Modelling photosynthesis from biochemistry to optimal stomatal control

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Modelling photosynthesis from biochemistry to
optimal stomatal control

• Pertti Hari
• Department of Forest Ecology
• University of Helsinki

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Two traditions of modelling photosynthesis at our
department

• Leaf level
• Biochemical approach

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Leaf level

• Field measurements and empirical modelling 1971 -
  1975
• high temperatures close stomata
• Optimal stomatal control 1985 -

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Optimal stomatal control model of photosynthesis

• Formulated by Cowan and Farquhar
• Reformulated and solved by us
• Scale
• 0.01 mm and 10 s
• Processes
• photosynthesis
• diffusion of CO2
• diffusion of water vapour
• stomatal regulation

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Summary model for photosynthesis ?

• Should be derived from undestanding of
  biochemical processes
• Derived intuitively 1985

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Photosynthesis
p photosynthesis I photosynthetically active
radiation, PAR Ci CO2 concentration inside
stoma ? parameter, describing biochemical
activity
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Biochemival model

• History
• Thornley
• light reseptors
• two states
• Kaitala et al
• light receptors
• CO2 reseptors
• energy exchange
• diffusion

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• Development of new version 1995 -
• more detailed leaf structure
• detailed analysis of biochemical reactions
• connections between the reactions
• scale
• 10 nm, 1 ms

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Hienorakenne
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Example of typical reaction
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Submodels for each reaction

• Reactions occur usually between two substances
• Reaction rates are determined by the
  concentrations of raw materials
• Multiplicative submodels

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Biochemical model

• 12 - 20 reactions
• one parameter per reaction
• estimation intelligent quess
• initial state
• 12 - 20 state variabels
• estimation intelligent quess or measurements
• model is operational

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Light response of photosynthesis
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Mesophyl CO2 concentration (rel. unit) as
function of light intensity
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Relationship between photosynthesis and the
product of mesophyl CO2 and light intensity
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Relationship between photosynthesis and the
product of mesophyl CO2 and light intensity
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WHY ?
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Relationship between photosynthesis and the
product of mesophyl CO2 and saturating function
of light intensity
f(I) Ci
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Possible explanations

• Unrealistic parameter values

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Possible explanations

• Unrealistic parameter values
• Errors in the code

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Possible explanations

• Unrealistic parameter values
• Errors in the code
• Inadequate model structure
• photorespiration

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Relationship between photosynthesis and the
product of mesophyl CO2 and light intensity
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Diffusion of CO2

• Diffusion transports CO2 and water vapour

i inflow of CO2 Ca ambient CO2
concentration Ci CO2 concentration in stomatal
concavity
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• Diffusion and respiraton increases CO2
• Photosynthesis consumes CO2
• CO2 concentration is stable
• Michaelis-Menten type model of photosynthesis

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Transpiration

• Stomatal concavity is saturated with water vapour
• Diffusion transports water out
• Simple model for transpiration

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Optimality principle

• Assume that transpiration of 1 kg water costs??
  kg of CO2
• Stomatal regulation maximises photosynthetic gain
  minus transpiration costs

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• Solution with the Lagrange method
• The solution depends on
• light
• temperature
• ambient water vapour concentration
• costs of transpiration
• biochemical activity

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Analysis of field measurements

• SMEAR I
• About 900 km from here to north-east
• 400 m a.s.l.
• at timberline
• near by the real home of Santa
• monitoring of photosynthesis, PAR, temperature
  etc. from late April to middle November in 1997
• 120 observations per day for about 150 days

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Chamber in Värriö
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CO2 exchange, g m-2 s-1
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Summary

• The derivation of the summary model from the
  biochemical model failed
• The fit of the optimal stomatal control model of
  photosynthesis is exelent
• How to explain
• Photorespiration gives hope

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Ristos comment

• At the end of a research project we try to
  explain results to others which we do not
  understand

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