**6. Theoretical modeling for describing stomatal delays**

To describe the dynamics of *g*s and *P*N in response to an abrupt change in light, piecewise linear, logistic, and exponential models have been frequently employed [25, 76–78]. For instance, in terms of stomatal dynamics in time scales during closing (*τ*cl) and opening phases (*τ*op), significant variation insensitivity and responsiveness is known to exist among different species [25, 32, 33]. As described above, when switching from high to low light, stomata always performed a lag relative to photosynthetic reduction, and to simplify, linearizing imputation between specific time period (stepwise) on photosynthetic dynamics could be a better option to define the amplitude and speed of stomata. In Arabidopsis, Wang et al. [79] have developed a dynamic model of stomatal responses, taking into consideration ion channel and kinetic effects as components controlling *g*<sup>s</sup> under steady-state and dynamic conditions. This model integrated the biophysical, molecular, and biochemical characteristics of guard cell transport, malate metabolism, and H+ and Ca2+, to predict stomatal aperture, which can be used to explore inherent interaction between different factors controlling *g*s [79, 80]. This model provided a good framework to incorporate new knowledge about controls over guard cell movements and hence help design engineering options to gain optimal steady state *g*<sup>s</sup> and also optimal dynamic responses of *g*s to light levels.

## **Author details**

Mingnan Qu1,2, Saber Hamdani1 and James A. Bunce2

1 CAS-Key Laboratory for Computational Biology, CAS-MPG Partner Institute for Computational Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, Shanghai, China

2 USDA ARS, Crop Systems and Global Change Laboratory, Beltsville, MD, USA

## **References**


[8] Demmig B, Winter K, Kruger A, Czygan FC. 1988. Zeaxanthin and the heat dissipation of excess light energy in *Nerium oleander* exposed to a combination of high light and water stress. *Plant Physiol*ogy 87: 17–24.

inherent interaction between different factors controlling *g*s [79, 80]. This model provided a good framework to incorporate new knowledge about controls over guard cell movements and hence help design engineering options to gain optimal steady state *g*<sup>s</sup> and also optimal

and James A. Bunce2

Computational Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of

1 CAS-Key Laboratory for Computational Biology, CAS-MPG Partner Institute for

2 USDA ARS, Crop Systems and Global Change Laboratory, Beltsville, MD, USA

[1] Willmer C, Fricker M. 1996. Stomata, 2nd edn. London: Chapman & Hall.

[2] Petersona KM, Rychela AL, Toriia KU. Out of the mouths of plants: The molecular basis of the evolution and diversity of stomatal development. *The Plant Cell* 22: 296–306.

[3] McKown AD, Guy RD, Klateps J, Geraldes A, Friedmann M, Cronk QCB, El-Kassa YA, Mansfield SD, Douglas CJ. 2014a. Geographical and environmental gradients shape phenotypic trait variation and genetic structure in *Populus trichocarpa*. The New

[4] Taub , DR, Seemann JR, Coleman JS. 2000. Growth in elevated CO2 protects photosyn‐ thesis against high-temperature damage. *Plant, Cell & Environment* 23: 649–656.

[5] Wang D, Heckathorn SA, Barua D, Joshi P, Hamilton EW, LaCroix JJ. 2008. Effects of elevated CO2 on the tolerance of photosynthesis to acute heat stress in C3, C4, and CAM

[6] Wang D, Heckathorn SA, Hamiton EW, Frantz J. 2014. Effects of CO2 on the tolerance of photosynthesis to heat stress can be affected by photosynthetic pathway and

[7] Yang Y, Han C, Liu Q, Lin B, Wang J. 2008. Effect of drought and low light on growth and enzymatic antioxidant system of *Picea asperata* seedlings. *Acta Physiologiae Planta‐*

dynamic responses of *g*s to light levels.

84 Applied Photosynthesis - New Progress

Mingnan Qu1,2, Saber Hamdani1

Phytologist 201: 1263–1276.

*rum* 30: 433–440.

species. *American Journal of Botany* 95: 165–176.

nitrogen. *American Journal of Botany* 101: 34–44.

Sciences, Shanghai, China

**References**

**Author details**


[33] Lawson T. 2009. Guard cell photosynthesis and stomatal function. The *New Phytolo‐ gist* 181: 13–34.

[19] Roden JS, Ball MC. 1996. Growth and photosynthesis of two eucalypt species during high temperature stress under ambient and elevated [CO2]. *Global Change Biology* 2: 115–

[20] Huxman TE, Hamerlynck EP, Loik ME, Smith SD. 1998. Gas exchange and chlorophyll fluorescence responses of three south-western Yucca species to elevated CO2 and high

[21] Chen JP, Burke JJ, Xin ZG. 2010. Role of phosphatidic acid in high temperature tolerance

[22] Eckardt NA, Snyder GW, Portis AR Jr, Ogren WL. 1997. Growth and photosynthesis under high and low irradiance of Arabidopsis thaliana antisense mutants with reduced ribulose-1,5-bisphosphate carboxylase/oxygenase activase content. *Plant Physiology*

[23] Crafts-Brandner SJ, Salvucci ME. 2002. Sensitivity of photosynthesis in a C4 plant,

[24] Chazdon RL. 1988. Sunflecks and their importance to forest understorey plants.

[25] Vico G, Manzoni S, Palmroth S, Katul G. 2011. Effects of stomatal delays on the economics of leaf gas exchange under intermittent light regimes. The *New Phytologist*

[26] Osterhout WJV, Haas ARC. 1918. On the dynamics of photosynthesis. *The Journal of*

[27] Walker DA. 1973. Photosynthetic induction phenomena and the light activation of

[28] Tang Y, Liang NS. 2000. Characterization of the photosynthetic induction response in a Populus species with stomata barely responding to light changes. *Tree Physiol* 20: 969–

[29] Lawson T, Weyers JDB. 1999. Spatial and temporal variation in gas exchange over the lower surface of *Phaseolus vulgaris* primary leaves. *Journal of Experimental Botany* 50:

[30] Pearcy RW. 1990. Sunflecks and photosynthesis in plant canopies. *Annual Review of*

[31] Lawson T, von Caemmerer S, Baroli I. 2010. Photosynthesis and stomatal behaviour. In: Luttge U, Beyschlag W, Budel B, Francis D, eds. Progress in Botany, Vol. 72.

[32] Lawson T, Blatt MR. 2014. Stomatal size, speed, and responsiveness impact on photo‐

synthesis and water use efficiency. *Plant Physiology* 164: 1556–1570.

ribulose diphosphate carboxylase. *The New Phytologist* 72: 209–235.

*Plant Physiology and Plant Molecular Biology* 41: 421–453.

temperature. *Plant, Cell & Environment* 21: 1275–1283.

maize, to heat stress. *Plant Physiology* 129: 1773–1780.

in maize. *Crop Science* 50: 2506–2515.

*Advances in Ecological Research* 18: 1–63.

128.

86 Applied Photosynthesis - New Progress

113: 575–586.

192: 640–652.

976.

1381–1391.

*General Physiology* 1: 1–16.

Heidelberg: Springer, 265–304.


[59] Wullschleger SD.1993. Biochemical limitations to carbon assimilation in C3 plants – a retrospective analysis of the *A*/*C* <sup>i</sup> curves from 109 species. *Journal of Experimental Botany* 44: 907–920.

[47] Wang D, Maughan MW, Sun J, Feng X, Miguez F, Lee D, Dietze MC. 2012. Impact of nitrogen allocation on growth and photosynthesis of Miscanthus (*Miscanthus ×*

[48] Merlot S, Leonhardt N, Fenzi F, Valon C, Costa M, Piette L, Vavasseur A, Genty B, Boivin K, Müller A. 2007. Constitutive activation of a plasma membrane H+

prevents abscisic acid-mediated stomatal closure. *The EMBO Journal* 26: 3216–3226.

[49] De Angeli A, Monachello D, Ephritikhine G, Frachisse JM, Thomine S, Gambale F, Barbier-Brygoo H. 2009. Review: CLC-mediated anion transport in plant cells.

[50] Gobert A, Isayenkov S, Voelker C, Czempinski K, Maathuis FJM. 2007. The two-pore

[51] Valliyodan B, Nguyen HT. 2006. Understanding regulatory networks and engineering for enhanced drought tolerance in plants. *Current Opinion in Biotechnology* 9: 189–195.

[52] Laanemets K, Wang YF, Lindgren O, Wu J, Nishimura N, Lee S, Caddell D, Merilo E, Brosche M, Kilk K. 2013. Mutations in the *SLAC1* anion channel slow stomatal opening and severely reduce Kþ uptake channel activity via enhanced cytosolic [Ca2þ] and increased Ca2þ sensitivity of Kþ uptake channels. *The New Phytologist* 197: 88–98. [53] Berger D, Altmann T. 2000. A subtilisin-like serine protease involved in the regulation of stomatal density and distribution in Arabidopsis thaliana. *Genes & Development* 14:

[54] Eisenach C, Chen ZH, Grefen C, Blatt MR. 2012. The trafficking protein SYP121 of

[55] Schlüter U, Muschak M, Berger D, Altmann T .2003. Photosynthetic performance of an Arabidopsis mutant with elevated stomatal density (*sdd1-1*) under different light

[56] Tanaka Y, Sugano SS, Shimada T, Hara-Nishimura I. 2013. Enhancement of leaf photosynthetic capacity through increased stomatal density in Arabidopsis. *The New*

[57] Büssis D, von Groll U, Fisahn J, Altmann TA. 2006. Stomatal aperture can compensate altered stomatal density in Arabidopsis thaliana at growth light conditions. *Funct Plant*

[58] Raven JA. 2002. Selection pressures on stomatal evolution. *The New Phytologist* 153: 371–

Arabidopsis connects programmed stomatal closure and K+

vegetative growth. *The Plant Journal* 69, 241–251.

regimes. *Journal of Experimental Botany* 54: 867–874.

homeostasis. *Proceedings of the National Academy of Sciences of the United States of*

*Philosophical Transactions of the Royal Society B: Biological Sciences* 364: 195–201.


conductance and plays a role in K+

channel activity with

*giganteus*). *GCB Bioenergy* 4: 688–697.

88 Applied Photosynthesis - New Progress

channel TPK1 gene encodes the vacuolar K+

*America* 104: 10726–10731.

1119–1131.

*Phytologist* 198: 757–764.

*Biol* 33: 1037–1043.

386.


physiology link stomatal patterning in *Populus trichocarpa* with carbon gain and disease resistance trade-offs. *Molecular Ecology* 23: 5771–5790.

