A new tool for fitting C₄ gas exchange response curves

Abstract

This article comments on:

Woodford R, Ermakova M, Furbank RT, von Caemmerer S. 2026. Fitting photosynthetic carbon dioxide and irradiance response curves for C₄ leaves. Journal of Experimental Botany 77, 4987–4999. https://doi.org/10.1093/jxb/erag223

This article comments on:

Woodford R, Ermakova M, Furbank RT, von Caemmerer S. 2026. Fitting photosynthetic carbon dioxide and irradiance response curves for C₄ leaves. Journal of Experimental Botany 77, 4987–4999. https://doi.org/10.1093/jxb/erag223

C₄ photosynthesis is responsible for nearly 20% of global primary productivity. Thus, understanding and predicting variability in C₄ photosynthesis across environments and taxa is critical. Woodford et al. (2026) present a much-needed tool that enables the use of C₄ leaf gas exchange data for extracting C₄ photosynthetic traits. These traits enable better understanding of C₄ biology and can be integrated into predictive models. Here, we highlight the utility of the tool, the advance it represents, and future directions for C₄ research. The tool enables improved harmonization of data and models, and will enable better understanding and more reliable and realistic future projections of C₄ photosynthesis.

Terrestrial flora can be characterized by the way in which they perform photosynthesis. The two most common groupings are C₃ and C₄ plant species. C₃ species comprise most of the Earth’s plant diversity and productivity. However, C₄ species, while only comprising ∼5% of all plant species on Earth, cover ∼17% of Earth’s surface and are responsible for ∼20% of global primary productivity (Luo et al., 2024). They also include many important agricultural species such as maize and sugarcane, as well as many forage grasses used by livestock. Given the numerous ecosystem services provided by C₄ species, it is imperative to understand how C₄ species function under present-day and future projected conditions.

To better understand and predict C₄ photosynthesis, mathematical models have been developed to describe processes and their responses to environmental conditions. One of the most used and cited models of C₄ photosynthesis is the von Caemmerer (2000) model, recently updated in 2021 (von Caemmerer, 2021). This model formulates many of the key processes underlying C₄ photosynthesis, but requires input parameters that may vary. These include parameters related to biochemical capacity and efficiency. The choice of model parameters can result in vastly different estimates of C₄ photosynthesis (Fig. 1). Additionally, data on these parameters can be useful for understanding variability in leaf and plant strategies across environments and lineages (Monson et al., 2025).

Fig. 1.

Variation in estimates of C₄ net photosynthesis resulting from parameter uncertainty. Net photosynthesis (A_net; y-axis) under different conditions (x-axis) using different biochemical parameters. The conditions represented on the x-axis are variation in atmospheric CO₂ (HC, high CO₂ = 1000 μmol mol^–1; LC, low CO₂ = 150 μmol mol^–1) and light [HL, high light=1500 μmol m^–2 s^–1 photosynthetically active radiation (PAR); LL, low light=400 μmol m^–2 s^–1 PAR]. Data were generated using the ‘AciC4’ function from the ‘plantecophys’ package (Duursma, 2015), which implements the von Caemmerer (2000) model of C₄ photosynthesis. The model was run 1000 times for each of the four conditions by randomly sampling parameter values from normal distributions for each condition. Parameter distributions were generated for the maximum rate of phosphoenolpyruvate carboxylase (PEPc) carboxylation (V_pmax), the maximum rate of Rubisco carboxylation (V_cmax), and the maximum rate of electron transport (J_max). Gaussian normal distributions were generated using the default value from ‘AciC4’ as the mean (V_pmax=120 μmol m^–2 s^–1, V_cmax=60 μmol m^–2 s^–1, J_max=400 μmol m^–2 s^–1) and 50% of that default value as the SD. Violin plots show the distribution of A_net values from each of the 1000 simulations and are colored by condition (HLHC = green, HLLC = yellow, LLHC = blue, LLLC = gray). Inset boxplots range from the first to third quartile, with whiskers defined as 1.5 times the interquartile range. Black points indicate the median value within a condition.

Leaf gas exchange data can be used to estimate biophysical parameters of C₄ photosynthesis. However, this requires tools that use mathematical formulations to derive these parameters from measurements. As noted, the mathematical formulations exist, but user-friendly tools for estimating model parameters from gas exchange have lagged behind their equivalents for C₃ leaves (e.g. Sharkey et al., 2007; Duursma, 2015). To fill this gap, Woodford et al. (2026) have developed a new Excel tool based on an improved version of the von Caemmerer (2021) model of C₄ photosynthesis. Below we describe the advance this tool makes over previous data-fitting approaches, highlight how this tool improves our ability to estimate photosynthetic processes in C₄ leaves, and provide some avenues for improving estimates of photosynthetic processes in C₄ leaves.

Current C₄ fitting tools

Gas exchange response curves for C₃ leaves are usually fit using the Farquhar, von Caemmerer, and Berry model (Farquhar et al., 1980) model of C₃ photosynthesis, from which fitting tools have been developed (e.g. Sharkey et al., 2007; Duursma, 2015). However, there has been a lack of an analogous approach for fitting curves taken on C₄ leaves. This is due to a variety of factors, including the added complexity of the CO₂-concentrating mechanisms (CCM) of C₄ species. This causes multiple limitation states to be indistinguishable from each other. It also causes the necessary addition of processes that may not have defined parameters, such as bundle sheath conductance and leakage of CO₂, and the flow of electrons through various stages of the photosynthetic processes.

As a result, previous simplified methodologies have been used for C₄ curve fitting. For CO₂ response curves, the initial linear portion of the curve at low intercellular CO₂ has been assumed to be the region where photosynthesis is limited by phosphoenolpyruvate carboxylase (PEPc) carboxylation and used to estimate the maximum rate of PEPc carboxylation (V_pmax). Then, because it is difficult to determine whether Rubisco carboxylation or the electron transport rate for regenerating ribulose-1,5-bisphosphate (RuBP) is limiting photosynthesis, a non-rectangular hyperbola has been used to estimate a maximum rate of photosynthesis (A_max). This has been used in past studies (e.g. Pignon and Long, 2020; Fan et al., 2025) to broadly understand environmental and species variation in photosynthetic processes, but does not provide the mechanistic detail needed to quantify the underlying biochemical processes or to parameterize predictive models. Specifically, it does not provide estimates of the maximum rate of Rubisco carboxylation (V_cmax) or the rate of electron transport (J). Woodford et al. (2026) demonstrate an approach for estimating these parameters that, particularly when combined with light response curves, provides a fuller picture of the photosynthetic strategy used by C₄ leaves than has been available before.

Description of this tool and its advances over previous tools

The new gas exchange fitting tool Woodford et al. (2026) is an advantage over previous C₄ parameter estimation methods. First, the tool is grounded in contemporary theory of C₄ photosynthesis (von Caemmerer, 2021). In fact, the parameterization of cyclic electron flow in this theory has been updated in Woodford et al. (2026). Full model equations, parameterizations, and assumptions are provided, allowing users to understand how the tool is getting to the parameter estimates.

Next, the tool provides parameter estimates for both CO₂ and light response curves, thus delineating what can be gleaned from each type of response curve. This is useful for researchers needing to determine the right protocol for their question. Importantly, Woodford et al. (2026) provide a reasonable and cautioned solution for the issue that C₄ photosynthetic rates at high CO₂ may be limited by electron transport for regeneration of RuBP or Rubisco carboxylation. That is, CO₂ response curves use these high CO₂ data to fit both the V_cmax and J values needed to sustain the measured photosynthetic rates at high CO₂. The authors suggest using light response curves to estimate the maximum rate of electron transport (J_max) and validate J estimates from CO₂ response curves. Researchers should consider taking both CO₂ and light response curves to fully estimate model parameters, also argued in Dietze (2014).

Finally, the tool is presented as an Excel (Microsoft Corporation) document where measured gas exchange values can be entered before estimating model parameters. The tool is simple and easy to use, particularly for those that are familiar with the tool for C₃ leaves of Sharkey et al. (2007). To our knowledge, this is the first such tool for C₄ leaves. We demonstrate the use of this tool to fit a C₄ CO₂ response curve using published data from the publicly available leaf carbon exchange dataset (Smith and Dukes, 2017) in Fig. 2.

Fig. 2.

Overview of input (left panels; light green background) and output (right panels; dark green background) windows of the Excel tool developed by Woodford et al. (2026) for CO₂ response curves. (A) Users first define measurement conditions, including leaf temperature (T_leaf), atmospheric pressure (P_atm), irradiance, atmospheric O₂ concentration, and the fraction of PSII active in the bundle sheath. (B) Users then input measured values of the CO₂ assimilation rate (A) and intercellular CO₂ (C_i) values obtained from gas exchange measurements. (C) The tool generates a plot of the measured A and C_i values (black squares). Overlaid on top of this are the estimated carboxylation rate-limited photosynthetic values (orange circles) and electron transport rate-limited photosynthetic values (red circles) at each measured C_i value. These numbers are also provided in a table (table not shown). (D) The tool provides a table with estimated parameter values, including the maximum rate of phosphoenolpyruvate carboxylase (PEPc) carboxylation (V_pmax), the maximum rate of Rubisco carboxylation (V_cmax), and the electron transport rate (J). Note that a similar approach is used for fitting light response curves. Data used in this curve-fitting are from Zea mays (Smith and Dukes, 2017).

Future directions

The C₄ gas exchange fitting tool of Woodford et al. (2026) is a needed step forward for understanding C₄ leaf physiology, arriving nearly two decades after the analogous tool for C₃ leaves (Sharkey et al., 2007). However, there is still follow-on work to be done. First, using this tool to develop an open-source, code-based version of the tool would increase accessibility and transparency of the tool—as was shown by Duursma (2015) for C₃ curves. Next, the tool struggles to ingest high-resolution response curves such as those created from the Dynamic Assimilation Technique (Saathoff and Welles, 2021). As these high-resolution curves become more common, it will be helpful to update the tool to allow a greater number of data points to be input. Additionally, Woodford et al. (2026) describe the necessary use of fixed parameters in the model underlying the tool. This should be a call for future research to test the sensitivity of the model to these parameters and design future studies to better quantify these and their variability. Finally, the tool provides an opportunity to harmonize parameters estimated from curves developed in previous studies, for example as was done in Fan et al. (2025). This would be helpful for meta-analyses aimed at comparing C₄ photosynthetic traits across taxa and environments, something that is sorely needed to better understand and predict C₄ photosynthesis now and into the future.

Funding

This work was supported by the US National Science Foundation (DEB-2045968).