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Pathways for loss of excitation from excited chlorophyll

1) Energy transfer to neighboring Chl of the same protein; rate constant k_e1
2) Energy transfer to neighboring Chl of different protein; rate constant k_e2
3) Fluorescence (radiative decay); rate constant k_f
4) Non-radiative decay (loss as heat); rate constant k_h
5) Formation of triplet state; rate constant k_t
6) Energy transfer to an open photochemical trap, and photochemical conversion; rate constant k_p

The open photochemical trap is represented here by P.Q_A, where P is the primary donor, usually a special chlorophyll or bacteriochlorophyll dimer, and Q_A is the primary acceptor. In many bacterial reaction centers, and in photosystem II of green plants, Q_A is a bound quinone; however, in the original nomenclature, Q stood for quencher (of fluorescence, see below).

Useful equations

Fluorescence intensity

F_I = f_f . I . B

F_I is fluorescence intensity, f_f is fluorescence yield (see below), I is incident light intensity, B is Einstein coefficient. Product I.B is rate of absorption of light.

Fluorescence yield.

Fluorescence yield is the fraction of the decay that proceeds through a fluorescence pathway. We can assume that all light harvesting centers have the same set of decay constants, and that all processes except photochemical trapping are first order:

f_f = k_f[Chl*] / (k_f[Chl*] + k_h[Chl*] + k_t[Chl*] + k_p[Chl*].[P.Q_A])

= k_f / (k_f + k_h + k_t + k_p.[P.Q_A])

f_f = fluorescence yield

[P.Q_A] = concentration of open traps

k_f, k_h, k_t, k_p are rate constants (see scheme above)

Intrinsic fluorescence lifetime

Intrinsic fluorescence lifetime is the lifetime fluorescence would have if there were no other competing processes.

t^o = 1 / k_f or k_f = 1 / t^o

Since probabilities of absorption and emission are related by the factor 8phcn3, to can also be calculated from the absorbance and fluorescence spectra:

1 / t^o » 2.9 × 10^-9 á n²ñav ò e × dn

Here n is the wavenumber (cm^-1) for the transition, á n²ñav is the mean wavenumber of the absortion band (near the center of the band), e is the molar extinction coefficient, and ò e × dn is the area under the absorption band plotted as e vs. n. The shapes of most absorption bands are symetrical, so that ò e × dn is approximately equal to the half-width of the band times the maximal (peak) extinction coefficient, Dn × e_max, so to a good approximation:

1 / t^o » 3 × 10^-9 á n²ñ_av Dn × e_max

Actual fluorescence lifetime

The actual or measured lifetime t, is determined by all the decay pathways:

ie., k' is the sum of the rate constants for all decay pathways.

By substitution:

f_f = k_f . t = t / t^o

and t = f_f . t^o

Closed and open traps, and their fluorescence yield

According to the equations above, the fluorescence expected from a photosynthetic system will reflect the the fraction of open photochemical traps. The inverse relationship implies that fluorescence is lowest when all traps are open, and maximal when all traps are closed. However, any process which directly affects the first-order rate constants for other competing processes will also effect fluorescence. In bacterial reaction centers, the main contribution to changes in fluorecence yield come from changes in the concentration of open traps. However, in green plants, the fluorescence also reflects the the presence of an additional quencher, P⁺, which effectively dumps the exciton energy as heat by providing an absorption band in the near IR which "absorbs" the fluorescence, and allows it all to decay through non-radiative pathways. Effectively, this allows the non-radiative decay rate constant, k_h, to dominate the decay of Chl*, and eliminates the fluorescence.

The scheme below summarizes the states of the reaction center of photosystem II, and the fluorescence levels associated with them. The transitions from low to high and high to low fluorescence yield allow the kinetics of the reactions associated with these transitions to be explored through fluorescence, using fluorimeters designed to operate in the µs range. In addition, many other processes giving rise to changes in fluorescence through secondary interactions can be explored through fluorescence. Most important are the processes associated with non-photochemical quenching (q_E-quenching), through which plants protect themselves against excess light.

Probability of exciton transfer between centers

If an absorbed photon can be transferred to more than one photochemical trap, the relation between variable fluorescence and [Q_A^-] is not linear. A correction factor can be calculated based on the probability, P, of transfer to another trap. P has a value of about 0.55 in green plants.

The variable fluorescence F_v is given by F_v = (F_t - F_o) / F_o, where F_t is the measured fluorescence, and F_o is the fluorescence which is not associated with closing of traps (ie., the fluorescence when all traps are open). F_max is the fluorescence when all traps are closed.