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Modelling the dynamics of the electron transport rate measured by PAM fluorimetry during Rapid Light Curve experiments

  • Original Paper
  • Published:
Photosynthetica

Abstract

We propose a dynamic model specifically designed to simulate changes in the photosynthetic electron transport rate, which is calculated from fluorescence measurements when plants are exposed, for a short time, to a series of increasing photon flux densities. This model simulates the dynamics of the effective yield of photochemical energy conversion from the maximum and natural chlorophyll fluorescence yields, taking into account a cumulative effect of successive irradiations on photosystems. To estimate a characteristic time of this effect on photosystems, two series of experiments were performed on two benthic diatom culture concentrations. For each concentration, two different series of irradiations were applied. Simplified formulations of the model were established based on the observed fluorescence curves. The simplified versions of the model streamlined the parameters estimation procedure. For the most simplified version of the model (only 4 parameters) the order of magnitude of the characteristic time of the residual effect of irradiation was about 38 s (within a confidence interval between 20 and 252 s). The model and an appropriate calibration procedure may be used to assess the physiological condition of plants experiencing short time-scale irradiance changes in experimental or field conditions.

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Abbreviations

a:

multiplication coefficient of I in the function δ(I) [m2 μmol−1(photon)]

b:

exponent of I in the function δ(I)

Chl:

chlorophyll

COV:

variance-covariance matrix

Et :

PFD received by the plant at the time t [μmol(photon) m−2 s−1]

ETR:

electron transfer rate between photosystems I and II

ETRmax :

maximum value of ETR during one RLC or LC experiment

F, f:

fluorescence yield in the ambient irradiance environment

Fm :

dark adapted maximum fluorescence yield

F0 :

dark-adapted minimum fluorescence yield

F0′:

minimum fluorescence yield during irradiation

g:

the rate of convergence between M and F [s−1]

I(t) = I:

integrated photon accumulation by the plant [μmol(photon) m−2]

i, j, q, r:

indices. i,j,q,r ∈ N*4

J:

the Jacobian matrix of Yt, described by r parameters p

JT :

transposed matrix of J, [JTJ]−1 is the inversed matrix [JTJ]

k:

the rate of attenuation of the residual light effect [s−1]

LC:

light curve

M:

the fluorescence yield reached during the saturation pulse

Mmin :

minimum fluorescence yield reached during saturation

m, n:

numbers of consecutive times defining the series of light exposure Et

nq :

numbers of experimental fluorescence data for the models q, q = 1... Q

p:

numbers of parameters to estimate, p ∈ N*

p1, p2, p3, p4 :

parameters describing the simplified dynamics of Y

PE:

photosynthesis-irradiance curve

PFD:

photon flux density

Q:

number of models

RC:

rebuilt curve

RLC:

rapid light curve

s2 :

the sum of the square residuals (ε2) divided by (n − p)

t:

forward time [s]

Δt:

discrete time step [s]

Y:

the effective yield of photochemical energy conversion [at t, Yt = (1 − F/M)t]

β:

the absorption factor of the plant [m2 μmol−1(photon)]

δ(I):

function describing the effect of I(τ) on the dnamics of M, F, and Y

θI :

vectors (or set) of parameters describing δ(I) in dynamics of F, M, and Y

θF :

vectors (or set) of parameters describing the dynamics of F

θM :

vectors (or set) of parameters describing the dynamics of M

θY :

vectors (or set) of parameters describing the dynamics of Y

Φ, ψ:

criteria functions used in optimisation processes

τ:

backward time [s]

ϕF :

the integrated function describing the dynamics of F

ϕM :

the integrated function describing the dynamics of M

ϕY :

the integrated function describing the dynamics of Y

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Authors and Affiliations

  1. Laboratoire d’océanographie biologique de Banyuls, Université Pierre et Marie Curie, Paris 6, CNRS; UMR7621, Avenue Fontaulé, BP44, F-66650, Banyuls-sur-Mer, France

    J.-M. Guarini & C. Moritz

  2. Laboratoire d’écologie, biodiversité et évolution, Université Pierre et Marie Curie, Paris 6, CNRS; UMR7625, Quai Saint-Bernard, F-75005, Paris, France

    J.-M. Guarini & C. Moritz

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  1. J.-M. Guarini
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  2. C. Moritz
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Correspondence to J.-M. Guarini.

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Guarini, JM., Moritz, C. Modelling the dynamics of the electron transport rate measured by PAM fluorimetry during Rapid Light Curve experiments. Photosynthetica 47, 206–214 (2009). https://doi.org/10.1007/s11099-009-0034-3

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  • DOI: https://doi.org/10.1007/s11099-009-0034-3

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