Time-dependent anisotropy

Time-dependent anisotropy measurements 6.2.7.1 Pulse fluorometry... 

We measured the time-dependent anisotropy of 1-pyrene carboxaldehyde in sulfonate A and B systems. The results are shown in Figure 2. Relaxation times determined from the unconvoluted anisotropy decays for sulfonates A and B in heptane solution were found to be 7 ns and 28 ns, respectively. 

The internal rotational relaxation times of 1-pyrene carboxaldehyde in sulfonate systems may offer some indication of the extent of probe binding to the inverted micelle. In the absence of any background fluorescence interference to the time-dependent anisotropy decay profile, the internal rotational relaxation time should correlate with the strength of binding with the polar material in the polar core. However, spectral interference from the aromatic moieties of sulfonates is substantial, so that the values of internal rotational relaxation time can only be used for qualitative comparison. 

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. 

The two most important depolarization mechanisms that give rise to a time-dependent anisotropy are fluorophore rotation and energy transfer. Energy transfer leads to depolarization as the hopping of excitation from one fluorophore to another, when not parallel, is equivalent to an angular displacement. 

Measurement of the correlation time, and provided the viscosity of the medium is known, allows the determination of the hydrodynamic volume, hence the size of the particle where the fluorophore is embedded. This may in turn reflect an association process. For non-spherical particles, the anisotropy decay is given by more complex relations [24]. A time-dependent anisotropy may also indicate intramolecular mobility. 

In these equations, r(t) is the time-dependent anisotropy function, which is proportional to CF(t) as... 

Figure 3. Time-dependent anisotropy for anthracene-labeled polyisoprene in dilute hexane solution. The experimental anisotropy was obtained by setting the delay between the excitation and probe pulses to a given position and then varying the polarization of the probe beam. In the bottom portion of the figure, the smooth curve through the data is the best fit to the Hall-Helfand model(Ti=236 ps, t2=909 ps, and r(0)=0.250). Unweighted residuals for the best fit to this model are shown along with the experimental error bars in the top portion of the figure. Note that the residuals are shown on an expanded scale (lOx). The instrument response function is indicated at the left.

Figure 4. Time-dependent anisotropy for anthracene-labeled polyisoprene in dilute cyclohexane solution. The smooth curve through the data is the best fit to the Bendler-Yaris model(Ti=210 ps, t2=2750 ps, and r(0)=0.243).

Figure 5. Time-dependent anisotropies for labeled polyisoprene chains in dilute 2-pentanone solutions. The smooth curves through the data points are the best fits to the Hall-Helfand model for 22.8 C, -8.6 C, and -26.5 °C (bottom to top). The data at 35.1 °C is omitted for clarity. Semilog plots of the best fit correlation functions are shown in the inset. Note that all the correlation functions are quite non-exponential.

Although both theories correctly predicted the shape of the time-dependent anisotropy, the EF theory predicted values for theta-condition PMMA which were lower than expected (as compared to determinations by light scattering and neutron scattering) while the FAF theory resulted in values which were too high. The reason for the disparities in the excitation transport size determinations has been shown to be due to Inadequate models of the spatial distribution of chromophores on a polymer chain (18). 

Our streak camera with a fused-silica lens was found to have less than 5% of intrinsic anisotropy for fluorescence collection, and this is taken into account when calculating r(t) by using both vertical and horizontal excitations. When such a correction is taken into account, we find that ultraviolet time-dependent anisotropy values can be measured to within 0.5% upon averaging up to 400 shots. 

Special attention is drawn to Andrews unified theory of radiative and radiationless molecular energy transfer processes. Hochstrasser and co-workers have achieved the remarkable feat of using fs fluorescence time-dependent anisotropy for the direct measurement of energy transfer between identical chromophores. 

Hence, for broadband excitation of a symmetric dimer, the initial anisotropy may fall anywhere from 0.4 to 0.7, depending on the transition moment geometry. This expression concurs with one derived by Wynne and Hochstrasser using Redfield theory. In the special case where 6 = 90°, the time-dependent anisotropy function r t) has the form ... 

In this expression r(/) is the time-dependent anisotropy, 0 the correlation times and g, the fraction of the total anisotropy (r ) which decays with this correlation time. In general we expect one component (tf,) due to rotational diffusion of the protein, and one due to torsional motions of the tryptophan residue, if such motions are significant. In proteins which contain more than a single fluorescent residue there can be energy transfer among the residues, which can appear as a component in the anisotropy decay. The timescale of energy transfer depends upon the distance and orientation between the residues, but there is little information on the timescale of energy transfer between intrinsic fluorophores in proteins. 

To illustrate the nature of the anisotropy decays the equivalent time-dependent anisotropies are shown as an insert. These were calculated from the frequency-do-main data. For Sj Nuclease the plot of log r(t) versus time is mostly linear with a slope of (12 nsec) This is the portion of the anisotropy decay due to overall rotational diffusion of the protein. The rapid component in the nuclease anisotropy decay is seen only near the t = 0 origin. The anisotropy decay of melittin is much more rapid, which reflects the greater motional freedom of the tryptophan residue in this disordered polypeptide. Because of the segmental motions which depolarize the... 

In the preceding ch t we described the measurement and interpretation of steady state fluorescence anisotropies. These values are measured using continuous illumination and r resent an average of the anisotropy decay ov - the intensity decay. Measurement of steady-state anisotropies is simple, but interpretation of the steady-state anisotropies usually d nds on an assumed form for the anisotropy decay, which is not directly observed in the experiment. Additional information is available if one measures the time-dependent anisotropy> that is, the values of r(t) following pulsed excitation. The form of the anisotropy decay depends on the size, shape, and flexibility of the labeled molecule, and the data can be compared with the decays calculated from various molecular models. Anisotropy decays can be obtained using the TD or the FD method. 

In the time domain, one measures the time-dqiendent decays of the polarized components of the emission (Ei)s. [ 11.1] and [ 11,2]). The polarized intensity decays are used to calculate the time-dependent anisotropy,... 

The time-dependent anisotropy decay is then analyzed to determine which model is most consistent with the data. 

Figure 17.15, FD anisotropy decays of RNase T (pH 5.S) at 5 ( ) and 52 C (O) and at 5 C wtdi 6M guanidine hydrochloride (a), buet Equivalent time-dependent anisotropies reconstructed from the FDdata. Simitar data were reported in Ref S. From Ref. 5.

Figure 20.17. Time-dependent anisotropy decay of DNA labeled with (Ru(bpy>2(< z)j. The data are shown as dots. The solid Ime and deviations (lower panel) are for the best three-condadon-time fit with correlation times of 3.1,22.2, and 189.9 ns. Rbm Rtf. 38.

The time-dependent anisotropy, r(r), in a fluorescence depolarization experiment is directly related to the reorientational correlation function ... 

We have investigated further the rotation of DMPC lipids by incorporating two eosin fatty acid probes (dodecanoyl- and hexadecanoyl-amidoeosin) and measuring the time-dependent phosphorescent anisotropies (37). The eosin moieties of these reporter molecules are located close to the membrane surface. Figure 7 shows typical experimental results at two temperatures. A number of features serve to illustrate the type of information provided by such studies. The phosphorescence emission at both temperatures displayed a time-dependent anisotropy which could be fit to an equation of the form... 

---