Relaxation spectral analysis in multi-contrast vascular magnetic particle imaging.

BACKGROUND: Magnetic nanoparticles (MNPs) are used as tracers without ionizing radiation in vascular imaging, molecular imaging, and neuroimaging. The relaxation mechanisms of magnetization in response to excitation magnetic fields are important features of MNPs. The basic relaxation mechanisms include internal rotation (Néel relaxation) and external physical rotation (Brownian relaxation). Accurate measurement of these relaxation times may provide high sensitivity for predicting MNP types and viscosity-based hydrodynamic states. It is challenging to separately measure the Néel and Brownian relaxation components using sinusoidal excitation in conventional MPI. PURPOSE: We developed a multi-exponential relaxation spectral analysis method to separately measure the Néel and Brownian relaxation times in the magnetization recovery process in pulsed vascular MPI. METHODS: Synomag-D samples with different viscosities were excited using pulsed excitation in a trapezoidal-waveform relaxometer. The samples were excited at different field amplitudes ranging from 0.5 to 10 mT at intervals of 0.5 mT. The inverse Laplace transform-based spectral analysis of the relaxation-induced decay signal in the field-flat phase was performed by using PDCO, a primal-dual interior method for convex objectives. Néel and Brownian relaxation peaks were elucidated and measured on samples with various glycerol and gelatin concentrations. The sensitivity of viscosity prediction of the decoupled relaxation times was evaluated. A digital vascular phantom was designed to mimic a plaque with viscous MNPs and a catheter with immobilized MNPs. Spectral imaging of the digital vascular phantom was simulated by combining a field-free point with homogeneous pulsed excitation. The relationship between the Brownian relaxation time from different tissues and the number of periods for signal averages was evaluated for a scan time estimation in the simulation. RESULTS: The relaxation spectra of synomag-D samples with different viscosity levels exhibited two relaxation time peaks. The Brownian relaxation time had a positive linear relationship with the viscosity in the range 0.9 to 3.2 mPa · s. When the viscosity was >3.2 mPa · s, the Brownian relaxation time saturated and did not change with increasing viscosity. The Néel relaxation time decreased slightly with an increase in the viscosity. The Néel relaxation time exhibited a similar saturation effect when the viscosity level was >3.2 mPa · s for all field amplitudes. The sensitivity of the Brownian relaxation time increased with the field amplitude and was maximized at approximately 4.5 mT. The plaque and catheter regions were differentiated from the vessel region in the simulated Brownian relaxation time map. The simulation results show that the Néel relaxation time was 8.33±0.09 µs in the plaque region, 8.30±0.08 µs in the catheter region, and 8.46±0.11 µs in the vessel region. The Brownian relaxation time was 36.60±2.31 µs in the plaque region, 30.17±1.24 µs in the catheter region, and 31.21±1.53 µs in the vessel region. If we used 20 excitation periods for image acquisition in the simulation, the total scan time of the digital phantom was approximately 100 s. CONCLUSION: Quantitative assessment of the Néel and Brownian relaxation times through inverse Laplace transform-based spectral analysis in pulsed excitation, highlighting their potential for use in multi-contrast vascular MPI.

Explicit Projection of Stokes Shifts onto Solvent Motion in an Aqueous Liquid and Linear Response Theory.

We investigate the molecular origin of the fluorescence Stokes shift in an aqueous liquid. By examining the speed of energy change, the solvation response function is explicitly projected onto the translational and rotational motions of water molecules for both nonequilibrium relaxation and equilibrium fluctuations. Molecular dynamics simulations of a tryptophan solution show that these two processes have highly consistent dynamics, not only for the total response function but also for the decomposed components in terms of specific molecular movements. We found that the rotational mode governs the relaxation of the Stokes shift, whereas the translational mode contributes non-negligibly with slower dynamics. This consistency implies the similarity of the underlying translational and rotational movements of water molecules as the system is far away from and at equilibrium, supporting the validity of the linear response theory at the molecular level. The decomposition methodology is also applicable to a rigid solvent.

Gradient-Based Pulsed Excitation and Relaxation Encoding in Magnetic Particle Imaging.

Magnetic particle imaging (MPI) is a radiation-free vessel- and target-imaging modality that can sensitively detect nanoparticles. A static magnetic gradient field, referred to as a selection field, is required in MPI to provide a field-free region (FFR) for spatial encoding. The image resolution of MPI is closely related to the size of the FFR, which is determined by the selection field gradient amplitude. Because of the limitations of existing gradient coil hardware, the image resolution of MPI cannot satisfy the clinical requirements of human in vivo imaging. Pulsed excitation has been confirmed to improve the image resolution of MPI by breaking down the 'relaxation wall.' This work proposes the use of a pulsed waveform magnetic gradient from magnetic resonance imaging to further improve the image resolution of MPI. Through alignment of the gradient direction along the field-free line (FFL), each location on the FFL is able to have a unique excitation field strength that generates a specific relaxation-induced decay signal. Through excitation of nanoparticles on the FFL with many gradient profiles, a high-resolution, one-dimensional (1D) image can be reconstructed on the FFL. For larger magnetic nanoparticles, simulation results revealed that a pulsed excitation field with a greater flat portion generates a 1D bar pattern phantom image with a higher correlation and spatial resolution. With parallel FFL and gradient coil movements, high-resolution, two-dimensional (2D) Shepp-Logan phantom and brain vessel maps were reconstructed through repetition of the spatially resolved measurement of magnetic nanoparticles on the FFL.

Development of Radiofrequency Saturation Amplitude-independent Quantitative Markers for Magnetization Transfer MRI of Prostate Cancer.

BACKGROUND: In the United States, prostate cancer has a relatively large impact on men's health. Magnetic resonance imaging (MRI) is useful for the diagnosis and treatment of prostate cancer. INTRODUCTION: The purpose of this study was to develop a quantitative marker for use in prostate cancer magnetization transfer (MT) magnetic resonance imaging (MRI) studies that is independent of radiofrequency (RF) saturation amplitude. METHODS: Eighteen patients with biopsy-proven prostate cancer were enrolled in this study. MTMRI images were acquired using four RF saturation amplitudes at 33 frequency offsets. ROIs were delineated for the peripheral zone (PZ), central gland (CG), and tumor. Z-spectral data were collected in each region and fit to a three-parameter equation. The three parameters are: the magnitude of the bulk water pool (Aw), the full width at half maximum of the water pool (Gw), and the magnitude of the bound pool (Ab), while, the slopes from the linear regressions of Gw and Ab on RF saturation amplitude (called kAb and kGw) were used as quantitative markers. RESULTS: A pairwise statistically significant difference was found between the PZ and tumor regions for the two saturation amplitude-independent quantitative markers. No pairwise statistically significant differences were found between the CG and tumor regions for any quantitative markers. CONCLUSION: The significant differences between the values of the two RF saturation amplitudeindependent quantitative markers in the PZ and tumor regions reveal that these markers may be capable of distinguishing healthy PZ tissue from prostate cancer.

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.

To unravel the connection between the non-equilibrium and equilibrium solvation dynamics of tryptophan: success and failure of the linear response theory of fluorescence Stokes shift.

The connections between the non-equilibrium solvation dynamics upon optical transitions and the system's equilibrium fluctuations are explored in aqueous liquid. Linear response theory correlates time-dependent fluorescence with the equilibrium time correlation functions. In the previous work [T. Li, J. Chem. Theory Comput., 2017, 13, 1867], Stokes shift was explicitly decomposed into the contributions of various order time correlation functions on the excited state surface. Gaussian fluctuations of the solute-solvent interactions validate linear response theory. Correspondingly, the deviation of the Gaussian statistics causes the inefficiency of linear response evaluation. The above mechanism is thoroughly tested in this study. By employing molecular simulations, multiple non-equilibrium processes, not necessarily initiated from the ground state equilibrium minimum, were examined for tryptophan. Both the success and failure of linear response theory are found for this simple system and the mechanism is analyzed. These observations, assisted by the width dynamics, the initial state linear response approach, and the variation of the solvation structures, integrally verify the virtue of the excited state Gaussian statistics on the dynamics of Stokes shift.

Magnetic resonance elastography of the brain: A study of feasibility and reproducibility using an ergonomic pillow-like passive driver.

Magnetic resonance elastography (MRE) can be used to noninvasively resolve the displacement pattern of induced mechanical waves propagating in tissue. The goal of this study is to establish an ergonomically flexible passive-driver design for brain MRE, to evaluate the reproducibility of MRE tissue-stiffness measurements, and to investigate the relationship between tissue-stiffness measurements and driver frequencies. An ergonomically flexible passive pillow-like driver was designed to induce mechanical waves in the brain. Two-dimensional finite-element simulation was used to evaluate mechanical wave propagation patterns in brain tissues. MRE scans were performed on 10 healthy volunteers at mechanical frequencies of 60, 50, and 40 Hz. An axial mid-brain slice was acquired using an echo-planar imaging sequence to map the displacement pattern with the motion-encoding gradient along the through-plane (z) direction. All subjects were scanned and rescanned within 1 h. The Wilcoxon signed-rank test was used to test for differences between white matter and gray matter shear-stiffness values. One-way analysis of variance (ANOVA) was used to test for differences between shear-stiffness measurements made at different frequencies. Scan-rescan reproducibility was evaluated by calculating the within-subject coefficient of variation (CV) for each subject. The finite-element simulation showed that a pillow-like passive driver is capable of efficient shear-wave propagation through brain tissue. No subjects complained about discomfort during MRE acquisitions using the ergonomically designed driver. The white-matter elastic modulus (mean ±â€¯standard deviation) across all subjects was 3.85 ±â€¯0.12 kPa, 3.78 ±â€¯0.15 kPa, and 3.36 ±â€¯0.11 kPa at frequencies of 60, 50, and 40 Hz, respectively. The gray-matter elastic modulus across all subjects was 3.33 ±â€¯0.14 kPa, 2.82 ±â€¯0.16 kPa, and 2.24 ±â€¯0.14 kPa at frequencies of 60, 50, and 40 Hz, respectively. The Wilcoxon signed-rank test confirmed that the shear stiffness was significantly higher in white matter than gray matter at all three frequencies. The ranges of within-subject coefficients of variation for white matter, gray matter, and whole-brain shear-stiffness measurements for the three frequencies were 1.8-3.5% (60 Hz), 4.7-6.0% (50 Hz), and 3.7-4.1% (40 Hz). An ergonomic pneumatic pillow-like driver is feasible for highly reproducible in vivo evaluation of brain-tissue shear stiffness. Brain-tissue shear-stiffness values were frequency-dependent, thus emphasizing the importance of standardizing MRE acquisition protocols in multi-center studies.

Theoretical Insights on Nonlinear Response Theory of Fluorescence Spectroscopy in Liquids.

Correlations between the nonequilibrium solvation dynamics upon the photon excitation of the chromophore and a system's equilibrium fluctuations are deeply studied. As the linear response of the solvent has been linked with Gaussian statistics of the energy fluctuations in the literature, we specifically explore the cases beyond the regime of the linear response theory due to deviation from Gaussian fluctuations. As a continuation of our previous work, an analytical formalism is presented to project the energy shift with various order moments, where the non-Gaussian statistics arise from the overlap of the energy basins on the perturbed potential energy surface. It is shown that the nonequilibrium dynamics still correlate with the spontaneous regressions at equilibrium and are controlled by the decay rates of those higher order components with the prevailing contributions to the energy shift. Molecular dynamics simulations were performed in the protein Staphylococcus nuclease, in which even the dynamics of the high order moments are available. The results further verify the above relationship. Our scheme is used to evaluate Stokes shift using the information on non-Gaussian statistics at equilibrium, thus presenting a broad picture on the correlation between the nonequilibrium process and equilibrium properties in liquids.

Effect of chemical structure of S-nitrosothiols on nitric oxide release mediated by the copper sites of a metal organic framework based environment.

The effect of chemical structure of different biologically compatible S-nitrosothiols on the solvation environment at catalytic copper sites in a metal organic framework (MOF) suspended in a solution of ethanol is probed using computational methods. The use of a copper based MOF as a storage vehicle and catalyst (copper sites of the MOF) in the controlled and sustained release of chemically stored nitric oxide (NO) from S-nitrosocysteine has been shown to occur both experimentally and computationally [J. Am. Chem. Soc., 2012, 134, 3330-3333; Phys. Chem. Chem. Phys., 2015, 17, 23403]. Previous studies on a copper based MOF, namely HKUST-1, concluded that modifications in the R-group of s-nitrosothiols and/or organic linkers of MOFs led to a method capable of modulating NO release. In order to test the hypothesis that larger R-groups slow down NO release, four different RSNOs (R = cysteine, N-acetylcysteine, N-acetyl-d,l-penicillamine or glutathione) of varying size were investigated, which in turn required the use of a larger copper based MOF. Due to its desirable copper centers and more extensive framework, MOF-143, an analog of HKUST-1 was chosen to further explore both the effect of different RSNOs as well as MOF environments on NO release. Condensed phase classical molecular dynamics simulations are utilized to study the effect of the complex MOF environment as well as the chemical structure and size of the RSNO on the species on the catalytic reaction. The results indicate that in addition to the size of the RSNO species and the organic linkers within the MOF, the reaction rates can be modulated by the molecular structure of the RSNO and furthermore combining different RSNO species can also be used to tune the rate of NO release.

Efficient Criterion To Evaluate Linear Response Theory in Optical Transitions.

The role of the Gaussian statistics on the solvation dynamics upon the photon excitation of the chromophore is deeply explored. The linear response theory for the fluorescence Stokes shift is investigated. An analytical formulism is presented to recast Stokes shift into the contributions of the equilibrium time correlation functions of the solute-solvent interactions on the excited-state surface, and the latter is further reformed and depicted by the time relaxation of the moment. As the first application of the formulism in the molecular dynamics simulations, it is verified that the efficiency of the linear response theory relies on the Gaussian characteristics of the dominant moments in terms of the Stokes shift, which is identified by the same relaxation dynamics between those moments and the linear order one. The comparisons between the above observations on the linearity of Stokes shift and the explanations in the literature are discussed. The key finding is the development of explicit criterion to measure the appropriateness of applying linear response theory.

Role of excited state solvent fluctuations on time-dependent fluorescence Stokes shift.

We explore the connection between the solvation dynamics of a chromophore upon photon excitation and equilibrium fluctuations of the solvent. Using molecular dynamics simulations, fluorescence Stokes shift for the tryptophan in Staphylococcus nuclease was examined using both nonequilibrium calculations and linear response theory. When the perturbed and unperturbed surfaces exhibit different solvent equilibrium fluctuations, the linear response approach on the former surface shows agreement with the nonequilibrium process. This agreement is excellent when the perturbed surface exhibits Gaussian statistics and qualitative in the case of an isomerization induced non-Gaussian statistics. However, the linear response theory on the unperturbed surface breaks down even in the presence of Gaussian fluctuations. Experiments also provide evidence of the connection between the excited state solvent fluctuations and the total fluorescence shift. These observations indicate that the equilibrium statistics on the excited state surface characterize the relaxation dynamics of the fluorescence Stokes shift. Our studies specifically analyze the Gaussian fluctuations of the solvent in the complex protein environment and further confirm the role of solvent fluctuations on the excited state surface. The results are consistent with previous investigations, found in the literature, of solutes dissolved in liquids.

A computational study of the effect of the metal organic framework environment on the release of chemically stored nitric oxide.

The use of copper based metal organic frameworks as a vehicle for the storage and delivery of chemically stored nitric oxide has been proposed based on recent experiments [J. Am. Chem. Soc., 2012, 134, 3330-3333]. In these experiments copper based metal organic frameworks (MOFs) suspended in ethanol catalytically convert chemically stored nitric oxide (in the S-nitrosothiol or RSNO form) to free nitric oxide at a slow and sustained rate, as compared to a quick release in a solution of ethanol containing free copper ions. In order to gain insight on the effect of the MOF environment on the catalytic activity, a combination of electronic structure calculations on representative clusters and classical simulations using a force-field (partly parameterized on the above calculations) is used to study a simple RSNO species, S-nitrosomethane (CH3SNO) as well as the biologically compatible S-nitrosocysteine, both in the MOF and free copper solution. The free energy profiles of bringing the RSNO species to the catalytic centers have been compared and related to the different solvation environments of the copper catalyst in the complex solvated MOF and in free copper solution. Surprisingly, in the case of the simple CH3SNO moiety as well as the S-nitrosocysteine case, the free energy profile of bringing the first RSNO from the center of one of the pores to the catalytic site in the pore is very similar to the free solution case. On the other hand, bringing a second RSNO molecule to the same catalytic site or to the adjacent catalytic copper site show relatively higher barriers. These studies help shed light on the sustained nitric oxide release in the MOF environment.

Hydration and vibrational dynamics of betaine (N,N,N-trimethylglycine).

Zwitterions are naturally occurring molecules that have a positive and a negative charge group in its structure and are of great importance in many areas of science. Here, the vibrational and hydration dynamics of the zwitterionic system betaine (N,N,N-trimethylglycine) is reported. The linear infrared spectrum of aqueous betaine exhibits an asymmetric band in the 1550-1700 cm(-1) region of the spectrum. This band is attributed to the carboxylate asymmetric stretch of betaine. The potential of mean force computed from ab initio molecular dynamic simulations confirms that the two observed transitions of the linear spectrum are related to two different betaine conformers present in solution. A model of the experimental data using non-linear response theory agrees very well with a vibrational model comprising of two vibrational transitions. In addition, our modeling shows that spectral parameters such as the slope of the zeroth contour plot and central line slope are both sensitive to the presence of overlapping transitions. The vibrational dynamics of the system reveals an ultrafast decay of the vibrational population relaxation as well as the correlation of frequency-frequency correlation function (FFCF). A decay of ∼0.5 ps is observed for the FFCF correlation time and is attributed to the frequency fluctuations caused by the motions of water molecules in the solvation shell. The comparison of the experimental observations with simulations of the FFCF from ab initio molecular dynamics and a density functional theory frequency map shows a very good agreement corroborating the correct characterization and assignment of the derived parameters.

[Analysis of Trace Inorganic Elements in Castor Oil by Inductively Coupled Plasma Mass Spectrometry].

A method for the determination of Na, Mg, Si, P, K, Ca, Cr, Mn, Fe, Co, Ni, Cu, Zn, As, Se, Sr, Mo, Cd, Hg and Pb in castor oil after direct dilution with ethanol by inductively coupled plasma mass spectrometry (ICP-MS) was established. The sample was diluted by ethanol before ICP-MS determination. The condensation and deposition of high concentrations of carbon in mass cone interface and ion lens, which will decrease the sensitivity of element analysis, were avoided effectively by introducing O2 to plasma. The mass spectral interferences were eliminated by octopole reaction system (ORS). The matrix effects were calibrated to using Sc, Ge, Rh and Ir as internal standard elements. Au standard solution, which could form amalgam alloy with Hg, was dropped to eliminate the memory effect of Hg. The results show that the correlation coefficient for analyte is no less than 0.999 5, the detection limits is in the range of 0.06 - 20.1 ng x L(-1), the recovery is in the range of 990.4% - 110.2%, and the RSD is less than 4.8%. This method was very fast, simple and accurate to simultaneously analyze multi-elements in castor oil.

Validity of linear response theory for time-dependent fluorescence in Staphylococcus nuclease.

We report a theoretical study on the relaxation dynamics of Staphylococcus nuclease following photon excitation. Molecular dynamics simulations were implemented for both ground state and excited state surface of Trp140. Over the course of 40 ns ground state simulation, a structural transition was observed from one isomeric protein configuration to another. No obvious isomerization process was exhibited in the excited state simulations. Using linear response theory and direct nonequilibrium approach, time-dependent Stokes shift, as well as its time-infinity value, was evaluated for both ground state isomers. Comparison between these methods exhibits severe disagreement. The nonequilibrium simulations show the similar relaxation dynamics as the excited state linear response approach, whereas they severely differ from the ground state linear response evaluation. Further examination reveals that the isomerization process breaks the characteristics of the energy gap histogram from Gaussian statistics. We also made the comparison between the experimental and simulation results. The significant inertial decay, in theory, is absent in the experiment. The ground state linear response evaluation provides a better agreement with the experimental results among all three approaches.

[Determination of impurity elements in edible phosphate by ICP-MS].

An octopole reaction system (ORS) inductively coupled plasma mass spectrometry (ICP-MS) was developed for the determination of Mg, Ti, V, Cr, Fe, Co, Ni, Cu, Zn, As, Cd and Pb in edible phosphate. The sample was digested by HNO3 followed by dilution with ultrapure water, then the above 12 impurity elements in the solution were analyzed directly by ICP-MS The use of ORS can eliminate the interference of polyatomic ions dramatically. Sc, Y, In and Bi were used to correct the matrix interference and drift. The detection limits of the 12 elements are in the range of 0.004-0.362 microg x L(-1). This method is rapid, simple and applicable for the analysis of trace elements in edible phosphate.

Mapping solvation dynamics at the function site of flavodoxin in three redox states.

Flavoproteins are unique redox coenzymes, and the dynamic solvation at their function sites is critical to the understanding of their electron-transfer properties. Here, we report our complete characterization of the function-site solvation of holoflavodoxin in three redox states and of the binding-site solvation of apoflavodoxin. Using intrinsic flavin cofactor and tryptophan residue as the local optical probes with two site-specific mutations, we observed distinct ultrafast solvation dynamics at the function site in the three states and at the related recognition site of the cofactor, ranging from a few to hundreds of picoseconds. The initial ultrafast motion in 1-2.6 ps reflects the local water-network relaxation around the shallow, solvent-exposed function site. The second relaxation in 20-40 ps results from the coupled local water-protein fluctuation. The third dynamics in hundreds of picoseconds is from the intrinsic fluctuation of the loose loops flanking the cofactor at the function site. These solvation dynamics with different amplitudes well correlate with the redox states from the oxidized form, to the more rigid semiquinone and to the much looser hydroquinone. This observation of the redox control of local protein conformation plasticity and water network flexibility is significant, and such an intimate relationship is essential to the biological function of interprotein electron transfer.

Ultrafast solvation dynamics at binding and active sites of photolyases.

Dynamic solvation at binding and active sites is critical to protein recognition and enzyme catalysis. We report here the complete characterization of ultrafast solvation dynamics at the recognition site of photoantenna molecule and at the active site of cofactor/substrate in enzyme photolyase by examining femtosecond-resolved fluorescence dynamics and the entire emission spectra. With direct use of intrinsic antenna and cofactor chromophores, we observed the local environment relaxation on the time scales from a few picoseconds to nearly a nanosecond. Unlike conventional solvation where the Stokes shift is apparent, we observed obvious spectral shape changes with the minor, small, and large spectral shifts in three function sites. These emission profile changes directly reflect the modulation of chromophore's excited states by locally constrained protein and trapped-water collective motions. Such heterogeneous dynamics continuously tune local configurations to optimize photolyase's function through resonance energy transfer from the antenna to the cofactor for energy efficiency and then electron transfer between the cofactor and the substrate for repair of damaged DNA. Such unusual solvation and synergetic dynamics should be general in function sites of proteins.

Origin of slow relaxation following photoexcitation of W7 in myoglobin and the dynamics of its hydration layer.

Molecular dynamics simulations are used to calculate the time-dependent Stokes shift following photoexcitation of Trp-7 (W7) in myoglobin. In agreement with experiment, a long time (approximately 60 ps) component is observed. Since the long time Stokes shift component is absent when we repeat the calculation with protein frozen at the instant of photoexcitation, we firmly establish that protein flexibility is required to observe slow Stokes shift dynamics in this case. A transition between sub-states near the middle of a 30 ns ground-state trajectory gave us an opportunity to compare solvation dynamics in two different environments. While some of the superficial features are different, we find that the underlying dynamics are shared by the two isomers. It is necessary to look beyond a decomposition of the Stokes shift into protein and water contributions and probe the underlying dynamics of protein side groups, backbone, and water dynamics to obtain a full picture of the relaxation process. We analyze water residence times, diffusion, and reorientation dynamics in the hydration layer. We find slow components in each of these quantities and critically examine their origin and how they affect the observed Stokes shift.

Hydration dynamics and time scales of coupled water-protein fluctuations.

We report experimental and theoretical studies on water and protein dynamics following photoexcitation of apomyoglobin. Using site-directed mutation and with femtosecond resolution, we experimentally observed relaxation dynamics with a biphasic distribution of time scales, 5 and 87 ps, around the site Trp7. Theoretical studies using both linear response and direct nonequilibrium molecular dynamics (MD) calculations reproduced the biphasic behavior. Further constrained MD simulations with either frozen protein or frozen water revealed the molecular mechanism of slow hydration processes and elucidated the role of protein fluctuations. Observation of slow water dynamics in MD simulations requires protein flexibility, regardless of whether the slow Stokes shift component results from the water or protein contribution. The initial dynamics in a few picoseconds represents fast local motions such as reorientations and translations of hydrating water molecules, followed by slow relaxation involving strongly coupled water-protein motions. We observed a transition from one isomeric protein configuration to another after 10 ns during our 30 ns ground-state simulation. For one isomer, the surface hydration energy dominates the slow component of the total relaxation energy. For the other isomer, the slow component is dominated by protein interactions with the chromophore. In both cases, coupled water-protein motion is shown to be necessary for observation of the slow dynamics. Such biologically important water-protein motions occur on tens of picoseconds. One significant discrepancy exists between theory and experiment, the large inertial relaxation predicted by simulations but clearly absent in experiment. Further improvements required in the theoretical model are discussed.