Understanding the energy transfer network with qE on requires a mathematical framework that
incorporates that information. The equation describing the changes in excitation population on any node in the network is given by the master equation: Nec-1s $$ \frac\rm dP(t)\rm dt = KP(t), $$ (6)where P(t) is a vector containing the populations of each node at a time t and K is a rate matrix that contains all of the information regarding energy transfer connectivity and rates, qE and RC quenching rates, and fluorescence and ISC rates. The fluorescence decay F(t) in this formalism is simply the sum of P(t) over all nodes in the network, weighted by the rate of fluorescence at each node (Yang et al. 2003). Knowing K is equivalent to knowing the
energy transfer network, and a full understanding of qE requires characterizing the changes in K between dark- and light-adapted grana membranes (see Fig. 6). To determine K in grana membranes with qE on, Holzwarth and coworkers measured and fit fluorescence lifetimes on quenched and unquenched leaves with closed RCs of wild type and npq4, npq1, and L17 leaves from A. thaliana. A kinetic model for energy quenching in thylakoid selleck chemicals membranes was fit to the fluorescence lifetime data using target analysis (Holzwarth et al. 2009). The kinetic model (K) contained the assumption that all the pigments in the grana membrane are connected, with excitation energy transfer between them occurring much faster Molecular motor than Batimastat nmr charge separation. The model was first fit to dark-acclimated leaves. Fitting the model with the data from light-acclimated
leaves required increasing the non-radiative decay rate of the antenna compartment and including an additional compartment with a decay time of ∼400 ps. The increase in the non-radiative decay rate correlated positively with the amount of zeaxanthin, and the amplitude of the detached compartment correlated positively with the amount of PsbS. These correlations led to the proposal that there are two mechanisms of qE: one that was zeaxanthin dependent that occurred in the antenna of the PSII supercomplex, and one that was PsbS dependent that occurred by detachment of LHCII trimers from PSII. A more complex model for energy transfer in the thylakoid membrane compared to that in Gilmore et al. (1995) resulted in more detailed information about the energy transfer network. It is still unclear what the appropriate model is for describing energy transfer in grana membranes. Recent work by van Oort et al. (2010) has suggested that the migration time of excitations in thylakoid membranes makes up ∼50 % of the average chlorophyll fluorescence lifetime. This result suggests that models that assume that energy transfer is instantaneous may not be sufficiently detailed to accurately describe energy transfer in grana membranes.