The net CO₂ assimilation (A) response to intercellular CO₂ concentration (C_i) is a fundamental measurement in photosynthesis and plant physiology research. The conventional A/Ci protocols rely on steady-state measurements and take 15-40 minute per measurement, limiting data resolution or biological replication. Additionally, there are several CO₂ protocols employed across the literature, without clear consensus as to the optimal protocol or systematic biases in their estimations. We compared the non-steady state Dynamic Assimilation Technique (DAT) protocol and the three most used CO₂ protocols in steady-state measurements, and tested whether different CO₂ protocols lead to systematic differences in estimations of the biochemical limitations to photosynthesis. The DAT protocol reduced the measurement time by almost half without compromising estimations accuracy or precision. The monotonic protocol was the fastest steady-state method. Estimations of biochemical limitations to photosynthesis were very consistent across all CO₂ protocols, with slight differences in ribulose 1·5- bisphosphate carboxylase/oxygenase carboxylation limitation. The A/Ci curves were not affected by the direction of the change of CO₂ concentration but rather the time spent under TPU-limited conditions. Our results suggest that maximum rate of ribulose 1·5- bisphosphate carboxylase/oxygenase carboxylation (V_cmax), linear electron flow for NADPH supply (J) and triose phosphate utilization (TPU) measured using different protocols within the literature are comparable, or at least not systematically different based on the measurement protocol used.

Photosynthetic gas exchange was measured with portable infrared gas analyzer (LI-6800, LI-COR, Lincoln, NE, USA) on fully developed leaves. Chamber conditions were set to mimic species growing conditions (Specific conditions outlined in Table S2). To increase battery life in these field measurements, temperature was controlled at the block level. Across all species, our measurements spanned from 20 – 30 °C and 1000 – 1500 μmol photons m^-2 s^-1. While we understand that these light intensities are likely slightly sub-saturating, we selected them to minimize the confounding effects of long-term build-up of non-photochemical quenching resulting from the longer total measuring times required to test all the regimes on the same leaf. Leaves were acclimated to this saturating light intensity for at least 5 minutes to ensure rubisco activation before the measurement commenced.

We used 10 biological reps in tobacco to fine-tune the different protocols. We then used 6 biological replicates for all other species. In tobacco, the 10 biological replicates were measured using multiple Li-6800 over multiple days. For all other species, all biological replicates were measured on the same day using three Li-6800 that were used to measure two separate leaves per day. The order in which all CO₂ protocols were implemented on the leaf was randomized separately for each replicate using the random variation in atmospheric data (Haahr, 2023), which outperforms computer algorithms that generate random numbers. An example random protocol for a single measurement is shown in figure S1. All steady-state CO₂ protocols controlled the CO₂ concentration in the reference channel. We tested the following protocols and CO₂ sequences; monotonic (400, 50, 100, 150, 200, 250, 300, 350, 400, 500, 600, 700, 800, 1000, 1250, 1500, 1750 μmol CO₂ mol^-1), split up-down (400, 500, 700, 1000, 1500, 1750, 1250, 800, 600, 400, 350, 250, 150, 50, 100, 200, 300 400 μmol CO₂ mol^-1), split down- up, (400, 300, 200, 100, 50, 150, 250, 350, 400, 600, 800, 1250, 1750, 1500, 1000, 700, 500, 400 μmol CO₂ mol^-1), random (with a different CO₂ sequence for each replicate) and, the non-steady state DAT-monotonic protocol (Fig. S1).

In tobacco measurements, we also implemented a random protocol and an abrupt CO₂ increase of CO₂ concentration. These random measurements were implemented to minimize the possibility that a previous measurement CO₂ concentration affected the subsequent measurement. These measurements included a period in between each concentration to return the leaf back to steady-state photosynthesis at 400 μmol CO₂ mol^-1 between each random CO₂ concentration. For the random protocol, the CO₂ levels were randomly ordered for each of the 10 plants CO₂ with two 400 μmol CO₂ mol^-1 steps in between each concentration to return the leaf to initial ambient CO₂. An abrupt increase of CO₂ concentration from 400 to 1500 μmol CO₂ mol^-1 was also performed to measure oscillations associated with CO₂ entry into TPU-limiting CO₂ concentrations (Oscillation test). The oscillation test ended once the leaves reach a new steady state at 1500 μmol CO₂ mol^-1.

The DAT-monotonic protocol ranged from 50 – 2000 μmol CO₂ mol^-1 at CO₂ concentration ramp speed of 200 μmol CO₂ mol^-1 min^-1. Leaves were left to acclimate at 50 μmol CO₂ mol^-1 for 5 minutes before starting the CO₂ ramp to allow the CO₂ concentrations in the chamber to reach a steady-state before the DAT curve is initiated. This pre-ramp wait time is included in the total time of the A/Ci measurement. Before clamping on the first leaf in the morning and afternoon a CO₂ and H₂O range matching, and a CO₂ dynamic tunning all with an empty chamber were performed (Saathoff and Welles, 2021; LI-6800 Operating Instructions, 2023). This time was not included in the total time of the A/Ci measurement.

A complete set of four or five (for tobacco only) CO₂ protocols was implemented on the same leaf without unclamping the leaf. A minimum of five minutes was allowed for leaves upon clamping to acclimate to chamber conditions and reach steady state before starting the A-C_i curves. A minimum of five minutes was also allowed in between A/Ci curves for the leaf to reach steady state again. At each step of the A/Ci measurements, CO₂ concentration in the reference channel remained constant, and gas exchange variables were recorded upon reaching steady state or the elapsed time reaching 3 min. The stability criteria for auto logging were for A slope < 1 and standard deviation < 0.5, and for slope < 0.2 and standard deviation < 0.01 over a 20 second period. For field measurements the period was extended to 30 seconds. In all steady-state protocols, gas analyzers in the reference and sample channel were matched after every measurement. For the DAT protocols, gas exchange variables were recorded every 5 seconds for tobacco and 1 second for all other species.

The parameters underlying the biochemical limitations to photosynthesis on each A/Ci measurement were estimated by fitting the Farquhar-von Caemmerer-Berry model of C3 photosynthesis (FvCB model; Farquhar et al., 1980) including TPU limitation (Harley and Sharkey, 1991) to the experimental data using the non-linear fitting procedure developed by Sharkey (2016) and implemented on the msuRACiFit R package (Gregory et al., 2021; McClain et al., 2023). The parameters for the three main photosynthesis limitations, Vcmax, J, and TPU, along with respiration in the light (RL), mesophyll conductance (gm) and carbon flow out of photorespiration as glycine (alpha_g) or serine (alpha_s) were estimated simultaneously. FvCB estimations also considered the leaf temperature at which the A/Ci was measured. Vcmax was also estimated as the initial slope of the A/Ci response curve for Ci < 300 μmol CO₂ mol^-1 (Vcmax).

The A oscillations in the Oscillation test were quantified using the following indices (Fig. S2); Amplitude (μmol CO₂ m^-2 s^-1), A difference between first A maximum and the projected A value of the linear trend of 1500-CO₂ steady state at the time of first maximum, Wavelength (min), average time between two consecutive maximum or minimum, Oscillation length (min), time elapsed between the first A minimum and the first observation at the new steady state at 1500 μmol CO₂ mol^-1 (1500-CO₂ steady state), Number of minimums (count), number of times the oscillation reached a local minimum or valley, Overshot CO₂ (μmol CO₂ m^-2), total area of CO₂ assimilated above the linear trend of the 1500-CO₂ steady state, Forgone CO₂ (μmol CO₂ m^-2), area between the linear trend of the 1500-CO₂ steady state and the assimilated CO₂ below the trend, and Total or Net CO₂ (μmol CO₂ m^-2), sum or difference between Overshot CO₂ and Forgone CO₂, respectively. For consistency, the first maximum of the oscillation was not included in the estimations, given its large variability across replicates.

The shapiro.test function was used to test the normality assumption, and plots of the residual variance across the fitted values to asses the homoscedasticity assumption. The emmeans function in the emmeans package (Lenth et al., 2018) was used for mean comparison, and emtrends in the same package to test for significant differences between slopes. For the linear regression we tested whether the slope of the regression was different from zero, and the intercept was different from zero. To investigate the correlation between A/Ci curves and A oscillations, we correlated the A/Ci parameters with the A oscillation indices. We used spearman correlation coefficient (r) to find significant correlations (P < 0.1).

We used R Statistical Software for all statistical analyses based on code developed by Mauricio Tejera-Nieves available at https://github.com/PerennialDr/ACi Methods

Please direct correspondence to Berkley Walker (berkely@msu)