A simple dynamic model of photosynthesis in oak leaves: coupling leaf conductance and photosynthetic carbon fixation by a variable intracellular CO2 pool
Steffen M. Noe A B and Christoph Giersch AA Institut für Botanik, Technische Universität Darmstadt, Schnittspahnstr. 3-5, D-64287 Darmstadt, Germany.
B Present address: Department of Plant Physiology, Institute of Molecular and Cell Biology, Riio 23, EE 51010 Tartu, Estonia.
C Corresponding author. Email: snoe@ut.ee
Functional Plant Biology 31(12) 1195-1204 https://doi.org/10.1071/FP03251
Submitted: 19 December 2003 Accepted: 27 October 2004 Published: 8 December 2004
Abstract
Modelling the diurnal course of photosynthesis in oak leaves (Quercus robur L.) requires appropriate description of the dynamics of leaf photosynthesis of which diurnal variations in leaf conductance and in CO2 assimilation are essential components. We propose and analyse a simple photosynthesis model with three variables: leaf conductance (gs), the CO2 partial pressure inside the leaf (pi), and a pool of Calvin cycle intermediates (aps). The environmental factors light (I) and vapour pressure deficit (VPD) are used to formulate a target function G(I, VPD) from which the actual leaf conductance is calculated. Using this gs value and a CO2 consumption term representing CO2 fixation, a differential equation for pi is derived. Carboxylation corresponds to the sink term of the pi pool and is assumed to be feedback-inhibited by aps. This simple model is shown to produce reasonable to excellent fits to data on the diurnal time courses of photosythesis, pi and gs sampled for oak leaves.
Keywords: leaf conductance, numerical model, oak, photosynthesis, Quercus robur.
Acknowledgments
We thank an anonymous referee for suggesting eqn 2 for the dependence of stomatal response on VPD. The photosynthesis model presented here was developed as part of a process-based model of isoprene emission by trees, which was initiated by Wolfgang Zimmer some time ago. He passed away in August 2002. Stimulating discussions with Wolfgang Zimmer during the earlier stages of this project are gratefully acknowledged.
This work was supported by the German Federal Ministry of Education and Research (BMBF) in context of BEWA2000 (Biogenic emissions of volatile organic compounds from forest ecosystems) which is a subproject of the national joint research project AFO2000 (Atmosphären-Forschungsprogramm 2000).
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Appendix
Consider a rectangular box with area F and thickness d. We assume that there is a flux Vin [mol m–2 s–1] into the box and a flux Vout leaving the box. The change in concentration n within the box, dn / dt, is then given by:
The change in pressure corresponding to that in n is from p = n RT:
so that (A1) may be written as:
with q = RT / d. Identifying the box with a leaf, F takes the role of the leaf surface and d that of leaf thickness (more exactly, that of a fictitious depth available to diffusion of CO2). Multiplying the flux term gs (pa – pi)/ Patm [μmol m–2 s–1] by RT / d [Pa m² μmol–1] gives the unit of Pa s–1. At T = 300 K and d = 0.1 mm, we have:
Alternatively, and more convenient when photosynthesis or respiration rates (mm s–1) are of interest, expressing the ps as concentrations (mol m–3), we have:
where q′ = RT / (d Patm). For standard pressure, T = 300 K and d = 0.1 mm, we have:
Using q or q′, a differential equation for pi may be formulated using the flux terms that are common in gas-exchange studies (e.g. eqn 11).
