Energy transfer orientational factor

The K factors in (C3.4.1) represent another very important facet of tire energy transfer [4, H]. These factors depend on tire orientations of tire donor and acceptor. For certain orientations tliey can reduce tire rate of energy transfer to zero—for otliers tliey effect an enhancement of tire energy transfer to its maximum possible rate. Figure C3.4.1 exhibits tire angles which define tire mutual orientation of a donor and acceptor pair in tenns of Arose angles the orientation factors and are given by [6, 7]... 

Dale, R., Eisinger, J. and Blumberg, W. (1979). The orientational freedom of molecular probes. The orientation factor in intramolecular energy transfer. Biophys. J. 26, 161-94. 

Thus, E is defined as the product of the energy transfer rate constant, ku and the fluorescence lifetime, xDA, of the donor experiencing quenching by the acceptor. The other quantities in Eq. (12.1) are the DA separation, rDA the DA overlap integral, / the refractive index of the transfer medium, n the orientation factor, k2 the normalized (to unit area) donor emission spectrum, (2) the acceptor extinction coefficient, eA(k) and the unperturbed donor quantum yield, QD. 

The optimal enhancement effect is observed when the localized surface plasmon resonance is tuned to the emission wavelength of a locally situated fluorophore [86]. This is consistent with the model suggesting a greatly increased efficiency for energy transfer from fluorophores to surface plasmons [78]. Since resonance energy transfer is involved, the important factors affecting the intensity of fluorescence emission must also be the orientation of the dye dipole moments relative to the... 

This section deals with a single donor-acceptor distance. Let us consider first the case where the donor and acceptor can freely rotate at a rate higher than the energy transfer rate, so that the orientation factor k2 can be taken as 2/3 (isotropic dynamic average). The donor-acceptor distance can then be determined by steady-state measurements via the value of the transfer efficiency (Eq. 9.3) ... 

Dale R. E., Eisinger J. and Blumberg W. E. (1975) The Orientational Freedom of Molecular Probes. The Orientation Factor in Intramolecular Energy Transfer, Biophys. J. 26, 161-194. 

Wu P. and Brand L. (1992) Orientation Factor in Steady-State and Time-Resolved Resonance Energy Transfer Measurements, Biochemistry 31, 7939-7947. 

With the exception of the orientation factor, all the parameters in this equation may be obtained within reasonable error by direct experimental measurement or by estimation. The problem of setting reasonable values for k2, which may vary from 0 to 4 for orientations in which the dipole moments are orthogonal or parallel, respectively, is nontrivial. A value of , which is an unweighted average over all orientations, is often used. Dale et al.(53) have examined this problem in great detail and have shown that a k2 value of is never justified for energy transfer in macromolecules because it is impossible for the donors and acceptors to achieve a truly isotropic distribution. They do provide an experimental approach, using polarized emission spectroscopy, to estimate the relative freedom of motion for the donor and acceptor that allows reasonable limits to be set for k2. 

An important parameter required for the calculation of R0 is the orientation factor k2 which takes into account the angular dependence of dipole-dipole energy transfer, as described by eq 22... 

The angular dependence of l(r) in eqn. (63) has not been discussed very widely. However, the pre-exponential factor, A, will depend on the mutual orientation of donor and acceptor molecules. For instance, in aromatic molecules the sign of the wave function changes as the molecular plane is crossed and, consequently, energy transfer between an aromatic donor (acceptor) and an acceptor (donor) in its molecular plane should be slower than for other orientations. Adamczyk and Phillips [182] have discussed this further (Sect. 3.5). 

Forster149 calculated that the rate of energy transfer kt should be proportional to the rate of fluorescence fcf, to an orientation factor X2, to the spectral overlap interval /, to the inverse fourth power of the refractive index n, and to the inverse sixth power of the distance r separating the two chromophores. 

Equation (18) may be derived in a manner similar to that described above for vibration-vibration energy transfer, with the difference that the product of the squared matrix elements of the two vibrations concerned, appears in the expression for transition probability. Since both molecules require suitable orientation for vibrational exchange, for two diatomic molecules the steric factor is usually taken to be ( )2. If AE - 0 (exact resonance), eqn. (18) is no longer valid and the following equation may be employed... 

Dosremedios CG, Moens PDJ. Fluorescence resonance energy-transfer spectroscopy is arehable ruler for measuring structural changes in proteins. Dispelling the problem of the unknown orientation factor. Journal of Structural Biology 1995, 115, 175-185. 

The energy E in Equation 6.86 has been replaced by the frequency v (in cm-1), FA E) has been replaced by the extinction coefficient sA v) of the acceptor, (pp is the fluorescence quantum yield, and k2 2/3 is an orientation factor. An expression similar to Equation 6.87 was deduced by Foster using a simpler mechanism of the energy transfer.41 The rate constant deduced from the dipole-quadmpole interaction is given in Equation 6.88, where a 1.266 and other parameters and functions are as defined above. 

Here, / is in amu A2, M is in amu, d is in A, a is in A-1, and v is in cm-1. The second exponential term results from a correction for the change in velocity due to the increase in rotational energy. The steric factor, Z0, is introduced as in V-T theory to account for noncolinear collision orientations. Moore tested this equation, along with two other more approximate forms, on a series of molecules having one or more H (or D) atoms. He also examined V-R transfer for collisions of dissimilar molecules, such as C02-CH4, C12-HC1, and CH4-Ar. Twenty-five different molecules having small moments of inertia were fitted with a single curve represented by equation (71) using a = 2.94 A-1 and Z0 = 5.0, with at least qualitative success. 

Wu P, Brand L. Orientation factor in steady-state and time-resolved resonance energy transfer measurements. Biochemistry 1992 31 7939-7947. 

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