Plant and Soil

, Volume 383, Issue 1–2, pp 111–138 | Cite as

Coupled carbon and water fluxes in CAM photosynthesis: modeling quantification of water use efficiency and productivity

  • Mark S. Bartlett
  • Giulia Vico
  • Amilcare Porporato
Regular Article


Background and Aims

Due to their high water use efficiency, Crassulacean acid metabolism (CAM) plants are of environmental and economic importance in the arid and semiarid regions of the world. Moreover, many CAM plants (e.g., Agave tequilana) have attractive qualities for biofuel production such as a relatively low lignin content and high amount of soluble carbohydrates. However, the current estimates of CAM productivity are based on empirical stress indices that create large uncertainties. As a first step towards a more accurate quantification of CAM productivity, this paper introduces a new model that couples both soil and atmosphere conditions to CAM photosynthesis.


The new CAM model is based upon well established C3 photosynthesis models coupled to a nonlinear circadian rhythm oscillator for the control of the photosynthesis carbon fluxes. The leaf-level dynamics are coupled to a simple, yet realistic description of the soil-plant-atmosphere continuum, including a plant water capacitance module.


The resulting model reproduces the four phases of CAM photosynthes is and the evolution of their dynamics during a soil moisture drydown, as a function of soil type, plant features, and climatic conditions.


The results help quantify the impact of soil water availability on CAM carbon assimilation and transpiration flux.


Crassulacean acid metabolism (CAM) Carbon assimilation Soil moisture Water stress Circadian rhythm oscillator Plant water capacitance 



This work was partially funded through the Agriculture and Food Research Initiative of the USDA National Institute of Food and Agriculture (2011-67003-30222); the National Science Foundation through grants CBET-1033467, EAR-1331846, and EAR-1316258; and by the U.S. Department of Energy (DOE) through the Office of Biological and Environmental Research (BER) Terrestrial Carbon Processes Program (DE-SC0006967). G. Vico acknowledges the support of “AgResource - Resource Allocation in Agriculture”, from the Faculty of Natural Resources and Agricultural Sciences, Swedish University of Agricultural Sciences. The comments and suggestions of the two anonymous reviewers are also gratefully acknowledged. The Wolfram Mathematica code for this CAM model is available upon request.


  1. Anderson CM, Wilkins MB (1989) Period and phase control by temperature in the circadian rhythm of carbon dioxide fixation in illuminated leaves of Bryophyllum fedtschenkoi. Planta 177(4):456–469PubMedCrossRefGoogle Scholar
  2. Aphalo P, Jarvis P (1991) Do stomata respond to relative humidity? Plant Cell Environ 14(1):127–132CrossRefGoogle Scholar
  3. Ball J (1987) A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions. In: Prog. Photosynthesis Res. Proc. Int. Congress 7th, Providence. 10-15 Aug 1986. Vol4:221–224Google Scholar
  4. Blasius B, Beck F, Lüttge U (1997) A model for photosynthetic oscillations in Crassulacean acid metabolism (CAM). J Theor Biol 184(3):345–351CrossRefGoogle Scholar
  5. Blasius B, Beck F, Lüttge U (1998) Oscillatory model of Crassulacean acid metabolism: structural analysis and stability boundaries with a discrete hysteresis switch. Plant Cell Environ 21(8):775–784CrossRefGoogle Scholar
  6. Blasius B, Neif R, Beck F, Lüttge U (1999) Oscillatory model of Crassulacean acid metabolism with a dynamic hysteresis switch. Proc Royal Soc Lond Ser B Biol Sci 266(1414):93–101CrossRefGoogle Scholar
  7. Borland AM, Griffiths H (1996) Variations in the phases of crassulacean acid metabolism and regulation of carboxylation patterns determined by carbon-isotope-discrimination techniques. In: Crassulacean acid metabolism, Springer, pp 230–249Google Scholar
  8. Borland A M, Hartwell J, Jenkins GI, Wilkins MB, Nimmo HG (1999) Metabolite control overrides circadian regulation of phosphoenolpyruvate carboxylase kinase and CO2 fixation in Crassulacean acid metabolism. Plant Physiol 121(3):889–896PubMedCrossRefPubMedCentralGoogle Scholar
  9. Borland A M, Griffiths H, Hartwell J, Smith J A C (2009) Exploiting the potential of plants with Crassulacean acid metabolism for bioenergy production on marginal lands. J Exp Bot 60(10):2879–2896PubMedCrossRefGoogle Scholar
  10. Brown E N, Choe Y, Luithardt H, Czeisler C A (2000) A statistical model of the human core-temperature circadian rhythm. Am J Physiol Endocrinol Metab 279(3):E669–E683PubMedGoogle Scholar
  11. Buchanan-Bollig I C (1984) Circadian rhythms in Kalanchoë: effects of irradiance and temperature on gas exchange and carbon metabolism. Planta 160(3):264–271PubMedCrossRefGoogle Scholar
  12. Calkin H W, Nobel PS (1986) Nonsteady-state analysis of water flow and capacitance for Agave deserti. Can J Bot 64(11):2556–2560CrossRefGoogle Scholar
  13. Carlson T N, Lynn B (1991) The effects of plant water storage on transpiration and radiometric surface temperature. Agric Forest Meteorol 57(1):171–186CrossRefGoogle Scholar
  14. Carter P J, Nimmo H, Fewson C, Wilkins M (1991) Circadian rhythms in the activity of a plant protein kinase. EMBO J 10(8):2063PubMedPubMedCentralGoogle Scholar
  15. Carter PJ, Fewson CA, Nimmo HG, Wilkins MB (1996) Roles of circadian rhythms, light, and temperature in the regulation of phosphoenolpyruvate carboxylase in Crassulacean acid metabolism. In: Crassulacean Acid Metabolism, Springer, pp 46–52Google Scholar
  16. Cockburn W, Ting I P, Sternberg L O (1979) Relationships between stomatal behavior and internal carbon dioxide concentration in crassulacean acid metabolism plants. Plant Physiol 63(6):1029–1032PubMedCrossRefPubMedCentralGoogle Scholar
  17. Comins H, Farquhar G (1982) Stomatal regulation and water economy in Crassulacean acid metabolism plants: an optimization model. J Theor Biol 99(2):263–284CrossRefGoogle Scholar
  18. Cowan I (1972) An electrical analogue of evaporation from, and flow of water in plants. Planta 106(3):221–226PubMedCrossRefGoogle Scholar
  19. Cushman J, Bohnert H (1996) Transcriptional activation of CAM genes during development and environmental stress. In: Crassulacean Acid Metabolism, Springer, pp 135–158Google Scholar
  20. Cushman J, Borland A (2002) Induction of Crassulacean acid metabolism by water limitation. Plant Cell Environ 25(2):295–310PubMedCrossRefGoogle Scholar
  21. Cushman J C (2001) Crassulacean acid metabolism. a plastic photosynthetic adaptation to arid environments. Plant Physiol 127(4):1439–1448PubMedCrossRefPubMedCentralGoogle Scholar
  22. Daly E, Porporato A, Rodriguez-Iturbe I (2004) Coupled dynamics of photosynthesis, transpiration, and soil water balance. Part I: Upscaling from hourly to daily level. J Hydrometeorol 5(3):546–558CrossRefGoogle Scholar
  23. Dodd A N, Borland A M, Haslam R P, Griffiths H, Maxwell K (2002) Crassulacean acid metabolism: plastic, fantastic. J Exp Bot 53(369):569–580PubMedCrossRefGoogle Scholar
  24. Escamilla-Treviño L L (2012) Potential of plants from the genus Agave as bioenergy crops. BioEnergy Res 5(1):1–9CrossRefGoogle Scholar
  25. Farquhar G, von Caemmerer S, Berry J (1980) A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta 149(1):78–90PubMedCrossRefGoogle Scholar
  26. FitzHugh R (1961) Impulses and physiological states in theoretical models of nerve membrane. Biophys J 1(6):445–466PubMedCrossRefPubMedCentralGoogle Scholar
  27. Flexas J, Ribas-Carbó M, Diaz-Espejo A, Galmes J, Medrano H (2008) Mesophyll conductance to CO2: current knowledge and future prospects. Plant Cell Environ 31(5):602–621PubMedCrossRefGoogle Scholar
  28. Forest L, Glade N, Demongeot J (2007) Liénard systems and potential–Hamiltonian decomposition–Applications in biology. Comptes rendus biologies 330(2):97–106PubMedCrossRefGoogle Scholar
  29. Friemert V, Heininger D, Kluge M, Ziegler H (1988) Temperature effects on malic-acid efflux from the vacuoles and on the carboxylation pathways in Crassulacean-acid-metabolism plants. Planta 174(4):453–461PubMedCrossRefGoogle Scholar
  30. Grams T E E, Borland A M, Roberts A, Griffiths H, Beck F, Luttge U (1997) On the mechanism of reinitiation of endogenous Crassulacean acid metabolism rhythm by temperature changes. Plant physiol 113(4):1309–1317PubMedPubMedCentralGoogle Scholar
  31. Griffiths H, helliker B, Roberts A, Haslam R P, Girnus J, Robe W E, Borland A M, Maxwell K (2002) Regulation of rubisco activity in Crassulacean acid metabolism plants: better late than never. Funct Plant Biol 29(6):689–696CrossRefGoogle Scholar
  32. Haag-Kerwer A, Franco A C, Luttge U (1992) The effect of temperature and light on gas exchange and acid accumulation in the C3-CAM plant Clusia minor L. J Exp Bot 43(3):345–352CrossRefGoogle Scholar
  33. Hartwell J, Smith L H, Wilkins MB, Jenkins GI, Nimmo HG (1996) Higher plant phosphoenolpyruvate carboxylase kinase is regulated at the level of translatable mRNA in response to light or a circadian rhythm. Plant J 10(6):1071–1078CrossRefGoogle Scholar
  34. Hartwell J, Gill A, Nimmo GA, Wilkins MB, Jenkins GI, Nimmo HG (1999) Phosphoenolpyruvate carboxylase kinase is a novel protein kinase regulated at the level of expression. Plant J 20(3):333–342PubMedCrossRefGoogle Scholar
  35. Hem JD (1985) Study and interpretation of the chemical characteristics of natural water, vol 2254, Department of the Interior, US Geological SurveyGoogle Scholar
  36. Herrera A (2009) Crassulacean acid metabolism and fitness under water deficit stress: if not for carbon gain, what is facultative CAM good forAnn Bot 103(4):645–653PubMedCrossRefPubMedCentralGoogle Scholar
  37. Holbrook NM, Putz F (1996) From epiphyte to tree: differences in leaf structure and leaf water relations associated with the transition in growth form in eight species of hemiepiphytes. Plant Cell Environ 19(6):631–642CrossRefGoogle Scholar
  38. Jackson R, Mooney H, Schulze ED (1997) A global budget for fine root biomass, surface area, and nutrient contents. Proc Natl Acad Sci 94(14):7362–7366PubMedCrossRefPubMedCentralGoogle Scholar
  39. Jones HG (1992) Plants and microclimate: a quantitative approach to environmental plant physiology. Cambridge University PressGoogle Scholar
  40. Katerji N, Hallaire M, Menoux-Boyer Y, Durand B (1986) Modelling diurnal patterns of leaf water potential in field conditions. Ecol Model 33(2):185–203CrossRefGoogle Scholar
  41. Kattge J, Knorr W (2007) Temperature acclimation in a biochemical model of photosynthesis: a reanalysis of data from 36 species. Plant Cell Environ 30(9):1176–1190PubMedCrossRefGoogle Scholar
  42. Katul G, Leuning R, Oren R (2003) Relationship between plant hydraulic and biochemical properties derived from a steady-state coupled water and carbon transport model. Plant Cell Environ 26(3):339–350CrossRefGoogle Scholar
  43. Kliemchen A, Schomburg M, Galla HJ, Lüttge U, Kluge M (1993) Phenotypic changes in the fluidity of the tonoplast membrane of Crassulacean-acid-metabolism plants in response to temperature and salinity stress. Planta 189(3):403–409PubMedCrossRefGoogle Scholar
  44. Kluge M (2008) Ecophysiology: Migrations between different levels of scaling. Prog Bot 5–34Google Scholar
  45. Kluge M, Kliemchen A, Galla HJ (1991) Temperature effects on crassulacean acid metabolism: EPR spectroscopic studies on the thermotropic phase behaviour of the tonoplast membranes of Kalanchoë daigremontiana. Botanica Acta 104(5):355–360CrossRefGoogle Scholar
  46. Lal R (2004) Carbon sequestration in dryland ecosystems. Environ Manag 33(4):528–544CrossRefGoogle Scholar
  47. Landsberg JJ, Sands P (2010) Physiological ecology of forest production: principles, processes and models, vol 4. Academic PressGoogle Scholar
  48. Larcher W (2003) Physiological plant ecology: ecophysiology and stress physiology of functional groups. SpringerGoogle Scholar
  49. Lee HS, Schmitt A K, Lüttge U (1989) The response of the C3-CAM tree, Clusia rosea, to light and water stress II. Internal CO2 concentration and water use efficiency. J Exp Bot 40(2):171–179CrossRefGoogle Scholar
  50. Leuning R (1990) Modelling stomatal behaviour and and photosynthesis of Eucalyptus grandis. Funct Plant Bio 17(2):159–175Google Scholar
  51. Leuning R (1995) A critical appraisal of a combined stomatal-photosynthesis model for C3 plants. Plant, Cell Environ 18(4):339–355CrossRefGoogle Scholar
  52. Lhomme JP, Rocheteau A, Ourcival J, Rambal S (2001) Non-steady-state modelling of water transfer in a Mediterranean evergreen canopy. Agric Forest Meteorol 108(1):67–83CrossRefGoogle Scholar
  53. Liguori G, Inglese G, Pernice F, Sibani R, Inglese P (2010) Co2 fluxes of opuntia ficus-indica mill. trees in relation to water status. In: VII International Congress on Cactus Pear Cochineal, 995, pp. 125–133Google Scholar
  54. Linton MJ, Nobel PS (2001) Hydraulic conductivity, xylem cavitation, and water potential for succulent leaves of Agave deserti and Agave tequilana. Int J Plant Sci 162(4):747–754CrossRefGoogle Scholar
  55. Lloyd J (1991) Modelling stomatal responses to environment in Macadamia integrifolia. Funct Plant Biol 18(6):649–660Google Scholar
  56. Lohammar T, Larsson S, Linder S, Falk S (1980) FAST: simulation models of gaseous exchange in Scots pine. Ecol Bull 505–523Google Scholar
  57. Long S, Postl W, Bolhar-Nordenkampf H (1993) Quantum yields for uptake of carbon dioxide in C3 vascular plants of contrasting habitats and taxonomic groupings. Planta 189(2):226–234CrossRefGoogle Scholar
  58. Lüttge U (2000) The tonoplast functioning as the master switch for circadian regulation of Crassulacean acid metabolism. Planta 211(6):761–769PubMedCrossRefGoogle Scholar
  59. Lüttge U (2002) CO2-concentrating: consequences in Crassulacean acid metabolism. J Exp Bot 53(378):2131–2142PubMedCrossRefGoogle Scholar
  60. Lüttge U (2004) Ecophysiology of Crassulacean acid metabolism (CAM). Ann Bot 93(6):629PubMedCrossRefGoogle Scholar
  61. Lüttge U, Beck F (1992) Endogenous rhythms and chaos in Crassulacean acid metabolism. Planta 188(1):28–38PubMedCrossRefGoogle Scholar
  62. Lüttge U, Duarte HM (2007) Morphology, anatomy, life forms and hydraulic architecture. In: Clusia, Springer, pp 17–30Google Scholar
  63. Manzoni S, Vico G, Porporato A, Katul G (2013) Biological constraints on water transport in the soil–plant–atmosphere system. Adv Water Resour 51:292–304CrossRefGoogle Scholar
  64. Medlyn B, Dreyer E, Ellsworth D, Forstreuter M, Harley P, Kirschbaum M, Le Roux X, Montpied P, Strassemeyer J, Walcroft A, Wang K, Loustau D (2002) Temperature response of parameters of a biochemically based model of photosynthesis. II. A review of experimental data. Plant Cell Environ 25(9):1167–1179CrossRefGoogle Scholar
  65. Nagumo J, Arimoto S, Yoshizawa S (1962) An active pulse transmission line simulating nerve axon. Proc IRE 50(10): 2061–2070CrossRefGoogle Scholar
  66. Neales T (1973) The effect of night temperature on CO2 assimilation, transpiration, and water use efficiency in Agave americana L. Aust J Biol Sci 26(4):705–714Google Scholar
  67. Nimmo G, Nimmo H, Fewson C, Wilkins M (1984) Diurnal changes in the properties of phosphoenolpyruvate carboxylase in Bryophyllum leaves: a possible covalent modification. FEBS Lett 178(2):199–203CrossRefGoogle Scholar
  68. Nimmo G, Wilkins M, Fewson C, Nimmo H (1987) Persistent circadian rhythms in the phosphorylation state of phosphoenolpyruvate carboxylase from Bryophyllum fedtschenkoi leaves and in its sensitivity to inhibition by malate. Planta 170(3):408–415PubMedCrossRefGoogle Scholar
  69. Nimmo HG (2000) The regulation of phosphoenolpyruvate carboxylase in CAM plants. Trends Plant Sci 5(2):75–80PubMedCrossRefGoogle Scholar
  70. Nobel P (1988) Environmental biology of agaves and cacti. Cambridge University Press, CambridgeGoogle Scholar
  71. Nobel P, Castaneda M, North G, Pimienta-Barrios E, Ruiz A (1998) Temperature influences on leaf CO2 exchange, cell viability and cultivation range for Agave tequilana. J Arid Environ 39(1):1–9CrossRefGoogle Scholar
  72. Nobel PS (1976) Water relations and photosynthesis of a desert CAM plant, Agave deserti. Plant Physiol 58(4):576–582PubMedCrossRefPubMedCentralGoogle Scholar
  73. Nobel PS (1991) Achievable productivities of certain cam plants: basis for high values compared with C3 and C4 plants. New Phytol 119(2):183–205CrossRefGoogle Scholar
  74. Nobel PS (1994) Remarkable agaves and cacti. Oxford University PressGoogle Scholar
  75. Nobel PS (2009) Physicochemical and environmental plant physiology. Academic PressGoogle Scholar
  76. Nobel PS, Cui M (1992) Hydraulic conductances of the soil, the root-soil air gap, and the root: changes for desert succulents in drying soil. J Exp Bot 43(3):319–326CrossRefGoogle Scholar
  77. Nobel PS, Hartsock T L (1978) Resistance analysis of nocturnal carbon dioxide uptake by a Crassulacean acid metabolism succulent, Agave deserti. Plant Physiol 61(4):510–514PubMedCrossRefPubMedCentralGoogle Scholar
  78. Nobel PS, Hartsock T L (1979) Environmental influences on open stomates of a Crassulacean acid metabolism plant, Agave deserti. Plant Physiol 63(1):63–66PubMedCrossRefPubMedCentralGoogle Scholar
  79. Nobel PS, Hartsock T L (1981) Shifts in the optimal temperature for nocturnal CO2 uptake caused by changes in growth temperature for cacti and agaves. Physiol. Plant. 53(4):523–527CrossRefGoogle Scholar
  80. Nobel PS, Hartsock T L (1984) Physiological responses of Opuntia ficus-indica to growth temperature. Physiol. Plant. 60(1):98–105CrossRefGoogle Scholar
  81. Nobel PS, Jordan P W (1983) Transpiration stream of desert species: resistances and capacitances for a C3, a C4, and a CAM plant. J. Exp. Bot. 34(10):1379–1391CrossRefGoogle Scholar
  82. Nobel PS, Valenzuela AG (1987) Environmental responses and productivity of the CAM plant, Agave tequilana. Agric Forest Meteorol 39(4):319–334CrossRefGoogle Scholar
  83. Nungesser D, Kluge M, Tolle H, Oppelt W (1984) A dynamic computer model of the metabolic and regulatory processes in Crassulacean acid metabolism. Planta 162(3):204–214PubMedCrossRefGoogle Scholar
  84. Ogburn R, Edwards EJ (2010) The ecological water-use strategies of succulent plants. Adv. Bot. Res 55:179–225CrossRefGoogle Scholar
  85. Osmond C (1978) Crassulacean acid metabolism: a curiosity in context. Annu. Rev. Plant Physiol. 29(1):379–414CrossRefGoogle Scholar
  86. Owen NA, Griffiths H (2013) A system dynamics model integrating physiology and biochemical regulation predicts extent of crassulacean acid metabolism (CAM) phases. New PhytologistGoogle Scholar
  87. Pavlidis T (1973) Biological oscillators: their mathematical analysis. Academic pressGoogle Scholar
  88. Ranney T, Whitlow T, Bassuk N (1990) Response of five temperate deciduous tree species to water stress. Tree Physiology 6(4):439–448PubMedCrossRefGoogle Scholar
  89. Rodríguez-Iturbe I, Porporato A (2004) Ecohydrology of water-controlled ecosystems: soil moisture and plant dynamics. Cambridge University PressGoogle Scholar
  90. Rompala K, Rand R, Howland H (2007) Dynamics of three coupled van der pol oscillators with application to circadian rhythms. Commun Nonlinear Sci Numer Simul 12(5):794–803CrossRefGoogle Scholar
  91. Schulte P, Nobel P (1989) Responses of a CAM plant to drought and rainfall: capacitance and osmotic pressure influences on water movement. J Exp Bot 40:61–70CrossRefGoogle Scholar
  92. Sheriff D (1984) Epidermal transpiration and stomatal responses to humidity: some hypotheses explored. Plant Cell Environ 7(9):669–677Google Scholar
  93. Smirnoff N (1996) Regulation of Crassulacean acid metabolism by water status in the C3/CAM intermediate Sedum telephium. In: Crassulacean Acid Metabolism, Springer, pp 176–191Google Scholar
  94. Smith J, Schulte P, Nobel P (1987) Water flow and water storage in Agave deserti: osmotic implications of crassulacean acid metabolism. Plant Cell Environ 10(8):639–648CrossRefGoogle Scholar
  95. Sperry J, Hacke U, Oren R, Comstock J (2002) Water deficits and hydraulic limits to leaf water supply. Plant Cell Environ 25(2):251–263PubMedCrossRefGoogle Scholar
  96. Strogatz S (2001) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineeringGoogle Scholar
  97. Surendran Nair S, Kang S, Zhang X, Miguez F E, Izaurralde R C, Post W M, Dietze M C, Lynd L R, Wullschleger S D (2012) Bioenergy crop models: descriptions, data requirements, and future challenges. GCB Bioenergy 4(6):620–633CrossRefGoogle Scholar
  98. Ting I, Patel A, Kaur S, Hann J, Walling L (1996) Ontogenetic development of Crassulacean acid metabolism as modified by water stress in peperomia. In: Crassulacean Acid Metabolism, Springer, pp 204–215Google Scholar
  99. Vico G, Porporato A (2008) Modelling C3 and C4 photosynthesis under water-stressed conditions. Plant Soil 313(1–2):187–203CrossRefGoogle Scholar
  100. Wilkins MB (1992) Tansley review No. 37 circadian rhythms: their origin and control. New Phytol 347–375Google Scholar
  101. Yamori W, Hikosaka K, Way DA (2014) Temperature response of photosynthesis in C3, C4, and CAM plants: temperature acclimation and temperature adaptation. Photosynth Res 119(1–2):101–117PubMedCrossRefGoogle Scholar
  102. Zañudo-Hernández J, González del Castillo Aranda E, Ramírez-Hernández BC, Pimienta-Barrios E, Castillo-Cruz I, Pimienta-Barrios E (2010) Ecophysiological responses of Opuntia to water stress under various semi-arid environments. J Prof Assoc Cactus Dev 12:20–36Google Scholar
  103. Zotz G, Patiño S, Tyree MT (1997) Water relations and hydraulic architecture of woody hemiepiphytes. J Exp Bot 48(10):1825–1833CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Mark S. Bartlett
    • 1
  • Giulia Vico
    • 2
  • Amilcare Porporato
    • 1
  1. 1.Department of Civil and Environmental EngineeringDuke UniversityDurhamUSA
  2. 2.Department of Crop Production EcologySwedish University of Agricultural SciencesUppsalaSweden

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