Shedding light on blue-green photosynthesis: A wavelength-dependent mathematical model of photosynthesis in Synechocystis sp. PCC 6803

Abstract

Cyanobacteria hold great potential to revolutionize conventional industries and farming practices with their light-driven chemical production. To fully exploit their photosynthetic capacity and enhance product yield, it is crucial to investigate their intricate interplay with the environment including the light intensity and spectrum. Mathematical models provide valuable insights for optimizing strategies in this pursuit. In this study, we present an ordinary differential equation-based model for the cyanobacterium Synechocystis sp. PCC 6803 to assess its performance under various light sources, including monochromatic light. Our model can reproduce a variety of physiologically measured quantities, e.g. experimentally reported partitioning of electrons through four main pathways, O2 evolution, and the rate of carbon fixation for ambient and saturated CO2. By capturing the interactions between different components of a photosynthetic system, our model helps in understanding the underlying mechanisms driving system behavior. Our model qualitatively reproduces fluorescence emitted under various light regimes, replicating Pulse-amplitude modulation (PAM) fluorometry experiments with saturating pulses. Using our model, we test four hypothesized mechanisms of cyanobacterial state transitions for ensemble of parameter sets and found no physiological benefit of a model assuming phycobilisome detachment. Moreover, we evaluate metabolic control for biotechnological production under diverse light colors and irradiances. We suggest gene targets for overexpression under different illuminations to increase the yield. By offering a comprehensive computational model of cyanobacterial photosynthesis, our work enhances the basic understanding of light-dependent cyanobacterial behavior and sets the first wavelength-dependent framework to systematically test their producing capacity for biocatalysis.

Fig 1. Computational model of the photosynthetic and respiratory chain allows simulating electron fluxes through main (linear), cyclic, alternate, and respiratory pathways in Synechocystis sp. PCC 6803.

Schematic representation of components and reactions included in the model of cyanobacterial photosynthesis. The model includes descriptions of protein complexes (e.g. PSII, PSI, Cb₆f and ATP synthase) and electron carriers in the photosynthetic electron transport chain and the reactions through them, enabling simulation of electron transfer through Linear Electron Transport (LET), Cyclic Electron Transport (CET), Respiratory Electron Transport (RET), and Alternate Electron Transport (AEF). With orange circles (Respiration, CBB, and photorespiratory salvage pathway (PR salvage)) we mark pathways represented in the model as lumped reactions. The top-right box shows gas exchange reactions (O₂ export and active CO₂ import) and metabolic ATP and reduced Nicotinamide adenine dinucleotide (NADH) consumption. Electron and proton flows are colored black and blue, respectively. Regulatory effects, such as Fd-dependent CBB activity, are represented with dotted lines. The two photosystems are described using Quasi-Steady-State (QSS) approximation. For the analyzes we assume internal quencher as the state transition mechanism, as marked on PSII. Various scenarios of PBS attachment can be simulated, on the figure attached to PSII. Abbreviations: 2PG: 2-phosphoglycolate, 3PGA: 3-phosphoglycerate, ADP: Adenosine diphosphate, ATP: Adenosine triphosphate, ATPsynth: ATP synthase, CBB: Calvin-Benson-Bassham cycle, CCM: Carbon Concentrating Mechanism, COX: Cytochrome c oxidase, Cyd: Cytochrome bd quinol oxidase, Cyt b₆f: Cytochrome b₆f complex, FNR: Ferredoxin-NADP⁺ Reductase, Fd: Ferredoxin, Flv 1/3: Flavodiiron protein dimer 1/3, NADP⁺: Nicotinamide adenine dinucleotide phosphate, NADPH: reduced Nicotinamide adenine dinucleotide phosphate, NAD⁺: Nicotinamide adenine dinucleotide, NADH: reduced Nicotinamide adenine dinucleotide, NDH-1: NAD(P)H Dehydrogenase-like complex 1, NDH-2: NAD(P)H Dehydrogenase complex 2, OCP: Orange Carotenoid Protein, Oxy: RuBisCO oxygenation, PC: Plastocyanin, PQ: Plastoquinone, PR: Photorespiration, PSI: Photosystem I, PSII: Photosystem II, SDH: Succinate dehydrogenase.

Fig 2. Simulation of the electron and gas fluxes in Synechocystis.

A-D: Simulated steady-state electron flux through linear (blue), cyclic (green), alternate (flavodiiron+terminal oxidases, orange) and respiratory (red) electron pathways for light intensities between 10 μmol(photons) m⁻² s⁻¹ and 300 μmol(photons) m⁻² s⁻¹. The model has been parameterized to yield approximately 15 electrons PSI⁻¹ s⁻¹ linear electron flow (blue) for a fraction of 65% under saturating CO₂ conditions, as measured in wild type (WT, A) [46]. The model predicts flux distributions under sub-saturating air CO₂ level (B) and for the flavodiiron (Flv1/3, C) and NAD(P)H Dehydrogenase-like complex 1 (NDH-1) knockout mutants (D). Each value represents a steady-state flux under continuous light exposure. Simulations were run using 670 nm light (Gaussian LED, σ = 10 nm). E: Barplot showing the mean flux distribution for light intensities over 10 μmol(photons) m⁻² s⁻¹ ± sd). F: Simulation of oxygen production and consumption (respiration + three terminal oxidases) rates for increasing light intensities, as compared to measured rates provided by Schuurmans et al. (2014) [47]. Data points are the mean from measurements of cells with 625 nm illumination with 50 mM NaHCO₃. Error bars show ± sd. G: The simulated carbon fixation rates are displayed with the measurement used for parameterization [48]. Simulations were run using a 625 nm light (gaussian LED, σ = 10 nm). We calculated light attenuation in the culture using Eq (S67) in S1 Appendix with default pigment concentrations and a constant 2 mg L⁻¹ sample chlorophyll concentration. H: O₂ production under variation of the external CO₂ concentration in vivo and in vitro. The data was used for parametrization by fitting the parameter fCin, representing the ratio of intracellular to extracellular CO₂ partial pressure which is increased by the carbon concentrating mechanism, which was varied in the simulation between 100 and 1000. Benschop et al. [49] measured oxygen evolution with 800 μmol(photons) m⁻² s⁻¹ light of Synechocystis sp. PCC 6803 grown under 20 ppm CO₂ and varied the dissolved CO₂ in the medium (C_i). The data was extracted from graphs using https://www.graphreader.com/. The simulation used a cool white LED. Our simulated O₂ evolution rates are ca. half of the measured rates. Within the CO₂ concentration range above ambient air (400 ppm) the rate dynamics are well reproduced with fCin = 1000. The model overestimates oxygen evolution at very low C_i concentrations. A black box with the letter “P” marks the data used for parameterization. RMSE quantifies the residuals of the respective simulation. In A and E, the residuals measure the difference to an experimentally measured LET flux of 15 electrons PSI⁻¹ s⁻¹ and 65% of the total PSI electron flux in the WT. The difference to the residuals of a model with initial parameters, not improved with the Monte Carlo results, is in parentheses.

Fig 3. Saturation pulse method using Pulse Amplitude Modulation (PAM) fluorescence measurement in vivo and in silico.

The simulated signal has been calculated using Eq (8). All experimental measurements were performed with a Multi-Color PAM (Walz, Effeltrich, Germany). A, B: Fit of simulated (black) to measured (red) PAM fluorescence dynamics during a saturation pulse light protocol. The simulation was manually fit the traces in A and improved by automated parameter variation using seven model parameters, and the parameters are used for all other model simulations. The experimental traces were measured in Synechocystis sp. PCC 6803 grown under 435 nm light (A, n = 2) or 633 nm light (B, n = 2) [59]. Simulations use the respectively measured pigment contents and ambient CO₂ (400 ppm). The shown light protocol includes several different light wavelengths and intensities to trigger a response from respective photosynthetic electron transport chain components. By monitoring cell responses to these light conditions, we captured light responses via state transitions and non-photochemical quenching and relaxation (as described in the upper bar). We calculated light attenuation in the culture using Eq (S67) in S1 Appendix with the measured pigment concentrations and sample chlorophyll content in Table D in S1 Appendix. C-J: Model prediction on emitted fluorescence signal. Light protocol in A is repeated with pigment contents measured in cells grown under different monochromatic lights [59]. We calculated light attenuation with the chlorophyll content measured in each culture. K,L: Model validation comparing PAM-SP fluorescence traces in vivo (K) and in silico (L). Four experimental replicates are shown. Simulations assume 1% CO₂ supplementation and use the default parameters (see A) and pigment set. The model reproduces the qualitative fluorescence dynamics during most of the experiment except for overestimating steady-state fluorescence during the strong blue light phase. The lower bar depicts the light wavelength and intensity (in parentheses, in μmol(photons) m⁻² s⁻¹) (lights used: 440 nm at 80 μmol(photons) m⁻² s⁻¹ and 1800 μmol(photons) m⁻² s⁻¹ and 625 nm at 50 μmol(photons) m⁻² s⁻¹, saturating pulse: 600 ms cool white LED at 15 000 μmol(photons) m⁻² s⁻¹). Cultures of Synechocystis sp. PCC 6803 were grown under bubbling with 1% CO₂ and 25 μmol(photons) m⁻² s⁻¹ of 615 nm light for ca. 24 h. For the measurement, 1.5 mL culture was transferred to a quartz cuvette and dark-acclimated for 15 min prior to each measurement. A black box with the letter “P” marks the data used for parameterization. RMSE quantifies the residuals of the respective simulation. The difference to the residuals of a model with initial parameters, not improved with the Monte Carlo results, is in parentheses.

Fig 4. Systematic analysis of the effect of various light sources on the rate of carbon fixation.

A-D: The light spectra of four light sources used in simulations, including common “white” light LED panels. E: Steady-state flux through the CBB under the lights in A-D, simulated over different light intensities. F,G: Results of Metabolic Control Analysis (MCA) performed for the given light sources with a range of intensities from 80 to 800 μmol(photons) m⁻² s⁻¹ to steady-state. By varying the photosystem concentrations and the maximal rate of the CBB by ± 1%, we quantified their control on the CBB flux by calculating flux control coefficients. We display the mean of absolutes of control coefficients. Higher values signify stronger pathway control.

Fig 5. In silico analysis of biotechnological compound production.

A: Monochromatic lights used in the analysis (Gaussian LED, σ = 0.001) shown as colored spikes. Relative absorption spectra of selected pigments are shown in the background. B-D: Simulated production capacities of biotechnological compounds under light variation. We created three models, each containing a sink reaction consuming energy carriers in the ratio corresponding to a biotechnological target compound, including the cost of carbon fixation. The models were simulated to steady-state under illumination with varying intensity of the lights in A. We disabled the CBB reaction and limited ATP and NADPH concentrations to 95% of their total pools. Thus we estimate the maximal production rate of energy carriers in a desired ratio, assuming optimal carbon assimilation for the process and no product inhibition. The shown sinks represent pure NADPH extraction (B), production of terpenes (C; 19 ATP, 11 NADPH, 4 Fd_red), and sucrose (D; 19 ATP, 12 NADPH). E,F: Comparison of measured isoprene production and simulated production capacity under light variation. We show the growth and isoprene production rates measured under monochromatic illuminations (405 nm, 450 nm, 540 nm and 630 nm at 50 (E) or 100 μmol(photons) m⁻² s⁻¹ (F)) by Rodrigues et al. [29]. The model was adapted to the measured pigment composition (see Table D in S1 Appendix) and simulated to steady-state under the respective monochromatic lights. We implemented the sink reaction representing isoprene as in C.

Fig 6. Testing possible mechanisms of state transitions.

Four possible mechanisms of state transitions have been implemented and parameterized randomly to quantify their performance by contributing to oxidising PQ pool. The fluorescence signal has been calculated using Eq (8). A: Schematic representation of four state transition models, as reviewed in [42]. B: The relative difference of PQ reduction under state 2 lighting to a model with no state transitions. The respective implementations’ parameters were systematically varied, and the distribution of relative reduction-alleviation is shown as violin plots with quantiles as boxplots. C: The reduction of maximal fluorescence in the light (${\text{F}}_{\text{m}}^{\prime }$) from state 1 to state 2 in the model variations. The distribution is also shown as violin plots with inset boxplots. D: The relative decrease in the reduction state of PQ was calculated for different intensities of 633 nm light. The distribution is shown for each combination of state transition model and light intensity. Dots mark the median. E: Results of the systematic parameter variation of the PSII-quenching model. Each point shows a model with varied parameters for the state transition model. The models were simulated for different light intensities on the x-axis, and we calculated how the activation of the state transition mechanism affected the reduction of the PQ pool (y-axis) and the rate of the CBB (z-axis). For higher light intensities, the state transition has less effect on the PQ pool and CBB rate.

Fig 7. Residuals of the model in Monte Carlo simulations.

We performed 10,000 simulations of the model with a subset of parameters being randomized: The 24 parameters marked as “manually fitted” in Table A in S1 Appendix were randomly varied within ±factor 2 (A) or ±10% (B) around their initially set value. We calculated ten residual functions for each simulation as described in the Methods. The x-axis shows the mean ratio of residuals compared to the initial parameter set, while the y-axis shows the highest ratio. Simulations with a y value below one, ca. 1.6% of the simulations in B and colored red improve all residual functions. We mark the parameter set with initial values for the randomized parameters and the set whose values were used to improve the model.

Fig 8. In silico analysis of gene overexpression.

Simulated change in the rate of the CBB under twofold overexpression of PSII (A), FNR (B), and Cb₆f (C) depending on the irradiance. Simulations were performed under increasing intensities of either 440 nm or 624 nm Gaussian LED light. The change in CBB rate differs both between the light colors and the low and high light intensity regimes.