Perrin equation

MEK diffusion is too slow to make a significant contribution to quenching in mixtures rich in PMMA. Quenching occurs only if a MEK molecule is close enough to a Phe group at the moment it absorbs light. Static quenching is described by the Perrin equation (26-27) ... 

The Perrin equation 48 describes the relationship between the rotational correlational time, 0, and the fluorescence lifetime, r, for steady-state measurements ... 

If the aromatic group is bound tightly within the protein molecule, then one may obtain information on the rotational diffusion of the whole molecule from fluorescence polarization studies. Such investigations, which were started by Weber,(68) were widely popular in the 1960s and 1970s. Correlation times D of macromolecule rotations were determined according to the Perrin equation ... 

The rx term is the anisotropy at times long compared to the fluorescence lifetime, whereas in Eq. (5.9) 2 will be long. If there is no rM, then Eq. (5.8) reduces to the familiar Perrin equation for an isotropic rotator. Earlier, some confusion existed in this field since it was not recognized that an rro term was required for the case of membrane lipid bilayers. For the most part, time-resolved anisotropy measurements have a short rotational correlation time and an term. However, it has been recognized that a more adequate description may be to use two rotational correlation times, where the second may be quite long but not infinite as the rm implies/35 36 ... 

Although the calculation of order parameters from r has become an area of intense interest, the current position is that it is better to quote steady-steady anisotropy data in terms of rs as well as possibly calculating an order parameter if this is useful, whereas calculations of microviscosities or rotational correlation times (from the Perrin equation) should be avoided. 

W. van der Meer, R. B. van Hoeven, and W. J. van Blitterswijk, Steady-state fluorescence polarization data in membranes. Resolution into physical parameters by an extended Perrin equation for restricted rotation of fluorophores, Biochim. Biophys. Acta 854, 38-44 (1986). 

Selected entries from Methods in Enzymology [vol, page(s)] Additive properties of polarization, 246, 286 angle-resolved, assessment of peroxidation effects on membranes, 233, 274-275, 281-283, 287-288 binding isotherm construction, 246, 287-288 effect of inner filter effects, 246, 288 incoherent systems, 246, 263-264 orientational averaging, 246, 265, 269-270 Perrin equation, 246, 284-285 polarization of emission, 246, 284 rotational diffusion, 246, 9, 260 time-resolved, assessment of peroxidation effects on membranes, 233, 274, 283-285, 285-287. 

The Perrin equation of static quenching is given in logarithmic form as... 

The tunneling distance, Rq, for various reactions of this type was obtained by fitting the static quenching of Ru(II)(LL)3 by various concentrations of D to the Perrin equation. R was found to depend on reaction exothermicity and to reach 20 A for the reaction between Ru(II)(ester)3 and TMPD (ester = 4,4/-diisopropyl ester 2,2 bipyridine). 

The emission intensity follows the so-called Perrin equation. 

FPA results obtained at different salt conditions may not be directly comparable because the fluorescence properties of 6-MI, including the lifetime (t), are salt dependent. The salt dependence of the FPA of a helix in a complex construct should thereby be normalized relative to the FPA of a short control duplex of the same sequence of the targeted helix to account for salt effects on the local environment of the 6-MI fluorophore. The normalization ratio, rnoml, can be calculated as the ratio between the apparent rotational correlation time, 9, of the constructs and the control duplex only, rnomi = construct/ control- is related to the rate of anisotropy decay, with larger 9 associated with higher anisotropy. If the basic Perrin equation for a sphere (Eq. (14.3)) is used to simplify calculation, then... 

The data points of Cs+-H above a loading of 2% of the CEC can also be fitted with the Perrin equation. The resulting effective surface area (Table III) is similar to that of K+-H. As there are only four data points, the value of the effective surface area is subject to some uncertainty. But, qualitatively, as for K+-H, proflavine probes only part of the surface due to aggregation. 

These values can then be used in conjunction with the Perrin equation [19] to estimate the rate of rotation of a spherical fluorescent molecule, Rs, as follows ... 

Fluorescence polarization cannot attain the +1 theoretical limits for maximum beam polarization owing to the nature of the absorption and emission processes, which usually correspond to electric dipole transitions. Although the excitation with linearly polarized radiation favours certain transition dipole orientations (hence certain fluorophore orientations, and the so-called photoselection process occurs), a fairly broad angular distribution is still obtained, the same happening afterwards with the angular distribution of the radiation of an electric dipole. The result being that, in the absence of fluorophore rotation and other depolarization processes, the polarization obeys the Lev shin-Perrin equation,... 

Researches on theoretical topics have not been reported very extensively. A few papers are mentioned here and some others at appropriate points later in the article. Weber has re-examined the famous Perrin equation for quantifying the rotational depolarization of fluorescence. The arguments presented in the paper are applied to the temperature dependence of the local motions of tyrosine and tryptophan residues observed in proteins. 

The Stern—Volmer and Perrin equations, (v) and (vi), both allow a quantitative characterization of the efficiency of non-radiative energy transfers. They are useful for the comparison of various donoi -acceptor systems, although they provide no information concerning the nature of the excited state involved and the mechanism of the energy transfer process. More appropriate theories have been established to describe non-radiative energy transfers that occur when there is close resonance between the initial and final states. 

The departure of the Perrin equation from linearity may be considered more generally. A curvature convex to the T/rj axis may result from the complete kinetic dissociation of rigid units or from increased rotational freedom within the polypeptide chain 26, 32, 65, 66, 68). A curvature concave to the T/rj axis may occur whenever more than one rotational relaxation time is present and may be detected when the two rotational relaxation times differ by more than fivefold 65). The initial slope, for small values of T/tj, depends upon the harmonic mean of the relaxation times involved and is determined practically by the shorter one. Such curvature has been reported in studies with DNS-labeled polyvinylamine and poly-p-amino-styrene 22, 33, 64). By applying a theory which deals with the case of an emitting group which has only one degree of rotational freedom, Gottlieb and Wahl 33) concluded that the rotations activated by temperature in... 

---