulted in Δψ : ΔpH of about 1 : 2 in the light. It is also clear from these simulations that, even in this simplified situation, Δψ : ΔpH can change with conditions, as is evident by the fact that Δψ : ΔpH increases as a result of the build-up of counter-ion gradients at higher pmf (see electronic electronic supplementary material,, Jupyter notebook in figure S1). The simulations in column C will be discussed below.

In any case, allowing counter-ion flow results in dissipation of Δψ (figure 3b.1), the build-up of ΔpH that acidifies the lumen (figure 3b.2) and activates q_E (figure 3b.3), which decreases the fraction of reduced Q_A (figure 3b.4). The combined effect of these changes is a decrease in ¹O₂ production when compared to the case with no counter-ion fluxes (figures 3b.4 and b.5), but at the expense of linear electron flow (LEF) (figure 3b.5).

From the above, we can conclude that the basic properties of the thylakoids allow Δψ to appear very rapidly upon illumination, whereas ΔpH is formed much more slowly, with a half time on the time-scale of several minutes [34], and that these kinetics are likely to affect the onset of photoprotective mechanisms. This kinetic mismatch can be exacerbated by the fact that at sub-saturating light, PSI and PSII centres will have access to relatively large pools of electron acceptors and donors, so that an abrupt increase in light may induce multiple turnovers, producing the large Δψ spikes that result in damaging back-reactions and recombination reactions.

Thylakoid properties also control the rate of ΔpH relaxation (and thus q_E recovery) when light is decreased, though the mechanism is more complex. As described in Cruz et al. [9,34], when the light is switched off, electron flow in the reaction centres is inhibited, but proton efflux through the ATP synthase continues, which causes rapid changes in Δψ (in the opposite direction to that induced by light-driven electron flow). Because of the low thylakoid capacitance and high lumen β, the changes in Δψ are far larger than ΔpH, and continue until an ‘inverted' Δψ is established. At this point, the total pmf (Δψ + ΔpH) is approximately equal to the backpressure from ATP hydrolysis (i.e. pmf ≈ ΔG_ATP/n), so the driving force for proton efflux is near zero, slowing down further proton efflux until counter-ion fluxes occur. When measuring Δψ changes in leaves using the electrochromic shift (ECS), this behaviour appears as the ‘negative' ECS_inv phase, which is used to estimate light-induced ΔpH [9,34], but it is important to note that these phases occur over the background level of Δψ from equilibration with ATP hydrolysis (ΔG_ATP) in the dark, as can be seen when the simulations are plotted without offsets in the pmf parameters (see electronic supplementary material, figure S3).

Under natural field conditions in a plant canopy or an aquatic environment, light can fluctuate over a wide range of time-scales, from less than a second for wind-induced leaf movements or sunflecks and water focusing, seconds–minutes for changes in cloud cover, and hours for the position of the sun [63]. Different regulatory processes contribute to photoprotection over these time-scales. Some photoprotection processes respond over the scale of many minutes to hours [64], including the xanthophyll cycle reactions, the PSII photoinhibition/repair cycle and chloroplast movements. These slow processes are unable to respond to the more rapid fluctuations, but will approach steady-states reflecting the conditions averaged over the many minutes-to-hours time-scale. Antenna state-transitions respond over the medium times-scales, but appear to be more important in green algae than higher plants [65]. Intriguingly, the remaining, rapidly responding photoprotective processes are all controlled (directly or indirectly) by lumen pH, most importantly the adjustment of q_E and the photosynthetic control of electron flow at the cytochrome b₆f complex, and are thus likely to be limited by the slow rates of ΔpH formation and decay.

This conclusion is in line with simulations in figure 3c.1–c.5, which shows that increasing the permeability of the thylakoid to counter-ions by 10-fold compared with ‘normal', increased the rate of relaxation of Δψ (figure 2c.1), leading to faster onset of ΔpH (figure 3c.1 and c.2) and thus q_E (figure 3c.3). The overall effect is a decrease in ¹O₂ production (figure 3c.4 and c.5) owing to both a decreased Δψ and (figure 3c.4). The potentially beneficial effects of increasing the permeability of the thylakoid to counter-ion movements can be seen by comparing figure 2b.5 and c.5, showing that the early, rapid accumulation of ¹O₂ is strongly supressed as ΔpH builds up. However, there is also a trade-off in loss of LEF, caused by increased control of PQH₂ oxidation (figure 3b.4 and c.4).

The effects of counter-ion permeability on photosynthesis are highly dependent on the rates of fluctuation of the light, as is seen in the simulations in figure 4 that compare the effects of low frequency light changes (a 1 hour sine wave, figure 4a.1–2 and b.1–2) or high frequency light changes (a 1 h duration of a sine wave with period of 10 min, figure 4c.1–2 and d1–2). Overall, the lower frequency changes produced lower rates of ¹O₂ production and increased linear electron flow (LEF) relative to the higher frequency changes, consistent with the expected frequency dependence of saturation effects. Increasing counter-ion permeability 10-fold (figure 4b.1–2) had almost no effect on the simulated photosynthetic parameters under the slowly changing sinusoidal light. By contrast, the same change in counter-ion permeability had large effects under the higher frequency square wave illumination (figure 4d.1–2), causing a twofold decrease in ¹O₂ under the fluctuating light, mainly due to the suppression of large Δψ spikes that occurred during the rapid increases in light intensity. This protection from ¹O₂ production, however, comes at the cost of approximately 20% decrease in LEF compared with the low frequency changes.

Figure 4.

Simulated responses of thylakoid pmf components, linear electron flow (LEF) and ¹O₂ production during a 1-h light sine wave. Simulations and annotations were as in figure 3, but with illumination set to a 1-h sine wave (a.1, a.2, b.1, b.2) or a 1-h square wave (c.1, c.2, d.1, d.2) both with peak intensity of 300 µmol photons m⁻² s⁻¹. Simulations were repeated with the thylakoid permeability to counter-ions set to ‘normal' (a.1, a.2, c.1, c.2) or ‘fast' (10-fold faster than normal, b.1, b.2, d.1, d.2). (a) Light-induced changes (with respect to the dark values) in pmf, Δψ and ΔpH, all expressed in units of volts, so that a ΔpH of one is equivalent to 0.06 V. (b) The cumulative LEF and ¹O₂ productions. Full datasets for these simulations are presented in the Jupyter notebook in electronic supplementary material, figure S3.

6. Can we improve photosynthesis by modifying pmf partitioning to make photosynthesis more robust?

The results from our model lead us to predict that increasing the rates of counter-ion fluxes across the thylakoid could, in principle, lead to improved photosynthetic performance, though the improvement is predicted to be the long-term advantage of decreased photodamage rather than the short-term gain from increased LEF [66].

Given that the slow rates of ion fluxes are likely due at least in part to low protein levels of ion transporters in the thylakoids, a strategy of overexpressing the rate-limiting channels could be suggested. However, if better photosynthesis could be achieved this simply, plants might be expected to have already evolved more rapid ion fluxes than those measured in laboratories. Indeed, exploring these properties in natural populations may reveal precisely these sorts of variations.

On the other hand, increasing ion fluxes may lead to secondary, deleterious effects. A basic tenet of the model is that ΔpH cannot form without the movements of counter-ions, and thus, for each proton that accumulates in the lumen, approximately an equal number of counter-ion charges must be moved to dissipate the Δψ. In effect, energy stored in Δψ is consumed, at least temporarily, in the movement of counter-ions, removing the ATP synthase driving force and preventing proton efflux through the ATP synthase. The diversion of protons away from ATP synthase efflux then allows protons to enter the lumen buffering pool, allowing ΔpH to form more rapidly as protons are no longer being driven out of the lumen by Δψ and the buffering capacity is overcome. Thus, one consequence of ΔpH formation will be a transient decrease in the LEF output ratio of ATP/NADPH due to the time-dependence of overcoming the lumen buffering capacity. Metabolic congestion and photodamage can occur if this ratio does not precisely match that needed to power assimilation, requiring alternative electron transfer processes, such as cyclic electron flow or the water–water cycle, to make up the balance [10]. Our simulations suggest that a slow ΔpH formation (half time of about 4 min) results in a counter-ion related deficit of about 0.05 ATP per CO₂ fixed by assimilation, which should be easily remedied by alternative electron transfer processes (figure 5). With a 10-fold faster ΔpH formation provided by increased counter-ion flux, the resulting ATP deficit caused by counter-ion movements can become severe, requiring a 10-fold higher input of ATP per CO₂ fixed (figure 5c), which may exceed the capacity for cyclic electron flow in some species.

Figure 5.

Effects of thylakoid counter-ion fluxes on the ATP/NADPH budget of photosynthesis. Data are taken from the simulations performed in figure 3, with x-axis origin set to the beginning of illumination. (a) The light-induced flux of counter-ions (K⁺), with positive values representing net flux out of the lumen. (b) The proton deficit, i.e. the protons deposited into the lumen but buffered so that they are unavailable to the ATP synthase. (c) The cumulative deficit in molecules of ATP relative to PSI turnover needed for CO₂ fixation by the Calvin–Benson cycle. The red, yellow, green and blue lines represent results with the thylakoid counter-ion permeability set to zero, ‘normal' (figure 3), 10× normal and 100× normal, respectively.

The osmotic balance of the chloroplast compartments must also be finely tuned to maintain their structure and the function of proteins residing within each compartment, and even small osmotic imbalances can lead to swelling-induced loss of thylakoid stacking, or shrinkage-induced inhibition of the interactions of plastocyanin with PSI [34,62,67]. Proton translocation by itself should not appreciably affect the osmotic potential of the lumen because most protons are buffered. By contrast, counter-ion movements will very likely change the concentrations of free counter-ions, and thus have a colligative effect on the osmolarities of the lumen and stroma. It is interesting to note that loss of the chloroplast potassium KEA (the potassium–proton antiporter in the thylakoid membrane) transporters leads to swelling and disordering of the thylakoid structure [37], suggesting that fine-tuning of the thylakoid ion balance is critical for osmoregulation. It is also suggestive that Chlamydomonas cells are able to compensate for severe hyperosmotic shock-induced lumenal shrinkage, but only over the same time-scale as ΔpH formation, i.e. about 5–10 min [68]. It is thus possible that the rate of pmf partitioning is limited by the need to prevent acute osmotic imbalances that could result in structural perturbations.

At this point, the model is not intended to reproduce all the reactions of photosynthesis. Nevertheless, using reasonable, published values for thylakoid properties (see electronic supplementary material, Appendix S1), the model qualitatively reproduced the FRIP behaviours observed by Davis et al. [4], including light fluctuation-induced Δψ spikes, that result in increased recombination, ¹O₂ production and the accumulation of photodamage.

This simplified model also suggests that accelerations in counter-ion fluxes will result in tuned increases in the rate of NPQ onset, which will have a potentially beneficial effect by decreasing ¹O₂-related photodamage and accelerating q_E responses, but this will be at the cost of decreasing LEF. This suggestion is interesting in the light of the recent work of Kromdijk et al. [6], who reported that more rapid NPQ responses can increase plant yield by increasing PSII quantum efficiency (and thus LEF). Our simulations suggest an alternative explanation: that the underlying benefit of more rapid responses will be decreases in both ROS production and photodamage, leading to more sustained photosynthesis and lower input costs over the long term. Interestingly, further modifications of photosynthetic parameters in our simulations show that the trade-off loss of LEF can be avoided by decreasing the pK_a for controlling the cytochrome b₆f complex to well below that for initiation of q_E, but this may lead to less control of electron flow at the cytochrome b₆f complex and over-reduction of PSI and subsequent PSI photodamage [19].

At the very least, recent results and the simulations they inspire suggest possible targets for plant improvement, and generate testable hypotheses. Ultimately, improving photosynthesis will require understanding the multiple constraints that life in the real world imposes on photosynthesis, as well as the multiple, interacting regulatory systems that have evolved to cope with them. Approaching this complex problem will require a larger scale investigation of the responses of pmf in a range of species, and under field-like conditions, as well as a deeper understanding of how the biophysical machinery of photosynthesis is integrated with the host organism to respond to the challenges of rapidly fluctuating environmental conditions.

From the simulations presented above, taking steps towards such an integrated view can reveal emergent properties of the system that were not apparent from studies of isolated complexes. Towards that end, it is hoped that future work (by us and others) will expand the model presented here to test the effects of important processes, including newly discovered ion transport systems and their regulation [69,70], effects on thylakoid osmotic balance [71], the PSII damage/repair cycle [72,73], the accumulation of electrons on the acceptor side of PSI (which can lead to irreversible PSI photodamage [74]), alternative modes of PSII regulation including the recent report of bicarbonate-mediated protective redox tuning [17], regulation of the ATP synthase, and the need for alternative electron transfer pathways.

Holistically, an expansive mechanistic model of photosynthetic regulation will likely provide immediate targets for testing the effects of engineered changes aimed at improving photosynthetic yields. When the model fails to replicate experimental results, it has the potential not only to focus attention on gaps in our understanding of photosynthesis and its regulation but also to provide insights that could help to fill these gaps.

Data accessibility

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Authors' contributions

D.M.K. designed and wrote the computational model. G.A.D., A.W.R., D.M.K. contributed to the design of simulation trials and the interpretation of results. G.A.D., A.W.R., D.M.K. contributed to drafting and revising the article.

Competing interests

We have no competing interests.

Funding

Work performed by G.A.D. and D.M.K. was supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under award number DE-FG02-91ER20021. A.W.R. was supported by the Biotechnology and Biological Sciences Research Council grant nos. BB/K002627/1 and BB/L011206/1 and the Royal Society Wolfson Research Merit Award.