Leaf chamber experiments on sunflowers indicate a temperature-dependent compensation point of carbonyl sulfide

Ara Cho; Linda M.J. Kooijmans; Steven M. Driever; Maarten Wassenaar; Gerbrand Koren; Sophie L. Baartman; Leon Mossink; Maarten C. Krol

doi:10.12688/openreseurope.20235.3

Leaf chamber experiments on sunflowers indicate a temperature-dependent compensation point of carbonyl sulfide

Ara Cho ,
Linda M.J. Kooijmans
,
Steven M. Driever ,
Maarten Wassenaar
,
Gerbrand Koren ,
Sophie L. Baartman ,
Leon Mossink
,
Maarten C. Krol

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April 10, 2026

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https://doi.org/10.12688/openreseurope.20235.3

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April 10, 2026 (Version of Record 1.0)
December 8, 2025 (Published Manuscript Under Review 2.0)
August 5, 2025 (Published Manuscript Under Review 1.0)

European Commission

Grant ID(s): 742798

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Leaf chamber experiment, Leaf conductance model, Carbonyl sulfide, Photosynthesis, Leaf relative uptake, Stomatal conductance, Compensation point

Abstract

Background

Carbonyl Sulfide (COS) is a potential tracer for estimating gross primary productivity (GPP), due to its co-uptake with CO ₂ in leaves and the assumed absence of re-emission. However, the effectiveness of COS as a GPP tracer depends on understanding the differential responses of COS and CO ₂ uptake to environmental factors such as temperature and humidity. Methods We conducted three sets of leaf gas exchange experiments on sunflower leaves. In each experiment, we varied only one environmental factor: COS mole fraction (at two temperatures), humidity, or temperature. During the experiments, COS and CO ₂ fluxes were measured, and the data were used to optimize a leaf conductance model.

Results

We identified the existence of a COS compensation point, which increases with higher temperatures, suggesting potential emissions at higher temperatures when atmospheric COS concentrations are low. Our gas exchange measurements detected a COS compensation point of 58.9 ± 52.4 pmol mol ⁻¹ at 20°C and 139.9 ± 26.0 pmol mol ⁻¹ at 25°C. As vapor pressure deficit increased and stomatal conductance decreased, we observed that COS leaf uptake decreased more rapidly than CO ₂ assimilation. Consequently, the leaf relative uptake ratio (LRU) of COS to CO ₂ also decreased when stomatal conductance decreased. The optimized conductance model indicated that the optimum temperature for COS and CO ₂ enzymatic uptake was around 35°. However, the maximum net deposition velocity for COS lies between 20 and 25°, due to its temperature-dependent compensation point.

Plain Language Summary

Carbonyl sulfide (COS) is a trace gas found in the atmosphere that plants take up in a way similar to carbon dioxide (CO ₂) during photosynthesis. Because of this shared pathway, COS has been widely used to estimate how much CO ₂ plants absorb from the atmosphere—a process known as gross primary production (GPP). In our study, we conducted experiments using sunflower leaves in controlled chambers and found that COS and CO ₂ respond differently to changes in temperature and humidity. Surprisingly, we also observed that sunflower leaves may release COS back into the atmosphere when COS levels are low and temperatures are high. This finding challenges the long-standing assumption that plants only absorb COS and do not emit it. Our research highlights that understanding how COS behaves in plants under different environmental conditions is crucial for using it as a reliable tool to estimate how much CO ₂ is absorbed by vegetation.

Corresponding author

Ara Cho

0000-0002-6440-4771

ara.cho@wur.nl

Grant information

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and Innovation programme (Grant agreement No. 742798).

© 2026 Ara Cho (Corresponding Author, Co-Author); Linda M.J. Kooijmans (Co-Author); Steven M. Driever (Co-Author); Maarten Wassenaar (Co-Author); Gerbrand Koren (Co-Author); Sophie L. Baartman (Co-Author); Leon Mossink (Co-Author); Maarten C. Krol (Co-Author)

This work is licensed under a Creative Commons Attribution 4.0 International License.

First version published

August 5, 2025 (https://doi.org/10.12688/openreseurope.20235.1)

Latest version published

April 10, 2026 (https://doi.org/10.12688/openreseurope.20235.3)

Revised

Amendment

The manuscript was revised in response to the reviewers’ comments as summarized below.
First, we clarified why the flux in Equation 2 is normalized using the outflowing mole fraction instead of the inflowing mole fraction. We added an explanation in the Methods section stating that, under the assumption of well-mixed chamber air, the outflowing mole fraction best represents the chamber air mole fraction experienced by the leaf.
Second, we expanded the description of plant growth conditions and experimental timing to improve reproducibility. The Methods section now specifies the greenhouse temperature regime during cultivation as well as the daytime window (10:00–17:00 local time) during which gas exchange measurements were conducted.
Third, the structure of several paragraphs was revised to improve readability and logical flow. In particular, Section 4.1 was reorganized to clearly distinguish experimental limitations from model-related uncertainties.
Finally, minor editorial revisions were made throughout the manuscript, including clarification of model interpretation, small wording improvements, and adjustments to table captions to ensure consistency with the manuscript text.

1. Introduction

Gross primary productivity (GPP) quantifies the largest terrestrial CO₂ uptake flux in the global carbon cycle. However, when measuring the net ecosystem exchange (NEE) of CO₂, separating the GPP signal from respiration is challenging (Reichstein et al., 2005; Wohlfahrt & Gu, 2015). To address this limitation, Carbonyl Sulfide (COS) is an atmospheric trace gas that has been identified as a promising tracer for GPP and several studies have explored its utility extensively (Asaf et al., 2013; Campbell et al., 2008; Kohonen et al., 2022; Montzka et al., 2007). COS primarily originates from anthropogenic sources and oceans, while vegetation predominantly acts as its sink (Berry et al., 2013; Kettle et al., 2002).

The application of COS to estimate GPP has been suggested because COS uptake by leaves proceeds through a stomatal pathway similar to uptake of CO₂. Importantly, COS is assumed not to be released by plants due to its irreversible hydrolysis catalyzed by carbonic anhydrase (CA) (Notni et al., 2007; Protoschill-Krebs et al., 1996; Stimler et al., 2010). With this advantage of COS, the leaf relative uptake ratio (LRU) of deposition velocities of COS and CO₂ has been introduced to scaling COS leaf uptake to photosynthesis (Campbell et al., 2008; Sandoval-Soto et al., 2005) (a detailed LRU description is provided in Section 2.1.2). However, previous studies have emphasized that LRU responds differently to environmental factors such as leaf temperature (T_leaf) and vapor pressure deficit (VPD), implying that it is not constant under varying conditions (Cochavi et al., 2021; Kooijmans et al., 2019; Stimler et al., 2010; Sun et al., 2018; Wohlfahrt et al., 2018).

Unlike photosynthesis, COS uptake by CA remains unaffected by light, rendering it a robust proxy for stomatal conductance to water vapor ( g_sw). Accordingly, recent studies have used ecosystem-level COS exchange as a proxy for g_sw, highlighting differences between stomatal and biochemical contributions to CO₂ uptake (Cochavi et al., 2021; Wohlfahrt et al., 2018).

Differences in COS and CO₂ responses to changes in T_leaf and VPD were observed under constant light conditions, but their causes remain unclear (Kooijmans et al., 2019; Stimler et al., 2010; Sun et al., 2018). Kooijmans et al. (2019) measured that LRU decreases with increasing temperatures (from 13 to 23°C) or increasing VPD (from 0.5 to 2.5 kPa) at the boreal forest site Hyytiälä in Finland, while CO₂ uptake remained relatively stable. Understanding these variations is imperative for utilizing COS measurements to infer information about GPP.

To address these open questions, we investigate three potential explanations for the different responses of COS and CO₂ uptake to increasing T_leaf and VPD under high-light conditions. First, the pronounced reduction in COS leaf uptake compared to CO₂ uptake at higher T_leaf might be due to a potential COS compensation point (Γ_COS) at higher T_leaf (Hypothesis 1), which occurs when uptake and production are equal. If the atmospheric mole fraction is higher than Γ_COS, it generally indicates a predominance of uptake over production. Conversely, below this point, production exceeds uptake, resulting in a net release of COS to the atmosphere.

Γ_COS have been reported in a few vascular plants, algae, crops, and lichen fields (Belviso et al., 2022; Geng & Mu, 2004; Goldan et al., 1988; Kesselmeier & Merk, 1993; Kuhn & Kesselmeier, 2000; Maseyk et al., 2014). These measured Γ_COS values are lower than typical atmospheric COS mole fractions (≈500 pmol mol⁻¹), which is why net COS uptake is observed. Stimler et al. (2010) also observed a Γ_COS of 60.7 pmol mol⁻¹, though statistically indistinguishable from zero, and interpreted it as a possible diffusional feedback under high COS mole fractions. More recently, Gimeno et al. (2017) demonstrated temperature-dependent COS emissions in nonvascular bryophytes, suggesting that biochemical processes such as protein degradation could contribute to COS release at elevated T_leaf. However, Γ_COS of vascular plants and its temperature dependence remain poorly constrained. We therefore hypothesize that the observed COS uptake results from the coexistence of uptake and production processes, with Γ_COS exhibiting temperature dependence.

Second, COS leaf uptake might respond more strongly to stomatal closure than CO₂ uptake (Hypothesis 2). Plants react to variations in VPD to optimize their water use efficiency (Farquhar & Sharkey, 1982). VPD-induced stomatal closure reduces CO₂ inflow, but CO₂ is still consumed within the mesophyll cells. Consequently, the leaf’s internal concentration of CO₂ is reduced, increasing the CO₂ gradient between internal and ambient air. This larger gradient could sustain CO₂ uptake despite stomatal closure.

In contrast, the internal COS concentration is assumed to be much lower than ambient levels due to the higher catalytic efficiency of the CA enzyme (Protoschill-Krebs et al., 1996; Seibt et al., 2010; Tcherkez et al., 2006). Assuming that the internal COS concentration is (near-)zero, this concentration cannot reduce much further when stomata close, unlike the CO₂ internal concentration. Consequently, in response to stomatal closure, the COS gradient between internal and ambient air will likely not reduce as much as the CO₂ gradient, and so the COS gradient will not counteract the stomatal closure as is the case for CO₂. Thus, decreasing g_sw is expected to reduce COS uptake more than CO₂ uptake.

Third, the enzyme CA could behave optimally at a lower temperature than the RuBisCO enzyme responsible for CO₂ fixation (Cho et al., 2023; Stimler et al., 2010). Consequently, when T_leaf rises above the optimum temperature of CA but is still below that of RuBisCO, COS uptake could decrease while CO₂ uptake still increases (Hypothesis 3). Enzyme activity typically increases with temperature until reaching an optimum temperature, and the rate and the optimum temperature might differ between enzymes. Optimum temperatures for the CA enzyme in previous models simulating leaf and soil COS uptake ranged from 15°C to 40°C (Cho et al., 2023; Ogée et al., 2016; Sun et al., 2015), significantly lower than the optimal temperature of 50°C reported for RuBisCO (Salvucci et al., 2001). Together, these hypotheses consider both stomatal and biochemical mechanisms that could explain the differential COS and CO₂ responses.

Disentangling these hypotheses using field measurements is challenging due to interrelated and simultaneous variations of environmental conditions (e.g. T_leaf, VPD, and g_sw). Laboratory experiments offer the advantage of observing COS and CO₂ uptake changes at a leaf level under controlled conditions while independently varying environmental factors. To complement the experimental analysis and mechanistically interpret the observed gas-exchange responses, we developed a coupled CO₂–COS– H₂O conductance model based on a leaf conductance model previously established for GPP tracers such as the ∆₁₇O and ∆₄₇ isotopic composition of CO₂ (Adnew et al., 2020; Adnew et al., 2021; Adnew et al., 2023). This model serves as a diagnostic tool that enables joint optimization of gas-exchange parameters through the shared stomatal pathway for the three gases and allows inference of internal variables, such as intercellular and chloroplast COS mole fractions, that are not directly measurable.

Finally, to validate the three hypotheses, we aim to investigate the existence of COS compensation points and responses of COS and CO₂ leaf uptake to varying g_sw and T_leaf. We will present measurement results from leaf gas exchange experiments with sunflowers under controlled environmental conditions. We will interpret the experimental results using the coupled leaf conductance model optimized using the experiments’ dataset.

2. Materials and methods

2.1 Leaf gas-exchange measurements

2.1.1 Leaf cuvette system. We measured deposition velocities of COS and CO₂ (V_COS and V_CO2), i.e. fluxes normalized by mole fractions in air, using a leaf cuvette system. These experiments were conducted using sunflower plants (Helianthus Annuus L. cv. ‘Sunsation’), which are C₃ photosynthesis type plants cultivated in a local plant nursery (Evanthia, Maasdijk, Netherlands). Plants were cultivated in a greenhouse under a day/night temperature regime of 18–21°C during the day and 15–18°C at night, with ventilation applied above 20°C. Germination occurred at 21–24°C. The species Helianthus annuus was originally described by Linnaeus (Species Plantarum, Vol. 2, p.904, 1753). Each sunflower plant was used for a maximum of 5 daytime hours to minimize physiological stress caused by prolonged exposure to experimental conditions. Gas exchange measurements were scheduled to align with the plants’ photosynthetic rhythm and were conducted during the local daytime window between 10:00 and 17:00 (local time, the Netherlands).

T_leaf was monitored within the leaf cuvette using a thermocouple touching the abaxial side of the leaf. A synthetic air mixture, composed of 79% nitrogen and 21% oxygen, was mixed and controlled using mass flow controllers (Bronkhorst, Veenendaal, the Netherlands) and humidified using a dew point generator (LI-610, Li-Cor). CO₂ and COS were supplied from controlled gas cylinders and then added to the air-stream entering the LI-6800 system. CO₂ mole fractions in the leaf cuvette were kept around 445.1 ± 3.5 μmol mol⁻¹. COS was introduced from a gas mixture with synthetic air with a COS mole fraction of around 700 nmol mol⁻¹, regulated by a mass flow controller (Analyt-MTC, Müllheim, Germany). Except for the first experiment to check Γ_COS, COS mole fraction levels were intentionally elevated (in the range of 900 to 1100 pmol mol⁻¹), relative to typically atmospheric mole fractions (approximately 500 pmol mol⁻¹) to improve the detectability of COS uptake. Air in the leaf cuvette was mixed by a fan, operated at approximately 10,000 rpm, and the boundary conductance near the leaf surface was maintained at about 2.44 mol m⁻² s⁻¹.

To control g_sw, adjustments were made to the VPD. Initial g_sw (mol m⁻² s⁻¹) values were estimated by measuring the total conductance of H₂O ( g_tw (mol m⁻² s⁻¹)) and applying a corresponding boundary conductance of H₂O ( g_bw (mol m⁻² s⁻¹)) according to the LI-6800 manual. We assumed equal distribution of stomata between the upper to lower side of the leaf and therefore applied a stomatal ratio of K = 0.5.

COS and CO₂ mole fractions of the inflowing and outflowing air were measured using a quantum cascade laser spectrometer (QCLS) (Aerodyne Research Inc., Billerica, MA, USA). The air subjected to QCLS analysis was initially passed through a magnesium perchlorate (Mg (ClO₄)₂) drying trap to eliminate water vapor. For this purpose, magnesium perchlorate hexahydrate (99% purity; Sigma-Aldrich, Product Code: 309303-100G, Linear Formula: Mg (ClO₄)₂·6H₂O) was used. The water vapor scrubber tubes employed were 50 cc stainless steel tubes with 0.25-inch tube fittings. Measurements of air from cylinders with known COS and CO₂ mole fractions were performed for hourly calibration.

Once a leaf reached steady-state under the given conditions, data were recorded. The LI-6800 measured every second and was set to log data automatically every 3 minutes. Each log consisted of an average taken over 15 measurements within the preceding 15 seconds. The QCLS was set to automatically record data every second, totaling 150 measurements over each 150-second period. Then, the median over this 150-second interval was taken as the “data point”. Each QCLS interval had a corresponding LI-6800 log.

The air was passed through the analyzer at an approximate flow rate (AF (mol s⁻¹)) of 0.35 mmol s⁻¹. Subsequently, leaf assimilation rates (F_gas) of COS (F_COS (pmol m⁻² s⁻¹)) and CO₂ (F_CO2 (μmol m⁻² s⁻¹)) were calculated by:

(1)

F_{g a s} = \frac{A F}{S} ({[g a s]}_{i n} - {[g a s]}_{o u t}) .

Here, the [gas]_in and [gas]_out represent the mole fractions of COS (pmol mol⁻¹) and CO₂ (μmol mol⁻¹) in the air entering and exiting the chamber, which are measured by the QCLS on a dry-air basis. The leaf area S (m²) was 9 cm². Although transpiration slightly increases the outlet air flow due to the addition of water vapor (von Caemmerer & Farquhar, 1981, Appendix 2), the resulting increase in total molar flow (<3% under [H₂O]_out = 15–30 mmol mol^–1) was neglected in Equation 1 for simplicity. This small effect was not considered in the flux calculations and was consistently omitted throughout the model analysis. The CO₂ leaf assimilation rates obtained from the QCLS measurements closely matched those from the LI-6800 (R = 0.96, mean difference = 0.18 μmol m⁻² s⁻¹), confirming the accuracy of the CO₂ flux measurements.

Hourly calibration corrected potential QCLS drift, and the data points were excluded when the dew point temperature approached or exceeded the air temperature in any experiment.

To account for COS emissions at higher temperatures from chamber material (Maseyk et al., 2014), we conducted empty chamber experiments using inflowing COS mole fractions of 750 – 900 pmol mol⁻¹, which were adequate for evaluating chamber emissions, across a similar range of temperatures with experimental conditions. Additional experiments with low mole fraction (40 – 75 pmol mol⁻¹) were conducted to evaluate potential emission increases originating from large concentration gradients between sampling air and chamber materials. Figure 1 shows a slight increase in COS emissions with rising temperature, with no significant effect from inflowing COS mole fractions. Measurements were conducted under 40% relative humidity (RH), to avoid potential condensation or other artifacts during the empty chamber experiment. Leaf COS flux measurements were corrected using a linear fit of emissions against temperature in the empty chamber (R² = 0.45) with chamber emissions averaging 6.7% of observed leaf COS flux.

Figure 1. Measurements of COS flux at different air temperatures in the empty chamber.

Dots represent measurement data points and their colors indicate injected COS mole fractions in a chamber, black lines are linear fit equations, and filled areas indicate 95% confidential interval.

2.1.2 Experiments. Table 1 lists the environmental factors that were used in the three experiments. We manipulated inflowing COS mole fractions, humidity, and air temperatures while keeping other environmental conditions constant, as specified in each experimental design. All environmental changes were introduced gradually to allow the leaf sufficient time to adapt to chamber conditions. For instance, we applied humidity (to achieve a desired g_sw) and temperature changes of approximately 0.8 mol m⁻² s⁻¹ and 10°C, respectively, over a period of two hours. This gradual adjustment ensured that measurements reflect steady-state conditions and minimize transient effects from rapid environmental changes. To exclude the effects of light on V_COS and V_CO₂, high light intensity similar to growth conditions (600 μmol m⁻² s⁻¹) was maintained throughout all experiments.

Table 1. Environmental conditions during the three experiments.

The range of controlled and constant variables for each experiment is expressed as minimum ~ maximum and mean ± standard deviation, respectively. Experiment 1 (Sunflower 1) aims to detect COS compensation points at two temperatures. Experiments 2 (Sunflower 2, 3, and 4) and 3 (Sunflower 2 and 4) are designed to investigate responses of V_COS and V_CO2 to stomatal conductance (g_s) and leaf temperature (T_leaf), respectively, with T_leaf acting as a primary driver of mesophyll conductance (g_m). We controlled a designated variable in each experiment while other variables including light intensity, air flow rate, and mixing fan speed were kept constant.

Experiment (Control)	Experiment 1 ([COS]_in)		Experiment 2 ( g_sw)			Experiment 3 (T_leaf)
Sunflower number (-)	1	1	2	3	4	2	3
g_sw (mol m⁻²s⁻¹)	0.8 ± 0.0	0.9 ±0.1	0.4 ~ 1.1	0.3 ~ 1.0	0.3 ~ 0.6	0.6 ± 0.1	0.6 ± 0.0
VPD (kPa)	0.5 ± 0.0	0.5 ± 0.0	0.6 ± 0.1	0.7 ± 0.2	0.9 ± 0.3	0.7 ± 0.2	0.9 ± 0.3
T_leaf (°C)	19.8 ± 0.0	25.0 ±0.3	25.1 ± 0.0	26.4 ± 0.1	24.8 ± 0.3	19.1 ~ 30.9	19.0 ~ 29.8
[COS]_in (pmol m⁻²s⁻¹)	94.11 ~ 589.05	104.50 ~ 706.96	1096.4 ± 12.6	1181.9 ± 11.1	914.4 ± 29.6	1087.7 ± 41.1	926.8 ± 14.0
[CO₂]_in (μmol m⁻²s⁻¹)	446.5 ± 0.1	449.1 ± 0.3	441.0 ± 0.4	446.2 ± 1.5	447.5 ± 1.7	439.9 ± 3.1	447.3 ± 1.4

The first experiment (Experiment 1) aimed to detect COS compensation points and their temperature dependence. To determine the existence of Γ_COS and its temperature response, we measured F_COS at four distinct inflow COS mole fractions ranging from 94 to 589 pmol mol⁻¹ at two different leaf temperatures (19.8°C and 25.0°C). As in Gimeno et al. (2017), the values of the Γ_COS were subsequently calculated for each temperature by extrapolating the COS mole fraction at which F_COS reaches zero using a linear regression.

The second experiment (Experiment 2) aimed to compare responses of COS and CO₂ uptake to stomatal closure. We examined the responses of V_COS and V_CO₂ to g_sw while keeping other environmental factors constant, including air temperature (approximately 25°C). Thus, changes in V_COS and V_CO2 predominantly reflect responses to changes in g_sw. The modulation of g_sw was accomplished by adjusting humidity within the leaf cuvette – hence modifying VPD – using the humidifier.

The last experiment (Experiment 3) aimed to compare responses of COS and CO₂ uptake to changing temperatures. We observed V_COS and V_CO₂ while controlling the air temperature (T_air) within the leaf cuvette and maintaining other variables constant, including g_sw. The desired g_sw value was sustained by manipulating chamber humidity and thus VPD when necessary. The resulting leaf temperatures varied between 19.0 and 30.9°C.

Regarding a repetition of experiments, Experiment 1 was executed once with a single sunflower plant (Sunflower 1), while Experiments 2 and 3 were replicated with three different sunflower plants over three days (Sunflower 2, 3, and 4). During the measurement of COS, CO₂, and H₂O mole fractions in Experiment 3, the complete temperature range could not be covered consistently across all three repetitions due to fluctuating g_sw conditions. Due to this limitation, data from Sunflower 3 were omitted from the analysis of Experiment 3. Overall, we collected 15 data points from Experiment 1 and 48 data points from Experiments 2 and 3.

The measured V_COS and V_CO₂ were used to calculate the LRU (-), which was used to characterize differing responses of COS and CO₂ from Experiments 2 and 3 (Sandoval-Soto et al., 2005; Campbell et al., 2008):

(2)

L R U = \frac{V_{C O S}}{V_{C O 2}} = \frac{A_{C O S}}{{[C O S]}_{o u t}} \frac{{[C O_{2}]}_{o u t}}{A_{C O 2}},

where A_COS (pmol m⁻² s⁻¹) and A_CO2 (μmol m⁻² s⁻¹) are assimilation rates of COS and CO₂, respectively. These rates were normalized by outflowing concentrations [COS]_out and [CO₂]_out, which are assumed to be the concentrations the plants are exposed to due to the well-mixed conditions (see Section 2.2.1).

2.2 Conductance model

2.2.1 General concept. Since the observations were somewhat limited in exploring internal leaf processes, we developed a conductance model and applied an optimization method using 48 data points from Experiments 2 and 3. Experiment 1 (15 data points) was used to provide initial information of Γ_COS and its temperature dependence to the model (Section 3.2.2). This modeling framework was designed to mechanistically link experimental observations to internal gas-exchange processes.

Our leaf conductance model simulates the concurrent exchange of COS, CO₂, and H₂O in a plant leaf with the conditions of the laboratory experiments. Since these gases share the same stomatal pathway, their simultaneous modeling stomatal pathway, their simultaneous modeling helps us understand the mechanisms of leaf conductance. The model calculates mole fractions on a wet-air basis, while the measurements are reported on a dry-air basis. Accordingly, conversions between dry- and wet-air mole fractions were applied when comparing modeled and observed concentrations (see Section 2.1.1). Additionally, the model assumes that gas exchange reaches an equilibrium that we tried to attain in the conducted experiments. All model variables that remain constant in the model are listed in Table 2. Variables that are excluded from Table 2 are targets for optimization as explained in Section 2.3.

Table 2. Model constants used in the model.

Variables in all gases were used for all models, while those specific to COS, CO₂, and H₂O were applied to their respective model. The molar volume (V_m) is at standard temperature (298 K) and pressure (100 kPa).

Gas	Symbol	Description	Unit	Value	Q₁₀
All	S	Leaf area	cm²	9.0
	R	Universal molar gas constant	J K⁻¹ mol⁻¹	8.314
	V_m	Molar volume	m³ mol⁻¹	0.0248
	V_cν	Cuvette volume	cm³	109^a
COS	∆ H_a,CA	Activation energy of CA	kJ mol⁻¹	40^b
COS	∆ H_eq,CA	Enthalpy change of CA	kJ mol⁻¹	100^b
CO₂	τ_{298 K}	Specificity factor between CO₂ and O₂ at 298 K	-	2600^c	0.57
	K_{c, 298 K}	Michaelis-Menten constant for carboxylation at 298 K	Pa	30^c	2.1
	K_{o, 298 K}	Michaelis-Menten constant for oxygenation at 298 K	Pa	30000^c	1.2
	R_d	Dark respiration at 298 K	μmol m⁻² s⁻¹	3.0^c	2.0
	p[O₂] _i	Partial pressure of internal O₂	Pa	20900^c
H₂O	g_mw	Mesophyll conductance for H₂O	mol m⁻² s⁻¹	10

a LI-COR-6800 documents.

b Cho et al. (2023).

c Collatz et al. (1991).

Figure 2a schematically illustrates the methodology for the gas exchange experiments. As described in Section 2.1.2, environmental conditions, including [COS]_in, T_air, and VPD, were manipulated to test the hypotheses while keeping other variables, such as light levels, constant. The cuvette received controlled mole fractions of the three gases via the airflow. Figure 2b depicts the exchange pathways of COS, CO₂, and H₂O within the sunflower leaf, which form the basis for the conductance model. We assumed that COS, CO₂, and H₂O production or consumption within the plant were governed by three conductances: boundary layer conductance ( g_b (mol m⁻² s⁻¹)), stomatal conductance ( g_s (mol m⁻² s⁻¹)), and mesophyll conductance ( g_m (mol m⁻² s⁻¹)) limited by physical or biochemical processes

Figure 2. Schemes of leaf cuvette experiments (a) and diffusion pathways of COS, CO₂, and H₂O into and out of a leaf in the conductance model (b).

A_gas and P_gas indicate the assimilation rate and production rate of each gas. g_b, g_s, and g_m represent boundary, stomatal, and mesophyll conductance, respectively.

With a designated set of conductance values, the model simulates the mole fractions of the three gases in each layer: ambient air ([gas]_a), boundary layer ([gas]_b), and inter-cellular airspace ([gas]_i)), and mesophyll level ([gas]_c). The mole fractions of COS, CO₂, and H₂O are represented in units of pmol mol⁻¹, μmol mol⁻¹, and mmol mol⁻¹, respectively.

The following rate equations describe the gas exchanges tendencies, assuming they achieve a steady state:

(3)

\frac{d {[g a s]}_{a}}{d t} (\frac{V_{c v}}{V_{m} S}) = - g_{b} ({[g a s]}_{a} - {[g a s]}_{b}) + \frac{A F}{S} ({[g a s]}_{i n} - {[g a s]}_{a}) = 0,

(4)

\frac{d {[g a s]}_{b}}{d t} (\frac{V_{c v}}{V_{m} S}) = g_{b} ({[g a s]}_{a} - {[g a s]}_{b}) - g_{S} ({[g a s]}_{b} - {[g a s]}_{i}) = 0,

(5)

\frac{d {[g a s]}_{i}}{d t} (\frac{V_{c v}}{V_{m} S}) = g_{S} ({[g a s]}_{b} - {[g a s]}_{i}) - g_{m} ({[g a s]}_{i} - {[g a s]}_{c}) = 0 .

Here, V_m (m³ mol⁻¹) is the molar volume, and V_cv (m³) is the effective air volume representing the gas-exchange region near the leaf surface. Under steady-state conditions, the first term on the left-hand side of Equation 3, Equation 4, and Equation 5, which represents the rate of gas accumulation, becomes negligible. To account for the different properties of COS and CO₂ to H₂O, the stomatal conductances ( g_s,COS and g_s,CO₂) and the boundary layer conductances ( g_b,COS and g_b,CO₂) are scaled proportionally to the conductance of water vapor ( g_sw and g_bw) ( g_s,CO₂ = g_sw/1.6, g_b,CO₂ = g_bw/1.4, g_s,COS = g_sw/1.94, g_b,COS = g_bw/1.56) (Bonan, 2008; Seibt et al., 2010; Stimler et al., 2010).

For the COS and CO₂ exchange at the stomatal level, a ternary system with H₂O and air should be considered, because the transpiration (F_H₂O (mol m⁻² s⁻¹)) is significantly larger than COS and CO₂ assimilation (Jarman, 1974; von Caemmerer & Farquhar, 1981). Thus, we added the ternary term in Equation 4 and Equation 5 for the COS and CO₂ models:

(6)

\frac{d {[g a s]}_{b}}{d t} (\frac{V_{c v}}{V_{m} S}) = g_{b} ({[g a s]}_{a} - {[g a s]}_{b}) - g_{S} ({[g a s]}_{b} - {[g a s]}_{i}) + \frac{F_{H_{2} O} ({[g a s]}_{b} + {[g a s]}_{i})}{2} = 0,

(7)

\frac{d {[g a s]}_{i}}{d t} (\frac{V_{c v}}{V_{m} S}) = g_{s} ({[g a s]}_{b} - {[g a s]}_{i}) - \frac{F_{H_{2} O} ({[g a s]}_{b} + {[g a s]}_{i})}{2} - g_{m} ({[g a s]}_{i} - {[g a s]}_{c}) = 0 .

Although accounting for the H₂O ternary system is important, its influence on the calculated mole fractions was found to be negligible. The smaller ternary effects within the leaf boundary layer were therefore not included, as they scale with E/g_bw (von Caemmerer & Farquhar, 1981, Equation B10) and are expected to be negligible under our experimental conditions (large g_bw and small E). Note that the mole fractions calculated by the model are expressed on a wet-air basis, whereas the observed mole fractions are reported on a dry-air basis. The moisture correction applied to model outputs is described at the end of this section.

To test Hypothesis 2, we analyzed how the intercellular mole fraction [gas]_i influences the net flux. The flux was computedusing Equation 3, Equation 6, and Equation 7 to determine [gas]_i, and then applied to the flux-gradient relationship:

(8)

F_{g a s} = g_{b \sim s} ({[g a s]}_{a} - {[g a s]}_{i}) .

Here, g_b∼s denotes the conductance from the leaf boundary layer to the stomata. The deposition velocity (V_gas (mol m⁻² s⁻¹)) can be calculated as follows:

(9)

V_{g a s} = g_{b \sim s} (1 - \frac{{[g a s]}_{i}}{{[g a s]}_{a}}) .

The term (1-[gas]_i [gas]_a⁻¹) represents the effect of changes between internal and ambient mole fractions on the gas conductance and deposition velocity, termed Ambient Fraction Remaining (AFR). This concept is utilized in Section 3.2.3 for interpreting Hypothesis 2. Strictly speaking, the mass flow difference between the inlet and outlet and the ternary effect should be considered in Equation 8 and Equation 9. However, these effects are expected to be minor under our experimental conditions (see above), and Equation 8 and Equation 9 were used only to examine the conceptual relationship between [gas]_i and flux. Therefore, for simplicity, these correction terms were omitted. Note that this omission does not affect the interpretation of AFR in Section 3.2.3.

This set of coupled rate equations can be solved analytically, resulting in mole fractions of the three gases in each layer. Conductance at the mesophyll level ( g_m) and [gas]_c were calculated using a different model for each gas. Descriptions of the individual biophysical processes at the mesophyll level for each gas are provided in subsequent sections.

From experiments, we measured [gas]_out, while the leaf conductance model calculates [gas]_a. Because the chamber air was well mixed, the modeled [gas] _out,est is considered equivalent to [gas]_a for model-observation comparison. Thus, [gas] _out,est is used for [gas]_a to interpret experimental data.

In the model, the estimated mole fractions for COS and CO₂ are based on wet air, whereas the QCLS measures dry-air mole fractions. Therefore, to compare model results with observations, the modeled wet-air mole fractions were converted to their dry-air equivalents using the observed outgoing H₂O mole fractions ([H₂O]_out,obs (mmol mol⁻¹)):

(10)

{[g a s]}_{o u t, e s t} = {[g a s]}_{a} {(1 - \frac{{[H_{2} O]}_{o u t, o b s}}{1000})}^{- 1} .

For [COS]_in,obs, which was measured after moisture removal, the same correction (Equation 10) was applied using [H₂O]_in,obs instead of [H₂O]_out,obs to convert from the dry-air to the wet-air basis before use in the conductance model.

Finally, net fluxes of the three gases were calculated using the same methodology as employed for the observations (Equation 1).

2.2.2 Water vapor model. In our experiments, we observed water evaporation from leaves. We aimed to model this evaporation at the mesophyll level and its subsequent transport out of the leaves, governed by g_sw. The unit of H₂O mole fractions in all layers is mmol mol⁻¹, and the unit of the flux is mmol m⁻² s⁻¹.

To represent the internal water vapor conditions, [H₂O]_c was calculated assuming that water vapor within the mesophyll intercellular airspace is saturated. However, we allowed for relative humidity within the intercellular airspace (RH_i (%)) to be less than 100%, based on previous studies (Cernusak et al., 2018; Wong et al., 2022). To achieve this, we introduced a mesophyll conductance for water vapor ( g_mw) and set it to an arbitrary value of 10 mol m⁻² s⁻¹, approximately ten times the largest observed value of g_sw. This parameter was included to test the sensitivity of the model to possible non-saturation within the intercellular airspace.

The expression for [H₂O]_c relies on T_leaf (°C) and air pressure (P_air (Pa)):

(11)

{[H_{2} O]}_{c} = 1000 \frac{P_{H_{2} O}}{P_{a i r}}, with

(12)

P_{H_{2} O} = 613.5 exp (\frac{17.502 T_{l e a f}}{T_{l e a f} + 240.97}) .

Using these assumptions, we calculated the water vapor mole fractions in the atmosphere ([H₂O]_a), boundary layer ([H₂O]_b), and interior ([H₂O]_i) by solving Equation 3, Equation 4, and Equation 5. Finally, we estimated the RH_i (%) from the calculated [H₂O]_c and [H₂O]_i:

(13)

R H_{i} = 100 \frac{{[H_{2} O]}_{i}}{{[H_{2} O]}_{c}} .

2.2.3 CO ₂ model. We aimed to simulate the gross CO₂ flux (F_CO₂, μmol m⁻² s⁻¹) and mole fractions of CO₂ in each layer (μmol mol⁻¹) using the model proposed by Farquhar et al. (1980). In this model, the gross CO₂ uptake rate is calculated as the minimum value among assimilation limited by enzymes (A_m), light (A_E), and sucrose synthesis (A_S), minus the dark respiration (R_d) :

(14)

F_{C O 2} \approx \min (A_{m}, A_{E}, A_{S}) - R_{d} .

Our experiments were conducted under a constant light intensity (PAR = 600 μmol m⁻² s⁻¹). We assumed that the A_E and A_S pathways were saturated, as light saturation points previously were obtained above 500 μmol m⁻² s⁻¹ (Lobo et al., 2013). Consequently, we calculated g_m,CO₂ ([CO₂]_i − [CO₂]_c) in Equation 7 with A_m −R_d. R_d was estimated by Collatz et al. (1991).

A_m is calculated by multiplying the maximum rate of RuBisCO carboxylation (V_max,Rub) with the partial pressure changes from RuBP partitioning between the CO₂ carboxylation and O₂ oxygenation reactions:

(15)

A_{m} = \frac{V_{m a x, R u b} f_{r u b} (T_{l e a f}) (p {[C O_{2}]}_{i} - Γ_{C O_{2}}^{*})}{p {[C O_{2}]}_{i} + K_{C} (1 + \frac{p {[O_{2}]}_{i}}{K_{o}})},

where p [CO₂]_i (Pa) and p [O₂]_i (Pa) are the partial pressures of CO₂ and O₂ in the inter-cellular air space. K_c (Pa) and K_o (Pa) are Michaelis-Menten constants for CO₂ and O₂, respectively. Γ^∗_CO₂ (Pa) stands for the CO₂ compensation point independent of dark respiration.

Strictly speaking, RuBisCO carboxylation occurs within the chloroplast stroma and should depend on the chloroplast CO₂ partial pressure (p [CO₂]_c), rather than p [CO₂]_i. However, our model does not explicitly include mesophyll conductance ( g_m,CO₂), and thus p [CO₂]_c cannot be directly resolved. Accordingly, p[CO₂]_i was used as a proxy for p [CO₂]_c, following the classical formulation of Farquhar et al. (1980).

The estimation of Γ^∗_CO2 is based on the partial pressure of oxygen linked to the side reaction of RuBisCO:

(16)

R_{2} = R_{1} Q_{10}^{\frac{(T_{2} - T_{1})}{10}} .

Here, T₂ corresponds to T_leaf, and T₁ is 25°C for the CO₂ parameters K_c, K_o, and Γ^∗_CO₂. The temperature function of V_max,Rub (μmol m⁻² s⁻¹) at T_leaf (°C) is calculated by (Badger & Collatz, 1977):

(17)

f_{R u b} (T_{l e a f}) = exp (\frac{((T_{l e a f} + 273.15) - T_{r e f, R u b}) Δ H_{a, R u b}}{T_{r e f, R u b} R (T_{l e a f} + 273.15)}),

where ∆ H_a,Rub (J mol⁻¹) is the activation energy of RuBisCO, valued at 60.0 kJ mol⁻¹ (von Caemmerer & Evans, 2015), and T_ref,Rub (K) is the reference temperature (298 K). R is the universal molar gas constant (8.314 J K⁻¹ mol⁻¹).

2.2.4 COS model. We constructed the COS model to estimate the gross COS flux rate (F_COS, pmol m⁻² s⁻¹) and mole fractions of COS in each layer (pmol mol⁻¹). Accurate modeling of COS leaf uptake requires representing mesophyll conductance, which integrates both the diffusional transport of COS and biochemical conversion by CA.

Earlier approaches treated mesophyll diffusion and CA activity as linearly proportional to Rubisco’s V_max (Berry et al., 2013). However, this simplification was shown to bias COS flux estimates, leading to the introduction of a revised CA-based temperature formulation (Cho et al., 2023). More recently, Lai et al. (2024) emphasized the importance of explicitly accounting for mesophyll diffusion in COS uptake models but also noted the lack of reliable parameterization for COS-specific mesophyll diffusion.

Building on these previous findings, we modeled biochemical conductance of COS in the mesophyll ( g_m,COS (mol m⁻² s⁻¹)) using the CA activity–based function proposed by Cho et al. (2023), which implicitly represents mesophyll diffusion while minimizing estimation bias through its revised temperature dependence. This function describes the temperature dependence of CA activity using a specified Arrhenius equation and Michaelis-Menten Kinetics (Cho et al., 2023; Daniel et al., 2010; Ogée et al., 2016; Sun et al., 2015):

(18)

g_{m, C O S} = V_{max, C A} f_{C A} (T_{l e a f}) = V_{max, C A} A_{T} \frac{(T_{l e a f} + 273.15) exp [- \frac{Δ H_{a, C A}}{R (T_{l e a f} + 273.15)}]}{1 + exp [- \frac{Δ H_{e q, C A}}{R} (\frac{1}{T_{l e a f}} - \frac{1}{T_{e q, C A} + 273.15})]} .

Here, V_max,CA (mol m⁻² s⁻¹) is the maximum catalyzation velocity of CA, ∆H_a,CA (J mol⁻¹) represents the activation free energy of CA and ∆ H_eq,CA (J mol⁻¹) is the enthalpy change when the enzyme transits from activation to inactivation. T_eq,CA (°C) stands for the optimum temperature at which the concentrations of activated and inactivated enzymes are equal (Daniel et al., 2010; Ogée et al., 2016; Sun et al., 2015). We adopted the normalization factor A_T as the value of f_CA (T_eq,CA)⁻¹.

To incorporate temperature-dependent compensation point behavior, applied the Γ_COS into [COS]_c. We proposed four temperature functions of Γ_COS based on Experiment 1 data. For model S1, Γ_COS was set to zero across all temperatures, assuming no compensation point effects. For model S2, Γ_COS was represented as a linear function:

(19)

Γ_{C O S} (T_{l e a f}) = f_{Γ C O S} (T_{l e a f}) = m_{C O S} (T_{l e a f} - T_{r e f}) .

where T_ref (°C) is the intercept temperature (16.4°C), determined from the linear regression of two Γ_COS values detected in Experiment 1 (Section 3.1.1). The slope m_COS (pmol mol⁻¹ K⁻¹) was set to 16.2 pmol mol⁻¹ K⁻¹, also derived from Experiment 1. At low temperatures, where Γ_COS becomes negative, we assumed Γ_COS = 0.

For model S3, Γ_COS was calculated using the Arrhenius function with a observation-based value of 55.0 pmol mol⁻¹ at 293 K from Experiment 1:

(20)

Γ_{C O S} (T_{l e a f}) = 55.0 exp (\frac{((T_{l e a f} + 273.15) - 293) Δ H_{a, Γ}}{293 R (T_{l e a f} + 273.15)}),

and for model S4, Γ_COS was similarly computed using a reference value of 138.7 pmol mol⁻¹ at 298 K:

(21)

Γ_{C O S} (T_{l e a f}) = 138.7 \exp (\frac{((T_{l e a f} + 273.15) - 298) Δ H_{a, Γ}}{298 R (T_{l e a f} + 273.15)}),

where ∆H_a,Γ (kJ mol⁻¹) represents the activation energy for Γ_COS. By solving for ∆H_a,
Γ using the two derived Γ_COS values, we determined an initial activation energy of 134.3 kJ mol⁻¹.

Figure 3 shows these four Γ_COS functions (S1–S4) representing the prior temperature-dependent parameterizations tested in the modeling framework with their imposed uncertainties. The figure also shows the experimental Γ_COS estimates from Experiment 1, included solely for reference to illustrate the initial parameter alignment.

Figure 3. Prior temperature functions of the COS compensation point (Γ_COS) (lines) with their error ranges (shaded area).

Blue triangles show the regression-derived Γ_COS from Experiment 1, included for reference to illustrate the initial parameter setup. The S1 model assumed Γ_COS = 0 pmol mol⁻¹. Model S2 describes Γ_COS as a linear relationship with T_leaf (a), while models S3 and S4 use an Arrhenius equation (b).

2.3 Indirectly derived COS compensation point

Because the temperature-dependent behavior of Γ_COS in Experiment 1 was derived from a limited set of measurements under a few temperature levels, additional validation was required to test whether the modeled Γ_COS functions are consistent across broader environmental conditions. To support this validation, we incorporated the indirectly derived Γ_COS from 48 data points in Experiments 2 and 3. By calculating [COS]_c using our optimized model parameters in Equation 3, Equation 6, and Equation 7, we were able to indirectly estimate Γ_COS and compare it with the modeled Γ_COS.

First, we calculated [COS]_b from the measured COS mole fractions with the rearranged Equation 3:

(22)

{[C O S]}_{b} = {[C O S]}_{a} + \frac{A F}{S g_{b, C O S}} ({[C O S]}_{a} - {[C O S]}_{i n}),

where [COS]_in and [COS]_a, along with AF, S, and g_b,COS, were applied from Experiments 2 and 3. Due to thorough mixing within the cuvette, we assumed [COS]_out to be equivalent to [COS]_a and used it accordingly (refer to Section 2.2). Although transpiration slightly increases the outlet air flow, this effect (<3%) was neglected to retain easy analytical expressions, consistent with the assumptions described in Equation 1. This formulation follows the same assumptions as in Equation 3 regarding ternary effects at the boundary layer, which were found to be negligible under our experimental conditions. Here, [COS]_in and [COS]_out were converted from a dry air basis to a wet air basis. We then used the derived [COS]_b to calculate [COS]_i using the rearranged Equation 6:

(23)

{[C O S]}_{i} = (- g_{b, C O S} {[C O S]}_{a} + g_{b, C O S} {[C O S]}_{b} + g_{s, C O S} {[C O S]}_{b} - 0.5 F_{H 2 O} {[C O S]}_{b}) {(g_{s, C O S} + 0.5 F_{H_{2} O})}^{- 1} .

F_H₂O was calculated using Equation 1 with the observed [H₂O]_in and the modeled [H₂O]_a obtained by the H₂O model. We used optimized g_sw value in the the H₂O model and g_s,COS. The reason for using the model-calculated [H₂O]_a instead of the observed [H₂O]_out is to consider the optimized g_sw in F_H₂O.

Finally, [COS]_i is used in Equation 7 to derive [COS]_c:

(24)

{[C O S]}_{c} = - \frac{g_{s, C O S}}{g_{m, C O S}} ({[C O S]}_{b} - {[C O S]}_{i}) + \frac{F_{H 2 O}}{g_{m, C O S}} ({[C O S]}_{b} + {[C O S]}_{i}) + {[C O S]}_{i},

where g_m,COS was determined using Equation 18 with optimized parameters V_max,CA and T_eq,CA. These indirectly calculated Γ_COS values vary depending on the chosen temperature-dependent functions of Γ_COS, which influence other parameters. Consequently, the indirectly derived Γ_COS values differ from Γ_COS functions due to their impact on the optimized parameters used in the calculations.

2.4 Parameter optimization

2.4.1 Optimization setting. Beginning with the model state parameter (x), we calculated [gas] _out,est and compared these to the observed values [gas] _out,obs on a dry-air basis. We aimed to minimize the differences between our model and the observations during each optimization step. To accomplish this, we defined a cost function (J_tot) consisting of a background term (J_bg) and three observational terms that account for the differences between model estimations and observations of COS (J_COS), CO₂ (J_CO₂), and H₂O (J_H₂O):

(25)

J_{t o t} = J_{b g} + J_{C O S} + J_{C O_{2}} + J_{H_{2} O} = \frac{{(x - x_{a})}^{2}}{W_{b g} σ^{2}} + \frac{{({[C O S]}_{o u t, e s t} - {[C O S]}_{o u t, o b s})}^{2}}{W_{C O S} {(σ_{C O S})}^{2}} + \frac{{({[C O_{2}]}_{o u t, e s t} - {[C O_{2}]}_{o u t, o b s})}^{2}}{W_{C O_{2}} {(σ_{C O_{2}})}^{2}} + \frac{{({[H_{2} O]}_{o u t, e s t} - {[H_{2} O]}_{o u t, o b s})}^{2}}{W_{H_{2} O} {(σ_{H_{2} O})}^{2}} .

The first term of the cost function penalizes deviations of the state x from the prior state vector x_a. This penalty depends on σ, which represents the prior error in the state vector. This background term is introduced to keep state variables within reasonable boundaries (Brasseur & Jacob, 2017). The last three terms of the cost function calculate the costs associated with deviations between modeled ([gas] _out,est) and observed mole fractions ([gas] _out,obs) for for COS, CO₂, and H₂O, respectively. Each term is normalized by its observational uncertainty to ensure consistent treatment of measurement errors, and each is scaled by optimization weights (W_bg, W_COS, W_CO₂, and W_H₂O) to balance the relative influence of each gas. These weights do not modify the observational errors but instead prevent any single gas—particularly CO₂—from dominating the total cost. The determination of these weights is described in the following section.

The costs related to observations (J_COS, J_CO₂ , and J_H₂O) are influenced by observational errors (σ_COS, σ_CO₂ , and σ_H₂O), derived from the measured COS, CO₂, and H₂O mole fractions. These observational errors were determined as the standard deviation of the measured mole fractions at outflow within the data point interval (150-second). Formally, σ_COS, σ_CO₂, and σ_H₂O should also reflect model errors caused by model parameters not included in the state or by processes that were not modeled (Brasseur & Jacob, 2017). Note that we excluded data from Experiment 1 to validate the optimized temperature function of Γ_COS in Section 3.2.2.

Due to the larger relative error in [H₂O]_out,obs and [COS]_out,obs than in [CO₂]_out,obs, the optimization procedure tended to focus on minimizing preliminary J_CO₂. To better utilize the non-CO₂ observations, we introduced optimization weights for each cost component. The observed [CO₂]_out,obs values ranged from 379.4 to 390.0 μmol mol⁻¹, with an average observational error of only 0.2 μmol mol⁻¹ (0.05%). [COS]_out,obs values ranged from 748.2 to 1032.4 pmol mol⁻¹, with an average error of 16.7 pmol mol⁻¹ (1.91%). [H₂O]_out,obs values ranged from 15.2 to 32.5 mmol mol⁻¹ with a mean error of 0.3 mmol mol⁻¹ (1.14%).

The targeted state parameters, along with their initial values and errors, are listed in Table 3. We assumed that the parameters related to the temperature response of mesophyll cells are consistent across all experiments, as all sunflowers were cultivated in a similar climate. We constructed state vectors with variables that significantly impact the total cost and better quantify the combined leaf exchanges: V_max,CA , T_eq,CA, and m_COS for COS, V_max,Rub and ∆ H_a,Rub for CO₂, and g_sw for all gases.

Table 3. State parameters (x) and their prior and posterior values with their errors based on model S2.

Posterior errors are calculated from 200 optimizations in a Monte Carlo method (Section 2.5). The last column denotes the error reduction. Prior and Posterior values for g_sw are averaged values across the dataset from Experiments 2 and 3. Values in “Bounds” column with brackets indicate lower and higher bounds provided to the optimization.

Parameter	Description	Unit	Bounds	Prior ± Error	Posterior ± Error	(b-a)/a¹ (%)
V_max,CA	Maximum velocity for CA	mol m⁻² s⁻¹	[0.01, 0.50]	0.125 ± 0.060	0.217 ± 0.037²	38
					0.189 ± 0.029³	52
					0.230 ± 0.042⁴	30
T_eq,CA	Optimum temperature for CA	°C	[1, 60]	30.0 ± 15.0	39.7 ± 5.0	66
m_COS	Slope of Γ_COS	pmol mol⁻¹ K⁻¹	[1, 300]	16.2 ± 16.2	22.4 ± 5.3	67
V_max,Rub	Maximum velocity for RuBisCO	μmol m⁻² s⁻¹	[1, 200]	90.0 ± 20.0	94.4 ± 0.3²	98
					87.4 ± 0.5³	98
					82.9 ± 0.3⁴	98
∆ H_a,Rub	Activation energy for RuBisCO	kJ mol⁻¹	[1, 100]	60.0 ± 12.0	54.5 ± 0.9	92
g_sw	Stomatal conductance of H₂O	mol m⁻² s⁻¹	[0, 3]	0.62 ± 0.09	0.64 ± 0.05	43

1 ‘a’ is a prior error and ‘b’ is a posterior error. They are used to calculate the error reduction.

2–4 The values are obtained for Sunflower 2, 3, and 4, respectively.

Although we selected sunflower leaves at similar development stages, variations in biochemical functioning existed among individual leaves. Therefore, we optimized V_max,CA and V_max,Rub for each individual plant, as these largely determine mesophyll conductance (Cho et al., 2023; Le Roux et al., 2001; Williams & Flanagan, 1996). The initial V_max,CA was based on the averaged V_max,CA across different phenological stages from two observation sites, Hyytiälä (Finland) and Harvard Forest (United States), as introduced by Cho et al. (2023). The standard deviation of V_max,CA was used as the state error. For V_max,Rub, we set the initial value as V_max,CA divided into the scaling factor 1400, derived from laboratory measurements of gas exchange in C₃ plants (Berry et al., 2013; Stimler et al., 2010; Stimler et al., 2011).

T_eq,CA is more crucial in determining CA’s temperature function compared to other kinetic variables (Cho et al., 2023). We adopted the initial value and state error of T_eq,CA directly from Cho et al. (2023), ensuring consistency with previous characterizations of CA kinetics.

To further evaluate the temperature dependence of Γ_COS , four temperature functions (S1 to S4) were tested within the conductance model. Each function was optimized and compared against observation-based Γ_COS. The S1 model excludes Γ_COS, while S2 applies a linear function with m_COS of 16.2 pmol mol⁻¹. Both S3 and S4 use a temperature dependence described by an Arrhenius relationship. All models were initialized with the same prior error for Γ_COS, including the zero-compensation point, as shown in Figure 3.

For the CO₂ parameters, we optimized ∆ H_a,Rub, as it is an unknown parameter for Sunflowers. We determine the initial value and error of ∆ H_a,Rub using the mean and standard deviation across nine species reported by von Caemmerer and Evans (2015). Other temperature-dependent parameters were adopted from Collatz et al. (1991).

The LI-6800 derives g_sw from water vapor exchange with its own uncertainties. Because g_sw similarly affects the exchange of H₂O, CO₂, and COS through the same shared stomatal pathway, we optimize g_sw in a coupled framework using flux information from all three gases to ensure internal consistency across species. The novelty of this framework lies in explicitly coupling these fluxes to derive a more physically consistent constraint on g_sw, while also addressing potential uncertainties in g_sw derived from LI-6800 measurements (e.g., stomatal ratio parameter K; Section 2.1.1).

Initial values for g_sw were taken from the LI-6800 measurements during Experiments 2 and 3. We applied a random error of 0.08 mol m⁻² s⁻¹, representing the standard deviation of g_sw from Experiment 3, despite efforts to maintain a constant g_sw (± 0.06 mol m⁻² s⁻¹). In addition, we considered an extra measurement uncertainty of 0.02 mol m⁻² s⁻¹, based on known sources of instrumental bias—such as the leaf temperature underestimation (Garen et al., 2022) and background total leaf conductance to water observed in empty chambers (Hussain et al., 2024). We also added individual [H₂O]_out,obs errors by normalizing [H₂O] _out,obs. The averaged initial g_sw value and its standard deviation (prior error) are 0.61 mol m⁻² s⁻¹ and 0.09 mol m⁻² s⁻¹, respectively.

Assuming a Gaussian probability density function for the state parameters could lead to nonphysical values in the optimization process. Thus, we minimized J_tot using the Sequential Least SQuares Programming optimizer (SLSQP) from the SciPy Python library. This optimizer enables the specification of lower and upper bounds on the state space and is well-suited for solving nonlinear problems. The parameter bounds are listed in Table 3.

2.4.2 Weight determination. We selected weights to achieve more balanced prior costs across four components in Equation 25. The prior chi-squared value (χ²_prior) was used to check the cost balance in prior condition. We set seven possible weights, and the corresponding χ²_prior value ranged from 3 to 200, as listed in Table 4. Then, we optimized parameters and calculated cost reduction rates for each part of the cost function. For H₂O, we found a χ²_prior value of about 3, indicating that the H₂O model already performs well with the prior parameter settings.

Table 4. Candidates for weights in the observational terms (W_COS, W_CO₂, W_H₂O) based on the chosen χ²_prior values.

χ²_prior	W_COS	W_CO₂	W_H₂O
3	0.337	238.8	3.24
10	0.101	71.6	0.97
30	0.034	23.9	0.32
50	0.020	14.3	0.19
100	0.010	7.2	0.10
150	0.007	4.8	0.06
200	0.005	3.6	0.05

We finally selected the weight combination that minimized the averaged reduction rates of J_COS and J_{CO 2} and ensured that each χ²_poste exceeded the value of 0.6 to avoid over-fitting, including J_bg. The selected weights (W_COS = 0.034, W_CO₂ = 7.2, W_H₂O = 3.24, W_bg = 1.0), correspond to χ²_prior values of 30, 100, and 3 for COS, CO₂, and H₂O, respectively. These weights lead to a more balanced ratio of χ² _prior across the observational parts (COS: CO₂: H₂O = 10: 33: 1), compared to the ratio without weights (1: 329: 4). Note that the prior value of J_bg is zero by design.

2.5 Error statistics

We evaluated the model performance using χ² values, mean bias errors (MBEs), and root mean square errors (RMSEs). The χ² metric was calculated by dividing the partial cost function by the number of observations or state variables (Tarantola, 2005). A posterior chi-squared value (χ²_poste) of 1 indicates a good fit, as the model predictions fall within the error distribution fall within the error distribution of the observations. A χ²_poste significantly greater than 1 indicates a poor fit, while a value smaller than 1 suggests potential overfitting. MBE indicates bias, with a positive value for overestimation and a negative value for underestimation. RMSE is the quadratic mean of the differences between estimation and observation, with a value of 0 indicating a perfect fit.

Note that the optimization process targets for χ²_poste to reach 1.0, but we also give the improvement in MBEs and RMSEs for completeness. To assess the posterior error associated with the optimized state, we employed a Monte Carlo method. In this process, we optimized the parameters using 200 distinct ensemble members, introducing random noise within the bounds of the respective state and observational errors (Bosman & Krol, 2023; Chevallier et al., 2007; Cho et al., 2023).

Furthermore, we conducted 500 perturbed forward simulations to assess the spread in both prior and posterior models. Parameters were randomly sampled from Gaussian distributions of both the prior and posterior. Prior uncertainties were assumed uncorrelated, while for the posterior parameters, we used the correlations that were determined using the Monte Carlo optimization. We quantified the posterior covariance matrix and considered the cross-parameter correlations when sampling the parameters to evaluate the posterior model. Parameters more than three standard deviations from the mean were discarded. These simulations were conducted with designated environmental input variables: pressure = 103,100 Pa, air flow rate (AF) = 0.00035 mol s⁻¹, [CO₂]_in = 400 μmol mol⁻¹, [COS]_in = 1000 pmol mol⁻¹, [H₂O]_in = 15 mmol mol⁻¹, g_bw = 2.44 mol m⁻² s⁻¹, g_sw = 0.6 mol m⁻² s⁻¹, and T_leaf = 25°C. We only varied one variable at the time, to evaluate its impact on the simulation.

3. Results

3.1 Experiments

3.1.1 COS Compensation Point (Experiment 1). Figure 4 presents the results from Experiment 1 with Sunflower 1, aimed at determining Γ_COS by measuring F_COS while controlling [COS]_out and maintaining constant g_sw and T_leaf. Minor fluctuations in g_sw occurred during temperature adjustments, increasing from 0.76 to 0.90 mol m⁻² s⁻¹ higher temperatures. F_COS shows a linear increase with increasing [COS]_out, in agreement with findings from earlier studies (Gimeno et al., 2017; Kesselmeier & Merk, 1993; Stimler et al., 2010).

We quantified the regression-based Γ_COS using a linear function at two temperatures: Γ_COS was 55.0 ± 53.2 pmol mol⁻¹ at 19.8°C and 138.7 ± 26.1 pmol mol⁻¹ at 25.0°C (error estimates denote 95% confidence interval). These results indicate that Γ_COS increases with rising T_leaf, suggesting a potential temperature dependence.

Figure 4. Observed mean COS net flux (F_COS) along an outflowing COS mole fraction ([COS]_out) in the light at 25.0°C (rectangle and red areas) and 19.8°C (circle and blue areas) in Experiment 1.

Lines and shaded areas represent linear fits with 95% confidence intervals. Positive values in F_COS (y axis) indicate COS uptake, and negative values indicate COS emissions.

Although the empty-chamber regression effectively removed the baseline COS emission, some residual variability likely remained (RMSE = 6.9 pmol mol⁻¹ for [COS] _a and 2.73 pmol m⁻² s⁻¹ for F_COS). To evaluate the potential influence of this unresolved background variability, we propagated these errors to the regression-derived Γ_COS. When the uncertainty is included, the 95% confidence interval of Γ_COS widened from ± 53.2 to ± 93.4 pmol mol⁻¹ at 19.8°C and from ± 26.1 to ± 48.9 pmol mol⁻¹ at 25.0°C.

The large uncertainty at 19.8°C indicates that the corresponding Γ_COS value is statistically indistinguishable from zero. By contrast, the Γ_COS measured at 25°C remains significant even when this is propagated and instrumental uncertainty is considered. Even accounting for the reported QCLS uncertainty of approximately 7.5 pmol mol⁻¹ for COS (Kooijmans et al., 2016), the Γ_COS value at 25°C remains statistically robust.

3.1.2 Responses to Stomatal Conductance (Experiment 2). Figure 5 illustrates the observed relationships of V_COS, V_CO₂, and LRU with optimized g_sw for three sunflower plants. The observed values show that both V_COS and V_CO₂ decrease with declining g_sw, albeit at a slower rate at higher g_sw values. Specifically, as g_sw decreases from 1.0 mol m⁻² s⁻¹ to 0.4 mol m⁻² s⁻¹, V_COS declines by approximately 40%, compared to a decline of about 10% in V_CO₂. This difference persists even after accounting for the g_sw ratio between COS and CO₂ (1.21).

Figure 5. COS (a) and CO₂ (b) deposition velocities and LRU changes (c) along the optimized g_sw under leaf temperatures of approximately 25°C for three different sunflower plants, each represented in a different color.

The circles and error bars represent the median values and standard deviations of the data points for their respective 150-second intervals.

The greater sensitivity of V_COS to changes in g_sw is also reflected in the LRU, which consistently increases with g_sw across all sunflowers. These findings support the hypothesis that COS uptake is more sensitive to variations in g_sw compared to CO₂ uptake. Meanwhile, slight differences in V_COS and V_CO₂ values among individual sunflowers result in variations in LRU as well.

3.1.3 Responses to Leaf Temperature (Experiment 3). Figure 6 shows the observed V_COS and V_CO₂, and LRU against T_leaf for two sunflowers, with g_sw held approximately constant. For all sunflowers, V_COS decreases when temperatures exceed 25°C, whereas V_CO2 increases with T_leaf up to approximately 30°C. The absolute rate of decrease in V_COS is larger than the rate of increase in V_CO₂. Consequently, LRU decreases as T_leaf increases. This trend can be attributed to the temperature responses of Γ_COS or/and the lower optimum temperature for CA than RuBisCO.

Figure 6. Same as Figure 5, but as a function of T_leaf with maintained stomatal conductance at 0.6 ± 0.1 mol m⁻² s⁻¹ (mean ± standard deviation).

The temperature-dependent variations in V_COS and V_CO2 also differ slightly between individual sunflower plants. While V_COS exhibited relatively large observational errors, V_CO2 showed minimal errors. This suggests that while experimental uncertainties may influence V_COS, the variations in both V_COS and V_CO₂ are likely driven by micro-environmental differences, plant-to-plant variability, or other natural conditions, even within the same species grown in similar environments.

3.2 Model-assisted analysis

3.2.1 Optimization Performance. We present the optimized results of model S2, which provides the best fit to the observations (Section 3.2.2).

Table 5 quantifies how well the optimized model estimates [COS]_out, [CO₂]_out, and [H₂O]_out compared to observations. The optimized model simulated the mole fractions of all three gases more accurately, reflected by mostly reduced values of χ², MSE, and MBE. Notably, the model biases were mitigated, as shown by the low posterior MBE values for [COS]_out (0.15 pmol mol⁻¹), [CO₂]_out (– 0.01 μmol mol⁻¹), and [H₂O]_out (0.07 mmol mol⁻¹). The χ²_poste values for [COS]_out, [CO₂]_out, [H₂O]_out, and the state variables are 6.65, 1.68, 2.24, and 1.00, respectively. The large χ²_poste and RMSE for [COS]_out likely result from its relatively larger observational error.

Table 5. The statistical indices of the prior and posterior estimated [COS]_out, [CO₂]_out, and [H₂O]_out from model S2 compared to the observations with χ² changes of state term (x).

The units of RMSE and MBE of [COS]_out are pmol mol⁻¹, [CO₂]_out is in μmol mol⁻¹, and [H₂O]_out is mmol mol⁻¹.

Index	[COS]_out		[CO₂]_out		[H₂O]_out		Background (State x)
Index	Prior	Posterior	Prior	Posterior	Prior	Posterior	Prior	Posterior
χ²	30.00	6.65	100.00	1.68	3.00	2.24	0.00	1.00
RMSE	16.71	7.93	3.63	0.71	0.30	0.45	-	-
MBE	11.77	0.15	-1.52	-0.01	-0.14	0.07	-	-

To visualize these improvements, Figure 7 presents scatter plots comparing the simulated atmospheric mole fractions from the prior and posterior models to the observed values. The optimized atmospheric mole fractions exhibit improved agreement with the observed values across all sunflowers, improving the performance of the prior simulations. The optimized model explains the variability in the observations with high R² values from 0.93 to 0.99. The simulation errors, represented by the standard deviation of 500 forward simulations, were substantially reduced after optimization. Specifically for [COS]_out, errors decreased from 47.4 pmol mol⁻¹ to 12.5 pmol mol⁻¹, for [CO₂]_out from 10.8 μmol mol⁻¹ to 0.8 μmol mol⁻¹, and for [H₂O]_out from 0.6 mmol mol⁻¹ to 0.3 mmol mol⁻¹. However, discrepancies remain, such as in Sunflower 2. Several posterior [COS]_out and [CO₂]_out values of Sunflower 2 fall outside the weighted observational error range, likely due to measurement uncertainties.

Figure 7. Scatter plots comparing the simulated (model S2) and observed atmospheric mole fractions of COS (a), CO₂ (b), and H₂O (c) with the prior parameters (left) and optimized parameters (right) with a 1:1 line indicating perfect agreement.

The vertical error bars represent weighted observational errors, taken as the standard deviations of measurements, and the horizontal error bars represent prior errors (left) and posterior errors (right). Colors indicate different sunflower plants (black: Sunflower 2, blue: Sunflower 3, red: Sunflower 4).

In addition to reproducing the observations well, the optimization also reduced the parameter uncertainties. The optimized state values and their posterior errors, along with error reductions, are presented in Table 2. As expected, errors associated with all target parameters were significantly reduced, with an average error reduction of 48%. An error reduction of more than 92% was achieved for CO₂ parameters ∆ H_a,Rub and V_max,Rub. Prior uncertainties of T_eq,CA, m_COS, and V_max,CA were reduced by more than 30%, and the error reduction for g_sw was about 43%.

Parameter values also shifted meaningfully after optimization. The optimized slope of Γ_COS (m_COS, 22.4 pmol mol⁻¹ K⁻¹) is slightly increased to the initial setting (16.2 pmol mol⁻¹ K⁻¹). With the optimized value of m_COS, the variable T_eq,CA was adjusted to 39.7°C, and the values of V_max,CA for each plant were optimized ranging from 0.189 to 0.230 mol m⁻² s⁻¹. These values increased significantly from their priors, 30.0°C and 0.125 mol m⁻² s⁻¹, indicating higher optimum temperatures and higher catalyzation velocities compared to the prior settings. The optimized V_max,Rub ranged from 82.9 to 94.4 μmol m⁻² s⁻¹, while ∆ H_a,Rub did not change substantially. The ratio of V_max,CA to V_max,Rub which is crucial for calculating CA activity from V_max,Rub based on the assumption of a linear relationship, ranges from 2160 to 2770.

The optimized g_sw also showed consistent behavior. Comparisons of the optimized mean g_sw values of 0.64 mol m⁻² s⁻¹ with the prior values of 0.62 mol m⁻² s⁻¹ reveal slight differences. Errors in g_sw were reduced from 0.09 to 0.05 mol m⁻² s⁻¹. The optimized model yielded an average relative humidity within the leaf (RH_i) of 98.82 ± 0.04%. These results confirm that allowing for slight non-saturation in the intercellular airspace (through g_m,H₂O) had a negligible impact on the modeled fluxes, validating the assumption that the air within the intercellular airspace was effectively saturated under our experimental conditions. Simulations further confirmed that varying g_mw (<10 mol m⁻² s⁻¹) did not alter the modeled fluxes or mole fractions, indicating that its effect was negligible under our experimental conditions.

Figure 8 illustrates the posterior covariance matrix derived from Monte Carlo calculations. Although several state variables were highly correlated after optimization (values above 0.7), they were retained as state parameters because their simulation errors were substantially reduced. For instance, three variables of COS parameters (T_eq,CA, m_COS, and V_max,CA) were highly correlated, with values ranging from 0.69 to 0.87, as these parameters are all related to the mesophyll uptake of COS.

Figure 8. The covariance matrix for state variables.

Regarding g_sw, only the first data point of each sunflower is marked.

3.2.2 COS Compensation Point (Hypothesis H1). Table 6 summarizes the changes in total cost (J_tot) between prior and posterior estimations for each Γ_COS temperature function. Among the tested models, the lowest total cost was achieved with the linear model (S2), followed by the Arrhenius models S4 and S3, and the model without a compensation point (S1). These results confirm that incorporating Γ_COS with a linear temperature function into the leaf exchange model provides the best agreement with observations, as it minimizes the overall cost function and improves model performance. However, the total cost difference between the S2 model and the S4 model was only 1 unit.

Table 6. Prior (Pri) and posterior (Poste) contributions to the cost function of the state term, H₂O, CO₂, and COS parts, depending on the prescription of Γ_COS and its temperature dependence.

J_tot is the sum of costs for the states (J_bg), H₂O (J_H₂O), CO₂ (J_CO₂), and COS (J_COS).

No.	Description of Γ_COS		Cost
No.	Description of Γ_COS		J_bg	J_H₂O		J_CO₂		J_COS		J_tot
	Function	Based T [ °C]	Post	Pri	Post	Pri	Post	Pri	Post	Post
S1	Γ_COS = 0	-	54	144	97	4800	80	2437	349	580
S2	Linear	16.4	57		107		81	1440	320	564
S3	Arrhenius	19.8	59		100		80	2634	335	574
S4	Arrhenius	25.0	61		106		80	2634	319	565

To further evaluate the performance of these models, Figure 9 compares estimated Γ_COS with two types of observation-based values across temperatures. The first type is regression-based measurements from 15 data points at two temperatures in Experiment 1 (blue triangles; see Figure 4). The second type is indirectly derived Γ_COS in Experiments 2 and 3.

Figure 9. Posterior temperature functions for Γ_COS from S1 to S4 models, shown with orange lines and error ranges from 200 Monte Carlo simulations.

These are compared with Γ_COS values from Experiment 1 (blue triangles, regression-derived from two temperature points) and Experiments 2 and 3 (black circles with red edges, derived indirectly). Regression-derived Γ_COS measurements are 55.0 ± 53.2 pmol mol⁻¹ at 19.8°C and 138.7 ± 26.1 pmol mol⁻¹ at 25.0°C, detailed in Section 3.1.1). Indirectly derived values are averages with standard deviation error bars, calculated from parameters optimized through 200 Monte Carlo simulations (See Section 2.5.).

The optimized S2 model best captures the Γ_COS measurements derived from both regression and indirect methods, compared to other models. Specifically, the S2 model achieved the lowest RMSE with the indirect derived Γ_COS (39 pmol mol⁻¹). The RMSE values for the other models were: S1 = 50 pmol mol⁻¹, S3 = 49 pmol mol⁻¹, and S4 = 41 pmol mol⁻¹, respectively.

3.2.3 Response to stomatal conductance (Hypothesis H2). In Experiment 2, we confirmed that V_COS responds more strongly than V_CO2 at low g_sw values. To further interpret this behavior mechanistically, we explore how changes in deposition velocity due to g_sw are influenced by interactions with mesophyll conductance. We calculated AFR values (1 –[gas]_i/[gas]_a) for both gases using the optimized S2 model, as these values cannot be directly measured ( Figure 10). Simulations were performed at a constant T_leaf of 25°C.

Figure 10. Simulated changes in (1 – [gas]_i/[gas]_a) for COS (red) and CO₂ (blue) averaged among sunflowers 2, 3, and 4, with LRU (black, secondary y-axis) as a function of g_sw each sunflower (Results from the S2 model).

The lines represent averages, and the filled areas indicate the standard deviation of 500 simulations using posterior error propagation.

The model results indicate that for both gases, AFR decreases as g_sw increases, which provides support for Hypothesis 2. However, contrary to Hypothesis 2, which assumes that [COS]_i is nearly zero thus resulting in AFR for COS close to 1, the actual modeled values range from 0.2 to 0.6 depending on g_sw. This deviation indicates that [COS]_i is not negligible and suggests a dynamic COS consumption within the leaf that does not bring [COS]_i close to zero.

The model also reveals a distinct LRU pattern, showing sharp increases at low g_sw values followed by stabilization at higher g_sw. This response is consistent with observations from Experiment 2, where LRU exhibited similar trends in response to g_sw. These results underscore the differing sensitivities of COS and CO₂ uptake to g_sw, as reflected in both experimental and modeled data.

3.2.4 Response to leaf temperature (Hypothesis H3). To investigate the temperature function of enzyme activity separated from Γ_COS in V_COS, we calculated g_m,COS and g_m,CO₂ using the optimized model S2. Figure 11 shows the temperature dependency of g_m,COS and g_m,CO₂ for three sunflowers. The magnitudes of these dependencies vary among plants due to differences in optimized V_max values. The optimum temperature for g_m,COS is around 35 to 40°C, while for g_m,CO₂ it is approximately 35°C, which contradicts Hypothesis 3, proposing a lower optimum temperature for g_m,COS than for g_m,CO₂.

Figure 11. Modeled response of mesophyll conductances ( g_m) to leaf temperatures (T_leaf) for COS (a) and CO₂ (b) with three sunflowers (black: sunflower 2, blue: sunflower 3, red: sunflower 4, results from the S2 model).

The lines represent averaged values, and the filled areas indicate the standard deviation from 500 simulations using posterior error propagation.

The observed decline in V_COS above 25°C in Experiment 3 ( Figure 6a) is explained by the model-predicted impact of Γ_COS on COS uptake. While the optimum temperature for g_m,COS is approximately 35 to 40°C, the influence of temperature-dependent Γ_COS results in a much lower optimum temperature for V_COS, around 20°C. This is significantly lower than the optimum temperature for V_CO₂, which is approximately 30°C.

Overall, the model results suggest that the temperature dependence of Γ_COS plays a critical role in shaping the distinct responses of V_COS and V_COS₂.

4. Discussion

This study aimed to investigate how leaf COS and CO₂ fluxes respond differently to environmental changes and to identify which internal processes within leaves govern these differences. Laboratory experiments were conducted under controlled conditions to isolate the effects of stomatal conductance and temperature. However, to provide more insights in the internal processes that control COS exchange, we developed and optimized a coupled CO₂–COS–H₂O conductance model to mechanistically interpret the measurement data. Although the model involves some simplified representations of internal processes, these simplifications are minor and do not affect the overall interpretation. In this section, we discuss the uncertainties in both observations and model representations, the physiological implications of the observed COS compensation points, and their broader significance for biochemical parameters and the global COS budget.

4.1 Uncertainties in measurements and models

Before discussing measurement uncertainties, we emphasize that potential leakage effects were minimized in our experimental setup. Through improvements in our experimental setup, especially with the LI-6800 system incorporating new gasket materials (Advanced Polymer, Polyethylene, and Neoprene) and optimized flow paths, we minimized the gas leakage issues prevalent in previous systems like the LI-6400. No significant pressure differentials were observed during experiments, supporting the effectiveness of these enhancements. Additionally, maintaining the cuvette under slight positive pressure reduces the risk of inward leakage.

Nevertheless, several experimental limitations remain. First, the temperature range explored in this study was relatively restricted. Our optimization was based on data from Experiments 2 and 3, conducted at temperatures ranging from 19.0°C to 29.8°C. Therefore, additional experiments across a broader temperature range are necessary to confirm the existence and assess the temperature dependence of Γ_COS.

The choice of elevated COS concentration in the cuvette also introduces interpretative considerations. In our experiment, we increased the COS mole fraction in the cuvette to approximately 1000 pmol mol⁻¹, significantly above natural ambient levels, to enhance signal detection and reduce noise. The primary purpose of our empty chamber experiments was to eliminate the effects of emissions from chamber materials. Conducting these tests at similarly high mole fractions also helped mitigate any emissions that could arise from this higher mole fraction setting.

This high COS mole fraction possibly contributed to slightly higher AFR ( Figure 10) because the high ambient mole fraction may influence the internal concentration. [COS]_i/[COS]_a values of about 0.63 ± 0.13 were observed under elevated ambient [COS]_a conditions (Stimler et al., 2010), aligning with our results. Stimler et al. (2010) also reported a linear relationship between [COS]_i/[COS]_a and [COS]_a, likely due to retro-diffusion from the leaves. Therefore, when applying our results to natural conditions ([COS]_a about 500 pmol mol⁻¹, the AFR may decrease. However, the high AFR is also possibly due to the influence of Γ_COS. The simulated [CO₂]_i/[CO₂]_a ranges from 0.4 to 0.9, consistent with values previously reported for C₃ plants (0.5 – 0.8) (Black & Jones, 1985; Seibt et al., 2010; Tanner & Sinclair, 2015). Nevertheless, in Experiments 2 and 3, despite the high COS mole fractions, their consistent level throughout the experiments likely negated any impact on analyzing how g_sw and temperatures relate to V_COS and V_CO₂.

In addition to the experimental limitations discussed above, a practical limitation arises from the mole fraction range used for model optimization. Model parameters were optimized using data obtained under relatively high COS mole fraction conditions (~1000 pmol mol⁻¹) to ensure stable and precise flux measurements, whereas Γ_COS was determined from experiments conducted at lower inflowing concentrations (100–600 pmol mol⁻¹). This discrepancy in concentration ranges may introduce some uncertainty when extrapolating parameters between optimization and compensation-point estimation. Nevertheless, the model formulation remains internally consistent, and the derived parameters are valid for interpreting the relative temperature-dependent behavior of COS exchange. Future experiments targeting near-ambient COS mole fraction levels will be valuable to further validate the applicability of these optimized parameters and to evaluate potential retro-diffusion effects under more natural conditions.

From a modeling perspective, only the enzyme CA is considered in determining the mesophyll conductance of COS. However, other enzymes, such as RuBisCO and phosphoenolpyruvate carboxylase (PEP-C), are known to also catalyze COS uptake (Lorimer & Pierce, 1989; Protoschill-Krebs & Kesselmeier, 1992). The contribution of RuBisCO to COS uptake is relatively minor compared to CA (Protoschill-Krebs et al., 1996), and its activity has not yet been quantified.

An additional source of uncertainty arises from the simplified representation of COS mesophyll conductance in our model. While mesophyll diffusion was not explicitly parameterized, it was implicitly represented through the temperature-dependent CA activity function (Cho et al., 2023) that integrates both diffusional and biochemical processes. Nevertheless, this implicit treatment may not fully capture variations in diffusional resistance under different environmental or structural conditions, and thus its influence on the temperature dependence of COS uptake cannot be completely excluded. Future modeling studies incorporating explicit mesophyll diffusion parameterization—beyond the current CA-based formulation—would help to disentangle the relative contributions of diffusional and biochemical controls, as well as potential COS emissions from leaves, in regulating COS exchange.

Beyond these structural uncertainties in the model, it is important to note that the conductance model was designed as an exploratory diagnostic tool. Its purpose was to integrate the coupled behavior of CO₂, COS, and H₂O exchange and to mechanistically interpret the observed fluxes. Despite its simplifications in not considering minor features, such as outlet mass flow change and boundary ternary effect, this framework represents the first attempt to jointly optimize gas exchange for the three gases, thereby providing a process-based means to independently estimate the COS compensation point. Overall, this approach highlights the potential of combined gas-exchange measurement and modeling to advance our understanding of COS biogeochemistry.

Taken together, the remaining uncertainties in both COS measurements and model structure require careful interpretation. Concerning Hypothesis 1, Model S2 was selected as the best model due to its minimal posterior costs and lowest RMSE with observation-based Γ_COS, despite higher H₂O and background costs compared to S1, as shown in Table 6. Furthermore, the minor differences in posterior costs and RMSE with indirectly derived Γ_COS between S2 and S4 suggest that S4 is a viable alternative. The strong correlation between the temperature dependence of Γ_COS (m_COS) and V_max,CA complicates the precise and independent determination of these two parameters. Although S2 and S4 employ different temperature-dependent formulations of Γ_COS, both model structures consistently support the presence of a COS compensation point.

Accordingly, the exact value and temperature dependence of Γ_COS remain uncertain, but including a compensation point in the models, as in models S2 and S4, significantly improves their alignment with observations. Even if S4 were to better represent the true underlying mechanism, both model structures indicate an increase in Γ_COS with temperature, although the optimum temperature derived under Hypothesis 3 may shift slightly depending on the assumed functional form of the temperature response of CA activity.

4.2 Possible causes of a COS compensation point

COS emission can occur due to leaf stress induced by external factors during experiments. To minimize the risk of mechanical damage or stress, the chamber was gently attached, and leaves were inspected post-experiment for physical damage such as bruising, desiccation, or discoloration. No visible damage was observed, and the limited measurement duration further reduced the likelihood of stress-induced COS emissions.

Previous studies on COS leaf exchange experiments have reported positive Γ_COS values, but often concluded these are statistically indistinguishable from zero due to high variability. For example, Stimler et al. (2010) observed a Γ_COS of 60.7 pmol mol⁻¹ at 25°C, and attributed it to potential retro-diffusion under high COS mole fractions. Similarly, our Γ_COS at 20.0°C (55.0 ± 53.2 pmol mol⁻¹) was statistically insignificant, whereas a significant Γ_COS (138.7 ± 26.1 pmol mol⁻¹) was detected at 25°C. Considering that our experiments, like those of Stimler et al. (2010), were conducted under relatively high COS mole fractions, this pattern suggests that higher temperature may enhance diffusion-driven feedbacks. It should also be noted that our COS model does not explicitly account for mesophyll diffusion conductance, and thus part of the apparent emission function could be interpreted as an effect of internal diffusion-related mechanisms (e.g., retro-diffusion) within the leaf.

In addition to retro-diffusion, temperature-induced stress could also contribute to the observed COS compensation point. Previous studies, typically conducted below 25°C, did not assess temperature dependence. Our modeling revealed a linear relationship between Γ_COS and temperature, consistent with Gimeno et al. (2017), who reported higher Γ_COS in mosses at elevated temperatures. Although no visible stress was observed in our plants, temperature stress may have influenced Γ_COS. Gimeno et al. (2017) suggested that COS emissions could result from protein degradation under stress, releasing COS through the breakdown of sulfur-containing amino acids. This highlights the role of temperature-driven biochemical pathways in shaping Γ_COS values and supports the inclusion of Γ_COS in leaf gas exchange models.

Beyond temperature-driven stress, differences in species physiology also contribute to Γ_COS. Mosses studied by Gimeno et al. (2017) exhibited higher Γ_COS values than in vascular plants, likely due to enzymatic activity of associated fungi and bacteria. While microbial activity is not directly applicable to vascular plants, it underscores the importance of species-specific factors in determining COS emissions. In vascular plants, rapeseed is known to produce COS due to its high sulfur content, with Γ_COS exceeding 100 pmol mol⁻¹ during ripening and senescence (Belviso et al., 2022). However, no experiments have previously been conducted to detect Γ_COS in sunflowers.

Previous studies (e.g., Maseyk et al., 2014; Belviso et al., 2022) reported that COS emissions occur during the ripening and senescence phases, indicating that senescence-related processes could explain COS emissions rather than active uptake from living tissues. In Maseyk et al. (2014) part of these emissions may have originated from the soil, whereas Belviso et al. (2022) provided strong evidence for plant-derived senescence emissions. Additionally, Kesselmeier and Merk (1993) reported Γ_COS values ranging from 57 to 328 pmol mol⁻¹ in rapeseed and corn during flowering. In our study, measurements were conducted during the flowering phase, which could explain the observed COS emissions, although the exact source remains unclear. Sulfur emissions during senescence have been linked to the translocation of sulfur-containing amino acids and sulfur regulation in plant cells (Rennenberg, 1991).

Apart from biological factors, methodological advances may explain the discrepancies between our results and previous studies. We employed the Li-6800 system, which offers improved measurement accuracy, and evaluated an optimized conductance model incorporating temperature-dependent Γ_COS. Our findings confirm that all observations support an increase in Γ_COS with temperature.

Taken together, the existence of Γ_COS and its increase at higher temperatures may result from a combination of the factors discussed above. However, our current formulation of Γ_COS is expressed solely as a temperature-dependent function and does not explicitly include retro-diffusion effects. As a result, while the observed increase in Γ_COS with temperature is consistent with thermally driven processes, the potential contribution of internal diffusion feedbacks—particularly under elevated COS mole fractions—cannot be fully excluded.

At present, reliable measurements can only be obtained under relatively high COS mole fractions, which limits our ability to fully constrain Γ_COS dynamics near ambient conditions. Improving detection precision at low COS concentrations and incorporating explicit representations of internal diffusion in future models would enable a more direct evaluation of whether Γ_COS variability originates from retro-diffusion or from physiological and biochemical processes. Moreover, extending such measurements to different phenological stages and species, and exploring interactions with microbial associations and environmental stressors, will be essential for developing a more mechanistic understanding of COS exchange in plants.

4.3 Impact of COS compensation point on V_max,CA

When Γ_COS was explicitly considered in the optimization, the optimized ratio between V_max,CA and V_max,Rub ranges from 2160 to 2770, which is higher than previously obtained values of approximately 1200 from laboratory measurements with C₃ plants (Berry et al., 2013). Kooijmans et al. (2021) reported an average ratio of 1616 ± 562 based on field observations in summer months. In contrast, when Γ_COS was excluded (model S1), the optimized V_max,CA became smaller, resulting in ratios of 1197–1327, closely matching the values reported in previous studies. Thus, models that incorporate Γ_COS result in higher optimized values of V_max,CA and consequently to higher ratios between V_max,CA and V_max,Rub, indicating a higher maximum catalyzation velocity of CA.

4.4 Consequences for the COS global budget

Our evidence of decreasing V_COS between 20 and 25°C ( Figure 6a) supports lower biosphere uptake in high temperature regions. The current COS budget has a missing source of roughly 400 GgS year⁻¹, mainly due to the large biosphere sink calculated by the Simple Biosphere model (SiB4) in the tropics (Berry et al., 2013). In warm tropical forests, biosphere uptake would be significantly reduced.

The presence of Γ_COS could have implications for the global COS budget and the utilization of COS in estimating GPP, especially under conditions such as drought, where high temperatures and low humidity persist. Despite the uncertainty concerning Γ_COS in our experiments, including Γ_COS in our model better reproduced CO₂ and COS observations. This suggests that incorporating Γ_COS into global biosphere models could enhance the accuracy of COS flux estimates. Differences in temperatures and humidity responses between CO₂ and COS should also be considered. To further improve the large-scale modeling, it is recommended to measure Γ_COS and enzyme activity across diverse plant types, specifically tropical plants.

While our study focused on controlled conditions with a single species, larger variations would indeed be expected under natural conditions and across different species. Consequently, future research should therefore explore these factors in more diverse environmental settings to validate and generalize these findings.

Ethics and consent

Ethical approval and consent were not required.

Data availability

All datasets generated from the experiments are available on GitHub and have been archived on Zenodo under a CC-BY 4.0 license.

- DOI: [ https://doi.org/10.5281/zenodo.15489794] (Cho et al., 2025)

- GitHub: [ https://github.com/dkfkcho/COS_sunflower]

Software availability

- Source code available from: [ https://github.com/dkfkcho/COS_sunflower]

- Archived software available from: [ https://doi.org/10.5281/zenodo.15489794] (Cho et al., 2025)

- License: MIT License

Acknowledgements

We gratefully acknowledge Steven van Heuven (Energy and Sustainability Research Institute Groningen) for his valuable technical contributions, including providing access to the gas chromatography system and advising on experimental setup and calibration. Additionally, we would like to express our sincere gratitude to Nerea Ubierna Lopez (Florida Department of Environmental Protection, FL, USA) and reviewers for their invaluable and insightful comments, which greatly improved the quality of this work. The manuscript was prepared with the assistance of ChatGPT (GPT-4, OpenAI), used for improving English readability.

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Adnew GA, Pons TL, Koren G, et al.: Leaf-scale quantification of the effect of photosynthetic gas exchange on δ¹⁷O of atmospheric CO₂. Biogeosciences. 2020; 17(14): 3903–3922. Publisher Full Text
Adnew GA, Pons TL, Koren G, et al.: Exploring the potential of ∆¹⁷O in CO₂ for determining mesophyll conductance. Plant Physiol. 2023; 192(2): 1234–1253. PubMed Abstract | Publisher Full Text | Free Full Text
Asaf D, Rotenberg E, Tatarinov F, et al.: Ecosystem photosynthesis inferred from measurements of carbonyl sulphide flux. Nat Geosci. 2013; 6(3): 186–190. Publisher Full Text
Badger M, Collatz G: Studies on the kinetic mechanism of ribulose-1,5-bisphosphate carboxylase and oxygenase reactions with particular reference to the effect of temperature on kinetic parameters.Carnegie Institution of Washington Yearbook;1977, 76(1961).
Belviso S, Abadie C, Montagne D, et al.: Carbonyl Sulfide (COS) emissions in two agroecosystems in central France. PLoS One. 2022; 17(12): e0278584. PubMed Abstract | Publisher Full Text | Free Full Text
Berry J, Wolf A, Campbell JE, et al.: A coupled model of the global cycles of carbonyl sulfide and CO₂: a possible new window on the carbon cycle. JGR. Biogeosciences. 2013; 118(2): 842–852. Publisher Full Text
Black VJ, Jones HG: Plants and microclimate. J Appl Ecol. 1985; 22(2): 605–606. Publisher Full Text
Bonan GB: Forests and climate change: forcings, feedbacks, and the climate benefits of forests. Science. 2008; 320(5882): 1444–1449. PubMed Abstract | Publisher Full Text
Bosman PJ, Krol MC: ICLASS 1.1, a variational Inverse modelling framework for the Chemistry land-surface atmosphere soil slab model: description, validation, and application. Geosci Model Dev. 2023; 16(1): 47–74. Publisher Full Text
Brasseur GP, Jacob DJ: Modeling of atmospheric chemistry.2017. Publisher Full Text
Campbell JE, Carmichael GR, Chai T, et al.: Photosynthetic control of atmospheric carbonyl sulfide during the growing season. Science. 2008; 322(5904): 1085–1088. PubMed Abstract | Publisher Full Text
Cernusak LA, Ubierna N, Jenkins MW, et al.: Unsaturation of vapour pressure inside leaves of two conifer species. Sci Rep. 2018; 8(1): 7667. PubMed Abstract | Publisher Full Text | Free Full Text
Chevallier F, Bréon FM, Rayner PJ: Contribution of the Orbiting Carbon Observatory to the estimation of CO₂ sources and sinks: theoretical study in a variational data assimilation framework. J Geophys Res Atmos. 2007; 112(9). Publisher Full Text
Cho A, Kooijmans LMJ, Driever SM, et al.: COS_sunflower: dataset and software for: leaf chamber experiments on sunflowers indicate a temperature (v1.0). Zenodo. 2025. Publisher Full Text
Cho A, Kooijmans LM, Kohonen KM, et al.: Optimizing the carbonic anhydrase temperature response and stomatal conductance of carbonyl sulfide leaf uptake in the Simple Biosphere model (SiB4). Biogeosciences. 2023; 20(13): 2573–2594. Publisher Full Text
Cochavi A, Amer M, Stern R, et al.: Differential responses to two heatwave intensities in a mediterranean citrus orchard are identified by combining measurements of fluorescence and carbonyl Sulfide (COS) and CO₂ uptake. New Phytol. 2021; 230(4): 1394–1406. PubMed Abstract | Publisher Full Text
Collatz GJ, Ball JT, Grivet C, et al.: Physiological and environmental regulation of stomatal conductance, photosynthesis and transpiration: a model that includes a laminar boundary layer. Agric For Meteorol. 1991; 54(2–4): 107–136. Publisher Full Text
Daniel RM, Peterson ME, Danson MJ, et al.: The molecular basis of the effect of temperature on enzyme activity. Biochem J. 2010; 425(2): 353–360. PubMed Abstract | Publisher Full Text
Farquhar GD, Sharkey TD: Stomatal conductance and photosynthesis. Annu Rev Plant Physiol. 1982; 33(1): 317–345. Publisher Full Text
Farquhar GD, von Caemmerer S , Berry JA: A biochemical model of photosynthetic CO₂ assimilation in leaves of C₃ species. Planta. 1980; 149(1): 78–90. PubMed Abstract | Publisher Full Text
Garen JC, Branch HA, Borrego I, et al.: Gas exchange analysers exhibit large measurement error driven by internal thermal gradients. New Phytol. 2022; 236(2): 369–384. PubMed Abstract | Publisher Full Text
Geng C, Mu Y: Carbonyl sulfide and dimethyl sulfide exchange between lawn and the atmosphere. J Geophys Res D: Atmos. 2004; 109(12). Publisher Full Text
Gimeno TE, Ogée J, Royles J, et al.: Bryophyte gas-exchange dynamics along varying hydration status reveal a significant Carbonyl Sulphide (COS) sink in the dark and COS source in the light. New Phytol. 2017; 215(3): 965–976. PubMed Abstract | Publisher Full Text | Free Full Text
Goldan PD, Fall R, Kuster WC, et al.: Uptake of COS by growing vegetation: a major tropospheric sink. J Geophys Res. 1988; 93(D11): 14186–14192. Publisher Full Text
Hussain SB, Stinziano J, Pierre MO, et al.: Accurate photosynthetic parameter estimation at low stomatal conductance: effects of cuticular conductance and instrumental noise. Photosynth Res. 2024; 160(2–3): 111–124. PubMed Abstract | Publisher Full Text | Free Full Text
Jarman PD: The diffusion of carbon dioxide and water vapour through stomata. J Exp Bot. 1974; 25(5): 927–936. Publisher Full Text
Kesselmeier J, Merk L: Exchange of Carbonyl Sulfide (COS) between agricultural plants and the atmosphere: Studies on the deposition of COS to peas, corn and rapeseed. Biogeochemistry. 1993; 23(1): 47–59. Publisher Full Text
Kettle AJ, Kuhn U, Von Hobe M, et al.: Global budget of atmospheric Carbonyl Sulfide: temporal and spatial variations of the dominant sources and sinks. J Geophys Res. 2002; 107(22): ACH 25-1–ACH 25-16. Publisher Full Text
Kohonen KM, Dewar R, Tramontana G, et al.: Intercomparison of methods to estimate gross primary production based on CO₂ and COS flux measurements. Biogeosciences. 2022; 19(17): 4067–4088. PubMed Abstract | Publisher Full Text | Free Full Text
Kooijmans LM, Cho A, Ma J, et al.: Evaluation of Carbonyl Sulfide biosphere exchange in the Simple Biosphere Model (SiB4). Biogeosciences. 2021; 18(24): 6547–6565. Publisher Full Text
Kooijmans LMJ, Sun W, Aalto J, et al.: Influences of light and humidity on Carbonyl Sulfide-based estimates of photosynthesis. Proc Natl Acad Sci U S A. 2019; 116(7): 2470–2475. PubMed Abstract | Publisher Full Text | Free Full Text
Kooijmans LMJ, Uitslag NAM, Zahniser MS, et al.: Continuous and high-precision atmospheric concentration measurements of COS, CO₂, CO and H₂O using a Quantum Cascade Laser Spectrometer (QCLS). Atmos Meas Tech. 2016; 9(11): 5293–5314. Publisher Full Text
Kuhn U, Kesselmeier J: Environmental variables controlling the uptake of Carbonyl Sulfide by lichens. J Geophys Res. 2000; 105(D22): 26783–26792. Publisher Full Text
Lai J, Kooijmans LMJ, Sun W, et al.: Terrestrial photosynthesis inferred from plant carbonyl sulfide uptake. Nature. 2024; 634(8035): 855–861. PubMed Abstract | Publisher Full Text
Le Roux X, Bariac T, Sinoquet H, et al.: Spatial distribution of leaf water-use efficiency and carbon isotope discrimination within an isolated tree crown. Plant, Cell and Environment. 2001; 24(10): 1021–1032. Publisher Full Text
Lobo FA, de Barros MP , Dalmagro HJ, et al.: Fitting net photosynthetic light-response curves with Microsoft Excel - a critical look at the models. Photosynthetica. 2013; 51(3): 445–456. Publisher Full Text
Lorimer GH, Pierce J: Carbonyl sulfide: an alternate substrate for but not an activator of ribulose-1,5-bisphosphate carboxylase. J Biol Chem. 1989; 264(5): 2764–2772. PubMed Abstract | Publisher Full Text
Maseyk K, Berry JA, Billesbach D, et al.: Sources and sinks of Carbonyl Sulfide in an agricultural field in the Southern Great Plains. Proc Natl Acad Sci U S A. 2014; 111(25): 9064–9069. PubMed Abstract | Publisher Full Text | Free Full Text
Montzka SA, Calvert P, Hall BD, et al.: On the global distribution, seasonality, and budget of atmospheric Carbonyl Sulfide (COS) and some similarities to CO₂. J Geophys Res. 2007; 112(9). Publisher Full Text
Notni J, Schenk S, Protoschill-Krebs G, et al.: The missing link in COS metabolism: a model study on the reactivation of carbonic anhydrase from its hydrosulfide analogue. ChemBioChem. 2007; 8(5): 530–536. PubMed Abstract | Publisher Full Text
Ogée J, Sauze J, Kesselmeier J, et al.: A new mechanistic framework to predict OCS fluxes from soils. Biogeosciences. 2016; 13(8): 2221–2240. Publisher Full Text
Protoschill-Krebs G, Kesselmeier J: Enzymatic pathways for the Consumption of Carbonyl Sulphide (COS) by higher plants. Bot Acta. 1992; 105(3): 206–212. Publisher Full Text
Protoschill-Krebs G, Wilhelm C, Kesselmeier J: Consumption of Carbonyl Sulphide (COS) by higher plant Carbonic Anhydrase (CA). Atmos Environ. 1996; 30(18): 3151–3156. Publisher Full Text
Reichstein M, Falge E, Baldocchi D, et al.: On the separation of net ecosystem exchange into assimilation and ecosystem respiration: review and improved algorithm. Glob Chang Biol. 2005; 11(9): 1424–1439. Publisher Full Text
Rennenberg H: The significance of higher plants in the emission of sulfur compounds from Terrestrial Ecosystems. Trace Gas Emissions by Plants.1991. Publisher Full Text
Salvucci ME, Osteryoung KW, Crafts-Brandner SJ, et al.: Exceptional sensitivity of Rubisco activase to thermal denaturation in vitro and in vivo. Plant Physiol. 2001; 127(3): 1053–1064. PubMed Abstract | Publisher Full Text | Free Full Text
Sandoval-Soto L, Stanimirov M, von Hobe M , et al.: Global uptake of Carbonyl Sulfide (COS) by terrestrial vegetation: estimates corrected by deposition velocities normalized to the uptake of carbon dioxide (CO₂). Biogeosciences. 2005; 2(2): 125–132. Publisher Full Text
Seibt U, Kesselmeier J, Sandoval-Soto L, et al.: A kinetic analysis of leaf uptake of COS and its relation to transpiration, photosynthesis and carbon isotope fractionation. Biogeosciences. 2010; 7(1): 333–341. Publisher Full Text
Stimler K, Berry JA, Montzka SA, et al.: Association between Carbonyl Sulfide uptake and ¹⁸∆ during gas exchange in C₃ and C₄ leaves. Plant Physiol. 2011; 157(1): 509–517. PubMed Abstract | Publisher Full Text | Free Full Text
Stimler K, Montzka SA, Berry JA, et al.: Relationships between Carbonyl Sulfide (COS) and CO₂ during leaf gas exchange. New Phytol. 2010; 186(4): 869–878. PubMed Abstract | Publisher Full Text
Sun W, Kooijmans LM, Maseyk K, et al.: Soil fluxes of Carbonyl Sulfide (COS), carbon monoxide, and carbon dioxide in a boreal forest in southern Finland. Atmos Chem Phys. 2018; 18(2): 1363–1378. Publisher Full Text
Sun W, Maseyk K, Lett C, et al.: A soil diffusion-reaction model for surface COS flux: COSSM v1. Geosci Model Dev. 2015; 8(10): 3055–3070. Publisher Full Text
Tanner CB, Sinclair TR: Efficient water use in crop production: research or re-search? In: Limitations to Efficient Water Use in Crop Production. 2015: 1–27. Publisher Full Text
Tarantola A: Inverse problem theory and methods for model parameter estimation.2005. Publisher Full Text
Tcherkez GG, Farquhar GD, Andrews TJ: Despite slow catalysis and confused substrate specificity, all ribulose bisphosphate carboxylases may be nearly perfectly optimized. Proc Natl Acad Sci USA. 2006; 103(19): 7246–7251. PubMed Abstract | Publisher Full Text | Free Full Text
von Caemmerer S , Evans JR: Temperature responses of mesophyll conductance differ greatly between species. Plant Cell Environ. 2015; 38(4): 629–637. PubMed Abstract | Publisher Full Text
von Caemmerer S , Farquhar GD: Some relationships between the biochemistry of photosynthesis and the gas exchange of leaves. Planta. 1981; 153(4): 376–387. PubMed Abstract | Publisher Full Text
Williams TG, Flanagan LB: Effect of changes in water content on photosynthesis, transpiration and discrimination against ¹³CO₂ and C¹⁸O¹⁶O in Pleurozium and Sphagnum. Oecologia. 1996; 108(1): 38–46. PubMed Abstract | Publisher Full Text
Wohlfahrt G, Gerdel K, Migliavacca M, et al.: Sun-induced fluorescence and gross primary productivity during a heat wave. Sci Rep. 2018; 8(1): 14169. PubMed Abstract | Publisher Full Text | Free Full Text
Wohlfahrt G, Gu L: The many meanings of gross photosynthesis and their implication for photosynthesis research from leaf to globe. Plant Cell Environ. 2015; 38(12): 2500–2507. PubMed Abstract | Publisher Full Text | Free Full Text
Wong SC, Canny MJ, Holloway-Phillips M, et al.: Humidity gradients in the air spaces of leaves. Nat Plants. 2022; 8(8): 971–978. PubMed Abstract | Publisher Full Text

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Publication information

Section

Research Article

Published

April 10, 2026

DOI

https://doi.org/10.12688/openreseurope.20235.3

Versions

April 10, 2026 (Version of Record 1.0)
December 8, 2025 (Published Manuscript Under Review 2.0)
August 5, 2025 (Published Manuscript Under Review 1.0)

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European Commission

Grant ID(s): 742798

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Keywords

Leaf chamber experiment, Leaf conductance model, Carbonyl sulfide, Photosynthesis, Leaf relative uptake, Stomatal conductance, Compensation point

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Ara Cho

Meteorology and Air Quality, Wageningen University & Research, Wageningen, Gelderland, The Netherlands

Roles

Corresponding Author, Co-Author, Conceptualization, Data Curation, Formal Analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – Original Draft Preparation, Writing – Review & Editing

0000-0002-6440-4771

ara.cho@wur.nl

Linda M.J. Kooijmans

Meteorology and Air Quality, Wageningen University & Research, Wageningen, Gelderland, The Netherlands

Roles

Co-Author, Conceptualization, Data Curation, Formal Analysis, Investigation, Methodology, Resources, Supervision, Validation, Writing – Original Draft Preparation, Writing – Review & Editing

info@lindakooijmans.nl

Steven M. Driever

Centre for Crop Systems Analysis, Wageningen University & Research, Wageningen, Gelderland, The Netherlands

Roles

Co-Author, Data Curation, Formal Analysis, Methodology, Resources, Writing – Original Draft Preparation, Writing – Review & Editing

0000-0003-4144-6028

steven.driever@wur.nl

Maarten Wassenaar

Horticulture and Product Physiology, Wageningen University & Research, Wageningen, Gelderland, The Netherlands

Roles

Co-Author, Data Curation, Formal Analysis, Methodology, Resources, Writing – Review & Editing

maarten.wassenaar@wur.nl

Gerbrand Koren

Copernicus Institute of Sustainable Development, Utrecht University, Utrecht, Utrecht, The Netherlands

Roles

Co-Author, Formal Analysis, Methodology, Software, Writing – Review & Editing

0000-0002-2275-0713

g.b.koren@uu.nl

Sophie L. Baartman

Meteorology and Air Quality, Wageningen University & Research, Wageningen, Gelderland, The Netherlands

Roles

Co-Author, Resources, Writing – Review & Editing

0000-0001-5394-0897

sophie.baartman@wur.nl

Leon Mossink

Centre for Crop Systems Analysis, Wageningen University & Research, Wageningen, Gelderland, The Netherlands

Roles

Co-Author, Resources, Writing – Review & Editing

leon.mossink@wur.nl

Maarten C. Krol

Meteorology and Air Quality, Wageningen University & Research, Wageningen, Gelderland, The Netherlands

Institute for Marine and Atmospheric Research, Utrecht University, Utrecht, The Netherlands

Roles

Co-Author, Conceptualization, Formal Analysis, Funding Acquisition, Investigation, Methodology, Project Administration, Software, Supervision, Writing – Review & Editing

0000-0002-3506-2477

maarten.krol@wur.nl

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[1] Adnew GA, Hofmann ME, Pons TL, et al.: Leaf scale quantification of the effect of photosynthetic gas exchange on ∆₄₇ of CO₂. Sci Rep. 2021; 11(1): 14023. PubMed Abstract | Publisher Full Text | Free Full Text

[2] Adnew GA, Pons TL, Koren G, et al.: Leaf-scale quantification of the effect of photosynthetic gas exchange on δ¹⁷O of atmospheric CO₂. Biogeosciences. 2020; 17(14): 3903–3922. Publisher Full Text

[3] Adnew GA, Pons TL, Koren G, et al.: Exploring the potential of ∆¹⁷O in CO₂ for determining mesophyll conductance. Plant Physiol. 2023; 192(2): 1234–1253. PubMed Abstract | Publisher Full Text | Free Full Text

[4] Asaf D, Rotenberg E, Tatarinov F, et al.: Ecosystem photosynthesis inferred from measurements of carbonyl sulphide flux. Nat Geosci. 2013; 6(3): 186–190. Publisher Full Text

[5] Badger M, Collatz G: Studies on the kinetic mechanism of ribulose-1,5-bisphosphate carboxylase and oxygenase reactions with particular reference to the effect of temperature on kinetic parameters.Carnegie Institution of Washington Yearbook;1977, 76(1961).

[6] Belviso S, Abadie C, Montagne D, et al.: Carbonyl Sulfide (COS) emissions in two agroecosystems in central France. PLoS One. 2022; 17(12): e0278584. PubMed Abstract | Publisher Full Text | Free Full Text

[7] Berry J, Wolf A, Campbell JE, et al.: A coupled model of the global cycles of carbonyl sulfide and CO₂: a possible new window on the carbon cycle. JGR. Biogeosciences. 2013; 118(2): 842–852. Publisher Full Text

[8] Black VJ, Jones HG: Plants and microclimate. J Appl Ecol. 1985; 22(2): 605–606. Publisher Full Text

[9] Bonan GB: Forests and climate change: forcings, feedbacks, and the climate benefits of forests. Science. 2008; 320(5882): 1444–1449. PubMed Abstract | Publisher Full Text

[10] Bosman PJ, Krol MC: ICLASS 1.1, a variational Inverse modelling framework for the Chemistry land-surface atmosphere soil slab model: description, validation, and application. Geosci Model Dev. 2023; 16(1): 47–74. Publisher Full Text

[11] Brasseur GP, Jacob DJ: Modeling of atmospheric chemistry.2017. Publisher Full Text

[12] Campbell JE, Carmichael GR, Chai T, et al.: Photosynthetic control of atmospheric carbonyl sulfide during the growing season. Science. 2008; 322(5904): 1085–1088. PubMed Abstract | Publisher Full Text

[13] Cernusak LA, Ubierna N, Jenkins MW, et al.: Unsaturation of vapour pressure inside leaves of two conifer species. Sci Rep. 2018; 8(1): 7667. PubMed Abstract | Publisher Full Text | Free Full Text

[14] Chevallier F, Bréon FM, Rayner PJ: Contribution of the Orbiting Carbon Observatory to the estimation of CO₂ sources and sinks: theoretical study in a variational data assimilation framework. J Geophys Res Atmos. 2007; 112(9). Publisher Full Text

[15] Cho A, Kooijmans LMJ, Driever SM, et al.: COS_sunflower: dataset and software for: leaf chamber experiments on sunflowers indicate a temperature (v1.0). Zenodo. 2025. Publisher Full Text

[16] Cho A, Kooijmans LM, Kohonen KM, et al.: Optimizing the carbonic anhydrase temperature response and stomatal conductance of carbonyl sulfide leaf uptake in the Simple Biosphere model (SiB4). Biogeosciences. 2023; 20(13): 2573–2594. Publisher Full Text

[17] Cochavi A, Amer M, Stern R, et al.: Differential responses to two heatwave intensities in a mediterranean citrus orchard are identified by combining measurements of fluorescence and carbonyl Sulfide (COS) and CO₂ uptake. New Phytol. 2021; 230(4): 1394–1406. PubMed Abstract | Publisher Full Text

[18] Collatz GJ, Ball JT, Grivet C, et al.: Physiological and environmental regulation of stomatal conductance, photosynthesis and transpiration: a model that includes a laminar boundary layer. Agric For Meteorol. 1991; 54(2–4): 107–136. Publisher Full Text

[19] Daniel RM, Peterson ME, Danson MJ, et al.: The molecular basis of the effect of temperature on enzyme activity. Biochem J. 2010; 425(2): 353–360. PubMed Abstract | Publisher Full Text

[20] Farquhar GD, Sharkey TD: Stomatal conductance and photosynthesis. Annu Rev Plant Physiol. 1982; 33(1): 317–345. Publisher Full Text

[21] Farquhar GD, von Caemmerer S , Berry JA: A biochemical model of photosynthetic CO₂ assimilation in leaves of C₃ species. Planta. 1980; 149(1): 78–90. PubMed Abstract | Publisher Full Text

[22] Garen JC, Branch HA, Borrego I, et al.: Gas exchange analysers exhibit large measurement error driven by internal thermal gradients. New Phytol. 2022; 236(2): 369–384. PubMed Abstract | Publisher Full Text

[23] Geng C, Mu Y: Carbonyl sulfide and dimethyl sulfide exchange between lawn and the atmosphere. J Geophys Res D: Atmos. 2004; 109(12). Publisher Full Text

[24] Gimeno TE, Ogée J, Royles J, et al.: Bryophyte gas-exchange dynamics along varying hydration status reveal a significant Carbonyl Sulphide (COS) sink in the dark and COS source in the light. New Phytol. 2017; 215(3): 965–976. PubMed Abstract | Publisher Full Text | Free Full Text

[25] Goldan PD, Fall R, Kuster WC, et al.: Uptake of COS by growing vegetation: a major tropospheric sink. J Geophys Res. 1988; 93(D11): 14186–14192. Publisher Full Text

[26] Hussain SB, Stinziano J, Pierre MO, et al.: Accurate photosynthetic parameter estimation at low stomatal conductance: effects of cuticular conductance and instrumental noise. Photosynth Res. 2024; 160(2–3): 111–124. PubMed Abstract | Publisher Full Text | Free Full Text

[27] Jarman PD: The diffusion of carbon dioxide and water vapour through stomata. J Exp Bot. 1974; 25(5): 927–936. Publisher Full Text

[28] Kesselmeier J, Merk L: Exchange of Carbonyl Sulfide (COS) between agricultural plants and the atmosphere: Studies on the deposition of COS to peas, corn and rapeseed. Biogeochemistry. 1993; 23(1): 47–59. Publisher Full Text

[29] Kettle AJ, Kuhn U, Von Hobe M, et al.: Global budget of atmospheric Carbonyl Sulfide: temporal and spatial variations of the dominant sources and sinks. J Geophys Res. 2002; 107(22): ACH 25-1–ACH 25-16. Publisher Full Text

[30] Kohonen KM, Dewar R, Tramontana G, et al.: Intercomparison of methods to estimate gross primary production based on CO₂ and COS flux measurements. Biogeosciences. 2022; 19(17): 4067–4088. PubMed Abstract | Publisher Full Text | Free Full Text

[31] Kooijmans LM, Cho A, Ma J, et al.: Evaluation of Carbonyl Sulfide biosphere exchange in the Simple Biosphere Model (SiB4). Biogeosciences. 2021; 18(24): 6547–6565. Publisher Full Text

[32] Kooijmans LMJ, Sun W, Aalto J, et al.: Influences of light and humidity on Carbonyl Sulfide-based estimates of photosynthesis. Proc Natl Acad Sci U S A. 2019; 116(7): 2470–2475. PubMed Abstract | Publisher Full Text | Free Full Text

[33] Kooijmans LMJ, Uitslag NAM, Zahniser MS, et al.: Continuous and high-precision atmospheric concentration measurements of COS, CO₂, CO and H₂O using a Quantum Cascade Laser Spectrometer (QCLS). Atmos Meas Tech. 2016; 9(11): 5293–5314. Publisher Full Text

[34] Kuhn U, Kesselmeier J: Environmental variables controlling the uptake of Carbonyl Sulfide by lichens. J Geophys Res. 2000; 105(D22): 26783–26792. Publisher Full Text

[35] Lai J, Kooijmans LMJ, Sun W, et al.: Terrestrial photosynthesis inferred from plant carbonyl sulfide uptake. Nature. 2024; 634(8035): 855–861. PubMed Abstract | Publisher Full Text

[36] Le Roux X, Bariac T, Sinoquet H, et al.: Spatial distribution of leaf water-use efficiency and carbon isotope discrimination within an isolated tree crown. Plant, Cell and Environment. 2001; 24(10): 1021–1032. Publisher Full Text

[37] Lobo FA, de Barros MP , Dalmagro HJ, et al.: Fitting net photosynthetic light-response curves with Microsoft Excel - a critical look at the models. Photosynthetica. 2013; 51(3): 445–456. Publisher Full Text

[38] Lorimer GH, Pierce J: Carbonyl sulfide: an alternate substrate for but not an activator of ribulose-1,5-bisphosphate carboxylase. J Biol Chem. 1989; 264(5): 2764–2772. PubMed Abstract | Publisher Full Text

[39] Maseyk K, Berry JA, Billesbach D, et al.: Sources and sinks of Carbonyl Sulfide in an agricultural field in the Southern Great Plains. Proc Natl Acad Sci U S A. 2014; 111(25): 9064–9069. PubMed Abstract | Publisher Full Text | Free Full Text

[40] Montzka SA, Calvert P, Hall BD, et al.: On the global distribution, seasonality, and budget of atmospheric Carbonyl Sulfide (COS) and some similarities to CO₂. J Geophys Res. 2007; 112(9). Publisher Full Text

[41] Notni J, Schenk S, Protoschill-Krebs G, et al.: The missing link in COS metabolism: a model study on the reactivation of carbonic anhydrase from its hydrosulfide analogue. ChemBioChem. 2007; 8(5): 530–536. PubMed Abstract | Publisher Full Text

[42] Ogée J, Sauze J, Kesselmeier J, et al.: A new mechanistic framework to predict OCS fluxes from soils. Biogeosciences. 2016; 13(8): 2221–2240. Publisher Full Text

[43] Protoschill-Krebs G, Kesselmeier J: Enzymatic pathways for the Consumption of Carbonyl Sulphide (COS) by higher plants. Bot Acta. 1992; 105(3): 206–212. Publisher Full Text

[44] Protoschill-Krebs G, Wilhelm C, Kesselmeier J: Consumption of Carbonyl Sulphide (COS) by higher plant Carbonic Anhydrase (CA). Atmos Environ. 1996; 30(18): 3151–3156. Publisher Full Text

[45] Reichstein M, Falge E, Baldocchi D, et al.: On the separation of net ecosystem exchange into assimilation and ecosystem respiration: review and improved algorithm. Glob Chang Biol. 2005; 11(9): 1424–1439. Publisher Full Text

[46] Rennenberg H: The significance of higher plants in the emission of sulfur compounds from Terrestrial Ecosystems. Trace Gas Emissions by Plants.1991. Publisher Full Text

[47] Salvucci ME, Osteryoung KW, Crafts-Brandner SJ, et al.: Exceptional sensitivity of Rubisco activase to thermal denaturation in vitro and in vivo. Plant Physiol. 2001; 127(3): 1053–1064. PubMed Abstract | Publisher Full Text | Free Full Text

[48] Sandoval-Soto L, Stanimirov M, von Hobe M , et al.: Global uptake of Carbonyl Sulfide (COS) by terrestrial vegetation: estimates corrected by deposition velocities normalized to the uptake of carbon dioxide (CO₂). Biogeosciences. 2005; 2(2): 125–132. Publisher Full Text

[49] Seibt U, Kesselmeier J, Sandoval-Soto L, et al.: A kinetic analysis of leaf uptake of COS and its relation to transpiration, photosynthesis and carbon isotope fractionation. Biogeosciences. 2010; 7(1): 333–341. Publisher Full Text

[50] Stimler K, Berry JA, Montzka SA, et al.: Association between Carbonyl Sulfide uptake and ¹⁸∆ during gas exchange in C₃ and C₄ leaves. Plant Physiol. 2011; 157(1): 509–517. PubMed Abstract | Publisher Full Text | Free Full Text

[51] Stimler K, Montzka SA, Berry JA, et al.: Relationships between Carbonyl Sulfide (COS) and CO₂ during leaf gas exchange. New Phytol. 2010; 186(4): 869–878. PubMed Abstract | Publisher Full Text

[52] Sun W, Kooijmans LM, Maseyk K, et al.: Soil fluxes of Carbonyl Sulfide (COS), carbon monoxide, and carbon dioxide in a boreal forest in southern Finland. Atmos Chem Phys. 2018; 18(2): 1363–1378. Publisher Full Text

[53] Sun W, Maseyk K, Lett C, et al.: A soil diffusion-reaction model for surface COS flux: COSSM v1. Geosci Model Dev. 2015; 8(10): 3055–3070. Publisher Full Text

[54] Tanner CB, Sinclair TR: Efficient water use in crop production: research or re-search? In: Limitations to Efficient Water Use in Crop Production. 2015: 1–27. Publisher Full Text

[55] Tarantola A: Inverse problem theory and methods for model parameter estimation.2005. Publisher Full Text

[56] Tcherkez GG, Farquhar GD, Andrews TJ: Despite slow catalysis and confused substrate specificity, all ribulose bisphosphate carboxylases may be nearly perfectly optimized. Proc Natl Acad Sci USA. 2006; 103(19): 7246–7251. PubMed Abstract | Publisher Full Text | Free Full Text

[57] von Caemmerer S , Evans JR: Temperature responses of mesophyll conductance differ greatly between species. Plant Cell Environ. 2015; 38(4): 629–637. PubMed Abstract | Publisher Full Text

[58] von Caemmerer S , Farquhar GD: Some relationships between the biochemistry of photosynthesis and the gas exchange of leaves. Planta. 1981; 153(4): 376–387. PubMed Abstract | Publisher Full Text

[59] Williams TG, Flanagan LB: Effect of changes in water content on photosynthesis, transpiration and discrimination against ¹³CO₂ and C¹⁸O¹⁶O in Pleurozium and Sphagnum. Oecologia. 1996; 108(1): 38–46. PubMed Abstract | Publisher Full Text

[60] Wohlfahrt G, Gerdel K, Migliavacca M, et al.: Sun-induced fluorescence and gross primary productivity during a heat wave. Sci Rep. 2018; 8(1): 14169. PubMed Abstract | Publisher Full Text | Free Full Text

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Leaf chamber experiments on sunflowers indicate a temperature-dependent compensation point of carbonyl sulfide

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Ara Cho

Linda M.J. Kooijmans

Steven M. Driever

Maarten Wassenaar

Gerbrand Koren

Sophie L. Baartman

Leon Mossink

Maarten C. Krol

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