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Chlorophyll a fluorescence induction kinetics in leaves predicted from a model describing each discrete step of excitation energy and electron transfer associated with Photosystem II

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Abstract

Chlorophyll a fluorescence induction (FI) is widely used as a probe for studying photosynthesis. On illumination, fluorescence emission rises from an initial level O to a maximum P through transient steps, termed J and I. FI kinetics reflect the overall performance of photosystem II (PSII). Although FI kinetics are commonly and easily measured, there is a lack of consensus as to what controls the characteristic series of transients, partially because most of the current models of FI focus on subsets of reactions of PSII, but not the whole. Here we present a model of fluorescence induction, which includes all discrete energy and electron transfer steps in and around PSII, avoiding any assumptions about what is critical to obtaining O J I P kinetics. This model successfully simulates the observed kinetics of fluorescence induction including O J I P transients. The fluorescence emission in this model was calculated directly from the amount of excited singlet-state chlorophyll in the core and peripheral antennae of PSII. Electron and energy transfer were simulated by a series of linked differential equations. A variable step numerical integration procedure (ode15s) from MATLAB provided a computationally efficient method of solving these linked equations. This in silico representation of the complete molecular system provides an experimental workbench for testing hypotheses as to the underlying mechanism controlling the O J I P kinetics and fluorescence emission at these points. Simulations based on this model showed that J corresponds to the peak concentrations of Q −A QB (QA and QB are the first and second quinone electron acceptor of PSII respectively) and Q −A Q −B and I to the first shoulder in the increase in concentration of Q −A Q 2−B . The P peak coincides with maximum concentrations of both Q −A Q 2−B and PQH2. In addition, simulations using this model suggest that different ratios of the peripheral antenna and core antenna lead to differences in fluorescence emission at O without affecting fluorescence emission at J, I and P. An increase in the concentration of QB-nonreducing PSII centers leads to higher fluorescence emission at O and correspondingly decreases the variable to maximum fluorescence ratio (F v/F m).

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Acknowledgements

This work was co-supported by the National Center for Supercomputing Applications, and the U. S. National Science Foundation IBN 04-17126.

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Authors and Affiliations

  1. Department of Plant Biology and Crop Sciences, University of Illinois at Urbana Champaign, 379 Madigan Laboratory, 1201 W. Gregory Drive, Urbana, IL, 61801, USA

    Xin-Guang Zhu, Donald R. Ort & Stephen P. Long

  2. Department of Plant Biology and Department of Biochemistry, 265 Morrill Hall, 505 S Goodwin Ave, Urbana, IL, 61801, USA

      Govindjee

  3. Department of Biological Sciences, University of Essex, Colchester, Essex, CO4 3SQ, UK

    Neil R. Baker

  4. Department of Computer Science, 4314 Thomas M. Siebel Center for Computer Science, University of Illinois at Urbana Champaign, Urbana, IL, 61801, USA

    Eric deSturler

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  1. Xin-Guang Zhu
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  2.   Govindjee
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  3. Neil R. Baker
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  4. Eric deSturler
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  5. Donald R. Ort
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Corresponding author

Correspondence to Stephen P. Long.

Appendices

Appendix 1

The ordinary differential equations representing the model of fluorescence induction (Fig. 1). This set of equations only includes the differential equations representing the change of concentrations of components associated with QB-reducing PSII reaction centers. Same set of different equations were used to describe the concentration changes of components associated with QB-nonreducing PSII reaction centers. The QB-nonreducing and QB-reducing reaction centers were assumed to share the same plastoquinol pool. The differential equation for [PQH2] in the full model combines the contributions from reactions associated with both QB-reducing and QB-nonreducing reaction centers. The rate equation for each velocity variable is listed in Appendix 2. The abbreviations of reaction velocities used in the system of differential equations are defined in Appendix 3.

$$\begin{aligned} \frac{{{\rm d}[A_{\rm p}]}}{{{\rm d}t}} & = I_{\rm a} - v_{\rm Af} - v_{\rm Ad} - v_{\rm AU} + v_{UA} - v_{\rm P680qA} - v_{\rm PQqA} \\ \frac{{{\rm d}[U]}}{{{\rm d}t}} & = I_{\rm c} + v_{\rm AU} - v_{\rm UA} - v_{\rm Uf} - v_{\rm Ud} - v_{\rm P680qU} - v_1 + v_{\_1} - v_{\rm PQqU} \\ \frac{{{\rm d}[{\rm P}_{680} ^ + {\rm Pheo}^ -]}}{{{\rm d}t}} & = v_1 - v_{-1} - v_{z\_1} - v_{2\_1} + v_{r2\_1}\\ \frac{{{\rm d}[{\rm P}_{680} ^ + {\rm Pheo}]}}{{{\rm d}t}} & = v_{2\_1} - v_{r2\_1} - v_{z\_2}\\ \frac{{{\rm d}[{\rm P}_{680} {\rm Pheo}^ -]}}{{{\rm d}t}} & = v_{z\_1} - v_{2\_2} + v_{r2\_2} \\ \end{aligned}$$
$$\begin{aligned} \frac{{{\rm d}[S_{1T}]}}{{{\rm d}t}} & = v_{s0\_s1} - v_{1Z} \\ \frac{{{\rm d}[S_{2T}]}}{{{\rm d}t}} & = v_{s1\_s2} - v_{2Z} \\ \frac{{{\rm d}[S_{3T}]}}{{{\rm d}t}} & = v_{s2\_s3} - v_{3Z} \\ \frac{{{\rm d}[S_{0T}]}}{{{\rm d}t}} & = v_{s3\_s0} - v_{0Z} \\ \frac{{{\rm d}[S_{{1T} _{\rm p}}]}}{{{\rm d}t}} & = v_{1Z} - v_{s1\_s2} \\ \frac{{{\rm d}[S_{{2T} _{\rm p}}]}}{{{\rm d}t}} & = v_{2Z} - v_{s2\_s3} \\ \frac{{{\rm d}[S_{{3T} _{\rm p}}]}}{{{\rm d}t}} & = v_{3Z} - v_{s3\_s0} \\ \frac{{{\rm d}[S_{{0T} _{\rm p}}]}}{{{\rm d}t}} & = v_{0Z} - v_{s0\_s1} \\ \end{aligned}$$
$$\begin{aligned} \frac{{{\rm d}[{\rm Q}_{\rm A} {\rm Q}_{\rm B}]}}{{{\rm d}t}} & = v_3 - v_{\_r3} - v_{2\_00\_1} - v_{2\_00\_2} + v_{r2\_00\_1} + v_{r2\_00\_2}\\ \frac{{{\rm d}[{\rm Q}_{\rm A} ^ - {\rm Q}_{\rm B}]}}{{{\rm d}t}} & = v_{2\_00\_1} + v_{2\_00\_2} - v_{r2\_00\_1} - v_{r2\_00\_2} - v_{\rm AB1} + v_{\rm BA1} + v_{3\_n} - v_{\_r3\_n}\\ \frac{{{\rm d}[{\rm Q}_{\rm A} {\rm Q}_{\rm B} ^ -]}}{{{\rm d}t}} & = v_{AB1} - v_{BA1} - v_{2\_01\_1} - v_{2\_01\_2} + v_{r2\_01\_1} + v_{r2\_01\_2}\\ \frac{{{\rm d}[{\rm Q}_{\rm A} ^ - {\rm Q}_{\rm B} ^ -]}}{{{\rm d}t}} & = v_{BA2} - v_{AB2} + v_{2\_01\_1} + v_{2\_01\_2} - v_{r2\_01\_1} - v_{r2\_01\_2}\\ \frac{{{\rm d}[{\rm Q}_{\rm A} {\rm Q}_{\rm B} ^2-]}}{{{\rm d}t}} & = v_{AB2} - v_{BA2} - v_3 + v_{\_r3} - v_{2\_02\_1} - v_{2\_02\_2} + v_{r2\_02\_1} + v_{r2\_02\_2}\\ \frac{{{\rm d}[{\rm Q}_{\rm A} ^ - {\rm Q}_{\rm B} ^2-]}}{{{\rm d}t}} & = v_{\_r3\_n} - v_{3\_n} + v_{2\_02\_1} + v_{2\_02\_2} - v_{r2\_02\_1} - v_{r2\_02\_2}\\ \frac{{{\rm d}[{\rm PQH}_2]}}{{{\rm d}t}} & = v_3 + v_{3\_n} - v_{\_r3} - v_{\_r3\_n} - v_{\_pq\_ox}\\ \end{aligned} $$

Appendix 2

The rate equations describing the reactions associated with QB-reducing reaction centers used in the model of fluorescence induction. The set of equations for the reactions associated with the QB-nonreducing reaction centers were similar to this set and not listed. See Appendix 3 for definition of abbreviations. The details for derivation of each rate equations are in the main text. The detailed description for each abbreviation is listed in Appendix 3 except that the rate constants are listed in Table 1.

$$\begin{aligned} I_{\rm a} & = \frac{220 I_{\rm in}}{(290 + 200 n)(1+ x)}\\ I_{\rm c} & = \frac{70 I_{\rm in}}{(290 + 200 n)(1+ {\it x})}\\ A_{\rm i} & = \frac{220 xI_{\rm in}}{(290 + 200 n)(1+ x)}\\ U_{\rm if} & = \frac{35 xI_{\rm in}}{(290 + 200 n)(1+ x)}\\ v_{\rm Af} & = [A_{\rm p}]k^{\rm a} _{\rm f}\\ v_{\rm Ad} & = [A_{\rm p}]k^{\rm a} _{\rm d}\\ v_{\rm AU} & = [A_{\rm p}]k_{\rm AU}\left(\frac{1 - x}{1+ x}\right)\\ v_{\rm UA} & = [U]k_{\rm UA}\\ v_{\rm Uf} & = [U]k^{\rm u} _{\rm f}\\ \end{aligned}$$
$$\begin{aligned} v_{\rm Ud} & = [U](1-q)k^{\rm Uc} _{\rm d}+ [U]qk^{\rm Uo} _{\rm d}\\ {\rm where}\; q & = [{\rm Q}_{\rm A}]/([{\rm Q}_{\rm A}]+ [{\rm Q}_{\rm A}^{-}])\\ \quad {\rm where}\;[{\rm Q}_{\rm A}] & = [{\rm Q}_{\rm A}{\rm Q}_{\rm B}]+[{\rm Q}_{\rm A}{\rm Q}_{\rm B}^{-}]+[{\rm Q}_{\rm A}{\rm Q}_{\rm B}^{2-}]\\ \quad [{\rm Q}_{\rm A}^{-}] & = [{\rm Q}_{\rm A}^{-} {\rm Q}_{\rm B}] + [{\rm Q}_{\rm A}^{-} {\rm Q}_{\rm B}^{-}] + [{\rm Q}_{\rm A}^{-} {\rm Q}_{\rm B}^{2-}]\\ \end{aligned}$$
$$\begin{aligned} v_{1} & = q[P_{680}^{*} {\rm Pheo}]k^{\rm o} _{1} + [P_{680}^{*} {\rm Pheo}](1-q)(1- {\it p})k^{\rm c} _{1}+[P_{680}^{*} {\rm Pheo}](1-q) {\it p}k^{\rm o} _{1} \quad {\rm where}\\ [P_{680}^{*} {\rm Pheo}] & = [U][P_{680}{\rm Pheo}](1 + \frac{{k_{- t}}}{{k_t}})^{-1} /70\\ {\rm and} \frac{{k_{- t}}}{{k_t}} & = \exp [- hc/(kT)(\lambda _{\rm Chl} ^{- 1} - \lambda _P ^{- 1})]\\ \end{aligned}$$
$$\begin{aligned} v_{-1} & = q[P_{680}^{+} {\rm Pheo}^{-}]k^{\rm o} _{-1} + (1-q)[P_{680}^{+} {\rm Pheo}^{-}]k^{\rm c} _{-1}\\ v_{\rm S1\_S2} & = [S_{\rm 1Tp}]k_{\rm o12}\\ v_{\rm S2\_S3} & = [S_{\rm 2Tp}]k_{\rm o23}\\ v_{\rm S3\_S0} & = [S_{\rm 3Tp}]k_{\rm o30}\\ v_{\rm S0\_S1} & = [S_{\rm 0Tp}]k_{\rm o01}\\ \end{aligned}$$
$$\begin{aligned} {\rm Coeff}1 & = \frac{[P_{680}^{+} {\rm Pheo}^{-}]}{[P_{680}{\rm PheoT}]}\\ \quad {\rm where}\; [P_{680}{\rm PheoT}] & = [P_{680}{\rm Pheo}] + [P_{680}^{+} {\rm Pheo}] + [P_{680}{\rm Pheo}^{-}] + [P680^{+} {\rm Pheo}^{-}]\\ v_{\rm 1z\_1} & = [S_{\rm 1T}]k_{\rm z}{\rm Coeff}1\\ v_{\rm 2z\_1} & = [S_{\rm 2T}]k_{\rm z}{\rm Coeff}1\\ v_{\rm 3z\_1} & = [S_{\rm 3T}]k_{\rm z}{\rm Coeff}1\\ v_{\rm 0z\_1} & = [S_{\rm 0T}]k_{\rm z}{\rm Coeff}1\\ v_{\rm z\_1} & = v_{\rm 1z\_1} + v_{\rm 2z\_1} + v_{\rm 3z\_1} + v_{\rm 0z\_1}\\ \end{aligned}$$
$$\begin{aligned} {\rm Coeff}2 & = \frac{[P_{680}^{+} {\rm Pheo}]}{[P_{680}{\rm PheoT}]}\\ v_{\rm 1z\_2} & = [S_{\rm 1T}]k_{\rm z}{\rm Coeff}2\\ v_{\rm 2z\_2} & = [S_{\rm 2T}]k_{\rm z}{\rm Coeff}2\\ v_{\rm 3z\_2} & = [S_{\rm 3T}]k_{\rm z}{\rm Coeff}2\\ v_{\rm 0z\_2} & = [S_{\rm 0T}]k_{\rm z}{\rm Coeff}2\\\end{aligned}$$
$$\begin{aligned} v_{\rm z\_2} & = v_{\rm 1z\_2} + v_{\rm 2z\_2} + v_{\rm 3z\_2} + v_{\rm 0z\_2}\\ v_{\rm 1z} & = v_{\rm 1z\_1} + v_{\rm 1z\_2}\\ v_{\rm 2z} & = v_{\rm 2z\_1} + v_{\rm 2z\_2}\\ v_{\rm 3z} & = v_{\rm 3z\_1} + v_{\rm 3z\_2}\\ v_{\rm 0z} & = v_{\rm 0z\_1} + v_{\rm 0z\_2}\\\end{aligned}$$
$$\begin{aligned} v_{\rm AB1} & = [{\rm Q}_{\rm A}^{-} {\rm Q}_{\rm B}]k_{\rm AB1}\\ v_{\rm BA1} & = [{\rm Q}_{\rm A}{\rm Q}_{\rm B}^{-}]k_{\rm BA1}\\ v_{\rm AB2} & = [{\rm Q}_{\rm A}^{-} {\rm Q}_{\rm B}^{-}]k_{\rm AB2}\\ v_{\rm BA2} & = [{\rm Q}_{\rm A}{\rm Q}_{\rm B}^{-2}]k_{\rm BA2}\\ \end{aligned}$$
$$\begin{aligned} {\text{[PQT]}} & = 6\\ v_{3} & = [{\rm Q}_{\rm A}{\rm Q}_{\rm B}^{2-}]k_{3}[{\rm PQ}]/[{\rm PQT}]\\ v_{\rm \_r3} & = [{\rm Q}_{\rm A}{\rm Q}_{\rm B}]k_{\rm r3}[{\rm PQH}_{2}]/[{\rm PQT}]\\ v_{\rm 3\_n} & = [{\rm Q}_{\rm A}^{-} {\rm Q}_{\rm B}^{2-}]k_{3}[{\rm PQ}]/[{\rm PQT}]\\ v_{\rm \_r3\_n} & = [{\rm Q}_{\rm A}^{-} {\rm Q}_{\rm B}]k_{\rm r3}[{\rm PQH}_{2}] /[{\rm PQT}]\\ v_{\rm \_pq\_ox} & = [PQH_{2}]k_{\rm ox}\\ v_{2\_1} & = [{P_{680}^{+}} {\rm Pheo}^{-}]k_{2}q\\ v_{2\_2} & = [{P_{680}}{\rm Pheo}^{-}]k_{2}q\\ \end{aligned}$$
$$\begin{aligned} a & = [{\rm Q}_{\rm A}{\rm Q}_{\rm B}]/([{\rm Q}_{\rm A}{\rm Q}_{\rm B}] + [{\rm Q}_{\rm A}{\rm Q}_{\rm B}^{-}] + [{\rm Q}_{\rm A}{\rm Q}_{\rm B}^{2-}])\\ b & = [{\rm Q}_{\rm A}{\rm Q}_{\rm B}^{-}]/([{\rm Q}_{\rm A}{\rm Q}_{\rm B}]+[{\rm Q}_{\rm A}{\rm Q}_{\rm B}^{-}] + [{\rm Q}_{\rm A}{\rm Q}_{\rm B}^{2-}])\\ c & = [{\rm Q}_{\rm A}{\rm Q}_{\rm B}^{2-}]/([{\rm Q}_{\rm A}{\rm Q}_{\rm B}]+[{\rm Q}_{\rm A}{\rm Q}_{\rm B}^{-}] + [{\rm Q}_{\rm A}{\rm Q}_{\rm B}^{2-}])\\ v_{2\_00\_1} & = v_{2\_1}a \\ v_{2\_01\_1} & = v_{2\_1}b \\ v_{2\_02\_1} & = v_{2\_1}c \\ v_{2\_00\_2} & = v_{2\_2}a \\ v_{2\_01\_2} & = v_{2\_2}b \\ v_{2\_02\_2} & = v_{2\_2}c \\ \end{aligned}$$
$$\begin{aligned} CE_{1} & = \frac{[P_{680}^{+} {\rm Pheo}]}{[P_{680}{\rm PheoT}]}\\ v_{\rm r2\_00\_1} & = CE_{1}[{\rm Q}_{\rm A}^{-} {\rm Q}_{\rm B}]k_{2}/{\rm Ke}\\ v_{\rm r2\_01\_1} & = CE_{1}[{\rm Q}_{\rm A}^{-} {\rm Q}_{\rm B}^{-}]k_{2} /{\rm Ke}\\ v_{\rm r2\_02\_1} & = CE_{1}[{\rm Q}_{\rm A}^{-} {\rm Q}_{\rm B}^{2-}]k_{2}/{\rm Ke}\\ v_{\rm r2\_1} & = v_{\rm r2\_00\_1} + v_{\rm r2\_01\_1} + v_{\rm r2\_02\_1}\\ \end{aligned}$$
$$\begin{aligned} CE_{2} & = \frac{[P_{680}{\rm Pheo}]}{[P_{680}{\rm PheoT}]}\\ v_{\rm r2\_00\_2} & = CE_{2}[{\rm Q}_{\rm A}^{-} {\rm Q}_{\rm B}]k_{2}/{\rm Ke}\\ v_{\rm r2\_01\_2} & = CE_{2}[{\rm Q}_{\rm A}^{-} {\rm Q}_{\rm B}^{-}]k_{2}/{\rm Ke}\\ v_{\rm r2\_02\_2} & = CE_{2}[{\rm Q}_{\rm A}^{-} {\rm Q}_{\rm B}^{2-}] \times k_{2}/{\rm Ke}\\ v_{\rm r2\_2} & = v_{\rm r2\_00\_2} + v_{\rm r2\_01\_2} + v_{\rm r2\_02\_2}\\ \end{aligned}$$
$$\begin{aligned} v_{\rm P680qU} & = [U]([P_{680}^{+} {\rm Pheo}] + [P_{680}^{+} {\rm Pheo}^{-}])k_{\rm c}\\ v_{\rm P680qA} & = [A]([P_{680}^{+} {\rm Pheo}] + [P_{680}^{+} {\rm Pheo}^{-}])k_{\rm c}\\ k_{\rm q} & = 0.15(k_{\rm f}+ k_{\rm h})/ [{\rm PQT}]\\ v_{\rm PQqU} & = [U][PQ]k_{\rm q}\\ v_{\rm PQqA} & = [A][PQ]k_{\rm q}\\ \Phi _{\rm f} & = k^{\rm a} _{\rm f}A_{\rm p}+ ([U]+[U_{\rm i}])k^{u} _{\rm f} + k^{\rm a} _{\rm f}[A_{\rm ip}] + k^{\rm u} _{\rm f}[U_{\rm ifc}]\\ \end{aligned}$$

Appendix 3

Definitions of all abbreviations except rate constants used in the model

Abbrev.

Description

Unit

[Ap]

Concentration of excitation energy on peripheral antenna of photosystem II

μmol m−2

[P *680 Pheo]

The concentration of excited P680 associated with Pheo

μmol m−2

[P +680 Pheo]

The concentration of P +680 associated with Pheo

μmol m−2

[P +680 Pheo−]

The concentration of P +680 associated with Pheo−

μmol m−2

[P680Pheo]

The concentration of P680 associated with Pheo

μmol m−2

[P680Pheo−]

The concentration of P680 associated with Pheo−

μmol m−2

[P680PheoT]

The total concentration of P680Pheo, P +680 Pheo, P680Pheo− and P +680 Pheo− .

μmol m−2

[PQ]

The concentration of plastoquinone

μmol m−2

[PQ]

The concentration of oxidized plastoquinone

μmol m−2

[PQH2]

The concentration of fully reduced plastoquinone

μmol m−2

[PQT]

The total concentration of plastoquinone and plastoquinol in thylakoid membrane

μmol m−2

[QA]

The concentration of oxidized QA

μmol m−2

[Q −A ]

The concentration of reduced QA

μmol m−2

[QAQB]

The concentration of oxidized QA associated with oxidized QB

μmol m−2

[Q −A QB]

The concentration of reduced QA associated with oxidized QB

μmol m−2

[Q −A QB]

The concentration of reduced QA associated with Q −B

μmol m−2

[Q −A QB]

The concentration of reduced QA associated with Q 2−B

μmol m−2

[QAQ −B ]

The concentration of oxidized QA associated with Q −B

μmol m−2

[QAQ 2−B ]

The concentration of oxidized QA associated with Q 2−B

μmol m−2

[S n]

The concentration of oxygen evolving complex at S n state

μmol m−2

[S nT ]

The concentration of oxygen evolving complex at S n state before donating electron to tyrosine (Y z)

μmol m−2

[S nTp ]

The concentration of oxygen evolving complex at S n state after donating electron to tyrosine (Y z)

μmol m−2

[U]

Concentration of excitation energy on core antenna of QB-reducing photosystem II

μmol m−2

[Ui]

Concentration of excitation energy on core antenna of QB-nonreducing photosystem II

μmol m−2

[Uifc]

The concentration of excitation energy on chlorophylls detached from core antenna of QB-nonreducing photosystem II

μmol m−2

[Y Z]

The concentration of primary electron donor for reaction center of PSII (P680)

μmol m−2

Ai

Incident photon flux density on peripheral antenna of QB-nonreducing photosystem II

μmol m−2 s−1

AiP

The concentration of excitation energy on peripheral antenna of QB-nonreducing photosystem II

μmol m−2

I a

The incident photon flux density on peripheral PSII antenna

μmol m−2 s−1

I c

The incident photon flux density on core antenna of QB-reducing reaction center

μmol m−2 s−1

I in

The total incident photon flux density

μmol m−2 s−1

n

The ratio of PSI to PSII

NA

P680

The reaction center chlorophyll of PSII. It can exist in native state (P680), excited state (P *680 ), or oxidized state (P +680 ).

NA

Pheo

Pheophytin, the first electron acceptor of primary charge separation in PSII. It can exist in either native state (Pheo) or reduced state (Pheo−).

NA

q

The proportion of oxidized QA

NA

QA

The first quinine electron acceptor of PSII

NA

QB

The second quinine electron acceptor of PSII

NA

Uif

Incident photon flux density on chlorophylls detached from core antenna of QB-nonreducing photosystem II

μmol m−2 s−1

v_pq_ox

The rate of PQH2 oxidation by Cyt b6f

μmol m−2 s−1

v_r3

The rate of the exchange of PQH2 with QB associated with QA

μmol m−2 s−1

v_r3_n

The rate of exchange of PQH2 with QB associated with Q −A

μmol m−2 s−1

v 1

The rate of charge separation in the QB-reducing PSII reaction center

μmol m−2 s−1

v −1

The rate of charge recombination in the QB-reducing PSII reaction center

μmol m−2 s−1

v2_0m_n

The rate of reactions relating to electron transfer from Pheo− to QA where m represents the redox state of QB with 0 for QB, 1 for Q −B and 2 for Q 2−B , and n represents the redox state of P680 with 1 for P +680 and 2 for P680, e.g. v2_00_1: the rate of reduction of QAQB by P +680 Pheo−

μmol m−2 s−1

v 2_1

The rate of QAreduction by P +680 Pheo−

μmol m−2 s−1

v 2_2

The rate of QAreduction by P680Pheo−

μmol m−2 s−1

v3

The rate of exchange of PQ with Q 2−B associated with QA

μmol m−2 s−1

v3_n

The rate of exchange of PQ with Q 2−B associated with Q −A

μmol m−2 s−1

vAB1

The rate of electron transfer from Q −A to QB

μmol m−2 s−1

vAB2

The rate of electron transfer from Q −A to Q −B

μmol m−2 s−1

v Ad

The rate of heat dissipation from the peripheral antenna

μmol m−2 s−1

v Af

The rate of fluorescence emission from the peripheral antenna

μmol m−2 s−1

v AU

The rate of excitation energy transfer from peripheral to core antenna

μmol m−2 s−1

vBA1

The rate of electron transfer from Q −B to QA

μmol m−2 s−1

vBA2

The rate of electron transfer from Q −2B to QA

μmol m−2 s−1

v nz

The rate of oxidation of Sn state of oxygen evolution complex

μmol m−2 s−1

v nz_1

The rate of electron transfer from oxygen evolution complex at Sn state to P +680 associated with Pheo− via Yz

μmol m−2 s−1

v nz_2

The rate of electron transfer from oxygen evolution complex at Sn state to P +680 associated with Pheo via Yz

μmol m−2 s−1

v P680qA

The rate of quenching of excitation energy in the peripheral antenna by P +680

μmol m−2 s−1

v P680qU

The rate of quenching of excitation energy in the core antenna by P +680

μmol m−2 s−1

v PQqA

The rate of quenching of excitation energy in the peripheral antenna by oxidized plastoquinone

μmol m−2 s−1

v PQqU

The rate of quenching of excitation energy in the core antenna by oxidized plastoquinone

μmol m−2 s−1

vr2_0m_n

The back reaction of v2_0m_n, see v2_0m_n for details

μmol m−2 s−1

v r2_1

The rate of Q −A oxidation by P +680 Pheo

μmol m−2 s−1

v r2_2

The rate of Q −A oxidation by P680Pheo

μmol m−2 s−1

vsm_sn

The rate of transition from S m state to S n state of oxygen evolution complex

μmol m−2 s−1

v UA

The rate of excitation energy transfer from core antenna to peripheral antenna

μmol m−2 s−1

v Ud

The rate of heat dissipation of excitation energy from the core antenna of QB-reducing PSII reaction center

μmol m−2 s−1

v Uf

The rate of fluorescence emission from the core antenna of QB-reducing reaction center

μmol m−2 s−1

v z_1

The rate of P +680 Pheo− reduction

μmol m−2 s−1

v z_2

The rate of P +680 Pheo reduction

μmol m−2 s−1

x

The ratio of the concentration of QB-nonreducing PSII reaction center to that of QB-reducing reaction center

NA

Φf

Fluorescence yield

μmol m−2 s−1

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Zhu, XG., Govindjee,  ., Baker, N.R. et al. Chlorophyll a fluorescence induction kinetics in leaves predicted from a model describing each discrete step of excitation energy and electron transfer associated with Photosystem II. Planta 223, 114–133 (2005). https://doi.org/10.1007/s00425-005-0064-4

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