Constraint-based modelling revealed changes in metabolic flux modes associated with the Kok effect

Constraint-based modelling was applied to provide a mechanistic understanding of the possible metabolic origins of the ‘Kok effect’ – the change in quantum yield of net photosynthesis at low light intensity. The well-known change in quantum yield near the light-compensation point (LCP) was predicted as an emergent behaviour from a purely stoichiometric model. From our modelling results, we discovered another subtle change in quantum yield at a light intensity lower than the LCP. Our model predicted a series of changes in metabolic flux modes in central carbon metabolism associated with the changes in quantum yields. We demonstrated that the Kok effect can be explained by changes in metabolic flux modes between catabolism and photorespiration. Changes in RuBisCO carboxylation to oxygenation ratio resulted in a change in quantum yield at light intensities above the LCP, but not below the LCP, indicating the role of photorespiration in producing the Kok effect. Cellular energy demand was predicted to have no impact on the quantum yield. Our model showed that the Kok method vastly overestimates day respiration – the CO2 released by non-photorespiratory processes in illuminated leaves. The theoretical maximum quantum yield at low light intensity was higher than typical measured values, suggesting that leaf metabolism at low light may not be regulated to optimise for energetic efficiency. Our model predictions gave insights into the set of energetically optimal changes in flux modes in low light as light intensity increases from darkness. One sentence summary The Kok effect can be explained by the changes in flux modes between catabolism and photorespiration.


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The gross daytime CO 2 production by a plant is traditionally thought to occur via the 25 processes of photorespiration and day respiration. Day respiration is usually defined as 26 the efflux rate of non-photorespiratory CO 2 in illuminated leaves, expressed on a leaf evolution rate did not response linearly with light intensity in unicellular algae (Kok, 1948; 38 Kok, 1949). The Kok method extrapolates the net CO 2 assimilation rate to zero 39 irradiance using data points above the break point to determine the day respiration, R d . 40 Kok found that the O 2 consuming respiratory flux in the dark was found to be higher 41 than that at low light (Kok, 1948;Kok, 1949). This effect, now commonly referred to as 42 the 'Kok effect', was interpreted as a consequence of dark respiratory inhibition by light. 43 Further studies had demonstrated that the Kok effect is highly variable and is affected  While it is often easy to predict the rate of photorespiration using equations for gas 53 exchange method and the internal CO 2 mole fraction, estimating day respiration is more 54 challenging as there is no equation that can predict its rate as a result of environmental 55 parameters, CO 2 mole fraction or photosynthesis. Despite being a difficult task, 56 research over the past-half century has been trying to estimate R d in the form of an  intensity of about 20 mol m -2 s -1 (Fig. 1). Coincidently, at this break point, the net CO 2 87 flux is zero and this point is also commonly referred to as the light compensation point 88 (LCP) where the CO 2 consumed during photosynthesis equals the CO 2 released during 89 respiration. LCP is also commonly used as the reference point to distinguish the dark 90 and the low light period. The region of no light to LCP (i.e. in this case, 0 -20 mol m -2 91 s -1 ) is classified as the dark / night period and is assigned as stage 1 and the region 92 thereafter is classified as the low light / day period and is assigned as stage 2 (Fig. 1).

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The intercepts of the resulting linear fits for the points in stage 1 and stage 2 represent 94 the apparent rates of respiration in the dark (night respiration, R n ) and in the day (day 95 respiration, R d ) respectively. R n and R d were predicted to be 2.98 mol m -2 s -1 and 1.44 96 mol m -2 s -1 respectively. It is worth noting that the break in linearity of the light curve  Photorespiration affects R d but not R n from the light curve 106 In order to understand the effect of photorespiration on the Kok effect, we repeated our 107 simulations with different RuBisCO carboxylation to oxygenation ratios ranging from 108 0.5:1 to 100:1. Our results showed that decreasing the ratio led to a more moderate 109 slope (lower gradient) in stage 2, i.e. lower quantum yield (amount of CO 2 fixed per 110 photon) (Fig. 2). This is expected since a decrease in the RuBisCO carboxylation to oxygenation ratio means an increase in photorespiration and thus more light will be 112 needed to fix the same amount of CO 2 as photorespiration is an energy-consuming 113 process.
Under predicted R d and R n to be 1.32 and 2.98 mol m -2 s -1 respectively using the Kok method.

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All subsequent simulations and analyses were performed using a RuBisCO carboxylase 134 to oxygenase ratio of 2.5:1 to investigate the various metabolic processes in C 3 leaf that 135 give raise to the Kok effect. We also noted that changing the ratio of RuBisCO the LCP in all simulated scenarios (Fig. 3), which explains why photorespiratory rate has no effect on R n . The increase in RuBisCO flux at the LCP indicated that Calvin-

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Benson cycle was predicted to only activate at light intensities higher than the LCP.

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Given that the objective function used optimises for maximum energy use efficiency, our 145 results suggest that it is energetically optimal for RuBisCO to only be active as light 146 intensity is higher than the LCP.   The TCA cycle is also involved in the production of ATP by producing NADH for the mitochondrial pyruvate dehydrogenase (33%) (Fig. 4b). predicted to be active at all times to produce the ATP needed by the leaf (Fig. S5). The

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From Point A to LCP, the production of NADPH was continued by the OPPP enzymes 342 in the cytosol (Fig. 8). On top of that, GAPN was also activated in this period and began 343 its production of NADPH needed for maintenance. Examining the predicted fluxes that 344 were affected by NADPH demand together, i.e. OPPP enzymes, GAPN and IDH, had 345 allowed us to understand the optimal regulation of these enzymes for energy efficiency 346 during the transition from dark to low light (Fig. 8). As light intensity increased from 0 347 mol m -2 s -1 , NADPH can start to be produced in the plastid by the photosynthetic light   Table S2). Notably, the ATP  Table S1. Manual curation log of the core metabolic model.

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Supplemental Table S2. Common constraints applied in all simulations.