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

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 Q_B (Q_A and Q_B 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 Q_B-nonreducing PSII centers leads to higher fluorescence emission at O and correspondingly decreases the variable to maximum fluorescence ratio (F _v/F _m).

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 Q_B-reducing PSII reaction centers. Same set of different equations were used to describe the concentration changes of components associated with Q_B-nonreducing PSII reaction centers. The Q_B-nonreducing and Q_B-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 Q_B-reducing and Q_B-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 Q_B-reducing reaction centers used in the model of fluorescence induction. The set of equations for the reactions associated with the Q_B-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