The measurement of the efficiency of Förster long-range resonance energy transfer between donor (D) and acceptor (A) luminophores attached to the same macromolecular substrate can be used to estimate the D-A separation, R. If the D and A transition dipoles sample all orientations with respect to the substrate (the isotropic condition) in a time short compared with the transfer time (the dynamic averaging condition), the average orientation factor less than K2 greater than is 2/3. If the isotropic condition is not satisfied but the dynamic averaging condition is, upper and lower bounds for less than K2 greater than, and thus R, may be obtained from observed D and A depolarizations, and these limits may be further narrowed if the transfer depolarization is also known. This paper offers experimental protocols for obtaining this reorientational information and presents contour plots of less than K2 greater than min and less than K2 greater than max as functions of generally observable depolarizations. This permits an uncertainty to be assigned to the determined value of R. The details of the D and A reoreintational process need not be known, but the orientational distributions are assumed to have at least approximate axial symmetry with respect to a stationary substrate. Average depolarization factors are derived for various orientational distribution functions that demonstrate the effects of various mechanisms for reorientation of the luminophores. It is shown that in general the static averaging regime does not lend itself to determinations of R.

SynopsisThe dependence of Forster long-range resonance energy transfer efficiency on the orientational freedom of donor D and acceptor A molecules attached to a macromolecular substrate is examined. The usefulness of polarized emission measurements in determining the mutual orientation as well as the degree of orientational freedom of D and A and thereby deriving maximum and minimum values for the D-A separation from the transfer efficiency is demonstrated. INTRODUCTlONAn exact theory of resonance transfer of electronic excitation energy between isolated donor D and acceptor A molecules of suitable spectroscopic properties was first presented almost a quarter of a century ago by Forster.'V2 The theory was immediately successfully applied to the phenomenon of quenching of donor fluorescence in mixed solutions of donor and acceptor dyestuffs3 and to that of concentration depolarization of viscous solutions of a single d y e~t u f f ,~ and has enjoyed continued success and widespread use in these5s6 and somewhat more s p e~i a l i z e d~-~~ systems. However, it was not until considerably later that the predicted dependence of transfer rate on the inverse sixth power of the intramolecular D-A separation R was demonstrated, in several laboratories, for isolated D-A pairs covalently attached to a neutral substrate molecule. [11][12][13][14] Only then did the practicability of using the energy transfer method as a "spectroscopic ruler"12 for the determination of intramolecular separations of the order of the dimensions of macromolecules (up to several tens of angstroms), which are of interest to physical organic chemists and more especially polymer chemists and biochemists, become widely recognized. Thus, the last few years have seen an increasing literature on the application of this technique to the determination of the topology of, in particular, biopolym e r~. l~-~* In almost all this work a major difficulty in interpretation has presented itself in that the mutual orientation of the D-A pair, which could * Present address:

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The ultraviolet-absorption spectrum of DNA closely resembles that of a mixture of its constituent nucleotidesl apart from the well-known hypochromism.2' I On the other hand, the emission spectra of DNA and its constituent nucleotides are qualitatively different.The phosphorescence from the excited triplet state of DNA has been shown4' to originate from thymine residues which after excitation have transferred a proton across the hydrogen bond to adenine.In this paper we present the results of a study of the fluorescence at 850K from the excited singlet states of dinucleotides, synthetic polynucleotides, and DNA. We show that the fluorescence of stacked dinucleotides originates in excimer states and differs considerably from the fluorescence of the component nucleotides. Furthermore, the emission from polynucleotides resembles that of the dinucleotide excimers and not that of the isolated mononucleotides.F6rster and Kasper6 showed that neighboring aromatic molecules in their excited singlet state may form an excited dimer or excimer. At the excimer equilibrium distance, the molecules attract each other in the excited state but repel each other in the ground state. Therefore,7 excimer 'fluorescence is red-shifted from the monomers and shows no vibrational fine structure, while the optical absorption remains the same as in monomers. Furthermore, because the energy minimum of the excimer is created by a covalent6-'0 interaction between the 7r-electron systems, the stacking of the aromatic molecules increases the probability of excimer formation. Excimers have been observed in many different solutes and solutions,7 in crystals of stacked aromatic molecules,8 11 and in solutes in glasses.12The dinucleotides 3'-5' ApG, GpC, UpA, CpC, and 2'-5' ApC were obtained from Gallard-Schlesinger Chemical Corp. and used without further purification. Synthetic TpT (deoxy) was obtained'3 from Dr. T. M. Jacob, and TpTp from Dr. F. J. Bollum. A chromatographic analysis of these samples in the isopropanolammonia-water system showed less than 2 per cent impurities in ApG, UpA, CpC, ApC, and TpT. Random poly A2U with s = 4.2, synthesized with M. lysodeikticus polymerase, was a gift from Professor J. Fresco. Poly d(AT) was extracted from the crab Cancer borealis by the method of Davidson et al.'4 The calf thymus DNA was from Worthington Biochemical Corp. (Freehold, N.J.) batch #606 and was dialyzed before use. Poly dA: dT, poly dG: dC, and poly rG:rC were prepared by Professor M. Chamberlin using E. coli polymerase enzymes as previously described. 15 The DNA from spX174 was generously supplied by Professor R. Sinsheimer.The optical emission was measured at 85°K with a spectrophosphorograph using Bausch and Lomb 0.5-m grating monochromators for excitation and emission. The experimental curves shown are not corrected for the wavelength dependence of the combined efficiency of the EMI 9558QC photomultiplier and the emission monochromator, but this varied by less than 20 per cent over the wavelength 1015

The fluorescence spectra and quantum yields of trytophan (TRP) and several tryptophan derivatives in water and a polar glass have been measured over wide temperature ranges. For TRP, the wavelength of maximum emission shifts from 310 nm at 80°K to 355 nm at room temperature with almost all of the red shift occurring between 170° and 230°K, which is the temperature range where the glass softens. The successively more red-shifted spectra have no isoemissive wavelength, which supports the view that reorientation of several solvent molecules in the solvent shell of the excited TRP molecule and not a 1:1 exciplex is responsible for the red shift. The quantum yield remains constant until a temperature is reached at which solvent reorientation is virtually complete. Above that temperature, the quenching of the 355-nm emission can be fitted with a nonradiative de-excitation having an activation energy of 7 kcal/mole. A model for these spectral changes and quenching mechanism will be offered. In deuterated solvents, a large isotope effect of fluorescence yield of TRP has been reported. This effect is clearly not caused by proton transfer in the excited state since it is found to be virtually the same for TRP and 1-Me-TRP. At temperatures below those at which solvent reorientation occurs, the isotope effect vanishes, and above them it approaches an asymptotic value, the quenching activation energy being independent of the isotopic constitution of the solvent. The fluorescence of most proteins and hormones originates in their tryptophan residues. The quantum yields, isotope effects, and emission spectra of such polypeptides are compared with the corresponding parameters for solvated TRP.

Binding energies and structure of transition metal negative ionsParamagnetic ions in water shorten the spin-lattice relaxation time Tl of the water protons. The effectiveness with which the relaxation takes place depends not only on the ion concentration, but also on the environment of the paramagnetic ion. In some cases where the paramagnetic ion is bound to a large molecule such as DNA, it shortens the proton relaxation time to a greater extent than when it is in solution. By measuring Tl by a pulsed nuclear magnetic resonance method, we have studied the binding of transition metal ions to DNA. We have obtained estimates for the number of available binding sites as well as information on the type of site which the various ions are bound to.

The lateral mobility of pyrenyl phospholipid probes in dimyristoylphosphatidylcholine (DMPC) vesicles was determined from the dependence of the pyrene monomeric and excimeric fluorescence yields on the molar probe ratio. The analysis of the experimental data makes use of the milling crowd model for two-dimensional diffusivity and the computer simulated random walks of probes in an array of lipids. The fluorescence yields for 1-palmitoyl-2-(1'-pyrenedecanoyl)phosphatidylcholine (py10PC) in DMPC bilayers are well fitted by the model both below and above the fluid-gel phase transition temperature (Tc) and permit the evaluation of the probe diffusion rate (f), which is the frequency with which probes take random steps of length L, the host membrane lipid-lipid spacing. The lateral diffusion coefficient is then obtained from the relationship D = fL2/4. In passing through the fluid-gel phase transition of DMPC (Tc = 24 degrees C), the lateral mobility of py10PC determined in this way decrease only moderately, while D measured by fluorescence photobleaching recovery (FPR) experiments is lowered by two or more orders of magnitude in gel phase. This difference in gel phase diffusivities is discussed and considered to be related either to (a) the diffusion length in FPR experiments being about a micrometer or over 100 times greater than that of excimeric probes (approximately 1 nm), or (b) to nonrandomicity in the distribution of the pyrenyl probes in gel phase DMPC. At 35 degrees C, in fluid DMPC vesicles, the diffusion rate is f = 1.8 x 10(8) s-1, corresponding to D = 29 microns2 s-1, which is about three times larger than the value obtained in FPR experiments. The activation energy for lateral diffusion in fluid DMPC was determined to be 8.0 kcal/mol.