Fluorescence Stokes Shift Experiments Research Articles

Linear Response Theory for Decomposition Energies of Stokes Shift in Proteins.

In aqueous solution, fluorescence Stokes shift experiments monitor the relaxation of the solute-solvent interactions upon photon excitation of the solute chromophore. Linear response (LR) theory expects the identical dynamics between the Stokes shift and the system's spontaneous fluctuations. Whether this identity guarantees similar dynamics between the nonequilibrated and equilibrium processes for the decomposition energy of the Stokes shift is the main focus of this study. In our previous work [Li, T. J. Chem. Theory Comput. 2017, 13, 1867-1873], Stokes shift is properly correlated with various order time-correlation functions. As a continuation, its decomposition energy from the subsystem is further represented as the full summation of all of the cross-time correlation functions between the decomposition energy and the total solute-solvent interactions. Gaussian statistics of the total solute-solvent interactions ensure the same decay rates among the odd orders not only for the time-correlation functions but also for the cross-time correlation functions, validating the LR of the Stokes shift and the decompositions, respectively. The above mechanism is verified by molecular dynamics simulations in the protein Staphylococcus nuclease and is robust even as the decomposed energy associated with an individual residue exhibits typical non-Gaussian properties. Further examinations reveal the consistent molecular motions for a specific residue over the nonequilibrium and equilibrium processes, which are responsible for the nonequilibrium dynamics of the associated decomposed energy. Our results show the appropriateness of LR on finer molecular scales.

Dynamics of water and ions around DNA: What is so special about them?

Water around biomolecules is special for behaving strangely - both in terms of structure and dynamics, while ions are found to control various interactions in biomolecules such as DNA, proteins and lipids. The questions that how water and ions around these biomolecules behave in terms of their structure and dynamics, and how they affect the biomolecular functions have triggered tremendous research activities worldwide. Such activities not only unfolded important static and dynamic properties of water and ions around these biomolecules, but also provoked heated debate regarding their explanation and role in biological functions. DNA, being negatively charged, interacts strongly with the surrounding dipolar water and positively charged counterions, leading to complex electrostatic coupling of water and ions with the DNA. Recent timeresolved fluorescence Stokes shift experiments and related computer simulation studies from our and other laboratories have unfolded some unique dynamic characteristics of water and ions near different structures of DNA. These results are discussed here to showcase the specialty of water and ion dynamics around DNA.

Vibrational Frequency Fluctuation of Ions in Aqueous Solutions Studied by Three-Pulse Infrared Photon Echo Method

In liquid water, hydrogen bonds form three-dimensional network structures, which have been modeled in various molecular dynamics simulations. Locally, the hydrogen bonds continuously form and break, and the network structure continuously fluctuates. In aqueous solutions, the water molecules perturb the solute molecules, resulting in fluctuations of the electronic and vibrational states. These thermal fluctuations are fundamental to understanding the activation processes in chemical reactions and the function of biopolymers. In this Account, we review studies of the vibrational frequency fluctuations of solute molecules in aqueous solutions using three-pulse infrared photon echo experiments. For comparison, we also briefly describe dynamic fluorescence Stokes shift experiments for investigating solvation dynamics in water. The Stokes shift technique gives a response function, which describes the energy relaxation in the nonequilibrium state and corresponds to the transition energy fluctuation of the electronic state at thermal equilibrium in linear response theorem. The dielectric response of water in the megahertz to terahertz frequency region is a key physical quantity for understanding both of these frequency fluctuations because of the influence of electrostatic interactions between the solute and solvent. We focus on the temperature dependence of the three experiments to discuss the molecular mechanisms of both the frequency fluctuations in aqueous solutions. We used a biexponential function with sub-picosecond and picosecond time constants to characterize the time-correlation functions of both the vibrational and electronic frequency fluctuations. We focus on the slower component, with time constants of 1-2 ps for both the frequency fluctuations at room temperature. However, the temperature dependence and isotope effect for the time constants differ for these two types of fluctuations. The dielectric interactions generally describe the solvation dynamics of polar solvents, and hydrodynamic theory can describe the slow component for the electronic states. Compared with the slow component of the solvation dynamics, however, the picosecond component for the vibrational frequency fluctuations is less sensitive to temperature. Therefore, the slow component of the vibrational frequency fluctuation is determined by different underlying dynamics, which are important for the solvation dynamics of the electronic state. The time constant for the picosecond component for the vibrational frequency fluctuation does not significantly depend on the solute. We propose that the vibrational frequency fluctuates because of the constant structural changes in the hydrogen-bonding network of water molecules around the solute.

Hydration Dynamics As Revealed By The Fluorescence Stokes Shift: The Origin Of Slow Hydration Dynamics And Breakdown Of Linear Response

Hydration dynamics in the immediate vicinity of a protein, probed by time-dependent fluorescence Stokes shift experiments, is critical to understand its biological function. Protein Stokes shifts typically exhibit biphasic relaxation following photo-excitation: fast relaxation occurs on a time scale of several picoseconds while slower components indicate additional hydration dynamics on a time scale of tens of picoseconds, or longer. Theoretical studies using both linear response and non-equilibrium molecular dynamics (MD) calculation qualitatively reproduce the observed biphasic behavior of time dependent Stokes shift for Trp-7 (W7) in myoglobin. Comparison with constrained MD simulations with protein frozen at the instant of photo-excitation reveals the molecular mechanism of slow hydration process and establishes the critical role of protein flexibility. Coupled protein-water motion is shown to be necessary for the observation of the slow component of hydration dynamics. Qualitatively similar results are found for a series of additional cases, such as monellin and staph. nuclease. We illustrate why tracking the separate contributions to the Stokes shift without constrained MD studies may not yield an accurate interpretation of protein hydration dynamics. Additionally, we examine the extent to which protein fluctuations obey Gaussian statistics and the linear response approximation to the Stokes shift is valid. Equilibrium fluctuations of the ground-excited energy difference, which control the absorption and fluorescence line shapes, in the ground and excited electronic states are not independent of each other. We illustrate how small differences from Gaussian statistics in one electronic state can be a signature of very significant deviations from linear response theory, such as isomerization, in the other electronic state.

A simple power-law approximation for the solvation time correlation function

In previous work we developed a new class of molecular theories of solvation, the “surrogate Hamiltonian” (SH) theories, to elucidate the structural, energetic, and dynamical aspects of the solvation process relevant to ultrafast time-domain spectroscopy and charge transfer reactions in solution. In these theories we represent both the solute and the solvent molecules by interaction site models of the sort already used in many computer simulation studies of solutions. Of special interest to the characterization of the nonequilibrium solvation process is the solvation time correlation function Z(t), that can be obtained in time-dependent fluorescence Stokes shift experiments. The experimental and theoretical studies of Z(t) in polar solvents have revealed an important dependence of the solvation time correlation function on the nature of the solute, especially with respect to the multipolar order of the charge jump. Here we investigate a simplified version of our theory of solvation dynamics, which is based on the straightforward application of a method previously developed by our group, the reference frequency modulation approximation (RFMA). In the earlier paper we showed that when applied to the solvation tcf, the RFMA leads to a simple interpretation of the power law equation for Z(t)found empirically by Maroncelli and coworkers. Here we propose a new power-law approximation to the solvation time correlation function that retains the dependence of Z(t) on the features of the solute. More specifically, the new application of the RFMA discussed here enables us to express the solvation tcf Zy(t) of solute Y in terms of the solvation tcf ZR(t) of another solute R in the same solvent. The solutes R and Y may differ in size, shape, and charge distribution. The consistency of Z(t) calculated with more accurate methods and the simpler RFMA theory is quite satisfactory.

CHROMOPHORE-SOLVENT DYNAMICS

▪ Abstract Experimental and theoretical studies of polar solvation dynamics and spectral line broadening are described. Photon echo and fluorescence Stokes shift experiments are discussed, and the relationship between the information content of the two techniques clarified. The interaction of the chromophore with its solvent bath is described by a spectral density, and the connection of this spectral density with the liquid's instantaneous normal modes discussed. The ubiquity of the ultrafast phase of solvation dynamics is demonstrated, and a discussion of its physical origin given. The slower phases of solvation vary strongly from solvent to solvent. Molecular theories of liquid dynamics are able to rationalize such variations over at least a 2000-fold range of time scale. The review concludes with a brief discussion of the relevance of ultrafast solvation to chemical dynamics.

An integral equation approximation for the dynamics of reversible electron-transfer reactions

The solution to an integral equation [J. Zhu and J. C. Rasaiah, J. Chem. Phys. 96, 1435 (1992)] for the survival probabilities in the Sumi–Marcus model of reversible electron-transfer (ET) reactions, in which ligand vibrations and fluctuations in the solvent polarization play important roles, is obtained numerically using a simple computer program suitable for use on a PC. The solutions depend on the time correlation function Δ(t) of the reacting intermediates along the reaction coordinate which is shown to be equal to the time correlation function of the Born free energy of solvation of these intermediates even in discrete molecular solvents provided its response is linear. This enables Δ(t) to be determined accurately from time-delayed fluorescence Stokes shift experiments or from dynamical theories of ion solvation; it is usually an exponential (Debye solvent) function of time or a sum of such exponentials (non-Debye solvent). The solutions to the integral equation, which can be obtained numerically for any given Δ(t), are found to predict the electron-transfer dynamics successfully over a wide range of model parameters. They can also be approximated by single or multiexponential interpolation formulas in which the thermally equilibrated rate constants are modified by a factor which reflects the relative importance of ligand (or inner-sphere solvent) vibration and outer-sphere solvation dynamics. The use of an effective longitudinal relaxation time in calculations of ET rates in solution is shown to be a poor assumption in some solvents. The theory is compared with an experiment in the inversion region, and its extension to include high-frequency vibrational modes that lead to an increased ET rate in other experiments is discussed.