**Appendix A**

#### *Calculating ATP and NADPH Ratios from Gas Exchange Data*

While the theory behind calculating ATP and NADPH demand ratios for rubisco carboxylation (*Vc*) and oxygenation (*Vo*) from gas exchange data has been published on previously [6,72], the underlying derivation and final equations have been admittedly lacking. Here, we present a complete derivation, complete with underlying assumptions, appropriate to allow the non-specialist to apply these calculations to their gas exchange data. We will not attempt a full derivation of the underlying biochemical model of leaf photosynthesis, but will instead refer to the relevant equations directly as presented completely previously [133,134].

The cornerstone equation for modelling net CO2 assimilation (A) is the mass balance subtracting from rates of carbon fixation via *Vc* and rates of CO2 loss from photorespiration and respiration in the light (Rl). Rates of photorespiratory CO2 loss are calculated by multiplying CO2 loss per rubisco oxygenation (usually assumed to be 0.5) by *Vo* and total A is represented by Equation (2.1) in von Caemmerer 2000 [133]:

$$A = V\_{\varepsilon} - 0.5V\_{\vartheta} - R\_{l} \tag{A1}$$

Since our goal is to use measured rates of A to estimate *Vc* and *Vo*, and subsequent ATP and NADPH demand, it becomes convenient to express Equation (A1) in terms of one unknown variable (*Vc*) and then solve for *Vo*. Equation (A1) is expressed in terms of *Vc* in principle by combining rubisco specificity for CO2 relative to O2 (Sc/o) with measured gas concentrations to determine what catalytic rates of *Vc* and *Vo* would produce the measured A. This is accomplished based on the following relationships (Equations (2.16) and (2.18) from von Caemmerer 2000 [133])

$$
\phi = \frac{V\_o}{V\_c} \tag{A2}
$$

$$
\phi = \frac{2\Gamma'}{\mathbb{C}\_c} \tag{A3}
$$

where Cc is the partial pressure of CO2 at the site of rubisco catalysis and Γ\* is the CO2 compensation point in the absence of Rl defined as

$$
\Gamma^\* = \frac{0.5O}{S\_{c/o}} \tag{A4}
$$

where O is the oxygenation partial pressure. Note that since O is part of the definition of Γ\*, it must be scaled according to the measurement concentration if an altered oxygen background is used during the experiment. In using Equation (A1), Rl is assumed or independently measured under the experimental conditions using a variety of gas exchange approaches and treated as a constant [98,135,136]. With Equations (A1)–(A3) we are able to represent the relationship between A and *Vc* with no other unknown variables

$$V\_c = \frac{A + R\_l}{1 - \frac{\Gamma^\*}{\overline{C\_c}}} \tag{A5}$$

The solution for *Vc* can then be used with Equation (A1) to solve for *Vo*.

$$V\_o = \frac{V\_c - A - R\_l}{0.5} \tag{A6}$$

With *Vc* and *Vo* determined from the above, the rate of demand for ATP (VATP) and NAD(P)H (VNADPH) can then be determined based on the requirements for the C3 cycle (3 ATP and 2 NADPH) and photorespiration (3.5 ATP and 2 NAD(P)H, [66,67]) according to

$$V\_{ATP} = \Im V\_c + \Im \mathcal{S} V\_o \tag{A7}$$

And

$$V\_{NADPH} = 2V\_{\mathcal{E}} + 2V\_{\mathcal{O}} \tag{A8}$$

Of course additional energy demanding processes can be added to Equations (A6) and (A7) to determine total leaf energy demand [72], but we have limited these calculations to those most directly measured using gas exchange.

It should be noted that several of the constants assumed above require additional interpretation depending on the species and conditions they are measured under. These calculations depend on Cc to account for the chloroplastic supply of CO2, but standard gas exchange measurements can only practically resolve the concentration of CO2 in the intercellular airspace (Ci). Ci can be converted to Cc assuming a simple linear conductance using Fick's law as

$$\mathbf{C}\_{\mathbf{c}} = \mathbf{C}\_{\mathbf{i}} - \frac{A}{\mathcal{g}\_{\mathbf{m}}} \tag{A9}$$

where gm is the mesophyll conductance to CO2 diffusion. Selecting an appropriate gm to use experimentally is complicated since it varies by species, temperature and the underlying theory used for it estimation [137–145]. Fortunately, under most conditions, VATP and VNADPH are not extremely sensitive to small errors in gm assumptions, but a sensitivity analysis can be performed to confirm that the findings of a study are robust. Note that stomatal conductance has a similar impact on changing Ci for a given photosynthetic rate. Since stomata close during drought, this means that the ratio *Vo*/*Vc* increases under these water-limiting conditions, increasing metabolic demand for ATP/NADPH. Additionally, the temperature response of Γ\* should be accounted for in addition to its linear dependence on O [138].
