Distribution donor-acceptor distance

The survival probability Gs(t) of the donor molecule (i.e. the probability that when excited at t = 0, it is still excited at time t) is obtained by summation over all possible rate constants kT (given by Eq. 9.1), each corresponding to a given donor-acceptor distance r. For a donor molecule surrounded with n acceptor molecules distributed at random in a spherical volume whose radius is much larger than the Forster critical radius R0, Gs(t) is given by... 

The native state conformation of the freely diffusing polypeptide is seen to be a helical dimer (Cf. Fig. 3). Assuming that the donor-acceptor distance R is given by the end-to-end distance, the corresponding distribution of R clearly shows that surface-immobilization does not affect the conformations in the folded state, regardless of whether the surface is repulsive or attractive (Cf. Fig. 4). This can be explained by the fact that the two helices are held together by the attractive nonbonding B-B interactions so that the B residues form a hydrophobic core, and therefore cannot effectively interact with the surface. 

When the distance R between D and A can be calculated or measured by other methods in relatively rigid systems, it has been amply demonstrated that remarkably consistent values of Rapp are obtained from FRET measurements. However, Rapp may differ somewhat from the actual donor acceptor distance in a flexible macromolecule with a broad distribution of donor acceptor distances. The distance Rapp derived from steady-state FRET measurements then considerably overestimates the true mean distance.76 To treat flexible macromolecules or conformational mixtures, time-resolved measurements of FRET are necessary.75... 

In the simplest case, the R mode is characterized by a low frequency and is not dynamically coupled to the fluctuations of the solvent. The system is assumed to maintain an equilibrium distribution along the R coordinate. In this case, ve can exclude the R mode from the dynamical description and consider an equilibrium ensemble of PCET systems with fixed proton donor-acceptor distances. The electrons and transferring proton are assumed to be adiabatic with respect to the R coordinate and solvent coordinates within the reactant and product states. Thus, the reaction is described in terms of nonadiabatic transitions between two sets of intersecting free energy surfaces ( R, and ej, Zp, corresponding to... 

Valeur et al. have calculated the distribution of donor-acceptor distances in flexible bichromophonic molecules. The rotational isomer theory for a 3 or 4 bond sequence is found to be in good agreement with experimental results. 

However maquettes for the design of redox proteins were proposed, based on a three helix bundle with a capping Co(III) (bipyridine)3 electron acceptor at the N-terminus and an electron donor at the C-terminus (199, 200). These proteins were tested for LRET. The a-helical percent was adjusted by addition of urea or trifluoroethanol (201, 202). Intriguingly, studies of one of the proteins (l6-mer-three helix bundle) shows a 2-fold higher LRET rate constant when the percent of helicity is 77% than when it is 0% (denatured in urea). However authors indicate that the kinetics is not a simple first-order one in the presence of urea. They interprete these data as coming from different donor-acceptor distances. The distribution of distances was determined by fluorescence lifetimes fit. Both when helicity is 0% or 77%, distributions peak around 18 A for the Ru(II) (16-mer)3-A (where A=5-((((2-acetyl)amino]ethyl)amino)-naphthalene-l sulfonic acid). Actually the distance appears 0.7A shorter for a-helix which is found consistent with the increased rate constant, by the authors. 

If the signal/noise ratio in the data is sufficiently high, a distribution of donor-acceptor distances P R)) can be extracted by fitting the fluoresence decay kinetics to a function of the form... 

Eis, P.S., Lakowicz, J.R. Time-resolved energy transfer measurements of donor-acceptor distance distributions and intramolecular flexibility of a CCHH zinc finger peptide. Biochemistry 32, 7981-7993 (1995)... 

Fig. 15.7 Probability distributions of donor-acceptor distances at the TS of the hydride transfer reaction in wild type EcDHER (continuous line) and N23PP-S148A mutant (dashed line)...

Figure 13, Donor-acceptor distance distribution functions in DNP-ENA-RNase calculated from donor fluorescence decay curves using Eq 6 in three states Native (N), denatured by guanidine HCl (D), and denatured and reduced by 0.1 M DTT (R).

Chapter 9 is devoted to resonance energy transfer and its applications in the cases of donor-acceptor pairs, assemblies of donor and acceptor, and assemblies of like fluorophores. In particular, the use of resonance energy transfer as a spectroscopic ruler , i.e. for the estimation of distances and distance distributions, is presented. 

L channels. We assume that in all channels a situation can be prepared as illustrated in Figure 1.30, at the beginning of the experiment. Immediately after all dye molecules have entered the zeolite channels, the maximum energy transfer is observed because the donor-to-acceptor distance is short. The donor-to-acceptor distance increases, and hence the energy-transfer rate decreases, when the molecules diffuse deeper into the channels. From this, the following relation for diffusion kinetics is found under the condition that the initial distributions of the donors and the acceptors are the same, [)py+ p x+, denoted as p°. Experimental details can be found in [77],... 

Donor and acceptors can be covalently linked using a chemical spacer. Assume that we have the same D-A pair Eosin-Phenol Red. In this case we will have a mixture of two linked donor-acceptor species (Eosin-Phenol Red protonated and Eosin-Phenol Red unprotonated) characterized by the same distance distribution and different critical distances (ftoi = 28.3 A and Rm = 52.5 A) for FRET. A distribution of D- to -A distances will be present because the linker is typically flexible. The fractional intensity of the first species at time t = 0 is gi and that of the second species is (1 - 1). The fractional intensity at time t = 0 is equal to fractional concentration of each form, which can be in case of pH indicator (Phenol Red) calculated using Eq. (10.31). The donor fluorescence intensity decay of the mixture is described by the equation... 

J. R. Lakowicz, R. F. Steiner, and I. Gryczynski, The distribution of donor-to-acceptor distances in troponin C from frequency-domain fluorometry, Biophys. J. 49, 106a (1986). 

The shape of the I(t) curves of the donor centers carries very useful information about the nature of the interaction process. Assuming that the acceptors A are randomly distributed at various distances from the donor centers D, the Japanese scientists Inokuti and Hirayama (1965) investigated the shape of the donor decay-time curves for the different multipolar interactions and also for the exchange interaction. 

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