Fluorescence Anisotropies

Anisotropy measurements are commonly used in the biochemical applications of fluorescence. Anisotropy measurements provide information on the size and shape of proteins or the rigidity of various molecular envinm-ments. Anisotropy measurements have been used to measure protein-protein associati ms and fluidity of mrai ranes and for Immunoassays c nunMtHis substances. 

Several phenomena can decrease the measured anisotropy to values lower than the maximum theoretical values. The most common cause is rotational diffusion. Such diffusion occurs during the lifetime of the excited state and displaces the emission dipole of the fluorophOTe. Measurement of this parameter provides information about the relative angular displacement of the fluorophore between the times of absorption and emission. In fluid solution, most fluorophores rotate extensively in 50-100 ps. nce, the molecules can rotate many times during the 1 - to 10-ns excited-state lifetime, and the orientation of the polarized emission is randomized. For this reason, fluorophores in ueous nonviscous solution typically display anisotropies near zero. Transfer of excitation between fluorophores also results in decreased anisotrc ies. 

The effects of rotational diffusion can be decreased if the fluorophore is bound to a macromolecule. For instance, it is known that the rotational correlation time for the protein human serum albumin (HSA) is near 50 ns. Suppose HSA is covalently labeled with a fluorophore whose lifetime is 10 ns. Assuming no other processes result in loss of anisot ropy, the expected anisotropy is given by the Perrin equation  

15 900 cm bottom the anisotropy of fluorescence excitation measured at (a) 293 K and (b) 7.5 K. (C) Time-domain fluorescence (top) and anisotropy decays measured for porphycene in glycerol at 293 K and in ERA glass at 77 K. 

The polarization properties of light in combination with fluorescence can be used as a powerful tool for determining motional properties of membranes. This is possible due to the fact that the time scale of interest for membrane lipids falls within the time frame of the fluorescence decay phenomena (0-100+ ns). This, coupled with high sensitivity, low perturbing properties of fluorescent probes, and the large number of available probes, makes the fluorescence approach the method of choice for membrane motional studies. 

The motional characteristics of interest are typically those governed by the phospholipid fatty acyl chains and head-group region and the neutral lipid or protein components of membranes. Rotational motion can be subdivided into a structural component, the order or degree of orientational constraint, 

The first decision to be made in designing an experiment to measure the motional properties of membrane lipids concerns the type of probe molecule. Too often, this choice is made from the point of view of convenience or tradition rather than suitability, although there is now a considerable range of suitable fluorophores from which to choose. The second consideration is the type of measurement to be made. The most detailed and complete motional information is obtained from a time-resolved fluorescence anisotropy measurement which is able to separate the structural or orientational aspects from the dynamic aspects of fluorophore motion. Steady-state anisotropy measurements, which are much easier to perform, provide a more limited physical parameter relating to both of these aspects. 

If the fluorescence of a sample is exeited by linearly polarised light the fluores-eenee is partially polarised (see Fig. 5.7 and Fig. 5.8). The fluorescence anisotropy, r, is defined as 

The fluoreseenee anisotropy deeays with the rotational relaxation time, The relaxation time is an indieator of the size of the dissolved molecules, dye-solvent interaetions, aggregation states, and the binding state to proteins [102, 308, 549]. Typieal rotational relaxation times of free fluorophores in water are in the range from 50 to 500 ps. 

Time-resolved measurements of anisotropy are difficult because I (t) -1Jt) is small eompared to the fluoreseenee components 7 (t)and7/t) themselves. Ip(t) and IJt) are deteeted with different efficiency, especially if a monochromator is used. The effect depends on the angle of the grating, i.e. on the wavelength, and on the slit width and the beam geometry. Anisotropy measurements therefore require calibration of the efficiency of the I (t) and7/t) detection channels. The relative efficiency, EJE, of the Ip and f detection channels is the G factor  

There are two ways to determine the G factor [308, 389]. The first one is to ran a measurement with horizontal polarisation of the excitation beam. For an angle of 90° between the optical axis of excitation and emission, the excited-state distribution is oriented towards the axis of observation. Consequently both channels measure equal perpendicular components. The ratio of the measured intensities represents the G factor. 

The second way to obtain G is tail matching . A sample with a depolarisation time substantially shorter than the fluorescence lifetime is measured. The G factor is obtained from the intensities in the later parts of the decay curves. The advantage of tail matching is that it can be used also for optical systems with excitation and detection along the same optical axis. 

The timescale of fluorescence emission is comparable to that of rotational diffusion of proteins and the timescale of segmental motions of protein domains or individual amino acid residues. The polarization or anisotropy of the emission provides a measure of these processes. Suppose a sample is excited with vertically polarized light (Fig. 11), and that the sample is viscous so that the fluorophores do not rotate during the lifetime of the excited state. Then the emission is polarized, usually also in the vertical direction. This polarization occurs because the polarized excitation selectively excites those fluorophores in the isotropic solution whose absorption 

A number of processes can result in the loss of anisotropy, the most common being rotational diffusion. Melittin is expected to have rotational correlation times near 2 and 8 nsec in the monomeric and tetrameric states, respectively. The effect of rotational diffusion on the anisotropy is described by the Perrin equation. 

When Tg and 6 are of simil u magnitude then the measured anisotropy is dependent upon the correlation time. Self-association of melittin is expected to increase its correlation time about four-fold. Since the lifetime of melittin fluo-resence is near 3 nsec we expect self-association to have a dramatic effect on the 

Anisotropy measurements are generally useful for measuring any process which increases or decreases the rate or extent of rotational diffusion. These processes include domain motions of immunoglobulins [21], denaturation of proteins [22] and the association of proteins with membranes [10]. Additionally, there are numerous applications of anisotropy measurements to membranes, in which the phase state and apparent fluidity are estimated from the anisotropy of probes which are bound to the membranes [23,24]. 

Huorescence anisotropy measurements and their applications are covered in Chapter 3. Plane polarized exciting light can be obtained by placing a Polaroid sheet or a Clan Taylor prism in front of the sample holder. The polarization or anisotropy of the fluorescence of the sample is then determined by placing another polarizer in front of EmM. The fluorescence that is polarized parallel, J, and perpendicular, to the excitation polarization direction is then measured. 

The denominator is proportional to the total fluorescence intensity, r is in the main a measure of the rotational motion or dynamics of the molecule, the latter being very useful in obtaining flexibility parameters of local segments of a macromolecule. 

Another point to be aware of is that holographic grating monochromators have a polarization anomaly known as the Wood s anomaly. At certain wavelengths the light is polarized entirely in the horizontal plane. This can cause important spectral artefacts such as false maxima or false shoulders. The anomaly can be avoided by using an excitation depolarizer and emission polarizer as described above. 

The size of a supramolecular object, as well as the orientational mobility of fluorophores can be determined by the measurement of fluorescence anisotropy. Energy transfer between identical fluorophores, also studied by fluorescence anisotropy, gives information on their relative distance. Fluorescence anisotropy can also be used to evaluate the state of association and the location of a fluorophore. Such measurements require the use of polarized light. 

In classical terms, radiation is represented by an electromagnetic wave. The polarization of plane-wave radiation is defined by the way the oscillating electric field evolves in space, in a plane perpendicular to the direction of propagation. The most general polarization state is called elliptical polarization [23], but for luminescence applications the subset of linear polarization states usually suffices. In these cases the electric field vector oscillates along a well defined direction in a plane perpendicular to the direction of propagation. This direction is the polarization direction, and radiation with this characteristic is said to be linearly polarized. 

If a beam of polarized radiation is passed through a linear polarizing filter, the intensity transmitted is a function of the angle between the filter polarization axis and the polarization direction of the beam. When the angle is zero, all radiation is transmitted (for an ideal filter there are always losses by reflection, background absorption, etc) when the angle is 90°, all radiation is blocked (absorbed) by the filter. 

For intermediate angles, the fraction of intensity transmitted is given by the square of the co-sine of the angle (Malus law). This is easily understood as the electric field vector can be decomposed in two orthogonal components, one along the polarization axis that is transmitted, and one along the perpendicular direction that is absorbed. Since intensity is proportional to the square of the electric field amplitude, the Malus law follows. 

Ordinary incoherent) light is seldom fully polarized, and a beam of depolarized (or natural) light can be considered a mixture, in equal amounts, of two (incoherent) beams polarized in arbitrary but orthogonal directions. 

FRAP was used initially to smdy the dynamics of lateral diffusion of lipids and proteins on cell surfaces [159-163]. It was combined with total internal reflection (Box 3.2 and Sect. 5.10) to study interactions of immunoglobulin fragments with planar bUayer membranes supported on glass surfaces [164] and binding of ligands to immobilized receptors [165]. Its applications expanded rapidly with the development of confocal microscopy (Sect. 5.10) and GFP tags [147,166-168], and now include components of the nucleus [169, 170], mitochonrial matrix [171], endoplasmic reticulum [172], and Golgi apparatus [173]. 

We now discuss the use of fluorescence to study rotational motions of molecules on a finer scale. Suppose we have a sample of randomly oriented molecules that we illuminate with linearly polarized light. Let the polarizarimi be parallel to the laboratory s z-axis. The light will selectively excite molecules that have their transition dipole (/ a) oriented parallel to this same axis. However, molecules with off-axis orientations also will be excited with a probability that depends oti cos 0, where 0 is the angle from the z-axis (Eqs. 4.8a—4.8c). 

The fraction of the molecules that have fii,a oriented with angle 0 between 0 and 0 + d0, and with (p between j) and p + d(p, where (p is the angle of rotation in the xy plane, is proportional to the area element sin0 d0 d p on the surface of a sphere of unit radius (Box 4.6). The fractiOTi of the excited molecules with this orientation, W (0,4 )d0d(p, is given by  

The integral in the denominator, which simply counts all of the molecules that are excited, evaluates to 4jt/3, so 

Now suppose that an excited molecule fluoresces. If absorption and emission involve the same electronic transitimi Pa Pb) the excited molecule does not 

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In certain situations involving coherently interacting pairs of transition dipoles, the initial fluorescence anisotropy value is expected to be larger tlian 0.4. As mdicated by the theory described by Wyime and Hochstrasser [, and by Knox and Gtilen [, ], the initial anisotropy expected for a pair of coupled dipoles oriented 90° apart, as an example. 

Cross A J and Fleming G R 1984 Analysis of time-resolved fluorescence anisotropy decays Blophys. J. 46 45-56... 

Matro A and Cina J A 1995 Theoretical study of time-resolved fluorescence anisotropy from coupled chromophore pairs J. Phys. Chem. 99 2568-82... 

Figure 6-24 a shows the angular dependence of the fluorescence anisotropy (H-V) in films made at temperatures of 22 °C (ca. 200 nm grain diameter - case A), 104°C... 

Viovy,J.L. and Monnerie, L. Fluorescence Anisotropy Technique Using Synchroton Radiation as a Powerful Means for Studying the Orientation Correlation Functions of Polymer Chains. Vol. 67, pp. 99—122. 

Figure 4.6 shows an apparatus for the fluorescence depolarization measurement. The linearly polarized excitation pulse from a mode-locked Ti-Sapphire laser illuminated a polymer brush sample through a microscope objective. The fluorescence from a specimen was collected by the same objective and input to a polarizing beam splitter to detect 7 and I by photomultipliers (PMTs). The photon signal from the PMT was fed to a time-correlated single photon counting electronics to obtain the time profiles of 7 and I simultaneously. The experimental data of the fluorescence anisotropy was fitted to a double exponential function. 

Figure 4.7 Fluorescence anisotropy decay curves for the PMMA brush swollen in benzene (filled circles) and the free PMMA chain in benzene solution at concentrations of 0.33 (triangles) and 2.9 X 10 g (open circles). The graft density of the brush is 0.46 chains nm . The solid curve indicates the instrument response function. Reproduced with permission from the American Chemical Society.

Figure 4.8 shows the fluorescence anisotropy decay curves for PMMA brushes with various graft densities swollen in benzene and acetonitrile. Benzene and acetonitrile are good and 0 solvents for PMMA. As clearly shown in this figure. 

Figure 4.9 Correlation time of the fluorescence anisotropy decay for the PMMA brush. The open and closed circles indicate the correlation times for the brush in acetonitrile and benzene, respectively.

Figure 4.12 Fluorescence image of PMMA brush layer (a) and schematic drawing of the brush chain (b). The dark region (a) corresponds to the substrate surface exposed by scratching off the brush layer. The filled and open circles indicate the points where the fluorescence anisotropy decay was acquired.

In practice, fluorescence anisotropy measurements are carried out as described by Larsson et al. [134] using ... 

Rotational dynamics of a fluorescent dye adsorbed at the interface provides useful information concerning the rigidity of the microenvironment of liquid-liquid interfaee in terms of the interfacial viscosity. The rotational relaxation time of the rhodamine B dye was studied by time-resolved total internal reflection fluorescent anisotropy. In-plane... 

FIG. 11 Order parameter variation along acyl chains in red cell ghosts ( ), small unilamellar vesicles of egg phosphatidylcholine (V), and paraffin oil (+), as determined by the fluorescence anisotropy decay of the w-anthroyloxy fatty acid probes. (Reprinted by permission from Ref. 12.)... 

Figure 5. Fluorescence anisotropy of F-D labelled heparin-antithrombin interaction. F-D-heparin (0.02 fluoresceins per uronic acid) at 0.1 mg/ml was incubated with different concentrations of antithrombin (open circles) or bovine serum albumin (solid diamonds) in 20 mM sodium phosphate buffer, pH 7.4.

Nakano, M., Kamo, T., Sugita, A. and Handa, T. (2005) Detection of bilayer packing stress and its release in lamellar-cubic phase transition by time-resolved fluorescence anisotropy. Journal of Physical Chemistry B, 109 (10), 4754—4760. 

Tramier M, Coppey-Moisan M (2008) Fluorescence anisotropy imaging microscopy for homo-FRET in living cells. Methods Cell Biol 85 395-414... 

Before being able to study the nonlinear optical properties of any material, it is necessary to have a complete understanding of its linear optical properties. Therefore, we start this section with a brief discussion of the techniques used to measure some of the most important linear properties, e.g., linear absorption, fluorescence, anisotropy, and fluorescence quantum yield. 

Situation with H-bonding also demands to take into account the fact that alcohols have ability to form various associates or even clusters at normal conditions. The most efficient method for determination of inhomogeneity in the excited states is fluorescence polarization measurements. These methods also frequently applied for studying of solvent viscosity, they may be provided in two variants steady state and time-resolved. Relations for time-resolved and steady state fluorescence anisotropy may be given as [1, 2, 75] ... 

One of the most popular applications of molecular rotors is the quantitative determination of solvent viscosity (for some examples, see references [18, 23-27] and Sect. 5). Viscosity refers to a bulk property, but molecular rotors change their behavior under the influence of the solvent on the molecular scale. Most commonly, the diffusivity of a fluorophore is related to bulk viscosity through the Debye-Stokes-Einstein relationship where the diffusion constant D is inversely proportional to bulk viscosity rj. Established techniques such as fluorescent recovery after photobleaching (FRAP) and fluorescence anisotropy build on the diffusivity of a fluorophore. However, the relationship between diffusivity on a molecular scale and bulk viscosity is always an approximation, because it does not consider molecular-scale effects such as size differences between fluorophore and solvent, electrostatic interactions, hydrogen bond formation, or a possible anisotropy of the environment. Nonetheless, approaches exist to resolve this conflict between bulk viscosity and apparent microviscosity at the molecular scale. Forster and Hoffmann examined some triphenylamine dyes with TICT characteristics. These dyes are characterized by radiationless relaxation from the TICT state. Forster and Hoffmann found a power-law relationship between quantum yield and solvent viscosity both analytically and experimentally [28]. For a quantitative derivation of the power-law relationship, Forster and Hoffmann define the solvent s microfriction k by applying the Debye-Stokes-Einstein diffusion model (2)... 

Shi X, Basran J, Seward FIE, Childs W, Bagshaw CR, Boxer SG (2007) Anomalous negative fluorescence anisotropy in yellow fluorescent protein (YFP 10C) quantitative analysis of FRET in YFP dimers. Biochemistry 46 14403-14417... 

Transfer between identical molecules Fluorescence anisotropy... 

Figure 4.9 illustrates time-gated imaging of rotational correlation time. Briefly, excitation by linearly polarized radiation will excite fluorophores with dipole components parallel to the excitation polarization axis and so the fluorescence emission will be anisotropically polarized immediately after excitation, with more emission polarized parallel than perpendicular to the polarization axis (r0). Subsequently, however, collisions with solvent molecules will tend to randomize the fluorophore orientations and the emission anistropy will decrease with time (r(t)). The characteristic timescale over which the fluorescence anisotropy decreases can be described (in the simplest case of a spherical molecule) by an exponential decay with a time constant, 6, which is the rotational correlation time and is approximately proportional to the local solvent viscosity and to the size of the fluorophore. Provided that... 

Fig. 4.9. Schematic of time-resolved fluorescence anisotropy sample is excited with linearly polarized light and time-resolved fluorescence images are acquired with polarization analyzed parallel and perpendicular to excitation polarization. Assuming a spherical fluorophore, the temporal decay of the fluorescence anisotropy, r(t), can be fitted to an exponential decay model from which the rotational correlation time, 6, can be calculated.

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