Fluorescence Stokes shift function

Both experiments and theory show that solvation may proceed exceedingly rapidly. Figure 2 shows the fluorescence Stokes shift function S(f) for a coumarin dye in water obtained by experiment and simulation [4]. Here, S(t) is a normalized function describing the progress toward equilibrium ... 

Figure 2. Experimental and simulated fluorescence Stokes shift function 5(f) for coumarin 343 in water. The curve marked Aq is a classical molecular dynamics simulation result using a charge distribution difference, calculated by semiempirical quantum chemical methods, between ground and excited states. Also shown is a simulation for a neutral atomic solute with the Lennard-Jones parameters of the water oxygen atom (S°). (From Ref. 4.)...

To establish the connection between M(f) and the fluorescence Stokes shift function 5(f) defined in Eq. (1), we first rewrite 5(f) as... 

The definition of the spectral density [Eq. (15)] allows to connect the various correlation functions relevant to spectral broadening and spectral diffusion. For example, the fluorescence Stokes shift function S(t) can be written as... 

Thus Eqs. (17) and (22) establish the explicit correlation between the fluorescence Stokes shift function and the line-broadening function that gives linear absorption and emission spectra via... 

FIG. 4 Time-resolved fluorescence Stokes shift of coumarin 343 in Aerosol OT reverse micelles, (a) normalized time-correlation functions, C i) = v(t) — v(oo)/v(0) — v(oo), and (b) unnormalized time-correlation functions, S i) = v i) — v(oo), showing the magnitude of the overall Stokes shift in addition to the dynamic response, wq = 1.1 ( ), 5 ( ), 7.5 ( ), 15 ( ), and 40 (O) and for bulk aqueous Na solution (A)- Points are data and lines that are multiexponential fits to the data. (Reprinted from Ref 38 with permission from the American Chemical Society.)... 

Thus we see that the first moment of the spectral density multiplied by h is the reorganization energy (i.e., one half of the Stokes shift magnitude), whereas the time dependence of the first moment of p(w) corresponds to the fluorescence Stokes shift. Thus the time dependence of S t) is determined entirely by the spectral density. At high temperature [i.e., when p(w) contains frequencies less than 2kBT], S(t) becomes the classical correlation function [36] used by many previous authors [7-10], This follows from... 

We have done a study by time-resolved hole-burning spectroscopy for dye molecules in polar solvents and found that the time correlation function of the hole width decays much slower than that of the peak shift of the hole, which occurs very rapidly, as you observed in the case of the fluorescence Stokes shift [K. Nishiyama, Y. Asano, N. Hashimoto, and T. Okada, J. Mol. Liquids 65/66, 41 (1995)]. 

We recently developed a systematic method that uses the intrinsic tryptophan residue (Trp or W) as a local optical probe [49, 50]. Using site-directed mutagenesis, tryptophan can be mutated into different positions one at a time to scan protein surfaces. With femtosecond temporal and single-residue spatial resolution, the fluorescence Stokes shift of the local excited Trp can be followed in real time, and thus, the location, dynamics, and functional roles of protein-water interactions can be studied directly. With MD simulations, the solvation by water and protein (residues) is differentiated carefully to determine the hydration dynamics. Here, we focus our own work and review our recent systematic studies on hydration dynamics and protein-water fluctuations in a series of biological systems using the powerful intrinsic tryptophan as a local optical probe, and thus reveal the dynamic role of hydrating water molecules around proteins, which is a longstanding unresolved problem and a topic central to protein science. 

Unie resolved ground state hole spectra of cresyl violet in acetonitrile, methanol, and ethanol at room temperature have been measured in subpicosecond to picosecond time region. The time correlation function of the solvent relaxation expressed by the hole width was obtained. The main part of the correlation function decayed much slower compared with that of the reported correlation function observed in time dependent fluorescence Stokes shift. Some possible mechanisms are proposed for understanding of the time depencences of the spectral broadening under the condition with the distribution of the relaxation times in fluid solution based on the entropy term in the solvent orientation as well as the site dependent response of the solvent. 

A rather simple experimental teehnique involving measurement of the time-dependent fluorescence Stokes shift (TDFSS) after an initial exeitation has been applied to measure SD in a large number of liquids. TDFSS oceurs due to dipolar solvation of the excited probe and thus gives an estimate of the solvation timeseales. In an important paper, Jimenez et al. reported the results of SD of the exeited state of the dye coumarin 343 (C343) in liquid water [14]. Their result is shown in Figure 3.13. The initial part of the solvent response of water was found to be extremely fast (few tens of femtoseconds) and it constituted more than 60% of the total solvation energy relaxation. The subsequent relaxation was found to occur in the picosecond timescale. The decay of the solvation time correlation function, S t)y was fitted to a function of the following form... 

Fluorescent probes are divided in two categories, i.e., intrinsic and extrinsic probes. Tryptophan is the most widely used intrinsic probe. The absorption spectrum, centered at 280 nm, displays two overlapping absorbance transitions. In contrast, the fluorescence emission spectrum is broad and is characterized by a large Stokes shift, which varies with the polarity of the environment. The fluorescence emission peak is at about 350 nm in water but the peak shifts to about 315 nm in nonpolar media, such as within the hydrophobic core of folded proteins. Vitamin A, located in milk fat globules, may be used as an intrinsic probe to follow, for example, the changes of triglyceride physical state as a function of temperature [20]. Extrinsic probes are used to characterize molecular events when intrinsic fluorophores are absent or are so numerous that the interpretation of the data becomes ambiguous. Extrinsic probes may also be used to obtain additional or complementary information from a specific macromolecular domain or from an oil water interface. 

The variations of the simulated steady state solvatochromism, as a function of the polar solvent molarity, were found to be in good agreement with the experimental work of Krolicki et al. [4], both for absorption and fluorescence. The difference of Stokes-shifts between benzene and acetonitrile is 981 cm-1, compared to 1230 cm-1 obtained experimentally. These numbers are 870 cm-1 and 1910 cm-1, respectively, for methanol. 

We have examined also dynamic Stokes shift of the fluorescence of denatured PYP to compare with the results in Fig. 5 by obtaining the correlation function C(t) with the same procedure. C(t) can be reproduced exactly by a double exponential fit with 670 fs (85 %) and 60 fs (15 %) components. 

To measure solvation dynamics in a liquid we follow the rearrangement of surrounding solvent molecules after photo-excitation of a dissolved dye by recording its fluorescence as a function of time. The Stokes shift response function S(t) = (v(t), v(0), and v(oo) re-... 

Fluorescence spectra, 22 spectral density function for, 25 spectral shape function for, 25 time resolved, 22 reconstruction of, 24 Stokes shift in, 22... 

Solvation dynamics are measured using the more reliable energy relaxation method after a local perturbation [83-85], typically using a femtosecond-resolved fluorescence technique. Experimentally, the wavelength-resolved transients are obtained using the fluorescence upconversion method [85], The observed fluorescence dynamics, decay at the blue side and rise at the red side (Fig. 3a), reflecting typical solvation processes. The molecular mechanism is schematically shown in Fig. 5. Typically, by following the standard procedures [35], we can construct the femtosecond-resolved emission spectra (FRES, Stokes shifts with time) and then the correlation function (solvent response curve) ... 

Detailed measurements of the s-tetrazine gas-phase spectrum were made. With these data, measurement of the absolute Stokes shift S(t) is possible. Because the Stokes shift is zero in the absence of solvent nuclear dynamics, the magnitude of the Stokes shift at the earliest times represents the amount of relaxation within the experimental time resolution. The steady-state absorption and fluorescence spectra were also measured to provide an independent value of the equilibrium Stokes shift S< With this data, the absolute solvation response function... 

Figure 5.9. Anomalous Stokes shift illustrated by displacements of 0-0 transitions in absorption and fluorescence of p-amino-p -nitrobiphenyl in benzene/dioxane as a function of the dioxane content (by permission from Lippert, 1966).

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