Transport of excitation energy in a molecular aggregate. VIII. Numerical simulation of exciton processes in thylakoid membrane

Abstract

ABSTRACT:We investigate the exciton dynamics in a molecular crystal. The dynamics is based on the exciton Hamiltonian, the phonon Hamiltonian, and the exciton-phonon interaction linear in phonon coordinates. Using the interaction picture, expressions were previously obtained for the rate of coherent migration of the exciton clothed by phonons, and the rate of incoherent or hopping motion. In this work we derive an expression for the clothed exciton propagator, which permits an explicit calculation of the hopping rate. Thus, the rates of exciton generation, coherent transfer, and hopping are determined completely from theory. These velocity constants, along with the experimental fluorescence decay constants and reaction rate constants for the excited molecules, are used to write a generalized master equation that describes the rate of change of exciton population at each site. The master equation can be numerically solved by using a time step of the order of a few femtoseconds, while the excited-state reactions and exciton transfer occur in the picosecond scale. Exciton dynamics is numerically simulated for a simple model of thylakoid membrane in green plants. The model is based on the known characteristics of thylakoid architecture. The membrane is divided into 97 zones, each zone in the bulk containing 1,442 chlorophylls, one P700, and one P680. The latter two pigments are randomly placed in each zone, while keeping their distance between 55 and 60 Å. This accounts for the randomness in orientation. The disorder of the chlorophyll molecules within the domains of photosystems is neglected. Our findings are as follows. On average, about 6 million photons within the range of 655-681 nm pass through a membrane in 1 s. About 2.3% of incident photons are absorbed by the membrane chlorophyll molecules. For an excitation bandwidth of 70 -175 cm Ϫ1 , the coherent transfer rate between two adjacent molecules is 1.138 Ϯ 0.488 ps Ϫ1 . Because the Debye frequency is expected to be much smaller, the slow phonon limit applies. The exciton-phonon coupling constant that can be determined from the transition dipole-transition dipole interaction model leads to a hopping rate of 0.088 ps Ϫ1 at 300 K. A steady state is effectively achieved for each zone in the bulk in ϳ5 ns. After a period of 50 ns, P700 and P680 in average trap at the rate of 650 -702 and 629 -679 excitons per second, respectively. The average rate of charge separation and subsequent reactions of each excited photosystem varies as 592-639 per second for PSI and 630 -680 per second for PSII. These numbers lead to a reasonable estimate for the amount of glucose produced in each square meter of leaf area in a day.

Integrated Kinetics for the Production of Glucose in Plant Cells and the Effect of Temperature

“…Using these data, we have recently constructed a simple model of the thylakoid membrane for our work on exciton transfer.The details are given in ref , which reported a numerical simulation carried out for the exciton transport. Here, in this work, we retain the results of the numerical calculation from the same reference.…”

“…To start with, there is the so-called light reaction where NADPH is produced: where “mem” stands for the thylakoid membrane. The rate R 1 is determined from the numerical simulation of exciton dynamics . In ref , we considered a typical thylakoid membrane and simulated exciton generation, transport, and trapping on it.…”

“…The rate R 1 is determined from the numerical simulation of exciton dynamics . In ref , we considered a typical thylakoid membrane and simulated exciton generation, transport, and trapping on it. We also determined the rate of reaction ( r 1 ‘) at photosystems I and II (the rate of electron transfers from each photosystem).…”

“…Assuming that the electron transport is fast enough (in the millisecond range), the rate of NADPH production during photosynthesis can be directly related to the rate of transfer of excitation between the nearest-neighbor chlorophylls . Our previous work on exciton transport in thylakoid was based on the theory of molecule−medium interaction that was developed by Simons .…”

“…With this background, we make a synthesis of the light reaction rates with the kinetics of the dark cycle. The novelty of the present work is severalfold: (1) In ref , the rate of transfer of an exciton between nearest-neighbor molecules in the thylakoid membrane was theoretically predicted, and the consequent reaction rate of each photosystem was numerically evaluated. These two rates are obviously related to each other, and the necessary relationship is numerically formulated in this work, thereby generating an expression for the temperature dependence of the light reaction rate, that is, the rate of reaction of photosystem I with NADP + .…”