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THE TWO-ELECTRON GATE OF REACTION CENTERS

Following illumination of bacterial reaction centers in the open state, the following sequence of reactions occurs:

P.Q_A.Q_B --> P*.Q_A.Q_B --> P⁺.Q_A^-.Q_B <=> P⁺.Q_A.Q_B^-
                k_AP = 10 s^-1
       ^_______________________|

The photochemical products return to the ground state by back-reaction through a pathway which has a half-time (in reaction centers from Rb. sphaeroides) of about 70 -100 ms, when forward electron transfer from Q_A^- is prevented. When forward electron transfer can occur to the secondary quinone, the back- reaction time is longer, because the electron in the acceptor pool is shared between Q_A and Q_B. The ratio of back-reaction times is related to the fractional occupancy of the Q_A^-.Q_B state.

Relation between back-reaction rate constants and the equilibrium constant between the acceptor quinones can be approached as follows.

We start with the simplest case. Consider the reaction between Q_A and Q_B when Q_B is bound.

Q_A^-.Q_B <=> Q_A.Q_B^-

with equilibrium constant:

         [Q_A.Q_B^-]
K_E = ------------
         [Q_A^-.Q_B]

We normalize by setting the total reaction center concentration to 1 in arbitrary units. Then the concentration of Q_A^- formed on a saturating flash when forward electron transfer is prevented will be 1. We can prevent forward electron transfer by adding an inhibitor which binds instead of Q_B, or by preparing reaction centers without Q_B. Under these circumstances, the back- reaction, measured by disappearance of P⁺, will occur according to the following rate equation (P⁺ has been omitted from the right-hand term for clarity):

v_A = -d[P⁺]/dt = k_AP.[Q_A^-]

for the initial rate,

v_A^init = k_AP.[Q_A^-]_tot = k_AP

Apparent rate constant will be the same as the true rate constant, k_AP

In the presence of Q_B, the probability of an electron being on Q_A will be less because of the electron transfer reaction above, and will be described by the equilibrium constant K_E. Since equilibrium is rapid compared to the back-reaction, we can use the relative rates of the back-reactions under the two conditions to measure K_E.

Let f be the fraction of centers in which the electron is on Q_A. Assuming rapid equilibration, immediately after a saturating flash we will have:

f = [Q_A^-.Q_B]/[reaction center]_tot

K_E = (1 - f) / f

f = 1/(1 + K_E)

The rate of the back-reaction will be given by

v_B = -d[P⁺]/dt = k_AP.[ Q_A^-.Q_B]

for initial rate,

v_B^init = k_AP.f = k_AP / (1 + K_E)

The apparent rate constant will be changed to k_AP / (1 + K_E). Since the reaction is first-order, the half-times under both conditions will depend on the apparent rate constants, so that

v_A^init / v_B^init = t_½(B) / t_½(A) = 1 + K_E

K_E = t_½(B) / t_½(A) - 1

The ratio of the back-reaction half-times (or apparent rate constants) therefore provides a direct measurement of the equilibrium constant for the sharing of an electron between primary and secondary acceptors.

The true situation is more complicated, because of the need to take account of the following secondary reactions:

i) The fraction of centers with Q_B bound before the flash will be less than 1 because of the reaction

Q_A.[vacant] + Q_pool <=> Q_A.Q_B

ii) Formation of Q_B^- is stabilized by binding of a proton to a neighboring group on the protein, according to the reaction

Q_A.Q_B^- + H⁺ <=> Q_A.Q_B^- (H⁺)

iii) Reactions on the donor side may consume P⁺. A treatment similar to that for the acceptor side discussed above can be used to probe equilibria between primary and secondary donors.

Nevertheless, the above treatment can be readily extended to the more complicated situation, and has provided much information about equilibrium constants among components in acceptor and donor pools.