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Interpretation of fluorescence kinetics

The kinetics of Q_A^- oxidation as measured by fluorescence show different rates after the first and second flashes, reflecting the two different reactions of the two-electron gate.

Q_A.Q_B -> Q_A-Q_B = Q_AQ_B-          (1)

Q_AQ_B^- -> Q_A^-Q_B^- = Q_AQ_BH₂       (2)

The rate after the first flash is a convolution of two processes. The fast phase (150- 200µs) is due to centers in which Q_B is bound before the flash. The slow phase (1 - 2ms) reflects centers in which Q_B is not bound before the flash so that electron transfer has to wait for Q binding.

The equilibrium and rate constants for the forward and reverse electron transfer and for binding and dissociation of plastoquinone at the Q_B site can be calculated using the following assumptions:

1. The ratio of amplitudes of fast and slow components of the rapid biphasic decay kinetics of Q_A^- following an actinic flash was assumed to reflect the ratio of the initial fraction of Q_A.Q_B to Q_A.[vacant] centers.
2. The dissociation constant of plastoquinone from the Q_B site in the dark was assumed to remain unchanged after an actinic flash.
3. Binding of plastoquinone to the Q_B-site was assumed to follow a pseudo-first order reaction kinetics when the pool was initially oxidized (ten-fold excess of oxidized plastoquinone over reaction center).

The two following equations are solutions of the rate equations derived from the model.

r₁ + r₂ = k_on ( 1 + A_o / B_o ) + k_BA{ 1 + K_app ( 1 + A_o / B_o ) }          (1)

r₁ . r₂ = k_on . k_BA ( 1 + A_o / B_o ) ( 1 + K_app )          (2)

Variables r₁ and r₂ are the slow and fast rate constants obtained directly from the experimental data by fitting the kinetic traces of fluorescence decay after one actinic flash to two exponential components, and a residual; A_o and B_o are the amplitudes of the slow and fast component, respectively, of the fitted kinetic traces, also obtained from the two-exponential fit. K_O, the plastoquinone dissociation constant, is calculated as the ratio A_o/B_o (assumption i) above).

K_app is the apparent equilibrium constant for sharing an electron between Q_A and Q_B, defined (if protonated states are included) as:

                      [Q_AQ_B^-] + [Q_AQ_B^-(H⁺)]
K_app = -------------------------------------------------
            [Q_A^-] + [Q_A^-(H⁺)] + [Q_A^-Q_B] + [Q_A^-Q_B(H⁺)]

For simplicity, we can ignore the effects of protonation, and treat Kapp at any fixed pH as determined by the equilibrium constants for electron transfer, and the dissociation of Q from the site:

                [Q_AQ_B^-]
K_app = -------------------
             [Q_A^-] + [Q_A^-Q_B]

         = K_E / (1 + K_O)          (3)

Again, for simplicity we have ignored the contribution of the quinone pool, so that

K_O = Q_A^- / Q_A^-.Q_B

      = A_o / B_o

      = k_off / k_on

Also,

K_E = Q_A.Q_B^- / Q_A^-.Q_B

      = k_AB / k_BA

so that

K_app = k_AB / k_BA . ( 1 + A_o / B_o ) -1          (3')

The apparent equilibrium constant, K_app, can be determined experimentally from the ratio of the half-time of the back reaction S₂PQ_AQ_B^- -> S₁PQ_AQ_B to that of the back reaction S₂PQ_A^- -> S₁PQ_A. The measured parameters therefore allow us to determine the rate constants and equilibrium constants which define the two-electron gate mechanism.

By repeating the above experiments at different pH values, we can also determine the pK values which describe the role of protons in the mechanism, but this more extensive data set has so far been collected only in A. hybridis and its S264G mutant (7).