Time-dependent anisotropy measurements

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. 

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. 

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. 

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,... 

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... 

The present review shows how the microhardness technique can be used to elucidate the dependence of a variety of local deformational processes upon polymer texture and morphology. Microhardness is a rather elusive quantity, that is really a combination of other mechanical properties. It is most suitably defined in terms of the pyramid indentation test. Hardness is primarily taken as a measure of the irreversible deformation mechanisms which characterize a polymeric material, though it also involves elastic and time dependent effects which depend on microstructural details. In isotropic lamellar polymers a hardness depression from ideal values, due to the finite crystal thickness, occurs. The interlamellar non-crystalline layer introduces an additional weak component which contributes further to a lowering of the hardness value. Annealing effects and chemical etching are shown to produce, on the contrary, a significant hardening of the material. The prevalent mechanisms for plastic deformation are proposed. Anisotropy behaviour for several oriented materials is critically discussed. 

Instead of measuring only the time-dependent dipolar interaction via NOE, it is also possible to determine dipolar couplings directly if the solute molecule is partially aligned in so-called alignment media. The most important resulting anisotropic parameters are RDCs, but residual quadrupolar couplings (RQCs), residual chemical shift anisotropy (RCSA) and pseudo-contact shifts (PCSs) can also be used for structure determination if applicable. 

This problem does not exist with time-dependent fluorescence polarization measurements where the decay of the emission anisotropy r(t) is obtained by determining the decay of Iz and Ix according to eq 12. 

The simplified schematic in Figure 2a shows the essential features of the effect. Optically anisotropic molecules in the solution are preferentially oriented by the applied field E(t), resulting in a difference of refractive indices for components of polarized light parallel and perpendicular to the bias field which is measured as a birefringence. The basic theoretical problem is to evaluate this effect in terms of anisotropies of polarizability Aa. referred to molecular axes which produce a time dependent effect when the molecules are preferentially oriented by the field. For no anisotropy in absence of the field, the effect must be an evgn function of field strength, and at low fields proportional to E. A remarkable feature of the effect is that for molecules with permanent dipole moments the response af-... 

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. 

Using time-dependent perturbation theory and taking full account of the symmetry and commutation relations for the high-order dipolar Hamiltonians, Hohwy et al.61 69 gave a systematic analysis of homonuclear decoupling under sample rotation and proposed a novel approach to the design of multiple-pulse experiments. Based on the theoretical analysis, they proposed a pulse sequence that can average dipolar interaction up to the fifth order. One example of these pulse sequences is shown at the top of Fig. 3. This sequence is sufficiently powerful that it is possible to obtain precise measurement of proton chemical shift anisotropies, as shown in Fig. 3. 

To experimentally probe the CO trajectory after dissociation, ultrafast time-resolved polarized mid-IR spectra of photolyzed h-MbCO in G/W were recorded (34), the results of which are plotted in Fig. 8A. This study was performed in G/W primarily because the flatness of the solvent absorbance spectrum near 2100 cm-1 minimizes temporal distortion of the transmitted femtosecond IR probe pulse, thereby maximizing the effective time resolution of the measurement. Two features are already apparent at 0.2 ps, the earliest time shown, and these features rapidly develop into the docked states denoted Bi and B2. The development of the docked CO spectrum is further quantified by the time dependence of the polarization anisotropy, as defined in Equation (2). The B and B2 polarization anisotropies, plotted in Fig. 8B, evolve exponentially with time constants of 0.20 0.05 ps and 0.52 0.10 ps, respectively, and converge to the same anisotropy of approximately 0.2. According to Fig. 8C, ligand translocation is accompanied by a 1.6 0.3 ps growth of the integrated isotropic B-state absorbance. 

Dynamic fluorescence anisotropy is based on rotational reorientation of the excited dipole of a probe molecule, and its correlation time(s) should depend on local environments around the molecule. For a dye molecule in an isotropic medium, three-dimensional rotational reorientation of the excited dipole takes place freely [10]. At a water/oil interface, on the other hand, the out-of-plane motion of a probe molecule should be frozen when the dye is adsorbed on a sharp water/oil interface (i.e., two-dimensional in respect to the molecular size of a probe), while such a motion will be allowed for a relatively thick water/oil interface (i.e., three-dimensional) [11,12]. Thus, by observing rotational freedom of a dye molecule (i.e., excited dipole), one can discuss the thickness of a water/oil interface the correlation time(s) provides information about the chemi-cal/physical characteristics of the interface, including the dynamical behavioiu of the interfacial structure. Dynamic fluorescence anisotropy measurements are thus expected... 

An important advantage of the depolarization technique is that it allows one to measure the molecular ordering, as well as the motional parameters. For this purpose, it is necessary to detect the time dependence of the anisotropy. In the presence of ordering constraints, the r value does not decay to zero, but to some limiting value foo r = (ro — roo)e / c - - poo. The rate of decay defines a rotational correlation time, and Poo is a direct measure of the order parameter through the following relation s = Poo/ o (29). The fluorescence depolarization method works well as long as fluorescence lifetimes, which are typically 10 s, are not too different from the rotation relaxation times to be measured. When the rotational correlation time... 

By using nonlinear least squares fitting, the orientation relaxation time (to,), fluorescence lifetime (r/), and the initial value of anisotropy (r(0)) were obtained. The typical results of the fitting to the time dependence of polarized fluorescence of I in n-nexane is shown in Fig. 1. In order to confirm the validity of the data analysis, the fluorescence lifetime was also measured with the magic angle arrangement. 

There are many uncertainties in this procedure, and it seems clear that direct measurement of the time dependence of emission anisotropy throu l (t) and Ix(t) is preferable. Such measurements are described in a later section. 

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