Analysis of initial chlorophyll fluorescence induction kinetics in chloroplasts in terms of rate constants of donor side quenching release and electron trapping in photosystem II

Abstract

The fluorescence induction F(t) of dark-adapted chloroplasts has been studied in multi-turnover 1 s light flashes (MTFs). A theoretical expression for the initial fluorescence rise is derived from a set of rate equations that describes the sequence of transfer steps associated with the reduction of the primary quinone acceptor Q _A and the release of photochemical fluorescence quenching of photosystem II (PSII). The initial F(t) rise in the hundreds of μs time range is shown to follow the theoretical function dictated by the rate constants of light excitation (k _L) and release of donor side quenching (k _si ). The bi-exponential function shows sigmoidicity when one of the two rate constants differs by less than one order of magnitude from the other. It is shown, in agreement with the theory, that the sigmoidicity of the fluorescence rise is variable with light intensity and mainly, if not exclusively, determined by the ratio between rate of light excitation and the rate constant of donor side quenching release.

Appendices

Appendices

A. Derivation of the rFv(t) expression when light excitation rate k _L for fluorescence emission is equal to the rate constant of the release of donor side quenching $k_{s_1 }$

Equation 3 gives the general expression for the normalized variable fluorescence rFv(t) = y ₂(t) upon light excitation at a rate k _L and under control of donor side quenching of which the release occurs with a rate constant $k_{s_1 }$

$$ y_2 (t) = 1 - \frac{{k_{s_1 } }} {{k_{s_1 } - k_{\text{L}} }}{\text{e}}^{ - k_{\text{L}} t} + \frac{{k_{\text{L}} }} {{k_{s_1 } - k_{\text{L}} }}{\text{e}}^{ - k_{s_1 } t} $$

(11)

The equation is not applicable when $k_{\text{L}} = k_{s_1 } .$ Here I give the derivation for the expression of y ₂(t) for this particular condition. After rewriting Eq. 3 and series expansion of the function ${\text{e}}^{ - (k_{s_1 } - k_{\text{L}} )t}$ (rows 2 and 3, respectively, in the derivation below) one obtains with substitution $k_{\text{L}} = k_{s_1 }$ at the end of the third row:

$$ \begin{gathered} y_2 (t) \hfill \\ = 1 - {\text{e}}^{ -k_{\text{L}} t} \times \left [ 1 - \frac{{k_{\text{L}} }}{{(k_{s_1 } - k_{\text{L}} )}}[{\text{e}}^{ - (k_{s_1 } -k_{\text{L}} )t} - 1] \right ] \hfill \\ = 1 - {\text{e}}^{ -k_{\text{L}} t} \times \left [ 1 - \frac{{k_{\text{L}} }}{{(k_{s_1 } - k_{\text{L}} )}}[1 - (k_{s_1 } - k_{\text{L}} )t +\frac{{(k_{s_1 } - k_{\text{L}} )^2 t^2 }} {2} - \{{\text{higher}}\;{\text{order}}\;{\text{terms\} }} - {\text{1}}]\right ] \hfill \\ = 1 - {\text{e}}^{ - k_{\text{L}} t} (1 +k_{\text{L}} t) \hfill \\ \end{gathered} $$

(A.1)

The plot of this relation is shown as the bold curve in Fig. 2a.

The relative variable fluorescence rFv in relation to the fraction q of (‘closed’) centers with Q ⁻_A for the particular case $k_{\text{L}} = k_{s_1 }$ is easily obtained after substitution Eq. 4 in Eq. A.1. This gives

$$ {\text{rFv}} = y_2 (t) = q - k_{\text{L}} t \times {\text{e}}^{ - k_{\text{L}} t} = q + (1 - q)\ln (1 - q) $$

(A.2)

The plot of this rFv versus q relation for $k_{\text{L}}=k_{s_1 }$ is shown as the bold curve in Fig. 2b.

B. Is the non-linear relation between rFv and the fractionq of centers with Q ⁻_A (‘closed’ RCs) (or between V and B, respectively, in Strasser’s terminology) a decisive indicator of energetic connectivity between RCs of PSII?

The answer is no, it is not. This will become clear from a closer look at the experimental procedure with which the fraction q (or B in Strasser’s terminology) of (closed) centers with Q ⁻_A is determined. B(t) is obtained, in the presence of DCMU, by numerical determination of the normalized area S(t) above the rFv(t) curve which gives the B(t) curve. The shape of the rFv(t) versus B(t) plot finally is used as a criterion for a nongrouping- (linear relation with rFv(t) = B(t)), or grouping- (hyperbolic relation between rFv(t) and B(t)) behavior of the PSII systems. In the latter case the connectivity) of the RCs of PSII is related to the empirically derived grouping parameter p by fitting the experimental rFv versus B relation with the hyperbolic relation

$$ {\text{rFv}}(t) = \frac{{B(t)}} {{[1 + C_{{\text{hyp}}} (1 - B(t))]}} $$

(B.1)

This relation (Strasser 1978), which is similar to one derived by Joliot and Joliot (1964), simplifies for C _hyp = 0 (no grouping, or noncooperativity) to a linear relation rFv(t) = B(t). Equation B.1 is identical with Eq. 7 with B(t) = q(t). So far so good.

However, it should be realized that B(t) determined from the area above an experimental rFv curve gives the fraction q ^dsq of RCs in which the donor side quenching is released. As has been derived (see text and Eqs. 1 and 3) q ^dsq (= y ₂) < q (= 1 − y ₀). The unknown fraction y ₁ of RCs with Q ⁻_A and rFv = 0 (due to quenching by donor side components) cannot be detected by the experimental area determination method; it remains hidden due to its quenched properties. Thus what in these graphic analyses routinely is considered as the rFv versus q relation in fact is the non-linear relation between rFv and q ^dsq fraction of RCs in which fluorescence quenching is released. Its non-linearity is quantitatively related to the release of donor side fluorescence quenching of which the rate constant becomes apparent as an approximately exponential rise in the tens of μs time range in ultra short STFs (Steffen 2003). Theoretically one would have found (see text) a linear relation between rFv and the fraction of closed centers if (i) the fraction q could have been estimated instead of q ^dsq and (ii) the effect of other inductors is comparatively small. In general the discrepancy between the outcome of the theoretical and experimental rFv versus q relation (with exclusion of improbable systematic errors in the experimental approach) might be caused by (impact factor is presumed to descend with order):

• 1. Neglecting fluorescence quenching by redox intermediates at the donor side of PSII (donor side quenching).

• 2. The fact that the closure of RCs in PSII is a double hit trapping process in which closure occurs via semi-open RCs (with 100% Q ⁻_A ) formed from open centers (100% Q _A) in the first hit, as described in the Three State Trapping Model (TSTM).

• 3. As yet unknown processes including that associated with (changes in) photo-electric fields.

• 4. A variable and time dependent excitation rate k _L caused for instance by intersystem energy transfer (connectivity) between PSUs of PSII.

• 5. A combination of 1–4.

C. On the significance of the rFv versus complementary area (B) relation in the concept of the double hit trapping model (TSTM)

The normalized area B(t) above an experimental rFv curve measured in the presence of DCMU does not bear a simple relation to the fraction of closed PSII centers q(t) when the concept of TSTM is adopted. Here it is shown that, within this concept, the rFv versus B relation is non-linear, even under conditions at which k _L is time independent (no connectivity) and the effect of donor side quenching is negligible, for instance at $k_{\text{L}} \ll k_{s_1 } .$ In that case (see Hiraki et al. 2003; Vredenberg 2004 for illustration of scheme and meaning of subscript numbering) the reaction pattern can be represented by the scheme y ₀ → y ₂ → y ₄ with rate constant k _L for both steps; y ₀ (=1), y ₂ and y ₄ refer to the open (y₀), semi-open(-closed) and closed state of PSII systems with relative fluorescence yields rFv equal to 0, 0.5 and 1, respectively. In this simple form and assuming a time-independent excitation rate k _L, the solution of the ODEs for y ₀, y ₂ and y ₄ are identical to those given in Eqs. 1–3 with the proper substitutions of the subscripts for the y-states in Eqs. 2 and 3 and substituting $k_{s_1 }=k_{\text{L}} {\text{.}}$ This gives (see also Eqs. 3a and A.1]), according to definitions:

$$ y_2 (t) = k_{\text{L}} te^{ - k_{\text{L}} t} $$

(C.1)

$$ y_4 (t) = 1 - {\text{e}}^{ - k_{\text{L}} t} (1 + k_{\text{L}} t) $$

(C.2)

$$ {\text{rFv}}(t) = 0.5y_2 (t) + y_4 (t) = 1 - {\text{e}}^{ - k_{\text{L}} t} \left( {1 + \frac{{k_{\text{L}} t}} {2}} \right) $$

(C.3)

and

$$ B(t) = \frac{{\int\limits_0^t {[1 - {\text{rFv}}(t)]{\text{d}}t} }} {{\int\limits_0^\infty {[1 - {\text{rFv}}]{\text{d}}t} }} = 1 - {\text{e}}^{ - k_{\text{L}} t} \left( {1 + \frac{{k_{\text{L}} t}} {3}} \right) $$

(C.4)

Equations C.3 and C.4 show that rFv is non-linearly related to the area B above rFv under conditions in which donor side quenching and intersystem energy transfer can be excluded. Thus a double hit trapping mechanism like TSTM causes a non-linear relation between the relative variable fluorescence (rFv) and the area above the induction curve in the absence of donor side quenching and of connectivity between PSUs.