Predicting stomatal conductance and its contribution to the control of photosynthesis

A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions

Ball J. T., Woodrow I. E., Berry J. A. (1987)

John Timothy Ball, Ian E. Woodrow, Joseph A. Berry,

In J Biggins, ed, Progress in Photosynthesis Research 4 – Proceedings of the VIIth International Congress on Photosynthesis Providence, Rhode Island, USA, August 10–15, 1986 – Springer, Dordrecht, The Netherlands –


In the past, stomatal responses have generally been considered in relation to single environmental variables in part because the interactions between factors have appeared difficult to quantify in a simple way.

A linear correlation between stomatal conductance (g) and CO2 assimilation rate (A) has been reported when photon fluence was varied and when the photosynthetic capacity of leaves was altered by growth conditions, provided CO2, air humidity and leaf temperature were constant (1). Temperature and humidity are, however, not consistent in nature.

Lack of a concise description of stomatal responses to combinations of environmental factors has limited attempts to integrate these responses into quantitative models of leaf energy balance, photosynthesis, and transpiration. Moreover, this lack has hindered progress toward understanding the stomatal mechanism.

We have taken a multi-variant approach to the study of stomatal conductance and we show that under many conditions the responses of stornata can be described by a set of linear relationships.

This model can be linked to models of leaf carbon metabolism and the environment to predict fluxes of CO2, H2O and energy.

In this paper, we show how the model of conductance can be linked to a description of CO2 assimilation as a function of intercellular CO2 (whether empirical or the output of a model) to predict the distribution of flux control between the stornata and leaf “biochemistry” under conditions in a gas-exchange cuvette.

There was no relationship between the sensitivity of stomata to COS and the rate of COS uptake (or, by inference, hydrogen sulfide production)

Effects of carbonyl sulfide and carbonic anhydrase on stomatal conductance

by Stimler K., Berry J. A., Yakir D. (2012)

Keren Stimler, Joseph A. Berry, Dan Yakir,


In Plant Physiol. 158: 524–530 – doi: 10.1104/pp.111.185926


The potential use of carbonyl sulfide (COS) as tracer of CO2 flux into the land biosphere stimulated research on COS interactions with leaves during gas exchange. We carried out leaf gas-exchange measurements of COS and CO2 in 22 plant species representing deciduous and evergreen trees, grasses, and shrubs, under a range of light intensities, using mid-infrared laser spectroscopy. A narrow range in the normalized ratio of the net uptake rates of COS (As) and CO2 (Ac), leaf relative uptake (As/Ac × [CO2]/[COS]), was observed, with a mean value of 1.61 ± 0.26, which is advantageous to the use of COS in photosynthesis research. Notably, increasing COS concentrations between 250 and 2,800 pmol mol−1 (enveloping atmospheric levels) enhanced stomatal conductance (gs) to a variable extent in most plants examined (up to a normalized enhancement factor [ fe = (gs-max − gs-min)/gs-min] of 1). This enhancement was completely abolished in carbonic anhydrase (CA)-deficient antisense lines of both C3 and C4 plants. We suggest that the stomatal response is mediated by CA and may involve hydrogen sulfide formed in the reaction of COS and water with CA. In all species examined, the uptake rates of COS and CO2 were highly correlated, but there was no relationship between the sensitivity of stomata to COS and the rate of COS uptake (or, by inference, hydrogen sulfide production). The basis for the observed stomatal sensitivity and its variations is still to be determined.

Stomatal closure in groups

Topography of Photosynthetic Activity of Leaves Obtained from Video Images of Chlorophyll Fluorescence

by Daley P. F., Raschke K., Ball J. T., Berry J. A. (1989)

In Plant Physiol. 90: 1233-1238 –


Comparing optimal and empirical stomatal conductance models

Comparing optimal and empirical stomatal conductance models for application in Earth system models

by Franks P. J., Bonan G. B., Berry J. A., Lombardozzi D. L., Holbrook N. M., Herold N., Oleson K. W. (2018)

Peter J. Franks, Gordon B. Bonan, Joseph A. Berry, Danica L. Lombardozzi, N. Michele Holbrook, Nicholas Herold, Keith W. Oleson,


In Global Change Biol.,24: 5709–5723 –


Earth system models (ESMs) rely on the calculation of canopy conductance in land surface models (LSMs) to quantify the partitioning of land surface energy, water, and CO2 fluxes. This is achieved by scaling stomatal conductance, gw, determined from physiological models developed for leaves. Traditionally, models for gw have been semi‐empirical, combining physiological functions with empirically determined calibration constants. More recently, optimization theory has been applied to model gw in LSMs under the premise that it has a stronger grounding in physiological theory and might ultimately lead to improved predictive accuracy. However, this premise has not been thoroughly tested. Using original field data from contrasting forest systems, we compare a widely used empirical type and a more recently developed optimization‐type gw model, termed BB and MED, respectively. Overall, we find no difference between the two models when used to simulate gw from photosynthesis data, or leaf gas exchange from a coupled photosynthesis‐conductance model, or gross primary productivity and evapotranspiration for a FLUXNET tower site with the CLM5 community LSM. Field measurements reveal that the key fitted parameters for BB and MED, g1B and g1M, exhibit strong species specificity in magnitude and sensitivity to CO2, and CLM5 simulations reveal that failure to include this sensitivity can result in significant overestimates of evapotranspiration for high‐CO2 scenarios. Further, we show that g1B and g1M can be determined from mean ci/ca (ratio of leaf intercellular to ambient CO2 concentration). Applying this relationship with ci/ca values derived from a leaf δ13C database, we obtain a global distribution of g1B and g1M, and these values correlate significantly with mean annual precipitation. This provides a new methodology for global parameterization of the BB and MED models in LSMs, tied directly to leaf physiology but unconstrained by spatial boundaries separating designated biomes or plant functional types.

Stomatal conductance based on energy balance

Stomatal conductance based on energy balance

by Pieruschka R., Berry J. A. (2009)

Roland Pieruschka (Forschungszentrum Jülich), Joseph A. Berry (Carnegie Institution for Science)

In Comparative Biochemistry and Physiology, Part A 153 (2009) S174–S183 – doi:10.1016/j.cbpa.2009.04.382 –



Evaporation of water inside a leaf into the humid air of the intercellular spaces is driven, in part, by absorbed radiation. A light beam interacting with a leaf penetrates the epidermis with little interaction and the largest part of the energy is absorbed by mesophyll cells. This asymmetric absorption of energy leads to the mesophyll becoming warmer than the epidermis and causes a temperature gradient which may drive evaporation and condensation within the leaf, carrying heat with it. We present data showing that variation in stomatal conductance at constant humidity and CO2 is closely propor- tional to changes in fluxes of energy (W m− 2) absorbed by the leaf. We developed a model of energy exchange between the mesophyll and the atmosphere with different regimes of heat and water exchange operating on the inner and outer sides of the epidermis. The rate at which water is delivered to the inner side of the epidermis is determined by the radiation load on the leaf while the rate of water loss to the atmosphere is controlled by stomata. We posit that energy driven changes in water vapor delivery to the epidermis affect the water potential of the epidermis influencing the water potential gradient between mesophyll and epidermis. Water and solutes are transported within the apoplast along this gradient and stomatal conductance adjusts such that the epidermis is neither gaining nor losing water in steady-state. The model realistically simulates stomatal response to changes in radiation, temperature and, water vapor, and has the potential for upscaling water fluxes in ecosystems.

Regulation of stomatal conductance

Screen Shot 2018-10-01 at 12.18.13
Fig. 1. A scheme showing the mass and energy fluxes along with the interactions between these considered in the complete model. Fluxes are shown as solid lines. Regulatory interactions are shown as dashed lines, c, e and T stand for CO2, H20 vapor concentrations and temperature, respectively. The subscripts a, s and 1, refer to properties in ambient air, at the leaf surface and of the leaf, respectively. Rsky specifies the long-wave length radiation input from the sky and Rso~ar represents solar radiation.


Physiological and environmental regulation of stomatal conductance, photosynthesis and transpiration: a model that includes a laminar boundary layer

by Collatz G. J., Grivet C., Ball J. T., Berry J. A. (1991)

G. James Collatz, J. Timothy Ball, b  Cyril Grivet, a  Joseph A. Berry, a

Carnegie Institution of Washington, Department of Plant Biology, 290 Panama Street, Stanford, CA 94305, USA
Desert Research Institute, PO Box 60220, Reno, NV 89622, USA


in Agricultural and Forest Meteorology 54 – 107-136 – –


This paper presents a system of models for the simulation of gas and energy exchange of a leaf of a C3 plant in free air. The physiological processes are simulated by sub-models that: (a) give net photosynthesis (An) as a function of environmental and leaf parameters and stomatal conductance (gs); (b) give g, as a function of the concentration of CO2 and H2O in air at the leaf surface and the current rate of photosynthesis of the leaf. An energy balance and mass transport sub-model is used to couple the physiological processes through a variable boundary layer to the ambient environment.

The models are based on theoretical and empirical analysis of gs, and An measured at the leaf level, and tests with intact attached leaves of soybeans show very good agreement between predicted and measured responses of gs and An over a wide range of leaf temperatures (20–35°C), CO2 concentrations (10–90 Pa), air to leaf water vapor deficits (0.5–3.7 kPa) and light intensities (100–2000 μmol m−2s−1).

The combined models were used to simulate the responses of latent heat flux (λE) and gs for a soybean canopy for the course of an idealized summer day, using the ‘big-leaf’ approximation. Appropriate data are not yet available to provide a rigorous test of these simulations, but the response patterns are similar to field observations. These simulations show a pronounced midday depression of λE and gsat low or high values of boundary-layer conductance.

Deterioration of plant water relations during midday has often been invoked to explain this common natural phenomenon, but the present models do not consider this possibility. Analysis of the model indicates that the simulated midday depression is, in part, the result of positive feedback mediated by the boundary layer. For example, a change in gs affects An and λE. As a consequence, the temperature, humidity and CO2concentration of the air in the proximity of the stomata (e.g. the air at the leaf surface) change and these, in turn, affect gs.

The simulations illustrate the possible significance of the boundary layer in mediating feedback loops which affect the regulation of stomatal conductance and λE. The simulations also examine the significance of changing the response properties of the photosynthetic component of the model by changing leaf protein content or the CO2 concentration of the atmosphere.

Stomata and models to develop a multi-scale assessment of the impact of changing c(a) on CO2 uptake and water use



Sensitivity of plants to changing atmospheric CO2concentration: from the geological past to the next century

by Franks P. J., Adams M. A., Amthor J. S., Barbour M. M., Berry J. A., Ellsworth D. S., Farquhar G. D., Ghannoum O., Lloyd J., McDowell N., Norby R. J., Tissue D. T., von Caemmerer S. (2013)


Faculty of Agriculture and Environment, University of Sydney, Sydney, NSW, Australia


in New Phytol. 197(4): 1077-1094 – – 

CrossRefPubMedWeb of ScienceGoogle Scholar


The rate of CO(2) assimilation by plants is directly influenced by the concentration of CO(2) in the atmosphere, c(a). As an environmental variable, c(a) also has a unique global and historic significance. Although relatively stable and uniform in the short term, global c(a) has varied substantially on the timescale of thousands to millions of years, and currently is increasing at seemingly an unprecedented rate. This may exert profound impacts on both climate and plant function.

Here we utilise extensive datasets and models to develop an integrated, multi-scale assessment of the impact of changing c(a) on plant carbon dioxide uptake and water use.

We find that, overall, the sensitivity of plants to rising or falling c(a) is qualitatively similar across all scales considered. It is characterised by an adaptive feedback response that tends to maintain 1 – c(i)/c(a), the relative gradient for CO(2) diffusion into the leaf, relatively constant.

This is achieved through predictable adjustments to stomatal anatomy and chloroplast biochemistry. Importantly, the long-term response to changing c(a) can be described by simple equations rooted in the formulation of more commonly studied short-term responses.

An ortholog of the stomatal regulator AtMUTE defines the stomatal precursor fate



Mobile MUTE specifies subsidiary cells to build physiologically improved grass stomata

by Raissig M. T., Matos J. L., Anleu Gil M. X., Kornfeld A., Bettadapur A., Abrash E., Allison H. R., Badgley G., Vogel J. P., Berry J. A., Bergmann D. C. (2017)

Michael Raissig, Universität Heidelberg, Germany

Juliana L Matos, Stanford University, USA

M. Ximena Anleu GilStanford University (Stanford, United States)

Ari KornfeldCarnegie Institution for ScienceWashington, United States

Akhila BettadapurStanford University (Stanford, United States)

Emily Abrash, Stanford University (Stanford, United States)

Grayson BadgleyCarnegie Institution for Science (Washington, United States)

John P. Vogel,

Joseph A Berry, Carnegie Institution for Science (Washington, United States)

Dominique C. Bergmann, Stanford University (Stanford, United States)


in Science 355(6330):1215-1218 – doi:10.1126/science.aal3254 –

Making more of your stomata

Stomata on grasses are made up of two guard cells and two subsidiary cells, and they perform better than stomata on broad-leaved plants, which are made up only of two guard cells. Raissig et al. found that the MUTE transcription factor in the wheat-like grass Brachypodium is a little bigger than the equivalent protein in the model broad-leaved plant Arabidopsis. The extension in the grass protein promotes its movement into adjacent cells, prompting them to become subsidiary cells. Mutant Brachypodium whose MUTE protein could not move between cells lacked stomatal subsidiary cells and grew poorly.


Plants optimize carbon assimilation while limiting water loss by adjusting stomatal aperture. In grasses, a developmental innovation—the addition of subsidiary cells (SCs) flanking two dumbbell-shaped guard cells (GCs)—is linked to improved stomatal physiology.

Here, we identify a transcription factor necessary and sufficient for SC formation in the wheat relative Brachypodium distachyon. Unexpectedly, the transcription factor is an ortholog of the stomatal regulator AtMUTE, which defines GC precursor fate in Arabidopsis.

The novel role of BdMUTE in specifying lateral SCs appears linked to its acquisition of cell-to-cell mobility in Brachypodium. Physiological analyses on SC-less plants experimentally support classic hypotheses that SCs permit greater stomatal responsiveness and larger range of pore apertures.

Manipulation of SC formation and function in crops, therefore, may be an effective approach to enhance plant performance.

Stomata-specific regulators can alter mesophyll properties



Disruption of stomatal lineage signaling or transcriptional regulators has differential effects on mesophyll development, but maintains coordination of gas exchange.

by Dow G. J., Berry J. A., Bergmann D. C. (2017)

Graham J. Dow, Joseph A. Berry, Dominique C. Bergmann,


in New Phytol. 2017 Oct;216(1):69-75. – doi: 10.1111/nph.14746. – Epub 2017 Aug 21. – PMID: 28833173


  • Stomata are simultaneously tasked with permitting the uptake of carbon dioxide for photosynthesis while limiting water loss from the plant. This process is mainly regulated by guard cell control of the stomatal aperture, but recent advancements have highlighted the importance of several genes that control stomatal development.
  • Using targeted genetic manipulations of the stomatal lineage and a combination of gas exchange and microscopy techniques, we show that changes in stomatal development of the epidermal layer lead to coupled changes in the underlying mesophyll tissues. This coordinated response tends to match leaf photosynthetic potential (Vcmax) with gas-exchange capacity (gsmax), and hence the uptake of carbon dioxide for water lost.
  • We found that different genetic regulators systematically altered tissue coordination in separate ways: the transcription factor SPEECHLESS (SPCH) primarily affected leaf size and thickness, whereas peptides in the EPIDERMAL PATTERNING FACTOR (EPF) family altered cell density in the mesophyll. It was also determined that interlayer coordination required the cell-surface receptor TOO MANY MOUTHS (TMM).
  • These results demonstrate that stomata-specific regulators can alter mesophyll properties, which provides insight into how molecular pathways can organize leaf tissues to coordinate gas exchange and suggests new strategies for improving plant water-use efficiency.

Model of stomatal development and leaf physiology



An integrated model of stomatal development and leaf physiology

by Dow G. J., Bergmann D. C., Berry J. A.  (2013) 

Graham J. Dow, Dominique C. Bergmann, Joseph A. Berry,


in New Phytologist. 201: 1218-1226 – DOI: 10.1111/nph.12608 – PMID: 24251982 –


  • Stomatal conductance (gs) is constrained by the size and number of stomata on the plant epidermis, and the potential maximum rate of gs can be calculated based on these stomatal traits (Anatomical gsmax). However, the relationship between Anatomical gsmax and operational gs under atmospheric conditions remains undefined.
  • Leaf-level gas-exchange measurements were performed for six Arabidopsis thaliana genotypes that have different Anatomical gsmax profiles resulting from mutations or transgene activity in stomatal development.
  • We found that Anatomical gsmax was an accurate prediction of gs under gas-exchange conditions that maximized stomatal opening, namely high-intensity light, low [CO2], and high relative humidity. Plants with different Anatomical gsmax had quantitatively similar responses to increasing [CO2] when gs was scaled to Anatomical gsmax. This latter relationship allowed us to produce and test an empirical model derived from the Ball–Woodrow–Berry equation that estimates gs as a function of Anatomical gsmax, relative humidity, and [CO2] at the leaf.
  • The capacity to predict operational gs via Anatomical gsmax and the pore-specific short-term response to [CO2] demonstrates a precise link between stomatal development and leaf physiology. This connection should be useful to quantify the gas flux of plants in past, present, and future CO2 regimes based upon the anatomical features of stomata.