The role of bundle sheath extensions and life form in stomatal responses to leaf water

37 Bundle-sheath extensions (BSEs) are key features of leaf structure with currently little- 38 understood functions. To test the hypothesis that BSEs reduce the hydraulic resistance from the 39 bundle sheath to the epidermis ( r be ), and thereby accelerate hydropassive stomatal movements, 40 we compared stomatal responses to reduced humidity and leaf excision among 20 species with 41 heterobaric or homobaric leaves, and herbaceous or woody life forms. We hypothesised that low 42 r be due to presence of BSEs would increase the rate of stomatal opening ( V ) during transient 43 wrong-way responses (WWRs), but more so during WWRs to excision ( V e ) than humidity ( V h ), 44 thus increasing the ratio of V e to V h . We predicted the same trends for herbaceous relative to 45 woody species given greater hydraulic resistance in woody species. We found that V e , V h and 46 their ratio were 2.3-4.4 times greater in heterobaric than homobaric leaves and 2.0 to 3.1 times 47 greater in herbaceous than woody species. To assess possible causes for these differences, we 48 simulated these experiments in a dynamic compartment/resistance model, which predicted larger 49 V e and V e / V h in leaves with smaller r be . These results support the hypothesis that BSEs reduce r be 50 Comparison of our data and simulations suggested r be is approximately 4-16 times larger in 51 homobaric than heterobaric leaves. Our study provides new evidence that variations in the 52 distribution of hydraulic resistance within the leaf and plant are central to understanding dynamic 53 stomatal responses to water status and their ecological correlates, and that BSEs play several key 54 roles in the functional ecology of heterobaric leaves. 55 56


This work was supported by startup funding from the Dean of the School of Science and 26
Technology at Sonoma State University, and by support from the SSU NoGAP program. 27 28 * Corresponding author; email tom.buckley@sonoma.edu, +1 707 664 3286 29 30 The author responsible for distribution of materials integral to the findings presented in this 31 article in accordance with the policy described in the Instructions for Authors 32 Franks, 2001). Similarly, stomata can respond to changes in transpiration rate in distant regions 90 of the same leaf (Buckley and Mott, 2000) or plant (Pataki et al., 1998;Pepin et al., 2002;91 Brooks et al., 2003). Long-distance responses include transient wrong-way opening movements 92 similar to those generated by local hydraulic perturbations, which suggests the long-distance 93 responses are mediated by hydraulic signals. However, Mott (2007) reported that stomatal 94 responses to humidity were independent on the two surfaces of amphistomatous leaves of Vicia 95 faba and Xanthium strumarium: when humidity was changed at one surface only, stomata on that 96 surface responded but stomata on the other surface did not. This suggests changes in water 97 potential near one surface may not propagate to the opposite surface, which in turn suggests that 98 stomata in opposing epidermes on broad leaves might be hydraulically sequestered from one 99 another and from the xylem. Peak and Mott (2011) hypothesised that guard cells themselves are 100 hydraulically sequestered from the epidermis, and instead sense humidity in the stomatal pore 101

INTRODUCTION
directly. An alternative explanation is that the hydraulic resistance between the epidermis and 102 the bulk leaf tissue, including the xylem, can be very large -consistent with the observation that 103 epidermal turgor pressure responded to humidity at the perturbed surface but not at the 104 unperturbed surface in V. faba (Mott 2007; turgor was not measured for X. strumarium). 105 The hydraulic resistance between the epidermis and the rest of the leaf may vary strongly 106 across species, and especially between homobaric and heterobaric leaves. The latter possess 107 bundle sheath extensions (BSEs) that connect the epidermis and vascular bundles (Wylie, 1952). 108 BSEs can help distribute light through thicker leaves, enhancing photosynthesis (Nikolopoulos et 109 al., 2002), and they may limit lateral CO 2 diffusion within the leaf (Terashima, 1992;Morison et 110 al., 2007). BSEs are more common in xeric, high light species and upper canopy trees (Kenzo et 111 al., 2007) and in deciduous woody species than in herbs (Wylie, 1952;McClendon, 1992). 112 Well-known features of stomatal behaviour can provide insight about the role of BSEs in 120 leaf hydraulics and the control of water loss. In most angiosperm leaves, stomatal closure 121 following either increased evaporative demand or reduced water supply is preceded by opening 122 movements known as "wrong-way responses" (WWRs; e.g., Fig. 1). The WWR is caused by an 123 initial reduction in epidermal backpressure on stomata (Darwin, 1898;Cowan, 1972), whereas 124 the subsequent closure ("right-way response," RWR) results from a slower but larger decline in 125 guard cell turgor pressure that may be caused by solute release from guard cells (Losch and 126 Schenk, 1978;Ehret and Boyer, 1979;Grantz and Zeiger, 1986;Buckley and Mott, 2002;Powles 127 et al., 2006). The rate of stomatal opening during the WWR depends on the time constant for 128 changes in epidermal turgor pressure, P e . The rate of change of P e is: 129 Eqn (1) suggests stomatal opening rate due to reduced P e will scale with 1/r be for a step change in 137 supply (ψ b ), and with f e for a step change in demand (E). However, increased demand may also 138 reduce ψ b , so the opening rate following a change in E may also scale with 1/r be , but to a lesser 139 extent. 140 This predicts low r be should increase WWR opening rates for both supply and demand 141 perturbations, but more so for supply responses. Thus, we hypothesised that the rates of stomatal 142 opening during excision WWRs (V e ) and humidity WWRs (V h ), as well as their ratio V e /V h , will 143 be greater in heterobaric than homobaric leaves. Similarly, because soil to leaf hydraulic 144 resistance is greater in woody than herbaceous species (Turner et al., 1984;Mencuccini, 2003;145 Sack et al., 2003), we hypothesised that V e , V h and V e /V h will be greater in herbaceous than 146 woody species. To assess the degree and functional significance of hydraulic sequestration of 147 the epidermis as affected by BSEs and plant growth habit, we tested these hypotheses by 148 measuring stomatal responses to humidity and leaf excision in leaves of 10 homobaric and 10 fold. These results are given in detail by species in Table S1 in the Supplementary Material, and  169 summarised by group (leaf type and life form) in Table II. A substantial part of the total 170 variance in the dataset, ranging from 22 to 60%, occurred within species (i.e., among replicates 171 of the same species), for all parameters except V h , V e and R h,rel (Table II). 172

WWR kinetics 174
Heterobaric and homobaric species (HE and HO, respectively) showed strong differences in 175 WWR parameters. Consistent with our hypothesis, the ratio of the rates of stomatal opening 176 during WWRs to excision and humidity (V e /V h ) was more than twice as large for HE than HO 177 species (3.23 ± 1.20 versus 1.40 ± 0.24; p<0.05; means ± SE; Fig 3 and Table II). This 178 difference arose because opening during WWRs to excision was 4.4 times faster in HE than HO 179 leaves (V e /10 -5 = 41.7 ± 15.8 vs 9.4 ± 1.9 mol m -2 s -2 ; p<0.001; Fig 3), and despite the fact that 180 opening during WWRs to humidity was also 2.5 times faster in HE leaves (V h /10 -5 = 20.2 ± 7.3 181 vs 8.1 ± 1.2 mol m -2 s -2 ; p<0.01; Fig 3). Notably, faster opening was not consistently associated 182 with shorter WWRs: although humidity WWRs were shorter in HE than HO species (p<0.05), 183 excision WWRs did not differ significantly in length (Table II). 184 We also found the hypothesised differences in WWR kinetics between woody and herbaceous 186 species: V h , V e , and V e /V h were 2.3, 3.1 and 2.0 times greater, respectively, in herbaceous than 187 woody plants (p<0.005, p<0.001, p<0.05, respectively; Fig 4 and Table II). In this case, faster 188 opening was associated with shorter humidity and excision WWRs (p<0.005 and p<0.05 189 respectively; Table II). 190 191 The faster opening we observed in HE than HO and in herbaceous relative to woody species was 192 linked partly, but not entirely with higher initial g s (Table II). Thus, V h and V e were correlated 193 with g 1 , with relationships that appeared to be exponential (equations V h = 0.00242 e 8.2472⋅g1 ; r 2 = 194 0.402; and V e = 0.00334 e 6.7698⋅g1 ; r 2 = 0.145; p<0.001 and p=0.005 respectively; Figure S1 in the 195 Supplementary Material). We determined whether BSEs and life form affected V e and V h 196 independently of g 1 by determining the residuals of V h and V e against g 1 from these equations, and 197 testing for difference in these residuals using the nested ANOVAs (see Methods). For V h and V e 198 the residuals differed between HE and HO (p = 0.064 and p<0.001 respectively) and between 199 woody and herbaceous species (p<0.005 and p<0.001 respectively). Figure S2 shows mean 200 residuals by species, leaf type and life form. These findings indicated differences in rates of 201 stomatal opening between leaf and plant types that were independent of differences in g 1 . 202

WWR and RWR sizes 204
The sizes of WWRs differed between plant types in some cases. Thus, WWRs in response to 205 excision were 3.7 times larger in HE than HO species (W e,rel = 138 ± 78 vs 38 ± 9%, respectively; 206 p<0.001; Fig 5), but WWRs to humidity did not differ significantly in size between HE and HO 207 species (W h,rel = 43 ± 20 vs 25 ± 6%, respectively; Fig 5,

Modeling analysis 218
Using the baseline parameter set (Table III), in which the resistance from the bundle sheath to 219 the epidermis, r be , was assumed equal to that between the bundle sheath and mesophyll, the 220 model predicted V e /V h = 3.58 ("1× r be " under "Simulated" in Table II). Using the same 221 parameters but with resistance to the epidermis increased 10-or 20-fold ("10× r be " and "20× r be " 222 under "Simulated" in Table II), the model predicted V e /V h = 2.32 and 1.62 respectively. All three 223 simulations predicted larger WWRs to excision than humidity, but this difference declined as r be 224 increased (W e /W h = 2.14, 1.68 and 1.33 at 1×, 10× and 20×r be , respectively). The absolute rates 225 of opening and WWR sizes predicted by the model were smaller than we observed (Table II). 226

227
We assessed parameter sensitivity by a series of simulations (Fig 7) in which individual 228 parameter values were doubled relative to their baseline values in Table III. This analysis 229 suggested that V e /V h should be sensitive to changes in several parameters, including r be . 230 Specifically, increases in epidermal osmotic pressure at incipient plasmolysis (π eo ), guard cell 231 volume fraction (v go /v total ) or maximum mesophyll elastic modulus (ε m ) would strongly increase 232 V e /V h , whereas increases in either the rate constant for guard cell osmoregulation (α), the 233 sensitivity of guard cell osmotic pressure to epidermal turgor at steady state (B), or the soil-leaf 234 xylem resistance (r sx ) would strongly reduce V e /V h . Doubling epidermal transpiration fraction 235 (f e ) reduced V e /V h by a similar degree as doubling r be . V e /V h was minimally sensitive to other 236 parameters. The absolute sensitivities of V e and V h differed widely among parameters. Notably, 237 doubling α had no effect on V h but reduced V e by over 30%. Doubling symplastic volume (v total ) 238 reduced both V h and V e by about 45%. The similar effects of f e and r be on V e /V h had different 239 causes: f e increased V h with little effect on V e , whereas r be reduced V e with little effect on V h . 240 Increasing π eo enhanced V e much more than V h ; the opposite was true for B (Fig 7).

242
We also assessed the sensitivity of V e /V h to a wider range of r be values (Fig 7). These simulations 243 used a range of values of B and α, because we could not estimate these parameters from the (4) and α (0.005 s -1 ); at approximately 1 and 16 times baseline r be for high B (6); and at 6 and 26 248 times baseline r be for low α (0.0025). (Similar trends were predicted at low B (2) and high α 249 (0.01), but in neither case could simulations span the range of observed mean V e /V h values for 250 both leaf types if r be were constrained to 30 times baseline.) From these three ranges we 251 tentatively estimated that a 4-to 16-fold reduction of r be by BSEs (

DISCUSSION 261
We hypothesised that bundle sheath extensions (BSEs) and growth habit would impact strongly 262 on stomatal responses. Thus, BSEs in heterobaric leaves should increase the rates of stomatal 263 opening during transient wrong-way responses to leaf excision (V e ) and humidity (V h ), but more 264 so for excision, such that the ratio of V e /V h should be greater in heterobaric than homobaric 265 leaves. Our hypotheses were based on inspection of Eqn (1) in the Introduction, and therefore 266 unavoidably omitted some dynamical complexity. However, a more rigorous analysis based on a 267 dynamical compartment-resistance model (Figs 7 and 8) also predicted that V e and V e /V h should 268 be larger in plants with low r be . 269 Our results supported these hypotheses for the impacts of BSEs. The V e , V h and the ratio 270 V e /V h were greater in heterobaric than homobaric leaves, as predicted. These results suggest that 271 BSEs reduce the sensitivity of epidermal turgor (P e ) to changes in either hydraulic supply or 272 demand for the epidermis, but more so for changes in hydraulic supply. We also predicted larger 273 V e , V h and V e /V h in herbaceous than woody plants because of the smaller total resistance of water 274 supply to the epidermis in woody species. Our results supported those predictions as well. 275 Our data and model analyses support the hypothesis that BSEs substantially reduce 276 hydraulic resistance to the epidermis. To estimate the size of that effect, we determined how 277 widely r be needed to vary to reproduce the mean values of V e /V h observed for heterobaric and 278 heterobaric leaves (Fig 8). On this basis, we estimated that a 4-16 fold reduction in r be by BSEs 279 could explain our observations. This is consistent with previous estimates of the extravascular 280 fraction of r leaf (30-50%, Sack et al., 2005) and of the effects of high irradiance on r leaf in 281 heterobaric leaves (reductions of 58 versus 20%, respectively, Scoffoni et al., 2008), which 282 suggest BSEs reduce r be by 5-24 fold (this is derived in the Supplemental Material). 283 284

Effect of parameters other than r be on WWR properties 285
Comparison of our results with the model suggested that parameters other than r be may 286 also vary systematically between heterobaric and homobaric leaves. Parameter sensitivity 287 analysis showed that increasing total symplastic volume per unit leaf area (v total ) would reduce 288 both V h and V e independent of their ratio. This is also evident from inspection of Eqn (1), and it 289 reflects the ability of volume to buffer changes in turgor pressure. One study did in fact find 290 thicker leaves in homobaric than heterobaric woody species (Liakoura et al., 2009), which is consistent with higher v total and thus with our finding of smaller V e and V h in homobaric species. 292 Another possibility is that π eo and B covary and are larger in heterobaric leaves (these are, 293 respectively, epidermal osmotic pressure at incipient plasmolysis and the sensitivity of guard cell 294 osmotic gradient to P e in the steady-state), as these parameters both increase V e and V h but have 295 opposing effects on their ratio V e /V h (Fig 7). 296 Sensitivity analysis indicated three other parameters with greater effects than r be on V e /V h : 297 guard cell volume fraction (v go /v total ), maximum mesophyll elastic modulus (ε m ), guard cell 298 osmoregulatory rate constant (α) and soil-leaf xylem resistance (r sx ). Like π eo and B, v go and α 299 have strong but opposing effects on V e /V h in the model. However, α modulates rates of 300 adjustment in guard cell osmotic content, which v go translates into osmotic pressure; thus, one 301 may expect α and v go to covary, which would tend to cancel both parameters' effects on V e /V h .

302
Doubling ε m increased V e /V h by 10%, so a 10-fold increase in ε m could potentially explain the 303 observed ~100% difference in V e /V h between heterobaric and homobaric leaves. This is unlikely, 304 however, because even doubling ε m increased it to 30.6 MPa, which exceeds the range of values 305 commonly reported in plants (e.g., Niinemets, 2001;Saito and Terashima, 2004). Increases in 306 another parameter, r sx, reduced the absolute magnitudes of both V e and V h , with a greater impact 307 on V e than V h . These effects are qualitatively identical to those of r be , and can be understood on a 308 similar basis. 309 Doubling the epidermal transpiration fraction (f e ) reduced V e /V h by a similar degree as 310 doubling r be . This arose mainly from increased V h in the case of f e , but from decreased V e in the 311 case of r be (Fig 7). This bears out the analysis of Eqn (1) in the Introduction, which suggested 312 increased f e and decreased r be should accelerate stomatal opening after demand and supply 313 perturbations, respectively. The actual value of f e is unknown and highly debated (Tyree and 314 Yianoulis, 1980;Maier-Maercker, 1983;Grantz, 1990). Our analysis suggests that if f e differs 315 systematically with leaf type, one would expect larger f e in homobaric than in heterobaric leaves. 316 That seems reasonable, as BSEs prevent evaporation from the epidermal cells that they subtend. 317 However, evaporation from BSEs likely cannot explain trends in V e /V h with leaf type, because 318 the effect of bundle sheath transpiration fraction (f b ) was negligible in the model (not shown). 319 Other parameters generally had smaller effects than r be on V e , V h and V e /V h . Doubling the 320 resistance from the bundle sheath to the mesophyll (r bm ) slightly increased V e /V h due to a small 321 increase in V e and decrease in V h . These effects are opposite those of r be , and this is because the ratio r be /r bm essentially partitions water supply between the epidermis and mesophyll. Epidermal 323 volume fraction (v eo /v total ) very slightly reduced both V e and V h , consistent with Eqn (1), and 324 bundle sheath volume fraction (v bo /v total ) had negligible effects on V e and V h . Xylem to bundle 325 sheath resistance (r xb ) had effects qualitatively identical to, but much smaller than those of r sx -326 i.e., reduced V e and V h and increased V e /V h -which is logical, given that r sx and r xb are in series 327 and proximal to the bundle sheath. Increased epidermis to guard cell resistance (r eg ) slightly 328 increased V e but not V h . V h was minimally affected because r eg has two opposing effects: it slows 329 both the hydropassive and hydroactive declines in guard cell turgor (which increase and decrease 330 opening rate, respectively) by impeding water movement. However, whereas the humidity 331 WWR peaks when the hydroactive response overcomes the epidermal mechanical advantage, the 332 excision WWR peaks when the epidermis reaches zero turgor, which means hydroactive kinetics 333 have less influence on V e than on V h . 334 The model assumes a linear dependence of g s on guard cell turgor, whereas g s -and 335 WWR size -may be mechanically limited to a maximum upper value. Thus, if heterobaric and 336 homobaric species differed systematically in the proximity of their initial g s to that theoretical 337 maximum, this could introduce a bias in WWR size and, transitively, in the parameters of WWR 338 kinetics. Although we did not attempt to quantify maximum g s per se, we sought to minimise 339 variations in the proximity of initial to maximum g s by measuring all leaves at the same high 340 irradiance (600 μmol m -2 s -1 , which exceeded that prevailing in the greenhouse during plant 341 growth and acclimation prior to measurement). 342 343 The cause of wide variation in WWR parameters 344 Although we found strong effects of leaf type on most WWR parameters, there was large 345 variation in those parameters, both among and within species. This variation could not be 346 explained by differences in growing or measurement conditions. Some of this variation may 347 relate to the mechanical advantage (m) of epidermal cells, which varies among and within 348 species, the latter in relation to changing P e (Franks et al., 1995;Franks et al., 1998;Franks and 349 Farquhar, 2007). Technical challenges have limited measurements of m to few species. We note 350 that one would expect the qualitative effects of P e -dependent changes in m to be consistent 351 among replicate leaves from a given species; however, we found WWR parameters often 352 diverged even within species in this study, which suggests variation in factors other than m.
Notably, variation in WWR parameters has been reported previously. Powles et al 354 (2006) reported consistent differences in excision WWR size and duration between Photinia x 355 fraseri individuals kept outdoors vs in a glasshouse in the days prior to measurement. They used 356 a modeling analysis to attribute those effects to differences in the lag time preceding the guard 357 cell hydroactive response. They also found that WWR size and length were positively 358 correlated, as we did in this study. Those findings suggest that the time constant for relaxation of 359 xylem-epidermis water potential gradients is correlated with the lag time preceding the guard cell 360 hydroactive response (otherwise, longer WWRs would also be smaller). Thus, variation in 361 WWR such as observed in these studies is consistent with variation in the hydraulic resistance of 362 flow pathways proximal to the guard cells, including r be and r eg . 363 Some within-species variation in WWR kinetics may be genetic in origin. Sinclair et al 364 (2008)  Notably, not all land plants exhibit WWRs: they are apparently absent among extant ferns 381 and lycophytes, which are also insensitive to abscisic acid (ABA) (Brodribb and McAdam, 382 2011), a hormone known to induce stomatal closure in response to progressive soil drought in 383 most seed plants (Davies et al., 1987;Raschke, 1987). This suggests stomatal hydromechanics are fundamentally different in seedless plants and seed plants: whereas the former have strictly 385 passive control of g s in relation to water status, seed plants require metabolic or other 386 mechanisms to amplify passive changes in guard cell turgor to overcome the epidermal 387 mechanical advantage (Buckley, 2005). Not surprisingly, then, guard cell osmoregulation in 388 seed plants is highly complex and adaptable (Zeiger et al., 2002;Nilson and Assmann, 2007). 389 Our finding that BSEs can affect stomatal dynamics, together with evidence that extravascular 390 resistance is large and dynamic (Nardini et al., 2005;Sack et al., 2005;Cochard et al., 2007) and 391 located partly in BSEs (Scoffoni et al., 2008), suggests BSEs may contribute to the regulatory 392 challenges posed by seed plants' unique stomatal mechanics. 393 One likely role for a variable BSE resistance would be to reversibly amplify changes in 394 epidermal water potential caused by changes in evaporative demand or water supply. "Apparent 395 feedforward" behaviour of stomata (Franks et al., 1997) -in which water loss actually declines 396 at high evaporative demand -may be necessary for optimal stomatal control under certain 397 conditions (Buckley, 2005). Feedforward could result from increased hydraulic resistance (Oren 398 et al., 1999;Buckley and Mott, 2002;Buckley, 2005), perhaps via modulation of r be . Variation 399 in r be could also help reconcile the observation that stomata respond independently to humidity in 400 the two epidermes of amphistomatous leaves (Mott, 2007) with other data that showed strong 401 hydraulic coupling of stomatal behaviour over much greater distances (Heath and Russell, 1954;402 Schulze and Kuppers, 1979;Mott et al., 1997;Buckley and Mott, 2000). Clarity on this issue 403 awaits further study on the phenomenology of r be in relation to the external and leaf environment. 404 405

Differences in steady-state humidity responses 406
This study also provided measurements of steady-state stomatal responses (RWRs) to reduced 407 humidity. Relative RWR size (R h,rel ) did not differ significantly between heterobaric and 408 homobaric leaves, but it was greater in woody than herbaceous species. This is consistent with 409 an earlier study comparing humidity responses in 6 non-woody and 7 woody species (Franks and 410 Farquhar, 1999). For a step change from Δw low to Δw high in our model, R h,rel is 411 where M is net epidermal mechanical advantage, χ is a turgor-to-conductance scaling factor, and 415 R is the effective hydraulic resistance from the soil to the epidermis. (Eqn (2) is derived in the 416 Supplemental Material.) Thus, greater R h,rel may reflect greater R, a more sensitive guard cell 417 response (B), smaller mechanical advantage or higher stomatal density (which largely determines 418 χ) in woody plants. The latter is unlikely, as high χ also implies high initial g s , whereas we 419 found lower g 1 in woody than herbaceous plants. The model predicted greater R h,rel in plants 420 with greater r sx , r xb , r be and f e (all of which influence R) and greater B, confirming Eqn (2), and 421 smaller R h,rel in plants with high π eo (not shown). However, the effects of r sx and B were about 422 25-30 times greater than those of r be and f e , and the next-largest effects were 30 times smaller still 423 -suggesting RWRs to humidity are primarily affected by R and B. As whole plant resistance is 424 generally greater in woody species (Turner et al., 1984;Mencuccini, 2003;Sack et al., 2003)

CONCLUSION 428
We found that rates of stomatal opening during transient wrong-way responses were greater in 429 heterobaric than in homobaric leaves, and that this difference was greater during excision than 430 humidity responses. Theoretical analysis showed this pattern to be consistent with the 431 hypothesis that bundle sheath extensions reduce hydraulic resistance between the bundle sheath 432 and epidermis (r be ). We estimated r be to be on the order of 4-16 times greater in homobaric than 433 heterobaric leaves, by applying a theoretical model to our results; we estimated a similar range 434

Plant material 445
Plants of diverse herbaceous and woody species (Table I)  photodiode (G1118, Hamamatsu, Bridgewater, NJ) previously calibrated to a quantum sensor 474 . 475 476

Experimental protocol 477
Each experiment measured a humidity response followed by an excision response for the same 478 leaf (e.g., Fig. 1). A plant was brought to the laboratory in the morning (0700-0830h) and one 479 healthy, young, fully expanded leaf was clamped in the chamber and allowed to equilibrate at 480 600 μmol m -2 s -1 PPFD, 25 o C leaf temperature, 15 mmol mol -1 leaf-air water vapour mole 481 fraction difference (Δw) (=52% relative humidity), and 370 ppm ambient CO 2 (c a ). Stomatal 482 conductance (gs) was logged every second. After g s reached a steady state (defined as 10 min 483 without a directional trend), Δw was increased to 25 mmol mol -1 (=20% relative humidity) in a 484 single step by adjusting the mixing ratio of humidified and dry air with MFCs. After g s reached a 485 new steady state, the leaf was excised at the petiole and gas exchange was logged for 60 more 486 minutes. 487 488

Correction for mixing and desorption lags 489
After humidity is reduced, mixing lags and vapour desorption can affect water vapour 490 differential for a time. To correct for this, we measured timecourses of IRGA output after a step 491 reduction in humidity identical to that applied in leaf experiments, with and without the leaf 492 chamber in the sample line. We characterised the lag due to chamber mixing and desorption by 493 comparing sample signals with and without the chamber, and fit a two-phase exponential model 494 to their difference between 1 and 5 min after the humidity change (r 2 = 0.9987); that model 495 showed a half-time of 9 sec and a 95% time of 51 sec. The half-time for mixing and des We 496 characterised differences in sample vs reference line mixing lags by comparing sample and 497 reference signals without the chamber, and fit a second-order polynomial to their difference, 498 between 1 and 5 min after the change (r 2 = 0.994; p < 0.0001). For each leaf experiment we 499 discarded data from less than 1 min after the Δw change, and applied the corrections to measured 500 water vapour differentials over the remaining timecourse. We quantified features of stomatal movements during WWRs and RWRs as described below and 504 illustrated in Fig 1. For humidity responses, we recorded the initial value of g s (g 1 ) at the time of 505 the humidity change (t 1 ), the time and value of g s at the peak of the WWR (t 2 and g 2 ), and the 506 time at the end of the WWR (t 3 , defined as the time at which g s first dropped below g 1 ; note g 3 ≡ 507 g 1 ). For excision responses, we recorded the g s value (g 4 ) at the time of excision (t 4 ), the time and 508 g s value at the WWR peak (t 5 and g 5 ) and the time at the end of the WWR (t 6 ). We calculated the 509 absolute size of each WWR (W) as W h = g 2 -g 1 for humidity and W e = g 5 -g 4 for excision, and the 510 length of each WWR (L) as L h = t 2 -t 1 and L e = t 5 -t 4 . We calculated the rate of opening during 511 each WWR (V) as V h = W h /L h and V e = W e /L e . We also calculated the size of humidity RWRs 512 (R h ) as R h = g 1 -g 4 ; we did not attempt to quantify an RWR to excision. To normalise for 513 differences in initial g s , we also calculated percent relative sizes of WWRs and RWRs and 514 opening rates (W rel , R rel and V rel ) by dividing W h , R h , V h and V e by g 1 and W e by g 4 , and 515 multiplying by 100. Data for each trait were analyzed using a nested ANOVA, with species 516 nested within heterobaric versus homobaric leaf type, nested within woody versus herbaceous 517 life form (Minitab Release 15). Data were incremented by 1 and log-transformed before 518 analyses, to allow inclusion of zero values and to increase normality and heteroscedasticity 519 (Sokal and Rohlf, 1995). Additionally, as WWR parameters were linked with g 1 (see Results) we 520 determined whether BSEs and life form affected V e and V h independently of g 1. We determined 521 correlations of V e and V h on g 1 and tested for difference in the residuals of those correlations 522 using the nested ANOVAs (Sokal and Rohlf, 1995). 523 524

Dynamic model of water flow and stomatal control 525
We simulated water flows, stomatal movements and transpiration in leaves subjected to the 526 experimental protocol described above, using a physical model based on conservation of mass in 527 an explicit compartment/resistance network (Fig 2). Complete details and parameter estimation 528 are given in the Supplemental Material, and briefly summarised here. 529

530
The model contains five state variables: symplastic volumes for four leaf water pools 531 (mesophyll, epidermis, guard cells and the bundle sheath, including bundle sheath extensions in 532 heterobaric species) and guard cell osmotic content (osmotic contents in other pools are assumed 533 constant). The volumes determine turgor and osmotic pressures passively. Flows are calculated from water potential differences and resistances among pools. Each pool supports a fixed 535 fraction of total evaporation (Table III), which is proportional to VPD and stomatal aperture. 536 Aperture is a function of guard cell and epidermal turgor pressures. Xylem capacitance is 537 assumed negligible, so xylem water potential is quasi-steady state with respect to other pools. 538 The only active process is dynamic modulation of guard cell osmotic content to seek a "target" 539 value of osmotic pressure (π g ) proportional to epidermal turgor (P e ), which overcomes the 540 epidermal mechanical advantage and causes a negative steady state relationship between g s and 541 VPD. WWRs arise because P e necessarily declines before π g . The existence of this hypothesised 542 "hydroactive feedback" is supported by a great deal of evidence (Losch and Schenk, 1978;Ehret 543 and Boyer, 1979;Grantz and Zeiger, 1986;Buckley and Mott, 2002;Powles et al., 2006) and is 544 the basis of previous models (Haefner et al., 1997;Buckley et al., 2003). 545

546
We derived a baseline set of parameter values (given in Table III) from the literature, for Vicia 547 faba where possible, as described in the Supplemental Material. V. faba is a homobaric species 548 in our study and is common in the stomatal literature. The parameter that captures the 549 hypothesized role of BSEs (r be , bundle sheath-epidermis resistance) has not been directly 550 measured. Therefore, we initially assumed r be was equal to the resistance from the bundle sheath 551 to the mesophyll (r bm ), and the baseline parameters represent a heterobaric leaf. However, we 552 varied r be among simulations to assess its potential role in stomatal dynamics. 553 554 We used this model to simulate our experimental protocol, and assessed the sensitivity of 555 predicted WWR kinetics to parameters in the model relative to a simulation using the baseline 556 parameter set.  Figure S1 (correlations of opening rates with initial conductance) 567 G. Figure S2   increase in evaporative demand from 15 to 25 mmol mol -1 (decrease in relative humidity from 52 738 to 20%) at t 1 , followed by leaf excision at the petiole at t 4 . The points in time and corresponding 739 g s values used to calculate the wrong-way response (WWR) and right-way response (RWR) 740 parameters (t 1 -t 6 and g 1 , g 2 , g 4 and g 5 ; note g 3 ≡ g 1 and g 6 ≡ g 4 ) as described in Materials and 741 Methods are represented diagrammatically.    to 20%) at t 1 , followed by leaf excision at the petiole at t 4 . The points in time and corresponding g s values used to calculate the wrong-way response (WWR) and right-way response (RWR) parameters (t 1 -t 6 and g 1 , g 2 , g 4 and g 5 ; note g 3 ≡ g 1 and g 6 ≡ g 4 ) as described in Materials and Methods are represented diagrammatically.        Table II. Parameters are ordered with respect to their effect on V e /V h .