Resolved Anisotropies

There ate significant advantages to the use of UCrtioK-tesolved measuiettmls. The lifetime can lineally be decreased with only a modest change in aoluiion oonditions. 

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Carotenoid radical intermediates generated electrochemically, chemically, and photochemically in solutions, on oxide surfaces, and in mesoporous materials have been studied by a variety of advanced EPR techniques such as pulsed EPR, ESEEM, ENDOR, HYSCORE, and a multifrequency high-held EPR combined with EPR spin trapping and DFT calculations. EPR spectroscopy is a powerful tool to characterize carotenoid radicals to resolve -anisotropy (HF-EPR), anisotropic coupling constants due to a-protons (CW, pulsed ENDOR, HYSCORE), to determine distances between carotenoid radical and electron acceptor site (ESEEM, relaxation enhancement). 

It should be noted that the calculated anisotropy may not be applied to fs time-resolved anisotropy measurements because fs time-resolved experiments involve pumping and probing conditions and may involve overlapping between the vibronic structures of several electronic states due to the use of fs laser pulses. Nevertheless, we think the calculated anisotropy using Eq. (2.54) can provide a reference in comparing models. 

Fast librational motions of the fluorophore within the solvation shell should also be consideredd). The estimated characteristic time for perylene in paraffin is about 1 ps, which is not detectable by time-resolved anisotropy decay measurement. An apparent value of the emission anisotropy is thus measured, which is smaller than in the absence of libration. Such an explanation is consistent with the fact that fluorescein bound to a large molecule (e.g. polyacrylamide or monoglucoronide) exhibits a larger limiting anisotropy than free fluorescein in aqueous glycerolic solutions. However, the absorption and fluorescence spectra are different for free and bound fluorescein the question then arises as to whether r0 could be an intrinsic property of the fluorophore. 

In principle, the shape parameters of asymmetric rotors can be estimated from time-resolved anisotropy decay measurements, but in practice it is difficult to obtain accurate anisotropy decay curves over much more than one decade, which is often insufficient to determine more than two rotational correlation times. 

The elucidation of the intramolecular dynamics of tryptophan residues became possible due to anisotropy studies with nanosecond time resolution. Two approaches have been taken direct observation of the anisotropy kinetics on the nanosecond time scale using time-resolved(28) or frequency-domain fluorometry, and studies of steady-state anisotropy for xFvarying within wide ranges (lifetime-resolved anisotropy). The latter approach involves the application of collisional quenchers, oxygen(29,71) or acrylamide.(30) The shortening of xF by the quencher decreases the mean time available for rotations of aromatic groups prior to emission. 

The results of fluorescence polarization studies of proteins were discussed above. Time-resolved anisotropy measurements often permit, without any additional variation of experimental conditions, intramolecular rotations to be distinguished from rotation of the whole protein molecule and characterized,... 

In time-resolved anisotropy measurements, the static or orientational components of motion and the rate of motion are derived. The time-resolved derivation of rs is revealed as... 

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 ... 

Since steady-state data are much easier to obtain, some effort has been directed to methods for deriving time-resolved anisotropy parameters from the steady-state anisotropy/2 4549-1 A number of relationships have been described, some of which require knowledge of r0 and the fluorescence lifetime (see, e.g., Ref. 48). An example(50) of such an empirical relationship is... 

At the present time, two methods are in common use for the determination of time-resolved anisotropy parameters—the single-photon counting or pulse method 55-56 and the frequency-domain or phase fluorometric methods. 57 59) These are described elsewhere in this series. Recently, both of these techniques have undergone considerable development, and there are a number of commercially available instruments which include analysis software. The question of which technique would be better for the study of membranes is therefore difficult to answer. Certainly, however, the multifrequency phase instruments are now fully comparable with the time-domain instruments, a situation which was not the case only a few years ago. Time-resolved measurements are generally rather more difficult to perform and may take considerably longer than the steady-state anisotropy measurements, and this should be borne in mind when samples are unstable or if information of kinetics is required. It is therefore important to evaluate the need to take such measurements in studies of membranes. Steady-state instruments are of course much less expensive, and considerable information can be extracted, although polarization optics are not usually supplied as standard. 

Many spectroscopic methods have been employed for the investigation of such systems For example, wide-band, time-resolved, pulsed photoacoustic spectroscopy was employed to study the electron transfer reaction between a triplet magnesium porphyrin and various quinones in polar and nonpolar solvents. Likewise, ultrafast time-resolved anisotropy experiments with [5-(l,4-benzoquinonyl)-10,15,20-triphenylpor-phyrinato]magnesium 16 showed that the photoinduced electron transfer process involving the locally-excited MgP Q state is solvent-independent, while the thermal charge recombination reaction is solvent-dependent . Recently, several examples of quinone-phtha-locyanine systems have also been reported . 

The limiting values of the fluorescence anisotropy are 0.4 and -0.2, corresponding to parallel and perpendicular absorption and emission dipoles, respectively. For a chromophore undergoing internal conversion, the change in angle between the two vectors can be instantaneous. It may also be caused by energy transfer or physical motion. On the laboratory scale, the time-resolved anisotropy decay is determined as ... 

In a layer-resolved or atomic analysis, the V operator in Eqs. (32-35) must be replaced by magnetization-angle differences, but a comparison with the continuum solution [95, 96] reveals only minor corrections due to the discrete nature of the layers. Note, however, that the layer resolved anisotropies and exchange constants may deviate from the respective bulk values. 

Anisotropy measurements yield information on molecular motions taking place during the fluorescence lifetime. Thus, measuring the time-dependent decay of fluorescence anisotropy provides information regarding rotational and diffusive motions of macromolecules (Wahl and Weber, 1967). Time-resolved anisotropy is determined by placing polarizers in the excitation and emission channels, and measuring the fluorescence decay of the parallel and perpendicular components of the emission. 

When a fluorophore exhibits segmental motions, time-resolved anisotropy decay must be analyzed as the sum of exponential decays ... 

TA-transient absorption TRANIP = time-resolved anisotropy TRPL = time-resolved photoluminescence TRIR = time-resolved IR TR = EPR-time-resolved electron paramagnetic resonance spectroscopy. 

Ludescher, R. D., Johnson, I. D., Volwerk, J. J., de Haas, G. H., Jost, P. C., and Hudson, B. S. (1988). Rotational dynamics of the single tryptophan of procine pancreatic phospholipase A2, its zymogen, and an enzyme/micelle complex. A steady-state and time-resolved anisotropy study. Biochemistry 27, 6618-6628. 

Energy transfer processes can be revealed by time-resolved anisotropy data. The large value for the limiting anisotropy (ro) of p-CIPi, p-C2P1 and m-CIPi... 

The time-resolved anisotropy. Fig. 7.13, decays from an initial value of 0.291 to a constant value (0.042) that is reached in about 2 ns. The final value is exactly one-... 

The Pauli Master equation approach to calculating RET rates is particularly useful for simulating time-resolved anisotropy decay that results from RET within aggregates of molecules. In that case the orientation of the aggregate in the laboratory frame is also randomly selected at each Monte Carlo iteration in order to account for the rotational averaging properly. 

Figure 7.7 Time-resolved hydration process for the proteins Sublitisin Carlsberg (SC) and Monellin (Mn). The time evolution of the constructed correlation function is shown for the protein SC (top), the Dansyl dye bonded SC (middle), and for the protein Mn (bottom). The inset of each part shows the corresponding time-resolved anisotropy r(t) decay [21].

To get more insight into the effect of confinement on the binding between HPMO and the host, time-resolved anisotropy measurements have been carried out [58]. The result (Fig. 7.12) shows a remarkable difference in the anisotropy decays, especially for the HSA protein case. While in dioxane, the rotational time constant (45 ps) is close to the expected one using hydrodynamic theory [58], this time increases with the rigidity of the host (97 ps for a micelle, 154 ps for yS-CD... 

Fluorescence anisotropy measurements can also be used to obtain the rates of the excited state tautomerization. Two variants can be applied. The first is based on the analysis of time-resolved anisotropy curves. These are constructed from measurements of the fluorescence decay recorded with different positions of the polarizers in the excitation and emission channels. The anisotropy decay reflects the movement of the transition moment and thus, the hydrogen exchange. For molecules with a long-lived Sj state, the anisotropy decay can also be caused by rotational diffusion. In order to avoid depolarization effects due to molecular rotation, the experiments should be carried out in rigid media, such as polymers or glasses. When the Sj lifetime is short compared to that of rotational diffusion, tautomerization rates can be determined even in solution. This is the case for lb, for which time-resolved anisotropy measurements have been performed at 293 K, using a... 

Time-resolved anisotropy measurements of excitation hopping between two anthryl moieties attached to both ends of alkane molecules have been interpreted by a model based on conformational... 

Time-Resolved Anisotropy Measurements Time-resolved anisotropy measurements (TRAMs) offer a distinct advantage over their steady-state... 

There are several analytical procedures available for derivation of relaxation information from time-resolved anisotropy experiments, the merits of which have been discussed at length elsewhere [25,112,114]. The salient points are covered here direct analysis of r(t) using a function such as Equation 2.31 is the most straightforward method but can become particularly problematic if the motion under study is comparable to the width of the excitation pulse [25,112,114]. Furthermore, as r(t) can suffer contamination from the polarizing effects of stray excitation from the source, particularly in weakly fluorescent samples, other methods are required to overcome such artifacts. Impulse reconvolution [115] allows mathematical removal of the instrumental pulse from the experimental data and involves an analysis of s(t) by a statistically adequate model function (e.g., Eq. 2.8). The best fit to s(t) is... 

Early time-resolved anisotropy experiments on PMAA used a combination of anthryl-based labels and probes [18,46,60,76] in an effort to fully characterize the conformational switch of the polyelectrolyte in aqueous solution. In their study of probes dispersed in and labels incorporated into PMAA, Treloar and coworkers [60,76] derived information from anisotropy experiments pertinent not only to the cluster size of the rotating units, but also to the structure of the hypercoil itself. 

Time-resolved anisotropy experiments reveal the dynamics of tumbling, and fast components may be assigned to local motions of the probe within the double helix (see below). The intensities of parallel and perpendicular polarized light are monitored as a function of time, and the time-resolved anisotropy is calculated as in Equation 2. Lakowicz [188] has described in great detail the data analysis for these kinds of experiments. Many data analyses rely on fitting the time-resolved data to sums of exponentials and considering limited physical states of the probe molecule (e.g., free vs. bound, solvent-exposed vs. buried) as appropriate. 

For example, 2-aminopurine (AP) has been used to probe the dynamics of mismatches in DNA [340]. AP can be excited at 320 nm, where the normal DNA bases do not absorb (much), and emits at 380 nm (Fig. 4.36). Time-resolved anisotropy decays of AP across from all four natural DNA bases were performed (Fig. 4.37). AP can hydrogen-bond to T nearly as well as the natural A. The data were fitted to sums of two exponential terms the long time corresponded to overall tumbling and the short time to local motions within the DNA base stack. It was found that the internal correlation time corresponding to local motions, at 4°C,... 

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