Parameter optimisation of fast chlorophyll fluorescence induction model

https://doi.org/10.1016/S0378-4754(01)00313-5Get rights and content

Abstract

Chlorophyll a fluorescence induction kinetics is commonly used as a probe of photosynthesis. Here, an ODE model developed by Stirbet et al. [J. Theor. Biol. 193 (1998) 131], describing the O–J–I–P fluorescence transient on the basis of the redox reactions occurring around photosystem II centres, is fitted using the software package PARFIT to the fluorescence induction data measured ‘in vivo’ on pea leaves. After a short review of the mathematical model of the fast chlorophyll a fluorescence induction process, the numerical results are presented. The approximations of the data are very good, but some model parameter values were not in agreement with those reported in the literature. In order to solve this problem we have also considered the presence of some non-QB active photosystem II units (around 20%), and postulated an exponential law for plastoquinone (PQ) exchange reaction. Moreover, the number of the PQ pool molecules was considered as model parameter in the fitting procedure. The results obtained after these improvements are closer to the reported data.

Introduction

The intensity of Chl a fluorescence emission in dark-adapted oxygen evolving systems shows a characteristic variation in time, known as fluorescence transient or induction, FI [1]. The fluorescence intensity rises quickly from an initial low value, F0 (the O level), to a higher one, FP (the P level). Two intermediary steps designated as FJ (the “J” level) and FI (the “I” level) normally appear under high light illumination conditions [2], [3], [4]. It is well established that the origin of FI of higher plants and green algae is the antenna system of photosystem II (PS II), and is due to the variation of the quantum yield of fluorescence emission (between 2 and 10%). Chl a fluorescence yield is principally influenced by the redox state of QA, the secondary electron acceptor of PS II, which is assumed to functions as a quencher in the oxidised state. As PS II function is highly sensitive to the environmental conditions (e.g. pollutants, heat and water stress, excess light, increasing carbon-di-oxide concentration, and so on), FI is expected to be very useful in plant biology research and related areas, as ecology, horticulture, agronomy, and biotechnology. In this view, it is essential to develop a special approach to characterise the plant samples, based on our knowledge about the processes leading to fast FI and the effect of external influences on it. Over the last few years a mathematical model of the fast FI has been proposed [5], [6], [7], [8], [9], [10], which is based mainly on the kinetics of the photochemical and redox reactions around the PS II centres. It consists of a reaction scheme that is translated to an ordinary differential equation system (ODEs) for the concentrations of the species using the law of mass action, and of an ‘output’ function describing the fluorescence yield for given concentrations of the redox species. Both, the ODE system and the output function, depend on unknown parameters (e.g. on the rate constants and other specific parameters [10]). After an appropriate choice of parameter values, this model was able to reproduce qualitatively the typical form of FI curves, with the characteristic O–J–I–P phases. But of course, a good model should also be able to reproduce experimental data quantitatively. Here, we present the results of parameter estimations, obtained using the software package PARFIT developed by Bock [11], [12], which consists of a discrete treatment of the DAE model by multiple shooting or collocation as a non-linear constraint of the optimisation problem. The fits of the experimental data are very good, but some of the parameter values deviate from those presented in the literature. We discuss the possible reason for these deviations, and we propose some ideas to be considered in the future development of the model.

Section snippets

The model of fast Chl a fluorescence induction

The model for the fast Chl a fluorescence induction proposed by Stirbet et al. [8] is based on six main assumptions:

(i) The Chl a fluorescence yield reflects the concentration of closed PS II centres with reduced QA.

(ii) The rate constants of QA reduction are modulated by the redox state of the oxygen evolving complex (OEC), the so-called S-states.

(iii) A so-called “two electron gate” process on the acceptor side of PS II unit is working.

(iv) The excitation energy of antenna can be exchanged

Experimental methods

Fast Chl a fluorescence induction measurements were performed at room temperature, on 15 min dark adapted Pisum sativum leaves, with a shutter-less fluorimeter (Plant Efficiency Analyser, built by Hansatech Ltd.).

The samples were illuminated 1 s with continuous light (600 W m−2 power; emission peak at 650 nm) provided by an array of six light-emitting diodes, focussed on a circle of 4 mm diameter of the sample surface. The fluorescence signals were detected using a PIN-photodiode after passing

Parameter optimisation procedure

The dynamic behaviour of the model depends on a set of unknown parameters contained in the right side of the ODEs system and in the output function (i.e. the function that maps the state variables and parameters to the observed quantity, fluorescence intensity F). These parameters have to be determined so that the experimental data are reproduced ‘as good as possible’. Here, we take the usual least squares approach, in which the sum of the squares of the differences between experimental data

Results and discussions

Three identical experiments on pea leaves were carried out. We have observed small, but non-stochastic differences between the three sets of data (results not shown). The numerical computations were carried out with a version of PARFIT based on multiple shooting, applied to the model presented in [8]. After few numerical experiments, we decided to use 10 multiple shooting nodes. During the iterations some of the parameters became negative, making the differential equations unstable. Instead of

Conclusions

The approximations of fast Chl a fluorescence induction curves O–J–I–P measured on pea leaves are quite good (see Fig. 1, Fig. 2). However, even after the introduction of three new insights in the model the estimates of model parameters obtained in this study are not always in agreement with the literature (see Table 2). Of course, in some cases we can blame the literature, as the related values are not always applicable. But there are also several possible explanations, related to the model

Acknowledgements

Supported by Swiss National Foundation Grant No. 3100-057046.99/1, and by SFB 359 of the Deutsche Forschungsgemeinschaft

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