Anisotropy decays correlation functions

The theory for rotational diffusion of nonspherical molecules predicts the anisotropy decays for ellipsoids and ellipsoids of revolution. The rotational correlation times in the anisotropy decay are functions of the rotational diffusion coefficients. 

Figure 8. Hydration correlation function c(f) of tripeptide-KWK. The c(t) can be fit with a stretched triexponential decay function as shown. For comparison, the hydration correlation function of tryptophan in bulk water is also shown. The inset shows the fluorescence anisotropy dynamics of KWK. The initial 100-fs dynamics resulted from the internal conversion between and states, and the free rotation time of KWK in bulk water is 127 ps.

Figure 19 shows the typical fluorescence transients of TBE from more than 10 gated emission wavelengths from the blue to the red side. At the blue side of the emission maximum, all transients obtained from four Trp-probes in the cubic phase aqueous channels drastically slow down compared with that of tryptophan in bulk water. The transients show significant solvation dynamics that cover three orders of magnitude on time scales from sub-picosecond to a hundred picoseconds. These solvation dynamics can be represented by three distinct decay components The first component occurs in about one picosecond, the second decays in tens of picoseconds, and the third takes a hundred picoseconds. The constmcted hydration correlation functions are shown in Fig. 20a with anisotropy dynamics in Fig. 20b. Surprisingly, three similar time scales (0.56-1.431 ps, 9.2-15 ps, and 108-140 ps) are obtained for all four Trp-probes, but their relative amplitudes systematically change with the probe positions in the channel. Thus, for the four Trp-probes studied here, we observed a correlation between their local hydrophobicity and the relative contributions of the first and third components from Trp, melittin, TME to TBE, the first components have contributions of 40%, 35%, 26%, and 17%, and the third components vary from 32%, to 38%, 43%, and 53%, respectively. The...

Strikingly, the solvation dynamics for all mutants are nearly the same. All correlation functions can be best described by a double exponential decay with time constants of 0.67 ps with 68% of the total amplitude and 13.2 ps (32%) for D60, 0.47 ps (67%) and 12.7 (33%) for D60G, and 0.53 ps (69%) and 10.8 ps (31%) for D60N. Relative to SNase above, the solvation dynamics are fast, which reflects the neighboring hydrophobic environment. We also measured the anisotropy dynamics and, as shown in the inset of Fig. 33, the local structure is very rigid in the time window of 800 ps. This observation is consistent with the inflexible turn (-T30W31-) in the transition from the second /1-sheet and the second x-helix (Fig. 31). Thus, the three mutants, with a charged, polar, or hydrophobic reside around the probe (Fig. 34) but with the similar time scales of... 

The evolution of the experimental anisotropy as a function of the temperature is shown in Fig. 8. As expected, the decay rate increases as the temperature increases. For the highest temperature (t > 50 °C), it can be noticed that the anisotropy decays from a value close to the fundamental anisotropy of DMA to almost zero in the time window of the experiment (about 60 ns). This means that the initial orientation of a backbone segment is almost completely lost within this time. This possibiUty to directly check the amplitude of motions associated with the involved relaxation is a very useful advantage of FAD. In particular, it indicates that in the temperature range 50 °C 80 °C, we sample continuously and almost completely the elementary brownian motion in polymer melts. Processes too fast to be observed by this technique involve only very small angles of rotation and cannot be associated with backbone rearrangements. On the other hand, the processes too slow to be sampled concern only a very low residual orientational correlation, i.e. they are important only on a scale much larger than the size of conformational jumps. 

ISS data have been recorded in many pure and mixed molecular liquids [34,49, 75, 83, 83-85], In most cases, the data are not described precisely by Eq. (27). Rather, an additional decay component appears at intermediate times (decay times 500 fs). This has been interpreted [49, 84] in terms of higher order polarizability contributions to C (t) which represent translational motions, an interpretation supported by observations in CCI4 (whose single-molecule polarizability anisotropy vanishes by symmetry). This interpretation is not consistent with several molecular dynamics simulations of CSj [71, 86]. An alternative analysis has been presented [82] that incorporates theoretical results showing that even the single-molecule orientational correlation function C (t) should in fact show decay on the 0.5-ps time scale of cage fluctuations [87, 88]. 

In a previous publication 17, we compared the experimental anisotropies for dilute solutions of labeled polyisoprene in hexane and cyclohexane to several theoretical models. These results are shown in Table II. The major conclusions of the previous study are 1) The theoretical models proposed by Hall and Helfand, and by Bendler and Yaris provide good fits to the experimentally measured correlation function for both hexane and cyclohexane. The model suggested by Viovy, et al. does not fit as well as the other two models. 2) Within experimental error, the shape of the correlation function is the same in the two solvents (i.e, the ratio of t2/ti is constant). 3) The time scale of the correlation function decay scales roughly with the solvent viscosity. 

Viovy, Monnerie, and Brochon have performed fluorescence anisotropy decay measurements on the nanosecond time scale on dilute solutions of anthracene-labeled polystyrene( ). In contrast to our results on labeled polyisoprene, Viovy, et al. reported that their Generalized Diffusion and Loss model (see Table I) fit their results better than the Hall-Helfand or Bendler-Yaris models. This conclusion is similar to that recently reached by Sasaki, Yamamoto, and Nishijima 3 ) after performing fluorescence measurements on anthracene-labeled polyCmethyl methacrylate). These differences in the observed correlation function shapes could be taken either to reflect the non-universal character of local motions, or to indicate a significant difference between chains of moderate flexibility and high flexibility. Further investigations will shed light on this point. 

The correlation function, <-P2[am(0) ( )]>. provides a measure of the internal motions of particular residues in the protein.324 333 Figure 46 shows the results obtained for Trp-62 and Trp-63 from the stochastic boundary molecular dynamics simulations of lysozyme used to analyze the displacement and velocity autocorrelation functions. The net influence of the solvent for both Trp-62 and Trp-63 is to cause a slower decay in the anisotropy than occurs in vacuum. In vacuum, the anisotropy decays to a plateau value of 0.36 to 0.37 (relative to the initial value of 0.4) for both residues within a picosecond. In solution there is an initial rapid decay, corresponding to that found in vacuum, followed by a slower decay (without reaching a plateau value) that continues beyond the period (10 ps) over which the correlation function is ex-... 

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].

Here, the parallel and perpendicular pump-probe signals due to component i are denoted by 7 and 7, respectively, and the respective orientational correlation functions are given by C2(i). When the two components display a large separation of timescales for both their vibrational lifetimes and orientational dynamics, then the long-time anisotropy decay can be an accurate representation of the anisotropy of the slow component. However, bofii of the two components can be mixed at intermediate times, making interpretation complicated. In such a case, a model hke Eq. (17.3) can be invoked to extraet information about the orientational dynamies. 

The data in Figure 17.18 illustrate another problem encountered when one is measuring protein anisotropy decays. Examination of the data reveals that the measured time-zero anisotropy [ 0)1 less than the fundamental anisotropy (ro=0.3) for the 300-nm excitation wavelength. This frequently occurs owing to the limited time resolution of the instrumentation. If the correlation time is too sh< t, the anisotropy decays within the instrument response function, and the apparent time-zero anisotropy is less than die actual value. ... 

In polymers, due to the constraint resulting from the connectivity of the chain, the local motions are usually too complicated to be described by a single isotropic correlation time x, as discussed in chapter 4. Indeed, fluorescence anisotropy decay experiments, which directly yield the orientation autocorrelation function, have shown that the experimental data obtained on anthracene-labelled polybutadiene and polyisoprene in solution or in the melt cannot be represented by simple motional models. To account for the connectivity of the polymer backbone, specific autocorrelation functions, based on models in which conformational changes propagate along the chain according to a damped diffusional process, have been derived for local chain... 

The anisotropy of segmental motion exhibited in Fig. 19 may arise, as noted above, either from the intramolecular or from the intermoleoilar ccmstraint to the rotational motion. The anisotropy d orioitational condadon decay was indeed noted already by Weber and Helfand [47] in their Brownian dynamics simulation of polyethylene of infinite chain length. Their orioitational time-correlation function of the chord vector ( = 0°) decayed much more slowly than those of either the bisector vector ( = 0°, = 0°) or the out-of-plane vector ( = 0°, = 90°). What they modeled was a phantom chain having no... 

ABSTRACT - The fluorescence anisotropy decay (FAD) technique is first described, then the different expressions ich have been proposed for the orientation autocorrelation function (OACF) of polymer chains are presented. Typical FAD curves of dilute and concentrated solutions of polystyrene labelled with an anthracene group in the middle of the chain are compared to the various OACF expressions and discussed. In the case of bulk polybutadiene, FAD results obtained either on anthracene labelled chains or on 9,10 dialkylanthracene probes free in the polymer matrix, show that the same type of OACF as for polymer solutions can account for the experimental data. Besides, the temperature dependence of the correlation time of the labelled polybutadiene appears to agree with the WLF equation derived from macroscopic viscoelastic measurements, proving that the segmental motions of about 20 bonds which lead to the FAD of labelled polybutadiene participate in the glass transition processes of this polymer. 

In bulk isotropic media, experiments such as IR and NMR spectroscopy and fluorescence anisotropy decay can give information about these correlation functions or their moments.At an interface with a cylindrical symmetry, SHG and SFG spectroscopies give information about out-of-plane and in-plane reorientation, and they involve more complicated time correlation functions.Nonetheless, the simple C/(t) are still useful for a direct comparison between bulk and surface reorientation. 

In DLS, the molecular anisotropy reflects the stmcture factor through rotational motions. The correlation function for lyv contains the decay by rotational diffusion. For example, the correlation functions for Jw and Ivh for a thin rod in dilute solution are, respectively, expressed as... 

Anisotropy describes the rotational dynamics of reporter molecules or of any sensor segments to which the reporter is rigidly fixed. In the simplest case when both the rotation and the fluorescence decay can be represented by single-exponential functions, the range of variation of anisotropy (r) is determined by variation of the ratio of fluorescence lifetime (xF) and rotational correlation time ([Pg.9]

There should exist a correlation between the two time-resolved functions the decay of the fluorescence intensity and the decay of the emission anisotropy. If the fluorophore undergoes intramolecular rotation with some potential energy and the quenching of its emission has an angular dependence, then the intensity decay function is predicted to be strongly dependent on the rotational diffusion coefficient of the fluorophore.(112) It is expected to be single-exponential only in the case when the internal rotation is fast as compared with an averaged decay rate. As the internal rotation becomes slower, the intensity decay function should exhibit nonexponential behavior. 

The limiting value of A0 is never achieved in practice, and partial depolarization can result from molecular motion. For a chromophore which moves with the motion of a rigid spherical macromolecule to which it is attached, the observed anisotropy will decay exponentially as a function of , the rotational correlation time, according to... 

Reticulum ATPase [105,106], Owing to the long-lived nature of the triplet state, Eosin derivatives are suitable to study protein dynamics in the microsecond-millisecond range. Rotational correlation times are obtained by monitoring the time-dependent anisotropy of the probe s phosphorescence [107-112] and/or the recovery of the ground state absorption [113— 118] or fluorescence [119-122], The decay of the anisotropy allows determination of the mobility of the protein chain that cover the binding site and the rotational diffusion of the protein, the latter being a function of the size and shape of the protein, the viscosity of the medium, and the temperature. 

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