Acclimation to fluctuating light impacts the rapidity and diurnal ... · PDF file02-02-2018 · Katul GG, Oren R, Manzoni S, Higgins C, Parlange MB (2012) Evapotranspiration: A process

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Acclimation to fluctuating light impacts the rapidity of response and 1

diurnal rhythm of stomatal conductance 2

Jack S.A. Matthews, Silvere Vialet-Chabrand, and Tracy Lawson* 3

School of Biological Sciences, University of Essex, Colchester, CO4 3SQ, UK. 4

* Corresponding author: [email protected] 5

JSAM, SVC & TL designed the experiments; JSAM performed the measurements; all 6 authors contributed to data analyses and writing the MS. 7

JSAM is funded by a PhD NERC DTP studentship (Env-East DTP E14EE). SV-C was supported 8 through a BBSRC grant BB/1001187/1 & BB/N021061/1 awarded to TL. 9

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Short title: Stomatal acclimatory response to growth light. 11

One-sentence summary: Fluctuating light influences stomatal responses in Arabidopsis 12

thaliana independently of the growth light intensity. 13

Key words: Acclimation, Circadian, Diurnal, Kinetics, Fluctuating Light, Stomatal 14

Conductance 15

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Abstract: 17

Plant acclimation to growth light environment has been studied extensively; however, the 18

majority of these studies have focused on light intensity and photo-acclimation, with few 19

studies exploring the impact of dynamic growth light on stomatal acclimation and behavior. 20

To assess the impact of growth light regime on stomatal acclimation, we grew Arabidopsis 21

thaliana plants in three different lighting regimes (with the same average daily intensity); 22

fluctuating with a fixed pattern of light, fluctuating with a randomized pattern of light 23

(sinusoidal), and non-fluctuating (square wave), to assess the effect of light regime dynamics 24

on gas exchange. We demonstrated that gs (stomatal conductance to water vapor) 25

acclimation is influenced by both intensity and light pattern, modifying the stomatal kinetics 26

at different times of the day and resulting in differences in the rapidity and magnitude of the 27

gs response. We also describe and quantify the response to an internal signal that 28

uncouples variation in A and gs over the majority of the diurnal period, and represents 25% 29

of the total diurnal gs. This gs response can be characterized by a Gaussian element and 30

when incorporated into the widely used Ball-Berry Model greatly improved the prediction of 31

gs in a dynamic environment. From these findings, we conclude that acclimation of gs to 32

Plant Physiology Preview. Published on February 2, 2018, as DOI:10.1104/pp.17.01809

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growth light could be an important strategy for maintaining carbon fixation and overall plant 33

water status, and should be considered when inferring responses in the field from 34

laboratory-based experiments. 35

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Abbreviations 38 39

A – Net CO2 assimilation rate per unit leaf area 40

Ai – Light saturated carbon assimilation rate at 1000 µmol m-2 s-1 41

FL – Plants grown under fluctuating light 42

FLH – Plants grown under fluctuating high light 43

FLL - Plants grown under fluctuating low light 44

FLHigh – Measurements under diurnal fluctuating high light conditions 45

FLLow – Measurements under diurnal fluctuating low light conditions 46

gs – Stomatal conductance to water vapor 47

Gd – Final values of gs at 100 µmol m2 s1 PPFD for stomatal closure 48

Gi – Final values of gs at 1000 µmol m2 s1 PPFD for stomatal opening 49

Gsin – Maximum gs reached in the Gaussian element during the diurnal measurement 50

PPFD – Photosynthetic photon flux density 51

Rsin – Relative percentage of Gaussian driven gs 52

SN – Plants grown under sinusoidal light 53

SNH – Plants grown under sinusoidal high light 54

SNL – Plants grown under sinusoidal low light 55

SNHigh – Measurements under diurnal sinusoidal high light conditions 56

SNLow – Measurements under diurnal sinusoidal low light conditions 57

SQ – Plants grown under square-wave light 58

SQH – Plants grown under square-wave high light 59

SQL – Plants grown under square-wave low light 60

SQHigh – Measurements under diurnal square wave high light conditions 61

SQLow – Measurements under diurnal square wave low light conditions 62

Tmsin – Time at the centre of the peak of the Gaussian element during the diurnal measurement 63

Tssin – Parameter related to the width of the peak of the Gaussian element during the diurnal 64 measurement 65

VPD – Vapor pressure deficit 66

Wi – Intrinsic water use efficiency 67

τai – Time constant for an increase in rate of carbon assimilation at 1000 µmol m2 s1 68

τd – Time constant for stomatal closure 69

τi – Time constant for stomatal opening 70

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Introduction 73 74 Despite typically occupying only 0.3–5% of the leaf surface, stomata control ca. 95% 75

of all gas exchange between the external environment and leaf interior, and it has been 76

estimated that 60% of all precipitation that falls on terrestrial ecosystems is taken up by 77

plants and transpired through stomatal pores (Morison, 2003; Katul et al., 2012). With the 78

global population continuing to rise and the need for increased crop yields, the excessive 79

allocation of water to agriculture, currently sitting at ca. 70–90% of all globally available 80

fresh water (Morison et al., 2008), highlights the need for sustainable crops with higher 81

water use efficiency and lower inputs of water. 82

Stomatal behavior regulates CO2 uptake for photosynthesis and water loss via 83

transpiration (which is also important for regulating leaf temperature). The balance between 84

these two fluxes can be characterized by intrinsic water use efficiency (Wi), the ratio 85

between CO2 assimilation (A) and stomatal conductance to water vapor (gs). Low gs can 86

restrict CO2 uptake into the leaf, thereby reducing A (Farquhar and Sharkey, 1982; Barradas 87

et al., 1994; McAusland et al 2016), whereas high gs enables higher rates of A but at a 88

greater cost of water loss via transpiration (Kirschbaum et al., 1988; Tinoco-Ojanguren and 89

Pearcy, 1993; Jones, 1998; Lawson et al. 2010; Lawson & Blatt, 2014). To maintain an 90

optimal balance between A and gs, stomata continually adjust aperture to external 91

environmental cues (e.g., PPFD (photosynthetic photon flux density)) and internal signals, 92

which can include hormonal (e.g., ABA (abscisic acid); Mencuccini et al., 2000; Tallman, 93

2004), circadian (Gorton et al., 1989, 1993; Dodd et al., 2005; Hubbard & Webb, 2015; 94

Hassidim et al., 2017) and/or a currently unidentified ‘mesophyll signal’ (Lee and Bowling, 95

1992; Mott et al., 2008; Fujita et al., 2013; Matthews et al., 2017). Many studies have 96

reported a strong correlation between A and gs (e.g., Wong et al., 1979) and it has been 97

theorized that synchronicity exists to optimize the trade-off between photosynthesis and 98

water loss (Buckley 2017). However, this synchronicity is often constrained by the temporal 99

stomatal response (Lawson & Blatt, 2014), i.e., the speed at which stomata open and close 100

to changing environmental cues, such as those experienced in a dynamic field environment 101

(Jones, 2013; Lawson et al., 2010; McAusland et al., 2016; Vialet-Chabrand et al., 2017a). 102

Stomatal responses to changing environmental cues are often an order of magnitude slower 103

than those observed in A (Tinoco-Ojanguren and Pearcy, 1993; Lawson et al., 2010; 104

McAusland et al., 2016), resulting in lags in stomatal behavior and a temporal disconnect 105

between A and gs, with implications for water use efficiency and crop productivity (Lawson 106

et al 2010; Lawson & Blatt, 2014; McAusland et al., 2013; 2016). The close relationship 107



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between A and gs has often been reported under steady state conditions and has been used 108

by many models to predict diurnal time courses of gs (Damour et al., 2010), such as the 109

widely used Ball-Berry model (Ball et al., 1987) and its derivatives. The use of steady state 110

models under fluctuating environmental conditions can lead to inaccurate predictions of the 111

diurnal response of gs, as these models do not really take into account the slow temporal 112

response of stomata (Vialet-Chabrand et al., 2013, 2017a; Matthews et al., 2017). Moreover, 113

the lack in temporal synchronicity between A and gs that cannot be predicted by these 114

models, has important implications for carbon gain and water use when integrated over the 115

diurnal period and/or entire growing season. Furthermore, as measurements of gs in the 116

field are highly variable they, correlate poorly with those measured under steady state 117

conditions in the laboratory (Poorter et al., 2016; Vialet-Chabrand et al., 2017a), which are 118

often taken in the middle of the day to maximize A and gs. In addition to the temporal 119

responses outlined above, diurnal variation in sensitivity and temporal kinetics to various 120

stimuli have been reported for both stomatal behavior and photosynthesis. For example, 121

there is evidence to suggest that the rapidity of stomatal responses may change at different 122

times of day (Mencuccini et al., 2000; Tallman, 2004). Additionally, changes in gs to 123

fluctuations in water status have been shown to restrict A depending on the time of day and 124

stomata have been reported to be more responsive to ABA in the morning compared with 125

the afternoon (Mencuccini et al., 2000). It has been recognized that the circadian clock at 126

least in part controls these diurnal modifications in A and gs responses over the diurnal 127

period (e.g. Dodd et al., 2005; Hassidim et al., 2017), through regulating the temporal 128

patterns of transcription in photosynthesis, stomatal opening and other physiological 129

processes (Gorton et al., 1989, 1993; Hubbard & Webb, 2015). Phase adjustment of the 130

circadian clock to environmental cues such as light or temperature is fundamental for 131

synchronizing plant biological processes with growth environment (Yin and Johnson, 2000; 132

Resco de Dios et al., 2016), which is important for photosynthesis and plant growth (Dodd et 133

al., 2005; Caldeira et al., 2014). However, there is also evidence, in Arabidopsis, that 134

endogenous signals such as accumulated photosynthates provide feedback mechanisms that 135

regulate the clock phase, and that these are essential for regulating carbon metabolism in 136

dynamic light environments (Seki et al., 2017; Resco de Dios et al., 2016; Ohara & Satake, 137

2017; Haydon et al., 2017). Although the mechanism(s) behind diurnal regulation of A and 138

gs and the impact on water use efficiency is (are) not fully understood, these studies 139

highlight the need for a greater understanding of the impact of temporal stomatal response 140



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over the entire diurnal period, as these will have important implications for cumulative A 141

and water loss as well as model predictions. 142

143

The speed and magnitude of the temporal response of gs is known to vary between species 144

(McAusland et al., 2016), although little is known about how growth light conditions may 145

affect stomatal responses at different times of the day. In the natural environment, the 146

response of A and gs is dominated by PPFD (Pearcy, 1990; Way & Pearcy, 2012), which varies 147

temporally over the course of seconds, minutes, days and seasons (Assmann and Wang, 148

2001), due to changes in cloud cover, sun angle, and shading from neighboring leaves and 149

plants (Pearcy, 1990; Chazdon and Pearcy, 1991; Way and Pearcy, 2012). Leaves therefore 150

experience short- and long-term fluctuations in light (sun/shade flecks) to which gs and A 151

respond. Although it is well established that photosynthesis and to some extent stomatal 152

behavior (including gs kinetics) acclimate to growth PPFD intensity, we have recently 153

demonstrated that photosynthesis acclimates to the pattern of growth irradiance as well as 154

intensity (Vialet-Chabrand et al., 2017b), with fluctuating light having a large impact on 155

photosynthetic performance (Kulheim et al., 2002; Alter et al., 2012; Suorsa et al., 2012; 156

Kromdijk et al., 2016; Yamori 2016; Kaiser et al., 2016, 2017a; Vialet-Chabrand et al., 2017b). 157

Additionally, a recent study by Kaiser et al. (2017b) demonstrated that leaf gas exchange 158

acclimates to light flecks; however, as growth light was kept constant this study focused on 159

dynamic acclimation of photosynthesis. It is not currently known if fluctuations in light 160

impact stomatal acclimation (as well as A) and potentially influence the magnitude and 161

temporal dynamics of gs and A over the diurnal period. To assess the influence of dynamic 162

light on temporal kinetics and diurnal responses of gs and A, we compared gas exchange in 163

Arabidopsis thaliana plants (Col-0) grown under dynamic light that mimics the ‘field’ 164

environment, with plants grown under square wave light regimes, representative of 165

‘laboratory’ growth conditions. We used controlled growth light environments to acclimate 166

plants to different light regimes, whilst maintaining the same time integrated daily light 167

intensity. Plants were grown under three light regimes; fluctuating with a fixed pattern of 168

light, fluctuating with a randomized pattern of light (sinusoidal), and non-fluctuating (square 169

wave), to assess the effect of light pattern on gas exchange. Two different average light 170

intensities (high and low) were used, to separate the effect of light intensity from light 171

pattern on stomatal acclimation and response. 172

To evaluate the impact of gs acclimation to growth light conditions, we assessed the 173

response of gs to a step change in light as well as the diurnal response of gs under constant 174



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light. This allowed us to quantify the periodicity, magnitude and rapidity of the response of 175

gs, and determine if these processes significantly impact stomatal behavior over the course 176

of the day. To separate the response of gs from environmental/external and non-177

environmental/internal signals, gas exchange measurements of A and gs were captured over 178

a 12-h period under a constant square wave light regime. As a result, any variation in the 179

response of gs will be due to the acclimatory response of internal signals to the pattern of 180

growth light. When used in conjunction with current steady state models of gs, a better 181

understanding of the gs response to internal signals could greatly improve their predictive 182

power. Our approach for quantifying the diurnal response of gs could prove useful for 183

rapidly quantifying the influence of circadian or diurnal elements relative to external signals 184

in a dynamic environment. 185

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Results 187

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Diurnal responses of gs, A, and Wi to a square wave pattern of light 189

190

To investigate the acclimation of diurnal stomatal responses in plants grown under the six 191

light treatments (FLH, fluctuating high light; SNH, sinusoidal high light; SQH, square high 192

light; FLL, fluctuating low light; SNL, sinusoidal low light; SQL, square low light), all 193

treatments were subjected to the square wave light regime corresponding to their growth 194

light intensity (SQHigh: high light treatments; SQLow: low light treatments), with net CO2 195

assimilation (A; Fig. 1A), stomatal conductance (gs; Fig. 1B), and intrinsic water use efficiency 196

(Wi; Fig. 1C) measured continuously over the diurnal period. When integrated over the 197

entire diurnal period, A was higher in SQH grown plants compared to FLH and significantly 198

higher (post hoc Tukey, P<0.05) in SQH compared to SNH grown plants (Fig. 1A), although 199

there was no difference between plants under low light treatments. After approx. 5 h into 200

the light regime, A started to decrease in all high light grown plants and this decrease 201

continued to the end of the light period (Fig. 1A). In all low light treatments a continuous 202

slow decrease in A was observed throughout the entire diurnal light period. In all growth 203

light treatments, gs responses were not coordinated with A, and displayed a Gaussian 204

pattern of response (Fig. 1B), whilst A displayed a more square wave response (Fig. 1A). FLH, 205

SQH and SNH grown plants displayed similar patterns of gs but differed in the maximum gs 206

achieved, and the time at which peak gs occurred over the diurnal period. Initial levels of gs 207

ca. 1 h after the light was turned on were comparable between all treatments dependent 208

on light intensity, whilst maximum values of gs in all treatments were reached approx. 4.5–209

6h into the diurnal period (Fig. 1B). In the evening (6–8pm) gs decreased to a value 210

approximately 0.06 mol m2 s1 lower than the initial value observed in the morning in SQH 211

and FLH treatments (ca. 0.3 to 0.24 mol m2 s1, morning and evening, respectively), 212

although this was not the case in SNH (0.27 to 0.26 mol m2 s1) grown plants. The maximum 213

value of gs reached during the diurnal period was higher in FLH (0.38 mol m2 s1) and SNH 214

(0.375 mol m2 s1) compared to SQH (0.32 mol m2 s1) grown plants (Fig. 1B). FLL and SNL 215

showed higher levels of gs than SQL grown plants throughout the day, with the maximum gs 216

reached significantly higher (post hoc Tukey, P<0.05) in FLL (0.27 mol m2 s1) and SNL (0.275 217

mol m2 s1) compared to SQL (0.19 mol m2 s1) grown plants (Fig. 1B). Intrinsic water use 218

efficiency (Wi) was greater in SQ grown plants compared to FL and SN treatments across the 219

entire diurnal light period, in both high and low light grown plants measured under their 220



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respective light intensities (Fig. 1C). When integrated over the entire diurnal period, Wi was 221

significantly higher (P<0.05) in SQH compared to SNH grown plants (data not shown). In high 222

light treatments, Wi remained relatively constant between morning and evening, assisted by 223

the fact that the decrease in A toward the end of the day was accompanied by a decrease in 224

gs. In low light treatments Wi decreased through the day driven by the continuous slow 225

decrease in A. All six treatments experienced a drop in Wi at midday due to the increase of gs 226

at this time with little or no change in A (Fig. 1C). The temporal response of gs to external 227

and internal cues was modeled using an exponential equation (Eq. 2; Materials and 228

Methods). Figures 1D-F display examples of the model fit on individuals of each high light 229

treatment (FLH, SNH, and SQH respectively). R2 and rmse of the relationship between 230

observed and predicted data were as follows for all treatments (R2, rmse respectively): FLH 231

(0.99, 0.008), SNH (0.99, 0.008), SQH (0.99, 0.005), FLL (0.99, 0.006), SNL (0.99, 0.006), SQL 232

(0.99, 0.002). 233

To further characterize the importance of the Gaussian response of gs relative to the diurnal 234

variation, we used a descriptive model to dissect the data into parameters that relate to 235

variation of the leaf internal signals. Using this model, we separated the Gaussian element of 236

the diurnal response of gs from the response to change in light intensity (Fig. 2A), and 237

determined the percentage of Gaussian driven gs (Rsin, Fig. 2B), the time at which peak gs 238

occurs (Tmsin, Fig. 2C), the width of the peak (Tssin, Fig. 2D), and magnitude (Gsin, Fig. 2E). 239

Significant differences in Rsin (Fig. 2B) were observed between plants grown under different 240

light regimes (post hoc Tukey, P<0.05), with the lowest values ca. 16% observed in SQL 241

grown plants, and the highest ca. 30% in SNL. When the results were grouped according to 242

light regime (not divided into intensity), a significant difference in the proportion of the 243

Gaussian driven gs response was observed between SQ and SN grown plants (post hoc 244

Tukey, P<0.05), with SQ (ca. 17%) lower than both FL (ca. 21%) and SN (25%) treatments 245

(Fig. 2B). There was no significant difference in the time at which peak gs occurred (Tmsin) 246

between treatments irrespective of light intensity and treatment (Fig. 2C), except for SNH 247

that took ca. 1 h longer to reach a maximum value of gs than all other treatments. Although 248

there was a noticeable trend of FL treatments having lower values of Tssin than SN 249

(irrespective of light intensity; Fig. 2D), no significant differences were observed; however, 250

Tssin was significantly lower in FL (ca. 2.1 h) than SN (ca. 2.35 h) when grouped by light 251

regime (post hoc Tukey, P<0.05; Fig. 2D). Large variation in the magnitude of the Gaussian 252

element (Gsin; Fig. 2E) was observed between and within treatments, with values ranging 253

from ca. 0.06 mol m2 s1 in SQL to ca. 0.15 mol m2 s1 in FLH. SQ grown plants exhibited 254



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lower values of Gsin than FL and SN under both light intensities, with SQL significantly lower 255

(post hoc Tukey, P<0.05) than all other treatments. When light intensities were grouped 256

together, SQ (ca. 0.08) grown plants were significantly lower (P<0.05) than FL (ca. 0.125) and 257

SN (ca. 0.13) treatments (Fig. 2E). 258

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260

Response of gs and A to a step change in PPFD as a function of time of day 261

262

To assess the impact of growth light regimes on stomatal responses, leaves were subjected 263

to a step increase in PPFD (100-1000 μmol m2 s1) followed by a step decrease (1000–100 264

μmol m2 s1), and the effect on A and gs measured using gas exchange. In the morning 265

period (8–10am) both high and low intensity fluctuating light treatments (FLH; Fig 3A and 266

FLL; Suppl Fig. 1A) and sinusoidal light treatments (SNH; Fig. 3A and SNL; Suppl Fig. 1A) 267

reached a new plateau of gs within 90 min after the light increase, whilst both the square 268

wave treatments, SQH (Fig. 3A) and SQL (Suppl. Fig. 1A), failed to reach a new plateau of gs 269

within this timeframe. In the midday (1–3pm) and evening (6–8pm) measurements, gs 270

reached a plateau in all light treatments (High; Fig. 3A and Low; Suppl. Fig. A), within 90 271

minutes. Following the increase in PPFD to 1000 μmol m2 s1 a near instantaneous increase 272

in A was observed in contrast with the slow initial increase in gs in all treatments, and at all 273

times of day (Fig. 3B and Suppl. Fig. 1B). In all treatments and three measurement times, gs 274

continued to increase during the measurement period despite the fact that A had reached 275

near steady state levels. Although all treatments displayed a predominantly uncoordinated A 276

and gs temporal response, final values of A and gs were strongly correlated, especially in the 277

morning where FLH exhibited the highest levels of operational maximum gs and A, whilst 278

SQH displayed the lowest values in each category (Fig. 3A and 3B). Intrinsic water use 279

efficiency (Wi), measured as A/gs, increased over the day in FL grown plants (Fig. 3C), 280

predominantly driven by the decrease in gs values over this period (Fig. 3A). Wi measured in 281

SQ and SN grown plants changed little between morning and evening, although SQ grown 282

plants always exhibited higher values than SN plants. Wi values were higher in the morning 283

for SQ and SN grown plants compared to FL treatments irrespective of light intensity (Fig. 3C 284

and Suppl. Fig. 1C), driven largely by the lower gs values (Fig. 3A). In the evening, the inverse 285

was evident with FL treatments displaying higher levels of Wi, driven by the higher A values 286

in FLH grown plants (Fig. 3B) and the lower final gs values in FLL grown plants (Suppl. Fig. 287

1A). In all treatments, final values of gs decreased through the day (morning to evening) 288



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when subjected to a step decrease in PPFD from 1000 to 100 μmol m2 s1 (Suppl. Fig. 2). In 289

the morning period, the highest final values of gs at 100 μmol m2 s1 were shown by FLH (ca. 290

0.26 mol m2 s1) grown plants, whilst SNH (0.14 mol m2 s1) displayed the lowest values 291

(Suppl. Fig. 2), which correlated strongly with the final values of gs at 1000 PPFD (Fig. 3A). In 292

the evening period final values of gs were comparable between all treatments (Suppl. Fig. 2). 293

294

295

Speed of gs response to a step change in PPFD 296

297

Stomatal responses to a step increase in PPFD were used to determine the influence of 298

acclimation to growth light regime and intensity on the speed of gs response at different 299

times of the day. Time constants for stomatal opening (τi, Fig. 4A) in response to a step 300

increase in light were significantly lower (post hoc Tukey, P<0.05) in SNH grown plants 301

compared with FLH and SQH grown plants when measured in the morning. The slower 302

responses observed in the FLH and SQH grown plants remained at the midday measurement 303

period; however, τi dropped significantly (P<0.05) in the evening measurements in both FLH 304

and SQH indicating a faster response similar to that observed for SNH throughout the day. In 305

low light treatments τi was significantly faster in SNL grown plants (P<0.05) compared to FLL 306

and SQL at all times of day (Suppl. Fig. 3A), with time constants decreasing at midday in all 307

treatments before returning in the evening to levels comparable to the morning. In contrast 308

to stomatal opening, time constants for stomatal closure (τd) significantly increased (post 309

hoc Tukey, P<0.05) through the day (morning to evening) in all FL and SN treatments 310

irrespective of light intensity (Fig. 4B and Suppl. Fig. 3B), although stomata of SN grown 311

plants closed in a significantly shorter time (post hoc Tukey, P<0.05) than FL at all times of 312

day. The time constant for stomatal closure (τd) was maintained at all times of day in SQ 313

grown plants irrespective of light intensity, whilst in both FL and SN treatments τd 314

significantly increased (P<0.05) from morning to evening. In general stomatal closure was 315

much slower in plants grown under FL than in SN and SQ, with SN gs responses slower than 316

SQ in the evening. 317

318

The time constant for light saturated rate of carbon assimilation at 1000 μmol m2 s1 PPFD 319

(τai, Fig. 4C and Suppl. Fig. 3C) was determined from the temporal response data (Fig. 3), 320

along with final values of gs at 1000 PPFD for stomatal opening (Gi, Fig. 4D and Suppl. Fig. 321

3D), stomatal closure (Gd, Fig. 4E and Suppl. Fig. 3E), and saturated rates of A at 1000 PPFD 322



12

(Ai, Fig. 4F and Suppl. Fig. 3F). Net CO2 assimilation was deemed saturated at 1000 PPFD 323

from analysis of light response curves on the same plants (see Vialet-Chabrand et al., 324

2017b). Time constants for light saturated A (τai, Fig. 4C) were significantly higher (post hoc 325

Tukey, P<0.05) in SNH compared to SQH and FLH at morning and midday, whilst in the 326

evening τai was significantly higher (P<0.05) in FLH. In low light treatments (Suppl. Fig. 3C) τai 327

significantly decreased (P<0.05) from morning to midday in SQL and SNL, and significantly 328

decreased (P<0.05) in all low light treatments from midday to evening. The final gs at 1000 329

μmol m2 s1 (Gi, Fig. 4D and Suppl. Fig. 3D), and following closure when light was reduced 330

from 1000 to 100 μmol m2 s1 (Gd, Fig. 4E and Suppl. Fig. 3E) differed significantly through 331

the day. Final gs at 1000 PPFD (Gi) decreased significantly (P<0.05) from morning to evening 332

in FLH grown plants (ca. 0.46 to 0.25 mol m2 s1, respectively; Fig. 4D), whereas SQH and 333

SNH treatments remained constant throughout the day displaying a trend of increased Gi at 334

midday. All low light treatments (FLL, SQL, SNL) displayed similar trends in Gi throughout the 335

day, with a significant decrease (P<0.05) from morning to evening; ca. 0.35 to 0.21 mol m2 336

s1 in FLL; ca. 0.34 to 0.23 mol m2 s1 in SQL; and ca. 0.33 to 0.23 mol m2 s1 in SNL 337

(morning and evening respectively, Suppl Fig. 3D). Final values of gs at 100 PPFD (Gd; Fig. 4E 338

and Suppl. Fig. 3E) displayed similar trends to that of Gi in all treatments, irrespective of light 339

intensity. Gd significantly decreased (P<0.05) from morning to evening in FLH grown plants 340

(ca. 0.27 to 0.11 mol m2 s1; Fig. 4E), though remained constant in SQH and SNH treatments 341

at all times of day. In all low light treatments, Gd significantly decreased (P<0.05) from 342

morning to evening (Suppl. Fig. 3E); ca. 0.17 to 0.1 mol m2 s1 in FLL; ca. 0.19 to 0.13 mol 343

m2 s1 in SQL; and ca. 0.15 to 0.1 mol m2 s1 in SNL (morning and evening respectively, 344

Suppl Fig. 3E). Saturated rates of A at 1000 PPFD (Ai; Fig. 4F and Suppl Fig. 3F) remained 345

constant from morning to midday in all treatments, irrespective of light intensity. In all light 346

treatments there was a decrease in Ai from midday to evening, although this was only 347

significant in SNH and SQL treatments (post hoc Tukey, P<0.05). A strong correlation was 348

observed in all treatments between the final value of gs (Gi) and A (Ai) under 1000 µmol m2 349

s1 PPFD. With regard to stomatal anatomy, significant differences in stomatal density (SD) 350

were observed between plants grown under high and low light intensity, though no 351

difference was observed between plants grown under the different patterns of growth light 352

of the same average intensity (data not shown). 353

354

Impact of diurnal stomatal behavior on predictive models of gs in a dynamic environment 355

356



13

The Ball-Berry model (Ball et al. 1987) is widely used in the literature as a basis for predicting 357

gs across leaf and global scales (Damour et al. 2010). Based on our findings and having 358

quantified and established the significance of gs response over the diurnal period, we 359

investigated whether adding a time of day effect (Gaussian element) to the Ball-Berry model 360

would improve predictive power and model fit when endeavoring to predict gs under 361

different light regimes and intensities. To exemplify the improvements in predictive power, 362

and display an example of the fit of the two models (with and without the Gaussian 363

element), we used a completely independent data set (Fig. 5A), measured under a dynamic 364

light environment previously described in Vialet-Chabrand et al. (2017b). By adding a 365

Gaussian element into the Ball-Berry model, our model exhibited improvements in the 366

prediction of gs at all times of day, especially at periods of high and low light where the 367

original Ball-Berry model failed to accurately predict the full range of variation in the data 368

(Fig. 5A). Figure 5 shows the difference between measured and predicted gs values using the 369

Ball-Berry model without (Fig. 5B) and with (Fig. 5C) a Gaussian element. We observed that 370

under all light conditions the best model fit was always that with the addition of the 371

Gaussian element. R2 of the relationship between observed and predicted data increased by 372

over 10% (0.837 to 0.941, respectively), and rmse was improved by ca. 40% (0.0527 to 373

0.0317, respectively), indicating a significant improvement in predictive power. This 374

indicates that although the Ball-Berry model and its derivatives have the ability to predict gs 375

under different light regimes, the addition of a Gaussian element significantly improves 376

performance, especially under a dynamic light environment. 377

378

379

Discussion 380 381

It is well-established that plants acclimate to growth light intensity by altering leaf anatomy 382

and biochemistry as well as physiology (Givnish, 1988; Walters and Horton, 1994; Weston et 383

al., 2000; Bailey et al., 2001; 2004). However, few studies have focused on stomatal 384

acclimation to the pattern of growth light. Although in a recent study we reported 385

photosynthesis and to some extent stomatal conductance, acclimate to the pattern and 386

intensity of growth irradiance (Vialet-Chabrand et al., 2017b), this study did not examine 387

how acclimation to fluctuating growth light influences the magnitude and temporal 388

dynamics of gs over the diurnal period. Here we demonstrate the impact of fluctuating 389

growth lighting regimes on stomatal behavior and show an acclimation of the rapidity and 390

magnitude of stomatal responses over the day. Additionally we report a previously 391



14

undescribed internally driven diurnal signal (referred to as the ‘internal signal’) that 392

uncouples gs from A, the magnitude and shape of which were modified by both light 393

intensity and light pattern. 394

395

Effect of acclimation to growth light on stomatal kinetics 396

397

Similar to previously published work (Gay & Hurd, 1975; Lake et al., 2001), our results 398

showed anatomical stomatal acclimation to light intensity, with significantly higher stomatal 399

density (SD) under high light. However, as we found no change in SD between growth 400

treatments of the same intensity, the physiological differences observed and reported here 401

are the result of alterations to guard cell biochemistry, sensitivity or signaling. 402

Both the rapidity and magnitude of gs responses to a step change in PPFD were 403

influenced by growth light regimes, and this was particularly evident at the start of the day. 404

Plants grown under dynamic (fluctuating and sinusoidal) high light showed a faster response 405

and in general a greater magnitude of change; however these differences in stomatal 406

responses diminished throughout the day. This has also been described previously by 407

Mencuccini et al. (2000), but not in the context of light acclimation. These authors used 408

detached leaves and pressurized them to simulate different levels of leaf water status, and 409

hypothesized that the magnitude of gs responses observed at different times of the day 410

were driven by changes in the osmotic regulation that altered stomatal aperture. Others 411

have also described a reduction in the magnitude of the gs response through time (Pfitsch 412

and Pearcy, 1989; Allen and Pearcy, 2000); however, faster responses towards the end of 413

the day were not reported. In contrast to opening, a slower closing response was observed 414

in plants grown under dynamic light, with slower time constants for closure in the evening 415

compared to the morning. This strategy was described previously by Ooba & Takahashi 416

(2003), and it is believed to improve light use efficiency by maintaining open stomata under 417

fluctuating light, reducing the limitation of A by gs. This may also represent a more 418

conservative strategy in energy (e.g., cost of stomatal movements; Raven, 2014) under 419

fluctuating light regimes. 420

The decrease over the course of the day in the absolute values of both A and gs 421

(observed in both the measurements following the step increase in light and over the diurnal 422

period) could be attributed to the accumulation of photosynthetic products, resulting in a 423

negative feedback on the Calvin cycle (Paul and Foyer, 2001; Paul and Pellny, 2003), or an 424

increase in apoplastic sucrose that accumulates in the guard cells, regulated by the rate of 425



15

transpiration (Lu et al., 1997; Outlaw 2003; Kang et al., 2007; Kelly et al., 2013; Lawson et al., 426

2014; Daloso et al., 2016). However, no significant acclimation of the slow decrease in A and 427

gs through the day by growth light intensity and pattern was observed in this experiment. 428

The acclimation of the rapidity of gs response was sensitive to light intensity as well 429

as pattern. Previous studies in forest (e.g., Pearcy, 2007) and crop canopies (Barradas et al., 430

1994; Qu et al., 2016) have reported stomatal acclimation to different light environments 431

with leaves at different heights or positions within the canopy receiving varying degrees of 432

light intensity (Barradas et al., 1998), resulting in different anatomical and biochemical 433

features (Givnish, 1988; Pearcy, 2007). In general, under lower light maximum gs 434

throughout the day is reduced and the speed of the gs response is dependent on species and 435

growth environment (Allen & Pearcy, 2000; Ooba and Takahashi, 2003; Vico et al., 2011; 436

Drake et al., 2013; Vialet-Chabrand et al., 2013; McAusland et al., 2016; Vialet-Chabrand et 437

al., 2017a). However, to date no study has clearly identified the environmental impact on 438

the rapidity of gs response. Here we quantify for the first time the impact of growth light on 439

the acclimation of the rapidity of the gs response at different times of the day. Our results 440

reveal that estimates of the rapidity of gs will depend on the micro-environment 441

experienced by the chosen leaf and the time at which the measurement is captured. 442

As stomatal responses to changing light are an order of magnitude slower than 443

photosynthetic responses (Jones 1998, 2013; Lawson et al. 2010), slower stomata can limit 444

CO2 diffusion for A (Barradas et al., 1998; Kaiser and Kappen 2000; McAusland et al., 2016; 445

Vialet-Chabrand et al., 2017a; Vico et al., 2011), whilst higher gs can be at the expense of Wi. 446

The different growth light regimes clearly elicited different acclimation responses, with 447

plants grown under fluctuating light regimes showing the greatest variation in Wi 448

throughout the day as observed in the light step measurements. Wi was lowest in the 449

morning in plants grown under fluctuating light and increased towards the evening. A 450

possible explanation for this could be that although these plants receive the same amount of 451

light as the other treatments throughout the day, the majority of this light was delivered 452

earlier in the day. This suggests that the pattern of light distribution leads to an acclimation 453

that will determine the kinetics and magnitude of the gs response at different times of day. 454

Although the stomatal acclimation described here in plants subjected to fluctuating light 455

may show a reduction in the efficiency of water use earlier in the day, it may be important 456

for light utilization of sun/shade flecks for photosynthesis, as previously shown by Vialet-457

Chabrand et al. (2017b) when these plants were measured under their growth light regime. 458

The variation in Wi over the diurnal period may represent a more conservative strategy that 459



16

potentially balances CO2 uptake and water loss over the diurnal period to optimize the 460

current needs at the whole plant level (Meinzer and Grantz, 1990). 461

462

Effect of growth light acclimation and the internal signal on diurnal responses 463

464

Diurnal gas exchange under constant light revealed an internally driven diurnal gs 465

response that was not only disconnected from A, but also strongly influenced by the 466

patterns of growth light regime and to a smaller extent the average light intensity. The 467

importance of the internal gs response over the diurnal period was unexpected with ca. 25% 468

of the total daily gs driven by this signal. This diurnal stomatal response could be considered 469

detrimental, as significant water is lost for no extra carbon gain; however, it may also play a 470

valuable role in translocation of photosynthates, nutrient uptake, and/or maintenance of 471

optimal leaf temperature through transpirational cooling (Caird et al., 2007; Hills et al., 472

2012). Although measured under constant light, all plants showed a characteristic sinusoidal 473

pattern of response of gs over the diurnal period similar to that reported by Dodd et al. 474

(2005). What is novel and intriguing about these findings is that gs was not only partially 475

uncoupled from A over a substantial part of the day, but that the characteristics (magnitude 476

and period) of this internal gs response are acclimating to the growth light intensity and the 477

pattern of the lighting regime. 478

Previous reports have suggested that such oscillations in gs are entrained by 479

circadian rhythms (Dodd et al., 2004; Hubbard & Webb, 2015; de Dios et al., 2016; Hassidim 480

et al., 2017). However, characterization of this response as circadian would require 481

continuous measurements over multiple days (3+ days) in a constant low light environment 482

to establish if the rhythm persists in each theoretical diurnal time period (e.g., Dodd et al. 483

2005). It is well established that regulation of temporal transcription patterns by the 484

circadian clock play an important role in rhythms of photosynthesis and stomatal opening 485

(Dodd et al., 2004, 2005; Hubbard & Webb, 2015; Hassidim et al., 2017), although the 486

pathways and signals that lead to this diurnal behaviour in gs are still largely unknown. Some 487

hypotheses involving ABA concentration (Mencuccini et al., 2000; Tallman et al., 2004), and 488

the level of sucrose and calcium signaling (Dodd et al., 2006; Haydon et al., 2017) have been 489

put forward to explain internally driven diurnal variations in gs. 490

Quantifying the impact of growth environment and acclimation on these patterns 491

and physiological responses under environmentally relevant conditions is extremely difficult. 492

To address this, we built a diurnal model of gs that allowed us to quantify this internal signal 493



17

as well as the influence of lighting regimes on the magnitude and periodicity. This model 494

was accurate (R2: 0.99) at describing the response of gs, and the parameters derived from 495

this model allowed us to quantify the relative importance of the internal signal on gs. Plants 496

grown under dynamic light regimes showed a higher magnitude of gs response under 497

constant light conditions, which highlights the importance of growth light pattern on the 498

acclimation of this internal signal. Interestingly, the duration of the gs response to the 499

internal signal was also dependent on growth light regime. These large changes in gs over 500

the course of the day represent a significant loss in water with little variation in CO2 501

assimilation over the same period, resulting in significantly reduced plant Wi. This 502

emphasizes the importance of the growth light regime as it potentially influences the 503

regulation of gs by an internal signal that may be under the control of the circadian clock and 504

alters gs over the course of the day. 505

506

Implications of the internal signal on the Ball-Berry model 507

508

Our results revealed that diurnal stomatal behavior is influenced by the pattern and 509

intensity of growth light, but this is often ignored in current steady-state models of gs 510

(Damour et al., 2010). Here we demonstrate that the addition of an equation describing the 511

‘internal’ signal to the widely used Ball-Berry model (Ball et al., 1987) greatly improves the 512

predictive power of the model. Using this new model and an independent data set (Vialet-513

Chabrand et al., 2017b) measured under a dynamic environment, we showed improvements 514

in both the R2 (ca. 10%) and a reduction in the error (rmse; ca. 40%) between observed and 515

predicted data, highlighting the importance of this process under dynamic fluctuating light. 516

Although integration of a diurnal signal to the Ball-Berry model was first attempted by de 517

Dios et al. (2016) and also showed an improvement in the prediction of gs, here, we provide 518

a more precise validation of our model with higher time resolution which enables us to 519

capture rapid variations under fluctuating light regimes. The unexplained variance by the 520

new model may be due to changes in the rapidity and magnitude of stomatal response at 521

different times of the day, as we have shown experimentally here, but could not be 522

integrated due to the steady state nature of the Ball-Berry model. To further improve model 523

predictions, a dynamic model that can integrate our findings will be required, that not only 524

includes the diurnal/circadian regulation of gs but altered gs kinetics at different times of 525

day. 526

527



18

CONCLUSION 528

In this study, we directly examined the impact of dynamic growth light regimes on 529

stomatal acclimation and diurnal behavior. We have demonstrated that growth light 530

environment modifies stomatal kinetics at different times of the day resulting in differences 531

in the rapidity and magnitude of this response. Importantly we also describe and quantify 532

the response to an internal signal that uncouples A and gs over the majority of the diurnal 533

period, with characteristics that are modified by growth light environment. The importance 534

of this signal on diurnal gs kinetics is demonstrated by the inclusion of the Gaussian element 535

describing the internal signal, which greatly improves the prediction of gs from the widely 536

used Ball-Berry Model. 537

Our quantification of the components of the diurnal kinetic of gs (response to light, 538

gradual temporal decrease, Gaussian element) provides an invaluable tool for assessing 539

diurnal patterns of stomatal behavior, as well as the effect of the circadian clock. A dynamic 540

model of gs that includes these components will be able to describe the contribution of each 541

element to the diurnal response of gs, even under a dynamic environment such as that 542

experienced by plants in the field. This has been illustrated by the improvement in predicted 543

gs from plants acclimated to different light environments and measured under dynamic 544

regimes. 545

Acclimation of the rapidity and response of gs to the internal signal, appears to be 546

determined by both the intensity and pattern of growth light, and is an important strategy 547

for maintaining carbon fixation and overall plant water status by conditioning the plant to 548

respond appropriately to future diurnal variations in light. 549

550



19

Material and Methods 551

552

Plant material and growth conditions 553

Fluctuating and square wave light growth conditions were delivered via a Heliospectra LED 554

light source (Heliospectra AB, Göteborg, Sweden). Fluctuating light regime (FLHigh) was 555

recreated from a natural light regime recorded at the University of Essex during a relatively 556

clear day in July (Fig. 1) (with the assumption of a constant spectral distribution). The 557

average light intensity over the 12 h fluctuating regime was calculated as 460 µmol m2 s1 558

and was used as the light intensity for the square wave high light treatment (SQHigh). This 559

value was then halved to 230 µmol m2 s1 for the fluctuating (FLLow) and square wave (SQLow) 560

low light conditions. Plants (Arabidopsis thaliana, Col-0) were grown in peat-based compost 561

(Levingtons F2S, Everris, Ipswich, UK) and were maintained under well-watered conditions in 562

a controlled environment, with growth conditions maintained at a relative humidity of 55–563

65%, air temperature of 21–22°C, and a CO2 concentration of 400 µmol mol–1. The position 564

of the plants under the light source was changed daily at random to remove any effect of 565

potential heterogeneity in the light quality and quantity. 566

567

Simulating daily light fluctuations for sinusoidal growth light regime 568

The sinusoidal light regime was simulated using a specific algorithm including a sinusoidal 569

variation with random alterations constrained to maintain the daily amount of light intensity 570

(PPFD) constant during the growth. The sinusoidal variation as a function of time (t) was 571

obtained by: 572

𝑃𝑃𝐹𝐷 = 𝑎𝑒−(𝑡−𝑏)2

2𝑐2 − 𝑎𝑒−(𝑡1−𝑏)2

2𝑐2 (1)

573

where a is the maximum PPFD reached during the peak, b is the time at which the peak is 574

reached and c a parameter related to the width of the peak. The value of a was arbitrarily 575

set to 1000 for convenience as the whole curve is rescaled at the final step of the algorithm. 576

Values of b and c where set to 7 and 13 respectively. 577

A random number of decreases in light intensity at different times throughout the diurnal 578

period were then added, and ranged between 0 and 80% of the original light level. This 579



20

guaranteed a minimum light intensity that mimics the daily variation of diffuse light 580

intensity. 581

The final step was to scale the curve to obtain an average light intensity of 460 µmol m2 s1 582

for the sinusoidal high light treatment (SNHigh) and 230 µmol m2 s1 for the sinusoidal low 583

light treatment (SNLow) as used in the other growth light regimes described previously. The 584

same process was repeated for the number of days required and was then programmed into 585

the Heliospectra lights. The five first days simulated are shown in Fig. S4, highlighting that 586

each day had a unique pattern of light intensity, mimicking a natural light environment. 587

588

Leaf gas exchange 589

All gas exchange (A and gs) parameters were recorded using a Li-Cor 6400XT portable gas 590

exchange system, with light delivered via a Li-Cor 6400-40 fluorometer head unit (Li-Cor, 591

Lincoln, Nebraska, USA). For all gas exchange measurements, a constant flow rate was set at 592

300 µmol s1, with cuvette conditions maintained at a CO2 concentration of 400 µmol mol1, 593

a leaf temperature of 25°C (unless otherwise stated), and to maintain a leaf to air water 594

vapor pressure deficit of 1 (±0.2) kPa, the system was connected to a Li-Cor 610 portable 595

dew point generator. All measurements were taken using the youngest, fully expanded leaf. 596

Intrinsic water use efficiency was calculated as Wi = A/gs. 597

598

Measurements and modelling of diurnal stomatal conductance under constant light 599

environment 600

On the day of measurement, plants were removed from the growth chamber prior to the 601

initiation of the diurnal regime of light. Leaves were placed in the Li-Cor cuvette (for 602

conditions see above) in darkness and both A and gs were allowed to stabilize for a minimum 603

of 15–30 minutes. After A and gs were at steady state for at least 5 minutes (<2% change 604

over this time period), the automatic 12 h light programs (SQHigh and SQLow) were started, 605

with A and gs recorded every 2 minutes. 606

The temporal response of gs to external and internal cues was modelled using an 607

exponential equation: 608



21

𝑑𝑔𝑠

𝑑𝑡=

(𝐺 − 𝑔𝑠)

𝜏

(2)

609

where G represent the steady state target of gs and 𝜏 the time constant to reach 63% of G. 610

Due to the asymmetry of response during a step increase or decrease in light intensity, a 611

different value of 𝜏 was used in each condition (𝜏𝑖 and 𝜏𝑑). 612

The steady state target (G) was calculated as the sum of three processes: the decrease of gs 613

through the diurnal period (D), the bell shape variation of gs through the diurnal period (S), 614

the response of gs to light intensity variation (G1, G2, G3). 615

Before and after the lighted period, G was set to G1 and G3 respectively, two values 616

representing the steady state gs at the end and beginning of the dark period (grey area in 617

Fig. 1). During the lighted period, 𝐺 was set to 𝐺2 + 𝐷 + 𝑆 assuming that the internal cues 618

were activated by light. 619

The decrease of gs (D) as a function of time (t) was modelled using an exponential function 620

constrained over the lighted portion of the diurnal period (between ton and toff): 621

𝐷 = {𝐺𝑠𝑙 (1 − 𝑒

−𝑡−𝑡𝑜𝑛

𝜏𝑠𝑙 ) , 𝑖𝑓 𝑡 > 𝑡𝑜𝑛 𝑎𝑛𝑑 𝑡 < 𝑡𝑜𝑓𝑓

0, 𝑖𝑓 𝑡 < 𝑡𝑜𝑛 𝑎𝑛𝑑 𝑡 > 𝑡𝑜𝑓𝑓

(3)

622

where Gsl is the steady state target of the decrease in gs and 𝜏𝑠𝑙 the time constant to reach 623

63% of Gsl. 624

The bell shape variation of gs (S) as a function of time (t) was modelled using a Gaussian 625

function: 626

𝑆 = 𝐺𝑠𝑖𝑛𝑒

−(𝑡−𝑇𝑚𝑠𝑖𝑛)2

(2𝑇𝑠𝑠𝑖𝑛2)

(4)

627

where Gsin is the maximum gs reached during the peak, Tmsin the time at the centre of the 628

peak and Tssin a parameter related to the width of the peak. On each parameter, a one-way 629

ANOVA with light treatment as factor was applied with a Tukey’s posthoc test for comparing 630

group means. Statistics were conducted using R statistical software (version 3.2.4). 631

632



22

This model was implemented using the stan language and adjusted on the observation using 633

R (www.r-project.org) and the RStan package (http://mc-stan.org/users/interfaces/rstan). 634

For each diurnal curve of gs measured, the model was adjusted using 3 chains starting with 635

different parameter sets. No divergent transitions were observed, meaning that the 636

simulations can be trusted, and Rhat values were all c.a. 1, meaning that all three chains 637

converged (Carpenter et al., 2016). 638

639

Temporal response of A and gs 640

For the step change in light, leaves were placed in the Li-Cor cuvette (for conditions see 641

above) and equilibrated at a PPFD of 100 µmol m2 s1 until both A and gs were at steady 642

state. Steady state in this case was defined as less than a 2% change of the given parameter 643

over a 10-minute period (this would take ca. 20–60 min). Once at steady state, PPFD was 644

increased to 1000 µmol m2 s1 for 1.5 h before returning to 100 µmol m2 s1 for a further 1 645

h. A and gs were recorded every 20 s. For measurements at the different times of day 646

(morning, midday, evening), plants were removed from the growth chamber at 8am, 1pm, 647

and 6pm, and the increase in PPFD from 100 to 1000 µmol m2 s1 was initiated at 648

approximately 9am, 2pm, and 7pm respectively. To prevent previous step changes in light 649

(e.g., morning) having an effect on the response to step changes later in the day (e.g., 650

midday), individual leaves that were subjected to a step change in light were not subjected 651

to another measurement until the following day. 652

653

Modelling rapidity of the stomatal conductance response 654

The rapidity of the stomatal response following a step change in light intensity was assessed 655

as a function of time (t) using a custom exponential equation including a slow linear increase 656

of the steady state target (G): 657

𝑔𝑠 = (𝐺 + 𝑆𝑙𝑡) + (𝑔0 − (𝐺 + 𝑆𝑙𝑡))𝑒−𝑡 𝜏⁄ (5)

658

where Sl is the slope of the slow linear increase of G observed during the response, g0 the 659

initial value of gs, and 𝜏 the time constant to reach 63% of G (when τ = t, gs−g0

((G+Slt)−g0)=660

1 − e−1~0.63). Due to the asymmetry of response during a step increase or decrease in 661

light intensity, a different value of 𝜏 was used in each condition (𝜏𝑖 and 𝜏𝑑). Even if gs did not 662


http://www.r-project.org/

http://mc-stan.org/users/interfaces/rstan


23

reach a plateau within the given timeframe, the model was able to predict the final 663

asymptotic response and therefore the time constant (𝜏𝑖 and 𝜏𝑑). This equation was 664

adjusted on response curves of each treatment at different times of the day using a 665

nonlinear mixed effect model. Parameter G, g0 and Sl were assumed to vary at individual 666

level (random effects) and 𝜏 was assumed to vary only at treatment level (fixed effect). R 667

and the nlme package were used to perform the analysis. On each parameter, a one-way 668

ANOVA with light treatment as factor was applied with a Tukey’s posthoc test for comparing 669

group means. Confidence intervals at 95% were reported at the treatment level. 670

671

Modelling rapidity of the net CO2 assimilation response 672

The rapidity of the photosynthesis response following a step change in light intensity was 673

assessed as a function of time (t) using an updated version of equation 5: 674

𝐴𝑡 = (𝐴𝑠 + 𝑆𝑙𝑡) + (𝐴0 − (𝐴𝑠 + 𝑆𝑙𝑡))𝑒−𝑡 𝜏⁄ (6)

675

where At is the net CO2 assimilation (A) at time t, As is the plateau of A reached in steady 676

state, Sl is the slope of the slow linear increase of A, A0 the initial value of A, and 𝜏 the time 677

constant to reach 63% of As. This equation was adjusted on response curves using the same 678

method described above for gs. 679

680

Including variation in diurnal stomatal behaviour in the Ball-Berry model for predicting gs 681

An addition was made to the original Ball-Berry model (Ball et al., 1987) to take into 682

consideration the time of the day (t) effect on gs: 683

𝑔𝑠 = 𝑔0 + (𝑔1

𝐴𝐻𝑠

𝐶𝑠) + (𝑔2𝑒

−(𝑡−𝑇𝑚)2

2𝑇𝑠2

) (7)

684

Where g0 is the minimal conductance or intercept, g1 the slope of the relationship between 685

gs and the Ball index (AHs/Cs), g2 the amplitude of the Gaussian function, Tm the time to 686

reach the peak of the Gaussian, Ts a parameter related to the width of the peak, and A the 687

net CO2 assimilation. The conditions imposed at the surface of the leaf are represented by 688

Hs, the relative humidity, and Cs, the CO2 concentration in the chamber. 689



24

Using R and the nls function, two versions (with and without the third term in equation 6) 690

were adjusted on an independent dataset described previously in Vialet-Chabrand et al. 691

(2017b). The fluctuating light regime and different light intensities applied on plants grown 692

in different conditions give a large range of variation to test the performance of the Ball-693

Berry model against our modified version. 694

The difference between observation (Obs.) and predictions (Mod.) of both models were 695

assessed using the root mean square error (rmse): 696

𝑟𝑚𝑠𝑒 = √∑(𝑂𝑏𝑠. −𝑀𝑜𝑑. )

𝑛

2

(8)

697

where n represents the number of recorded data. 698

699

Supplemental Data 700

The following supplemental materials are available. 701

Supplemental Figure 1. Temporal response of stomatal conductance (gs), net CO2 702 assimilation (A), and intrinsic water use efficiency (Wi), to a step increase in light intensity 703 (from 100 to 1000 µmol m-2 s-1), at different times of the day for the three low light 704 treatments. 705 706 Supplemental Figure 2. Temporal response of stomatal conductance (gs), to a step decrease 707 in light intensity (from 1000 to 100 µmol m-2 s-1), at different times of the day for all six light 708 treatments. 709 710 Supplemental Figure 3. Time constants for stomatal opening (τi), stomatal closure (τd), and 711 the light saturated rate of carbon assimilation (τai) following a step change in light intensity, 712 at different times of the day for the three low light treatments. 713 714 Supplemental Figure 4. First five days of the simulated sinusoidal high light regime (SNHigh), 715 highlighting the random fluctuations in light intensity unique to each day. 716 717 718 719 720 721 722 723 724 725 References 726 727 728



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Figure Legends 1001 1002 Figure 1. Diurnal measurements of net CO2 assimilation (A); stomatal conductance (gs); and 1003 intrinsic water use efficiency (Wi), measured under square wave regimes of light. Fluctuating 1004 (FLH, red), sinusoidal (SNH, green) and square wave (SQH, blue) high light treatments (Full 1005 lines) were measured under square wave high light regime (SQHigh); fluctuating (FLL, red), 1006 sinusoidal (SNL, green) and square wave (SQL, blue) low light treatments (Dashed lines) were 1007 measured under square wave low light regime (SQLow). Error bars represent mean ± SE, n = 5 1008 –7. Grey shaded areas indicate when light source is off. Represented are examples of FLH 1009 (D), SNH (E) and SQH (F) to highlight fit of the temporal response exponential model (black 1010 line). Pink shaded areas illustrate growth light regimes for FLH (D), SNH (E) and SQH (F). 1011 1012 Figure 2. Quantification of the Gaussian signal of stomatal conductance (gs) during diurnal 1013 measurements. Diurnal stomatal conductance measured under square wave light (A); the 1014 relative percentage of Gaussian driven gs (Rsin, B); the time at which peak gs occurs (Tmsin, C); 1015 the width of the peak (Tssin, D); and the magnitude of the Gaussian gs response (Gsin, E). 1016 Fluctuating (FLH, red), sinusoidal (SNH, green) and square wave (SQH, blue) high light 1017 treatments (Full lines) were measured under square wave high light regime (SQHigh); 1018 fluctuating (FLL, red), sinusoidal (SNL, green) and square wave (SQL, blue) low light 1019 treatments (Dashed lines) were measured under square wave low light regime (SQLow). Bars 1020 are combined data from high and low light treatments. Error bars represent mean ± SE, n = 1021 5–7. Colored letters represent the results of Tukey’s posthoc comparisons of group means 1022 from the individual light treatments and black letters are the result from combined high and 1023 low light treatments. 1024 1025 Figure 3. Temporal response of stomatal conductance (gs), net CO2 assimilation (A), and 1026 intrinsic water use efficiency (Wi), to a step increase in light intensity (from 100 to 1000 1027 µmol m2 s1), at different times of the day. Gas exchange parameters (gs, A; A, B; and Wi, C) 1028 were recorded at 20-s intervals, leaf temperature maintained at 25°C, and leaf VPD at 1 ± 1029 0.2 kPa. Plants grown under the three high light treatments; fluctuating (FLH, red); sinusoidal 1030 (SNH, green); square wave (SQH, blue). Error ribbons represent mean ± SE. n = 5–6. 1031 1032 Figure 4. Modelled temporal response of gs and A to a step change in light. Time constants 1033 for stomatal opening (τi, A), stomatal closure (τd, B), and light saturated rate of carbon 1034 assimilation (τai, C) to a step change in light intensity (from 100 to 1000 µmol m2 s1; and 1035 from 1000 to 100 µmol m2 s1 respectively), at different times of the day. Stomatal 1036 conductance following a step increase in light intensity (from 100 to 1000 µmol m2 s1) (Gi, 1037 D); and after light intensity returned to 100 µmol m2 s1 (Gd, E); and light saturated rate of 1038 net CO2 assimilation at 1000 µmol m2 s1 (Ai, F), at different times of the day (Morning, 1039 Midday, Evening). Plants grown under the three high light treatments; fluctuating (FLH, red); 1040 sinusoidal (SNH, green); square wave (SQH, blue). Error bars represent 95% confidence 1041 intervals. n = 5–6. 1042 1043 Figure 5. Comparison of the Ball-Berry model prediction of gs with and without a Gaussian 1044 element. An example of adjustment made on an existing independent data set (black circles) 1045 measured under a dynamic light environment (A; see Vialet-Chabrand et al., 2017b), for the 1046 Ball-Berry model without (blue line) and with (red line) a Gaussian element. Shown are the 1047 comparisons between measured and predicted gs values using the Ball-Berry model without 1048 (B; Blue dots) and with (C; Red dots) a Gaussian element. Open and closed circles are the 1049 Fluctuating and Square-wave treatments, respectively, from the independent data set. 1050 1051



32

1052 1053



1

Figure 1. Diurnal measurements of net CO2 assimilation (A); stomatal conductance (gs); and intrinsic water use efficiency (Wi), measured under square wave regimes of light. Fluctuating (FLH, red), sinusoidal (SNH, green) and square wave (SQH, blue) high light treatments (Full lines) were measured under square wave high light regime (SQHigh); fluctuating (FLL, red), sinusoidal (SNL, green) and square wave (SQL, blue) low light treatments (Dashed lines) were measured under square wave low light regime (SQLow). Error bars represent mean ± SE, n = 5-7. Grey shaded areas indicate when light source is off. Represented are examples of FLH (D), SNH (E) and SQH (F) to highlight fit of the temporal response exponential model (black line). Pink shaded areas illustrate growth light regimes for FLH (D), SNH (E) and SQH (F).



1

Figure 2. Gaussian signal of stomatal conductance (gs) during diurnal measurements of square wave light (A). Shown is the relative percentage of Gaussian driven gs (Rsin, B); the time at which peak gs occurs (Tmsin, C); the width of the peak (Tssin , D); and magnitude (Gsin, E), during the diurnal signal of gs. Fluctuating (FLH, red), sinusoidal (SNH, green) and square wave (SQH, blue) high light treatments (Full lines) were measured under square wave high light regime (SQHigh); fluctuating (FLL, red), sinusoidal (SNL, green) and square wave (SQL, blue) low light treatments (Dashed lines) were measured under square wave low light regime (SQLow). Colored bars are combined data from high and low light treatments. Error bars represent mean ± SE, n = 5-7. Letters represent the results of Tukey’s posthoc comparisons of group means.



1

Figure 3. Temporal response of stomatal conductance (gs), net CO2 assimilation (A), and intrinsic water use efficiency (Wi), to a step increase in light intensity (from 100 to 1000 µmol m-2 s-1), at different times of the day. Gas exchange parameters (gs, A; A, B; and Wi, C) were recorded at 20s intervals, leaf temperature maintained at 25°C, and leaf VPD at 1 ± 0.2

KPa. Plants grown under the three high light treatments; fluctuating (FLH, red); sinusoidal (SNH, green); square wave (SQH, blue). Error ribbons represent mean ± SE. n = 5-6.



1

Figure 4. Time constants for stomatal opening (τi, A), stomatal closure (τd, B), and light saturated rate of carbon assimilation (τai, C) to a step change in light intensity (from 100 to 1000 µmol m-2 s-1; and from 1000 to 100 µmol m-2 s-1 respectively), at different times of the day. Stomatal conductance following a step increase in light intensity (from 100 to 1000 µmol m-2 s-1) (Gi, D); and after light intensity returned to 100 µmol m-2 s-1 (Gd, E); and light saturated rate of net CO2 assimilation at 1000 µmol m-2 s-1 (Ai, F), at different times of the day (Morning, Midday, Evening). Plants grown under the three high light treatments; fluctuating (FLH, red); sinusoidal (SNH, green); square wave (SQH, blue). Error bars represent 95% confidence intervals. n = 5-6.



1

Figure 5. Comparison of the Ball-Berry model prediction of gs with and without a Gaussian element. An example of adjustment made on an existing independent data set (black circles) measured under a dynamic light environment (A; see Vialet-Chabrand et al., 2017b), for the Ball-Berry model without (blue line) and with (red line) a Gaussian element. Shown are the comparisons between measured and predicted gs values using the Ball-Berry model without (B; Blue dots) and with (C; Red dots) a Gaussian element. Open and closed circles are the Fluctuating and Square-wave treatments respectively, from the independent data set.



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http://www.ncbi.nlm.nih.gov/pubmed?term=Allen MT%2C Pearcy RW %282000%29 Stomatal behavior and photosynthetic performance under dynamic light regimes in a seasonally dry tropical rain forest%2E Oecologia 122%3A 470�??478&dopt=abstract

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http://search.crossref.org/?page=1&rows=2&q=Alter P, Dreissen A, Luo FL, Matsubara S (2012) Acclimatory responses of Arabidopsis to fluctuating light environment: comparison of different sunfleck regimes and accessions. Photosynth Res 113: 221?237

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http://scholar.google.com/scholar?as_q=Acclimatory responses of Arabidopsis to fluctuating light environment: comparison of different sunfleck regimes and accessions.&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_publication=&as_yhi=&as_allsubj=all&hl=en&lr=&c2coff=1

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http://www.ncbi.nlm.nih.gov/pubmed?term=Assmann SM%2C Wang XQ %282001%29 From milliseconds to millions of years%3A guard cells and environmental responses%2E Curr Opin Plant Biol 4%3A 421�??8&dopt=abstract

http://search.crossref.org/?page=1&rows=2&q=Assmann SM, Wang XQ (2001) From milliseconds to millions of years: guard cells and environmental responses. Curr Opin Plant Biol 4: 421?8

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http://www.ncbi.nlm.nih.gov/pubmed?term=Bailey S%2C Walters RG%2C Jansson S%2C Horton P %282001%29 Acclimation of Arabidopsis thaliana to the light environment%3A the existence of separate low light and high light responses%2E Planta 213%3A 794�??801&dopt=abstract

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http://scholar.google.com/scholar?as_q=Photosynthetic response to fluctuating environments and photoprotective strategies under abiotic stress&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_publication=&as_yhi=&as_allsubj=all&hl=en&lr=&c2coff=1

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http://www.ncbi.nlm.nih.gov/pubmed?term=Yin ZH%2C Johnson GN %282000%29 Photosynthetic acclimation of higher plants to growth in fluctuating light environments%2E Photosynth Res 63%3A 97�??107&dopt=abstract


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http://search.crossref.org/?page=1&rows=2&q=Yin ZH, Johnson GN (2000) Photosynthetic acclimation of higher plants to growth in fluctuating light environments. Photosynth Res 63: 97?107

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Documents

Acclimation to fluctuating light impacts the rapidity and diurnal ... · PDF file02-02-2018 · Katul GG, Oren R, Manzoni S, Higgins C, Parlange MB (2012) Evapotranspiration: A process