Modeling the light-induced electric potential difference ΔΨ across the thylakoid membrane based on the transition state rate theory

Dynamic modulation of transthylakoid electric potential by chloroplast ATP synthases

The light-induced transthylakoid membrane potential (ΔΨm) can function as a driving force to help catalyzing the formation of ATP molecules, proving a tight connection between ΔΨm and the ATP synthase. Naturally, a question can be raised on the effects of altered functioning of ATP synthases on regulating ΔΨm, which is attractive in the area of photosynthetic research. Lots of findings, when making efforts of solving this difficulty, can offer an in-depth understanding into the mechanism behind. However, the functional network on modulating ΔΨm is highly interdependent. It is difficult to comprehend the consequences of altered activity of ATP synthases on adjusting ΔΨm because parameters that have influences on ΔΨm would themselves be affected by ΔΨm. In this work, a computer model was applied to check the kinetic changes in polarization/depolarization across the thylakoid membrane (TM) regulated by the modified action of ATP synthases. The computing data revealed that under the extreme condition by numerically "switching off" the action of the ATP synthase, the complete inactivation of ATP synthase would markedly impede proton translocation at the cytb6f complex. Concurrently, the KEA3 (CLCe) porter, actively pumping protons into the stroma, further contributes to achieving a sustained low level of ΔΨm. Besides, the quantitative consequences on every particular component of ΔΨm adjusted by the modified functioning of ATP synthases were also explored. By employing the model, we bring evidence from the theoretical perspective that the ATP synthase is a key factor in forming a transmembrane proton loop thereby maintaining a propriate steady-state ΔΨm to meet variable environmental conditions.

From leaf to multiscale models of photosynthesis: applications and challenges for crop improvement

To keep up with the growth of human population and to circumvent deleterious effects of global climate change, it is essential to enhance crop yield to achieve higher production. Here we review mathematical models of oxygenic photosynthesis that are extensively used, and discuss in depth a subset that accounts for diverse approaches providing solutions to our objective. These include models (1) to study different ways to enhance photosynthesis, such as fine-tuning antenna size, photoprotection and electron transport; (2) to bioengineer carbon metabolism; and (3) to evaluate the interactions between the process of photosynthesis and the seasonal crop dynamics, or those that have included statistical whole-genome prediction methods to quantify the impact of photosynthesis traits on the improvement of crop yield. We conclude by emphasizing that the results obtained in these studies clearly demonstrate that mathematical modelling is a key tool to examine different approaches to improve photosynthesis for better productivity, while effective multiscale crop models, especially those that also include remote sensing data, are indispensable to verify different strategies to obtain maximized crop yields.

Effect of ion fluxes on regulating the light-induced transthylakoid electric potential difference

The light-induced transthylakoid membrane potential (ΔΨ) can not only drive the ATP synthesis through the ATP-synthase in chloroplasts but serve as an essential modifier in the acclimation of photosynthesis to fluctuating light conditions. It has been manifested that during photosynthesis, the light-induced ΔΨ is responsive to multiple factors among which the ion channels/transporters (e.g., V-K⁺, VCCN1, and KEA3) are key to adjust the ion distribution on the two sides of the thylakoid membrane and hence shape the kinetics of ΔΨ. However, an in-depth mechanistic understanding of ion fluxes on adjusting the transthylakoid electric potentials is still unclear. This lack of a mechanistic understanding is due to the experimental difficulty of closely observing ion fluxes in vivo and also hacking the evolution of parameters in a highly intertwined photosynthetic network. In this work, a computer model was applied to investigate the roles of ion fluxes on adjusting transthylakoid electric potentials upon a temporal cycle of a period of high illumination followed by a dark-adapted phase. The computing data revealed that, firstly, upon illumination, the dissipation of the steady-ΔΨ by ∼10 mV is contributed from the V-K⁺-driven K⁺ flux whilst ∼8 mV of the steady-ΔΨ is dissipated by the VCCN1-pumped Cl^- flux, but there were no appreciable KEA3-evoked variations on ΔΨ; secondly, on transition from high light to darkness, V-K⁺ and KEA3 are serving as major contributors whereas VCCN1 taking a counterbalancing part in shaping a standard trace of ECS (electrochromic shift), which commonly shows a sharp fall to a minimum before returning to the baseline in darkness. Besides, the functional consequences on components of ΔΨ adjusted by every particular ion channel/transporter were also explored. By employing the model, we bring evidence that particular thylakoid-harbored proteins, namely V-K⁺, VCCN1, and KEA3, function by distinct mechanisms in the dynamic adjustment of electric potential, which might be mainly importnat under fluctuating light conditions.

Insights on the regulation of photosynthesis in pea leaves exposed to oscillating light

Plants growing in nature often experience fluctuating irradiance. However, in the laboratory, the dynamics of photosynthesis are usually explored by instantaneously exposing dark-adapted plants to constant light and examining the dark-to-light transition, which is a poor approximation of natural phenomena. With the aim creating a better approximation, we exposed leaves of pea (Pisum sativum) to oscillating light and measured changes in the functioning of PSI and PSII, and of the proton motive force at the thylakoid membrane. We found that the dynamics depended on the oscillation period, revealing information about the underlying regulatory networks. As demonstrated for a selected oscillation period of 60 s, the regulation tries to keep the reaction centers of PSI and PSII open. We present an evaluation of the data obtained, and discuss the involvement of particular processes in the regulation of photosynthesis. The forced oscillations provided an information-rich fingerprint of complex regulatory networks. We expect future progress in understanding these networks from experiments involving chemical interventions and plant mutants, and by using mathematical modeling and systems identification and control tools.

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

The transthylakoid membrane potential (ΔΨm) 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 ΔΨm component is physiologically important in the acclimation of photosynthesis to environmental stresses. It has been shown that ΔΨm is the sum of the Donnan potential difference (ΔΨdn) and the diffusion potential difference (ΔΨd). Specifically, ΔΨdn, ΔΨd, and ΔΨm 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 (ΔΨdn, ΔΨd, and ΔΨm) 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 ΔΨm, 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.

Photosynthesis dynamics and regulation sensed in the frequency domain

Foundations of photosynthesis research have been established mainly by studying the response of plants to changing light, typically to sudden exposure to a constant light intensity after dark acclimation or light flashes. This approach remains valid and powerful, but can be limited by requiring dark acclimation before time-domain measurements and often assumes that rate constants determining the photosynthetic response do not change between dark and light acclimation. We show that these limits can be overcome by measuring plant responses to sinusoidally modulated light of varying frequency. By its nature, such frequency-domain characterization is performed in light-acclimated plants with no need for prior dark acclimation. Amplitudes, phase shifts, and upper harmonic modulation extracted from the data for a wide range of frequencies can target different kinetic domains and regulatory feedbacks. The occurrence of upper harmonic modulation reflects nonlinear phenomena, including photosynthetic regulation. To support these claims, we measured chlorophyll fluorescence emission of the green alga Chlorella sorokiniana in light that was sinusoidally modulated in the frequency range 1000-0.001 Hz. Based on these experimental data and numerical as well as analytical mathematical models, we propose that frequency-domain measurements can become a versatile tool in plant sensing.

Model quantification of the light-induced thylakoid membrane processes in Synechocystis sp. PCC 6803 in vivo and after exposure to radioactive irradiation

Measurements of OJIP-SMT patterns of fluorescence induction (FI) in Synechocystis sp. PCC 6803 (Synechocystis) cells on a time scale up to several minutes were mathematically treated within the framework of thylakoid membrane (T-M) model (Belyaeva et al., Photosynth Res 140:1-19, 2019) that was renewed to account for the state transitions effects. Principles of describing electron transfer in reaction centers of photosystems II and I (PSII and PSI) and cytochrome b₆f complex remained unchanged, whereas parameters for dissipative reactions of non-radiative charge recombination were altered depending on the oxidation state of Q_B-site (neutral, reduced by one electron, empty, reduced by two electrons). According to our calculations, the initial content of plastoquinol (PQH₂) in the total quinone pool of Synechocystis cells adapted to darkness for 10 min ranged between 20 and 40%. The results imply that the PQ pool mediates photosynthetic and respiratory charge flows. The redistribution of PBS antenna units responsible for the increase of Chl fluorescence in cyanobacteria (qT_{2 → 1}) upon state 2 → 1 transition or the fluorescence lowering (qT_{1 → 2}) due to state 1 → 2 transition were described in the model by exponential functions. Parameters of dynamically changed effective cross section were found by means of simulations of OJIP-SMT patterns observed on Synechocystis cells upon strong (3000 μmol photons m^-2s^-1) and moderate (1000 μmol photons m^-2s^-1) actinic light intensities. The corresponding light constant values kL_ΣAnt = 1.2 ms^-1 and 0.4 ms^-1 define the excitation of total antenna pool dynamically redistributed between PSII and PSI reaction centers. Although the OCP-induced quenching of antenna excitation is not involved in the model, the main features of the induction signals have been satisfactorily explained. In the case of strong illumination, the effective cross section decreases by approximately 33% for irradiated Synechocystis cells as compared to untreated cells. Under moderate light, the irradiated Synechocystis cells showed in simulations the same cross section as the untreated cells. The thylakoid model renewed with state transitions description allowed simulation of fluorescence induction OJIP-SMT curves detected on time scale from microseconds to minutes.

Photovoltage generation by photosystem II core complexes immobilized onto a Millipore filter on an indium tin oxide electrode

The light-induced functioning of photosynthetic pigment-protein complex of photosystem II (PSII) is linked to the vectorial translocation of charges across the membrane, which results in the formation of voltage. Direct measurement of the light-induced voltage (∆V) generated by spinach oxygen-evolving PSII core complexes adsorbed onto a Millipore membrane filter (MF) on an indium tin oxide (ITO) electrode under continuous illumination has been performed. PSII was shown to participate in electron transfer from water to the ITO electrode, resulting in ∆V generation. No photovoltage was detected in PSII deprived of the water-oxidizing complex. The maximal and stable photoelectric signal was observed in the presence of disaccharide trehalose and 2,6-dichloro-1,4-benzoquinone, acting as a redox mediator between the primary quinone acceptor Q_A of PSII and electrode surface. Long time preservation of the steady-state photoactivity at room temperature in a simple in design ITO|PSII-MF|ITO system may be related to the retention of water molecules attached to the PSII surface in the presence of trehalose.

Photosynthesis: basics, history and modelling

BACKGROUND

With limited agricultural land and increasing human population, it is essential to enhance overall photosynthesis and thus productivity. Oxygenic photosynthesis begins with light absorption, followed by excitation energy transfer to the reaction centres, primary photochemistry, electron and proton transport, NADPH and ATP synthesis, and then CO2 fixation (Calvin-Benson cycle, as well as Hatch-Slack cycle). Here we cover some of the discoveries related to this process, such as the existence of two light reactions and two photosystems connected by an electron transport 'chain' (the Z-scheme), chemiosmotic hypothesis for ATP synthesis, water oxidation clock for oxygen evolution, steps for carbon fixation, and finally the diverse mechanisms of regulatory processes, such as 'state transitions' and 'non-photochemical quenching' of the excited state of chlorophyll a.

SCOPE

In this review, we emphasize that mathematical modelling is a highly valuable tool in understanding and making predictions regarding photosynthesis. Different mathematical models have been used to examine current theories on diverse photosynthetic processes; these have been validated through simulation(s) of available experimental data, such as chlorophyll a fluorescence induction, measured with fluorometers using continuous (or modulated) exciting light, and absorbance changes at 820 nm (ΔA820) related to redox changes in P700, the reaction centre of photosystem I.

CONCLUSIONS

We highlight here the important role of modelling in deciphering and untangling complex photosynthesis processes taking place simultaneously, as well as in predicting possible ways to obtain higher biomass and productivity in plants, algae and cyanobacteria.

Chloride involvement in the synthesis, functioning and repair of the photosynthetic apparatus in vivo

Cl^- has long been known as a micronutrient for oxygenic photosynthetic resulting from its role an essential cofactor for photosystem II (PSII). Evidence on the in vivo Cl^- distribution in Spinacia oleracea leaves and chloroplasts shows that sufficient Cl^- is present for the involvement in PSII function, as indicated by in vitro studies on, among other organisms, S. oleracea PsII. There is also sufficient Cl^- to function, with K⁺ , in parsing the H⁺ electrochemical potential difference (proton motive force) across the illuminated thylakoid membrane into electrical potential difference and pH difference components. However, recent in vitro work on PSII from S. oleracea shows that oxygen evolving complex (OEC) synthesis, and resynthesis after photodamage, requires significantly higher Cl^- concentrations than would satisfy the function of assembled PSII O₂ evolution of the synthesised PSII with the OEC. The low Cl^- affinity of OEC (re-)assembly could be a component limiting the rate of OEC (re-)assembly.

Variable fluorescence of closed photochemical reaction centers

Chlorophyll fluorescence induction during 0.4 to 200 ms multiple-turnover pulses (MTP) was measured in parallel with O₂ evolution induced by the MTP light. Additionally, a saturating single-turnover flash (STF) was applied at the end of each MTP and the total MTP +STF O₂ evolution was measured. Quantum yield of O₂ evolution during the MTP transients was calculated and related to the number of open PSII centers, found from the STF O₂ evolution. Proportionality between the number of open PSII and their running photochemical activity showed the quantum yield of open PSII remained constant independent of the closure of adjacent centers. During the induction, total fluorescence was partitioned between F_o of all the open centers and F_c of all the closed centers. The fluorescence yield of a closed center was 0.55 of the final F_m while less than a half of the centers were closed, but later increased, approaching F_m to the end of the induction. In the framework of the antenna/radical pair equilibrium model, the collective rise of the fluorescence of centers closed earlier during the induction is explained by an electric field, facilitating return of excitation energy from the Pheo^- P680⁺ radical pair to the antenna.

Mg2+ homeostasis and transport in cyanobacteria - at the crossroads of bacterial and chloroplast Mg2+ import

Magnesium cation (Mg2+) is the most abundant divalent cation in living cells, where it is required for various intracellular functions. In chloroplasts and cyanobacteria, established photosynthetic model systems, Mg2+ is the central ion in chlorophylls, and Mg2+ flux across the thylakoid membrane is required for counterbalancing the light-induced generation of a ΔpH across the thylakoid membrane. Yet, not much is known about Mg2+ homoeostasis, transport and distribution within cyanobacteria. However, Mg2+ transport across membranes has been studied in non-photosynthetic bacteria, and first observations and findings are reported for chloroplasts. Cyanobacterial cytoplasmic membranes appear to contain the well-characterized Mg2+ channels CorA and/or MgtE, which both facilitate transmembrane Mg2+ flux down the electrochemical gradient. Both Mg2+ channels are typical for non-photosynthetic bacteria. Furthermore, Mg2+ transporters of the MgtA/B family are also present in the cytoplasmic membrane to mediate active Mg2+ import into the bacterial cell. While the cytoplasmic membrane of cyanobacteria resembles a 'classical' bacterial membrane, essentially nothing is known about Mg2+ channels and/or transporters in thylakoid membranes of cyanobacteria or chloroplasts. As discussed here, at least one Mg2+ channelling protein must be localized within thylakoid membranes. Thus, either one of the 'typical' bacterial Mg2+ channels has a dual localization in the cytoplasmic plus the thylakoid membrane, or another, yet unidentified channel is present in cyanobacterial thylakoid membranes.