Residual motion

There would remain some very small residual motion of the pendulum due to the air molecules striking it at random (Brownian motion), but that does not count in the game of perpetual motion. In the condition of residual motion, the pendulum is just another (big) molecule sharing equally in the average kinetic energy of all the individual air molecules. In other words, the pendulum eventually comes to thermal equilibrium with the air. 

Partitioning of Free Energy Contributions in the Estimate of Binding Constants Residual Motions and Consequences for Amide-Amide Hydrogen Bond Strengths. 

In vitrified solution and/or when fluorophore molecules do not show any residual motions, the measured polarization is equal to the intrinsic one, P0. This value is obtained at low... 

Equation (11.9) indicates the possibility of calculating the rotational correlation time of the fluorophore not only by varying the T/q ratio but also by adding a collisional quencher. Interaction between the quencher and fluorophore decreases the fluorescence lifetime and intensity of the fluorophore, and increases its fluorescence anisotropy. Plotting 1 /A as a function of r0 yields a straight line with a slope equal to r. If the fluorophore is tightly bound to the macromolecule and does not exhibit any residual motions, the measured 0r is equal to, and the extrapolated anisotropy is equal to that measured at a low temperature. 

The Perrin plot as a function of temperature (Figure 13.3) reveals the presence or absence of local motions of the fluorophore on the macro molecule. The absence of any residual motions yields a Perrin plot with a slope equal to that of the protein and an extrapolated polarization equal to the limiting one. 

Knowing that the value of the limiting polarization at the excitation wavelength is 0.24, the rotational correlation time of the protein is 20 ns, and the fluorescence lifetime of the Trp residue is 2.8 ns, can you tell whether the fluorophore presents residual motions or not ... 

The width of this broader absorption indicates that some types of residual motion are still in evidence. The effective quadrupole coupling constant qQlh) can be related to the splitting between the satellites, AHq, by (14)... 

Searle, M. Williams, D. H. Gerhard, U., Partitioning of free energy contributions in the estimation of binding constants Residual motions and consequences for amide-amide hydrogen bond strengths,./. Am. Chem. Soc. 1992,114, 10704-10710... 

The next question is to identify residues near the active site that may modulate the donor-acceptor distance. In Fig. 10 we show the active site and some nearby residues. In the spirit of the previous results, in order to predict the degree that the motion of these residues is correlated with the donor-acceptor motion, we can calculate the Fourier transform of the autocorrelation of the residue motion, and then order the residues according to the height of the peak of the spectral density.34 In Fig. 11 we show one result, the spectral densities for the motion, projected first along the residue-donor axis and then along the donor-acceptor direction, of three residues, two of them strongly correlated and one not correlated. 

A compression of residues facilitates catalysis. We have identified a compression-relaxation sequence of residue motions that facilitates catalysis. These are the residues 31 and 65, located behind the cofactor and transferring hydride, and 106 and 195, located on the acceptor side behind the substrate, as seen in Fig. 23. 

In this lowest energy state, there is still some motion of the oscillator. If the motion ceased altogether, this would require Px = and x = 0 precisely. This is not permitted. A compromise is reached, which leaves a small residual motion and uncertainties in both position and momentum in conformity with the uncertainty principle. 

This can be seen more clearly in a PEANUT stereo-view, in which the display shows the difference between the experimental adps and the calculated adps because of the rigid-body motion of the molecule as a whole. Fig. 8 shows the PEANUT plot for one of the independent molecules, the plot for the other molecule is very similar. Because the residual motion of the metal atoms is seen to be rather small,... 

Figure 5.7. Steady-state fluorescence polarization versus temperature over viscosity ratio for Trp residues of human aj -acid glycoprotein prepared by acetonic precipitation. Data were obtained by thermal variations in the range 7-35" C. Xex = 300 nm. Xem = 330 nm. Protein concentration is equal to 10 pM. The rotational correlation time determined from the Perrin plot is equal to 13 ns at 20°C is in the same range as that (17 ns) expected for the protein at the same temperature, indicates the presence of residual motions. Also, the extrapolated anisotropy (0.264) is equal to that measured at -35 C (0.267). Source Albani, J. R. 1998, Spectrochimica Acta, Part A. 54, 173-183.

Measiuements of the emission anisotropy A as a function of added collisional quencher are made with the steady fluorescence intensity, which integrates the different weighted fluorescence lifetimes. Quenching emission anisotropy plot of 1 /A vs I (Fig. 5.14) yields for A(o) a value of 0.246 and 0.243 for [L-Met2] DREK and DREK, respectively. These values, lower than that (0.278) measured at - 45 °C for tyrosine at 280 nm (Lakowicz and Maliwal, 1983), indicate that tyrosine residue in both peptides display residual motion independent of the global rotation of the peptide. It is possible to measure the relative importance of the mean residual motions of the tyrosine residues ... 

The two Trp residues are located in different microenvironments, one near the surface and the second in the core of the protein with a completely quenched fluorescence. In this case, the Trp residue located near the surface of the protein would be responsible of the observed fluorescence. The lifetimes would originate from the different relative orientations between the emission dipole of the Trp residue and the absorption dipole of the heme. The residual motion of the heme and / or that of the Trp residue would generate the different orientations. We notice from the values of the fractional intensities that the relative orientation between the dipoles is favorable to that where the energy transfer is the most efficient. 

Time resolved anisotropy decay performed at different temperatures, reveals the presence of two rotational correlation times, one Op, corresponding to the global rotation of the protein and the second Oa, a shorter one, reveals the presence of local residual motions around and / or near the two tryptophan residues. Oa is an apparent rotational time that is a mathematical combination of the global rotation of the protein and the segmental motion of the fluorophore. 

The amino acids themselves display residual motions that can originate from the motions of the backbone of the Trp residues itself and from the motion of the surrounding amino acids. 

Indeed, the Trp residues in a i-acid glycoprotein s exhibit residual motions but not free ones, because of the surrounding amino acids that constrained the motion of the fluorophore. Therefore, the increase in the anisotropy with the excitation wavelength will depend on the importance of these restrictions. 

Hemoproteins are also interesting to investigate because of the efficient energy transfer from tryptophans to heme. Although fluorescence parameters such as intensity, lifetime and polarization of tryptophans in hemoproteins are weak, they still can be measured. Energy transfer rate between a tryptophan and heme depends on the dipole -dipole orientation and the distance that separates the two chromophores. Thus, in a certain way, energy transfer will be affected by the internal dynamics of the protein. Anyway, residual motions will always affect energy transfer between a donor and an acceptor, independently of the chemical nature of the two molecules. 

Figure 8.20 displays the normalized fluorescence emission spectra of 10 pM of calcofluor in the presence of 15 pM of ai -acid glycoprotein obtained at three excitation wavelengths. The maximum (440 nm) of the Calcofluor fluorescence does not change with the excitation wavelength (9iex 385, 395 and 405 nm). The results obtained clearly indicate that the microenvironment of calcofluor has residual motions independent of the global rotation of the protein, and this may induce the local motions of calcofluor. 

Perrin plot and red-edge excitation spectra experiments performed on Trp residues of sialylated and asialylated ai-acid glycoprotein have shown that in both proteins the intrinsic fluorophore displays local motions and are surrounded by a flexible environment. However, the above two mentioned methods yield information on the mean residual motion and can in no way give an indication on the dynamics of each class of Trp residues. In fact, the exposed tryptophan residue should be expected to rotate much more freely than the hydrophobic residues. In order to study the dynamics behavior of each class of Ti p residues, steady-state measurements of emission anisotropy at different temperatures (-45 to + 30°C) can be carried out. This method (the Weber s method) known also as the Y-plot, allows deriving parameters characteristic of the environment of the rotating unit, such as the thermal coefficient of the frictional resistance to the rotation of the fluorophore. 

The anisotropies of both Trp-residues of apacid glycoprotein measured at 20°C are very close (Table 8.7), (a result identical to that obtained with the Weber method, see Table 8.6) indicating that the two Trp residues are highly mobile. This result is confirmed by the values of the rotational correlation times (3 and 5 ns) lower than the global rotational correlation time of a i-acid glycoprotein. When the Trp residue is embedded in the protein core and does not show any residual motions such as in the Lens culinaris agglutinin, its rotational con elation time will be close to that of the protein and its anisotropy will be higher than that of the surface Trp residue. 

The Oi term contains the global rotation of the protein, the residual motion of the Trp residues and the motion of the microenvironment around the Trp residues. In a system... 

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