Energy transfer, resonance

When two molecular species reside in proximity to each other and one is excited, the excitation energy can be transferred to the other. In the simplest experimental observation of this kind the emission from the originally excited species (donor) decreases, and emission from the other species (acceptor) increases with increasing acceptor concentration. This phenomenon, first analyzed theoretically by Forster, plays a central role in several fundamental processes such as sensitization and 

This statement is not obvious, but can be shown to be correct. Th Forster, Ann. Phys. 2, 55 (1948). 

In what follows we derive the Forster expression for the rate of electronic energy transfer between two chromophore molecules. We consider two such molecules, donor D and acceptor A, each represented by its ground and excited electronic states and the associated vibrational manifolds Id, 2D,/j ° ) forthe ground and excited state manifolds of molecule D and 1a, 2a, 

The distance between the two molecules D and A is large enough so that the relevant intermolecular coupling is electrostatic. Moreover, the intermolecular distance is assumed large relative to the spatial extent of the individual molecular charge distributions. Under these circumstances the dominant electrostatic interaction is dipole-dipole coupling 

In the absence of this coupling the two-molecule Hamiltonian is the sum of Hamiltonians of the individual chromophores. Consequently, the zero-order wavefunctions are products of terms associated with the individual molecules, for example, 

Furthermore the Bom-Oppenheimer approximation is used to describe the wavefunctions of the individual molecules, that is. 

Forster (1959) classifies the qualitative features based on which one can distinguish the various modes of energy transfer. Mainly, only collisional transfer depends on solvent viscosity (vide infra), whereas complexing between the donor and acceptor changes the absorption spectrum. On the other hand, the sensitizer lifetime decreases for the long-range resonant transfer process, whereas it should be unchanged for the trivial process. 

Developed into a power series in R 1, where R is the intermolecular separation, H exhibits the dipole-dipole, dipole-quadrupole terms in increasing order. When nonvanishing, the dipole-dipole term is the most important, leading to the Forster process. When the dipole transition is forbidden, higher-order transitions come into play (Dexter, 1953). For the Forster process, H is well known, but 0. and 0, are still not known accurately enough to make an a priori calculation with Eq. (4.2). Instead, Forster (1947) makes a simplification based on the relative slowness of the transfer process. Under this condition, energy is transferred between molecules that are thermally equilibriated. The transfer rate then contains the same combination of Franck-Condon factors and vibrational distribution as are involved in the vibrionic transitions for the emission of the donor and the adsorptions of the acceptor. Forster (1947) thus obtains 

Equation (4.3) gives the inverse sixth power law of Forster, 

Forster (1968) points out that R0 is independent of donor radiative lifetime it only depends on the quantum efficiency of its emission. Thus, transfer from the donor triplet state is not forbidden. The slow rate of transfer is partially offset by its long lifetime. The importance of Eq. (4.4) is that it allows calculation in terms of experimentally measured quantities. For a large class of donor-acceptor pairs in inert solvents, Forster reports Rg values in the range 50-100 A. On the other hand, for scintillators such as PPO (diphenyl-2,5-oxazole), pT (p-terphenyl), and DPH (diphenyl hexatriene) in the solvents benzene, toluene, and p-xylene, Voltz et al. (1966) have reported Rg values in the range 15-20 A. Whatever the value of R0 is, it is clear that a moderate red shift of the acceptor spectrum with respect to that of the donor is favorable for resonant energy transfer. 

The total coulombic interaction includes dipole—dipole, dipole— quadrupole and higher multipole interactions. Forster [164] in a quantum mechanical treatment of resonance energy transfer which takes place between two well-separated molecules has considered only dipole—dipole interaction. A quantitative treatment leads to the following equation for the transfer rate coefficient [164]  

K is an orientation factor which for a random distribution equalsy/2l.  

It is important to point out that the rate cofficient for the energy transfer is a function of the overlap of the emission spectrum of the donor 

An experimental value of R0 can be obtained by plotting f as a function of the logarithm of the acceptor concentration and fitting the theoretical curve calculated according to Forster s theory to the experimental results. An experimental value larger than the calculated one may be considered as evidence for migration of excitation prior to the transfer. Agreement was obtained between the experimental results and Forster s theory for the system polystyrene—tetraphenylbutadiene [165]. 

When donor and acceptor molecules are very close together, and the resonance condition is fulfilled, exchange interaction that results in electronic energy transfer can occur. Dexter [166] has given the following equation for the rate coefficient of transfer. 

The fidd of RET is large and com dex. The dieory is different for dcmors and accqitors that are covalenOy linked, firee in sdution, or ccntained in die restricted geometries of membranes or DNA. AdditicmaHy, dqiend-ing on the donor lifetime, diffusion can increase the extent of energy transfer beyond that predicted by Eq. [1.12]. 

Consider two identical molecules for which the wavefunctions of the ground states are (piJCia nd (f 2aZ2m where (f and x represent electronic and nuclear wavefunctions, respectively, and subscripts 1 and 2 denote the molecules. Suppose, first, that the two molecules do not interact. The Hamiltonian for the dimer then is just the sum of the Hamiltonians for the individual molecules  

If each of the individual molecules has energy Ea in the ground state, the energy of the dimer s ground state is simply 2Ea. 

If either molecule can be raised to an excited state (piXb with energy Ef, there are two possible excited states of the dimer  

As long as the two molecules do not interact, both y/i and y/2 are eigenfunctions of the total Hamiltonian, and both states will have the same energy, Ea+Ei In addition. 

This means that states iffi and 1 2 are stationary states the excitation has no tendency to hop from one molecule to the other. 

---

Juzeliunas G and Andrews D L 2000 Quantum electrodynamics of resonance energy transfer Adv. Chem. Rhys. 112 357-410... 

Deniz A A, Dahan M, Grunwell J R, Ha T, Faulhaber A E, Chemla D S, Weiss S and Schultz P G 1999 Single-pair fluorescence resonance energy transfer on freely diffusing molecules observation of Forster distance dependence and subpopulations Proc. Natl Acad. Sc/. USA 96 3670-5... 

With tlie development of femtosecond laser teclmology it has become possible to observe in resonance energy transfer some apparent manifestations of tire coupling between nuclear and electronic motions. For example in photosyntlietic preparations such as light-harvesting antennae and reaction centres [32, 46, 47 and 49] such observations are believed to result eitlier from oscillations between tire coupled excitonic levels of dimers (generally multimers), or tire nuclear motions of tire cliromophores. This is a subject tliat is still very much open to debate, and for extensive discussion we refer tire reader for example to [46, 47, 50, 51 and 55]. A simplified view of tire subject can nonetlieless be obtained from tire following semiclassical picture. 

Juzeliunas G and Andrews D L 1999 Unified theory of radiative and radiationless energy transfer Resonance Energy Transfer ed D L Andrews and A A Demidov (New York Wiley) pp 65-107... 

Mass resonant analyzer. A mass analyzer for mass-dependent resonant-energy transfer and measurement of the resonance frequency, power, or ion current of the resonant ions. 

C. Resonance energy transfer. The excitation energy can be transferred by resonance energy transfer, a radiationless process, to a neighboring molecule if their energy level difference corresponds to the quantum of excitation energy. In this process, the quantum, or so-called exciton, is transferred. 

F statistic, 239, 241 False negatives, 152—153 False positives, 152—153 Fenoximone, 188 First-order kinetics, 167 Fluorescence resonance energy transfer, 182... 

Fig. 4.1.17 Graphic illustration of Forster-type resonance energy transfer from aequorin to Aequorea GFP. In the vessel at left, a solution contains the molecules of aequorin and GFP randomly distributed in a low ionic strength buffer. The vessel at right contains a solution identical with the left, except that it contains some particles of DEAE cellulose. In the solution at right, the molecules of aequorin and GFP are coadsorbed on the surface of DEAE particles. Upon an addition of Ca2+, the solution at left emits blue light from aequorin (Xmax 465 nm), and the solution at right emits green light from GFP (Xmax 509 nm).

Heim, R., and Tsien, R. Y. (1996). Engineering green fluorescent protein for improved brightness, longer wavelengths and fluorescence resonance energy transfer. Curr. Biol. 6 178-182. 

Rothschild W. G. Vibrational resonance energy transfer and dephasing in liquid nitrogen near its boiling point molecular computations, J. Chem. Phys. 65, 2958-61 (1976). 

More recently, the method of scanning near-field optical microscopy (SNOM) has been applied to LB films of phospholipids and has revealed submicron-domain structures [55-59]. The method involves scanning a fiber-optic tip over a surface in much the same way an AFM tip is scanned over a surface. In principle, other optical experiments could be combined with the SNOM, snch as resonance energy transfer, time-resolved flnorescence, and surface plasmon resonance. It is likely that spectroscopic investigation of snbmicron domains in LB films nsing these principles will be pnrsned extensively. 

Isik N, Hereld D, Jin T (2008) Fluorescence resonance energy transfer imaging reveals that chemokine-binding modulates heterodimers of CXCR4 and CCR5 receptors. PLoS ONE... 

Percherancier Y, Berchiche YA, Slight 1, Volkmer-Engert R, Tamamura H, Fujii N, Bouvier M, Heveker N (2005) Bioluminescence resonance energy transfer reveals hgand-induced conformational changes in CXCR4 homo- and heterodimers. J Biol Chem 280 9895-9903... 

Toth PT, Ren D, Miller RJ (2004) Regulation of CXCR4 receptor dimerization by the chemokine SDF-lalpha and the HIV-1 coat protein gpl20 a fluorescence resonance energy transfer (FRET) study. J Pharmacol Exp Ther 310 8-17 Tran PB, Miller RJ (2005) HIV-1, chemokines and neurogenesis. Neurotox Res 8 149-158 Tran PB, Ren D, Veldhouse TJ, Miller RJ (2004) Chemokine receptors are expressed widely by embryonic and adult neural progenitor cells. J Neurosci Res 76 20-34... 

The intramolecular distances measured at room temperature with the AEDANS FITC pair were similar in the Ca2Ei and E2V states [297]. Ca and lanthanides are expected to stabilize the Ej conformation of the Ca -ATPase, since they induce a similar crystal form of Ca -ATPase [119,157] and have similar effects on the tryptophan fluorescence [151] and on the trypsin sensitivity of Ca -ATPase [119,120]. It is also likely that the vanadate-stabilized E2V state is similar to the p2 P state stabilized by Pi [418]. Therefore the absence of significant difference in the resonance energy transfer distances between the two states implies that the structural differences between the two conformations at sites recorded by currently available probes, fall within the considerable error of resonance energy transfer measurements. Even if these distances would vary by as much as 5 A the difference between the two conformations could not be established reliably. 

Ag Antigen FRET Forster resonance energy transfer... 

We have been developing methods to prepare and characterize supported attune catalysts nsing readily available commercial snpports. One potential means of depositing amines on oxide surfaces is shown in Scheme 38.1, in which the micelle s role is to space the amines on the snrface. Cnrrent work is directed towards characterizing these samples, particularly applying flnorescence resonance energy transfer (FRET) techniques. 

When the proteins are in close proximity the Europium-cryptate emission can be absorbed by the acceptor (such as allophycocyanin [APC], or XL) which emits at a higher wavelength. When the two proteins are far apart, no fluorescence resonance energy transfer (FRET) occurs. 

---