On the quantitative molecular analysis of electronic energy transfer within donor-acceptor pairs

An extended F?rster theory (EFT) on electronic energy transfer is presented for the quantitative analysis of time-resolved fluorescence lifetime and depolarisation experiments. The EFT, which was derived from the stochastic Liouville equation, yields microscopic information concerning the reorientation correlation times, the order parameters, as well as inter chromophoric distances. Weakly interacting donor and acceptor groups, which reorient and interact in a pair wise fashion, are considered, under isotropic and anisotropic conditions. For the analysis of experiments it is shown that not only do we need to consider the orientational distributions of the transition dipoles, but the internal reorienting molecular dynamics within the pair which is of even greater importance. The latter determines the shape as well as the rate of the observed donor fluorescence and depolarisation decays, which are most often not mono-exponential functions. It is shown that the commonly used F?rster theory is a special case of the EFT. Strategies are presented for applying the EFT, which makes use of Brownian dynamics simulation.     

Partial donor-donor energy migration (PDDEM) as a fluorescence spectroscopic tool for measuring distances in biomacromolecules

A theoretical model is presented, tested and applied for determining the rates of energy migration and distances within pairs of chemically identical fluorophores, so-called donors (D), which are exposed to different physical properties. The model is a general extension of the recently developed donor-donor energy migration (DDEM) model [J. Chem. Soc., Faraday Trans. 92 (1996)1563; J. Chem. Phys. 105 (1996) 10896] that applies to examining structure-function of biomacromolecules, such as proteins. Most fluorescent groups of the same kind incorporated at different positions (alpha and beta) in a macromolecule exhibit shifts of the absorption and/or emission spectra, as well as different relaxation rates of the photophysics. As a consequence, the energy migration between the D(alpha) and D(beta) groups will be partially reversible. We refer to this case, as the partial donor-donor energy migration (PDDEM). The models of PPDEM presented can be used for analysing time-resolved fluorescence relaxation, as well as fluorescence depolarisation experiments. To explore the limitations of the PDDEM model, we have generated and re-analysed synthetic data that mimic time-correlated single photon counting (TCSPC) experiments. It was found that slow and fast rates of energy migration are most accurately recovered from the fluorescence relaxation and the depolarisation experiments, respectively. At comparable transfer and fluorescence rates, both kinds of experiments are equally useful. Real experiments on PDDEM were performed on an asymmetrically quenched bichromophoric molecule (1,32-dihydroxy-dotriacontane-bis-(Rhodamine 101) ester), that spans across the lipid bilayer of a vesicle. The depolarisation data were analysed by the PDDEM model and provide a distance between Rhodamine 101 groups, which agrees with independent studies.     

General framework for studying the dynamics of folded and nonfolded proteins by NMR relaxation spectroscopy and MD simulation

A general framework is presented for the interpretation of NMR relaxation data of proteins. The method, termed isotropic reorientational eigenmode dynamics (iRED), relies on a principal component analysis of the isotropically averaged covariance matrix of the lattice functions of the spin interactions responsible for spin relaxation. The covariance matrix, which is evaluated using a molecular dynamics (MD) simulation, is diagonalized yielding reorientational eigenmodes and amplitudes that reveal detailed information about correlated protein dynamics. The eigenvalue distribution allows one to quantitatively assess whether overall and internal motions are statistically separable. To each eigenmode belongs a correlation time that can be adjusted to optimally reproduce experimental relaxation parameters. A key feature of the method is that it does not require separability of overall tumbling and internal motions, which makes it applicable to a wide range of systems, such as folded, partially folded, and unfolded biomolecular systems and other macromolecules in solution. The approach was applied to NMR relaxation data of ubiquitin collected at multiple magnetic fields in the native form and in the partially folded A-state using MD trajectories with lengths of 6 and 70 ns. The relaxation data of native ubiquitin are well reproduced after adjustment of the correlation times of the 10 largest eigenmodes. For this state, a high degree of separability between internal and overall motions is present as is reflected in large amplitude and collectivity gaps between internal and overall reorientational modes. In contrast, no such separability exists for the A-state. Residual overall tumbling motion involving the N-terminal beta-sheet and the central helix is observed for two of the largest modes only. By adjusting the correlation times of the 10 largest modes, a high degree of consistency between the experimental relaxation data and the iRED model is reached for this highly flexible biomolecule.     

High-resolution solid-state 2H NMR spectroscopy of polymorphs of glycine

High-resolution solid-state (2)H MAS NMR studies of the α and γ polymorphs of fully deuterated glycine (glycine-d(5)) are reported. Analysis of spinning sideband patterns is used to determine the (2)H quadrupole interaction parameters, and is shown to yield good agreement with the corresponding parameters determined from single-crystal (2)H NMR measurements (the maximum deviation in quadrupole coupling constants determined from these two approaches is only 1%). From analysis of simulated (2)H MAS NMR sideband patterns as a function of reorientational jump frequency (κ) for the -N(+)D(3) group in glycine-d(5), the experimentally observed differences in the (2)H MAS NMR spectrum for the -N(+)D(3) deutrons in the α and γ polymorphs is attributed to differences in the rate of reorientation of the -N(+)D(3) group. These simulations show severe broadening of the (2)H MAS NMR signal in the intermediate motion regime, suggesting that deuterons undergoing reorientational motions at rates in the range κ ≈ 10(4)-10(6) s(-1) are likely to be undetectable in (2)H MAS NMR measurements for materials with natural isotopic abundances. The (1)H NMR chemical shifts for the α and γ polymorphs of glycine have been determined from the (2)H MAS NMR results, taking into account the known second-order shift. Further quantum mechanical calculations of (2)H quadrupole interaction parameters and (1)H chemical shifts reveal the structural dependence of these parameters in the two polymorphs and suggest that the existence of two short intermolecular C-H···O contacts for one of the H atoms of the >CH(2) group in the α polymorph have a significant influence on the (2)H quadrupole coupling and (1)H chemical shift for this site.     

Temperature dependence of anisotropic protein backbone dynamics

The measurement of (15)N NMR spin relaxation, which reports the (15)N-(1)H vector reorientational dynamics, is a widely used experimental method to assess the motion of the protein backbone. Here, we investigate whether the (15)N-(1)H vector motions are representative of the overall backbone motions, by analyzing the temperature dependence of the (15)N-(1)H and (13)CO-(13)C(alpha) reorientational dynamics for the small proteins binase and ubiquitin. The latter dynamics were measured using NMR cross-correlated relaxation experiments. The data show that, on average, the (15)N-(1)H order parameters decrease only by 2.5% between 5 and 30 degrees C. In contrast, the (13)CO-(13)C(alpha) order parameters decrease by 10% over the same temperature trajectory. This strongly indicates that there are polypeptide-backbone motions activated at room temperature that are not sensed by the (15)N-(1)H vector. Our findings are at variance with the common crank-shaft model for protein backbone dynamics, which predicts the opposite behavior. This study suggests that investigation of the (15)N relaxation alone would lead to underestimation of the dynamics of the protein backbone and the entropy contained therein.     

Mechanisms for fluorescence depolarization in dendrimers

We have investigated the fluorescence properties of dendrimers (Gn is the dendrimer generation number) containing four different luminophores, namely terphenyl (T), dansyl (D), stilbenyl (S), and eosin (E). In the case of T, the dendrimers contain a single p-terphenyl fluorescent unit as a core with appended sulfonimide branches of different size and n-octyl chains. In the cases of D and S, multiple fluorescent units are appended in the periphery of poly(propylene amine) dendritic structures. In the case of E, the investigated luminophore is noncovalently linked to the dendritic scaffold, but is encapsulated in cavities of a low luminescent dendrimer. Depending on the photophysical properties of the fluorescent units and the structures of the dendrimers, different mechanisms of fluorescence depolarization have been observed: (i) global rotation for GnT dendrimers; (ii) global rotation and local motions of the dansyl units at the periphery of GnD dendrimers; (iii) energy migration among stylbenyl units in G2S; and (iv) restricted motion when E is encapsulated inside a dendrimer, coupled to energy migration if the dendrimer hosts more than one eosin molecule.     

Director reorientation in nematics studied by microwave dielectrometry

A new experimental method is presented which is a useful approach in studying the reorientational dynamics in liquid crystals by means of dielectric measurements at microwave frequencies. The theoretical model is developed to describe the motion of the director when it is driven by two orthogonal electric or magnetic fields. A specific set up for the experimental apparatus is described. Experiments in fairly good agreement with the theoretical model are given for a nematic mesophase at different temperatures and field values. The capabilities of the method in monitoring the slow reorientational properties of collective molecular motions in liquid crystals are demonstrated. Possible refinements of the experimental apparatus to allow more quantitative measurements of the different physical parameters of anisotropic media are indicated.     

NMR studies on effects of temperature, pressure, and fluorination on structures and dynamics of alcohols in liquid and supercritical states

We measured 1H NMR chemical shifts (delta H) and 1H and 2H NMR spin-lattice relaxation times (1H- and 2H-T1) of methanol, ethanol, 2-propanol, 2,2,2-trifluoroethanol, and 1,1,1,3,3,3-hexafluoro-2-propanol in the temperature range from 298 to 673 K at reduced pressures ( Pr = P/ Pc) of 1.22 and 3.14. The delta H values showed that the degree (X HB) of hydrogen bonding decreased in the order of methanol > ethanol >2-propanol > H2O, and that the hydrogen bonding was much affected by fluorination, because of the intramolecular H-F interactions in supercritical (sc) states. Moreover, 1H- T 1 measurements revealed that the relaxation processes of OH groups in nonfluoroalcohols are controlled by dipole-dipole (DD) and spin-rotation (SR) mechanisms below and above the critical temperature (Tc), while the cross-correlation effects connected with intramolecular DD interactions between a carbon atom and an adjacent proton played an important role for hydrocarbon groups (CHn, n = 1-3) under sc conditions. This interpretation was also supported by two other results. The first is that the intramolecular H-F interactions strongly inhibit the internal rotation of CH and CH2 groups of sc fluoroalcohols, and the second is that the molecular reorientational correlation times (tauc(D)) obtained from 2H- T 1 values of deuterated hydrocarbon groups (CDn ) at temperatures above T c have significantly less temperature dependence than those of OD groups. Actually, the apparent activation energy (DeltaEa) for molecular reorientational motions in sc alcohols was smaller compared with liquid alcohols, being about 1 order of magnitude.     

Model-free approach to the dynamic interpretation of residual dipolar couplings in globular proteins.

The effects of internal motions on residual dipolar NMR couplings of proteins partially aligned in a liquid-crystalline environment are analyzed using a 10 ns molecular dynamics (MD) computer simulation of ubiquitin. For a set of alignment tensors with different orientations and rhombicities, MD-averaged dipolar couplings are determined and subsequently interpreted for different scenarios in terms of effective alignment tensors, average orientations of dipolar vectors, and intramolecular reorientational vector distributions. Analytical relationships are derived that reflect similarities and differences between motional scaling of dipolar couplings and scaling of dipolar relaxation data (NMR order parameters). Application of the self-consistent procedure presented here to dipolar coupling measurements of biomolecules aligned in different liquid-crystalline media should allow one to extract in a "model-free" way average orientations of dipolar vectors and specific aspects of their motions.     

Optimization of the GB/SA solvation model for predicting the structure of surface loops in proteins

Implicit solvation models are commonly optimized with respect to experimental data or Poisson-Boltzmann (PB) results obtained for small molecules, where the force field is sometimes not considered. In previous studies, we have developed an optimization procedure for cyclic peptides and surface loops in proteins based on the entire system studied and the specific force field used. Thus, the loop has been modeled by the simplified solvation function E(tot) = E(FF) (epsilon = 2r) + Sigma(i) sigma(i)A(i), where E(FF) (epsilon = nr) is the AMBER force field energy with a distance-dependent dielectric function, epsilon = nr, A(i) is the solvent accessible surface area of atom i, and sigma(i) is its atomic solvation parameter. During the optimization process, the loop is free to move while the protein template is held fixed in its X-ray structure. To improve on the results of this model, in the present work we apply our optimization procedure to the physically more rigorous solvation model, the generalized Born with surface area (GB/SA) (together with the all-atom AMBER force field) as suggested by Still and co-workers (J. Phys. Chem. A 1997, 101, 3005). The six parameters of the GB/SA model, namely, P(1)-P(5) and the surface area parameter, sigma (programmed in the TINKER package) are reoptimized for a "training" group of nine loops, and a best-fit set is defined from the individual sets of optimized parameters. The best-fit set and Still's original set of parameters (where Lys, Arg, His, Glu, and Asp are charged or neutralized) were applied to the training group as well as to a "test" group of seven loops, and the energy gaps and the corresponding RMSD values were calculated. These GB/SA results based on the three sets of parameters have been found to be comparable; surprisingly, however, they are somewhat inferior (e.g, of larger energy gaps) to those obtained previously from the simplified model described above. We discuss recent results for loops obtained by other solvation models and potential directions for future studies.     

A solid-state NMR study of the fast and slow dynamics of collagen fibrils at varying hydration levels

We report solid-state NMR investigations of the effect of temperature and hydration on the molecular mobility of collagen isolated from bovine achilles tendon. (13)C cross-polarization magic angle spinning (MAS) experiments were performed on samples at natural abundance, using NMR methods that detect motionally averaged dipolar interactions and chemical shift anisotropies and also slow reorientational processes. Fast motions with correlation times much shorter than 40 micro s scale dipolar couplings and chemical shift anisotropies of the carbon sites in collagen. These motionally averaged anisotropic interactions provide a measure of the amplitudes of the segmental motions expressed by a molecular order parameter. The data reveal that increasing hydration has a much stronger effect on the amplitude of the molecular processes than increasing temperature. In particular, the Cgamma carbons of the hydroxyproline residues exhibit a strong dependence of the amplitude of motion on the hydration level. This could be correlated with the effect of hydration on the hydrogen bonding structure in collagen, for which this residue is known to play a crucial role. The applicability of 1D MAS exchange experiments to investigate motions on the millisecond time-scale is discussed and first results are presented. Slow motions with correlation times of the order of milliseconds have also been detected for hydrated collagen.     

Raman study of ratational diffusion in methyl iodide

The usefulness of Raman and NMR spin relaxation spectroscopic methods in probing the details of molecular motions in liquids is demonstrated in a study of methyl iodide. Analysis of the lineshape of the ν₃ Raman band of methyl iodide as a function of temperature yields values of the perpendicular component D_⊥ of the diffusion tensor D_i and an activation energy of reorientation perpendicular to the C₃ axis of the molecule of 2.1 kcal/mole. Coupling the Raman data with ²D NMR spin relaxation data yields values of D_| and an activation energy for reorientation about the C₃ axis of 0.4 kcal/mole indicating quasi-free rotation for this motion. Thus the reorientational motions of methyl iodide are shown to be highly anisotropic in the liquid state.     

Dielectric study of the slow motional processes in the polymorphic States of anhydrous caffeine

Molecular mobility in crystalline anhydrous caffeine was studied by the dielectric technique of thermally stimulated depolarization currents (TSDC). Two relaxational processes were found, one appearing at approximately -10 degrees C that is ascribed to a reorientational glass transition, and a higher temperature one that probably arises from local molecular motions that are precursors of diffusion and sublimation. The experimental results suggest that both crystalline phases II and I of caffeine, that have distinct crystal structures, are solid rotator phases. Furthermore, this dynamic reorientational disorder shows a reorientational glass transition at the same temperature in phase II and in metastable phase I.     

Effect of polymer microenvironment on excitation energy migration and transfer

Excitation energy transfer between the dye pair acriflavine (donor) to rhodamine-6G (acceptor) in various polymers [polyvinyl alcohol (PVA), cellulose acetate, and polymethyl methacrylate (PMMA)] was studied using steady-state and time-resolved fluorescence spectroscopy at room temperature. In all these polymers, at higher acceptor concentrations, direct energy transfer from acriflavine to rhodamine-6G followed the F?rster theory, which is indicated by the agreement in the values of the observed critical transfer distance with that calculated from spectral overlap. On the other hand, at low acceptor concentrations, the excitation energy migration influences the kinetics, resulting in a significantly higher value of the observed critical transfer distance, which is explained on the basis of Loring et al. (Loring, R. F.; Anderson, H. C.; Fayer, M. D. J. Chem. Phys. 1984, 80, 5731-5744) and Huber (Huber, D. L. Phys. Rev. B: Condens. Matter Mater. Phys. 1979, 20 2307-2314) theories. It was observed that the spectral overlap for donor-donor transport (excitation migration) and donor-acceptor transfer (energy transfer) and thereby other energy transfer parameters were influenced by the microenvironment of the polymers. The efficiency of energy transfer (eta) was the highest in PMMA and the lowest in PVA. Further, the study of acceptor dynamics under energy transfer showed that the rise time of the acceptor also depends on the nature of the polymer microenvironment.     

Reorientational dynamics of the dodecahydro-closo-dodecaborate anion in Cs2B12H12

Rapid reorientational motions of the B(12)H(12)(2-) icosahedral anion, a key intermediate in borohydride dehydrogenation, are revealed by quasielastic neutron scattering (QENS) measurements of Cs(2)B(12)H(12) between 430 and 530 K. At 430 K, over the range of momentum transfers collected, the elastic incoherent structure factor (EISF) is consistent with a model for reorientational jumps about a single molecular axis. At temperatures of 480 K and higher, however, the EISF suggests the emergence of multiaxis reorientation by dynamically similar, independent jumps about two axes, on average, preserving crystallographic order. Alternatively, if one assumes that the anions are undergoing temperature-dependent rotational trapping, then the EISF is also consistent with a jump model involving a temperature-dependent mobile fraction of anions statistically tumbling between discrete crystallographic sites. Although neutron vibrational spectra demonstrate that the anion torsional modes soften dramatically with increasing temperature, the QENS-derived activation energy of 333 meV for reorientation clearly shows that the anions are not undergoing isotropic rotational diffusion.     

Tyrosine 263 in Cyanobacterial Phytochrome Cph1 Optimizes Photochemistry at the prelumi‐R→lumi‐R Step

We report a low‐temperature fluorescence spectroscopy study of the PAS‐GAF‐PHY sensory module of Cph1 phytochrome, its Y263F mutant (both with known 3D structures) as well as Y263H and Y263S to connect their photochemical parameters with intramolecular interactions. None of the holoproteins showed photochemical activity at low temperature, and the activation barriers for the Pr→lumi‐R photoreaction (2.5–3.1 kJ mol^?1) and fluorescence quantum yields (0.29–0.42) were similar. The effect of the mutations on Pr→Pfr photoconversion efficiency (Φ_Pr→Pfr) was observed primarily at the prelumi‐R S₀ bifurcation point corresponding to the conical intersection of the energy surfaces at which the molecule relaxes to form lumi‐R or Pr, lowering Φ_Pr→Pfr from 0.13 in the wild type to 0.05–0.07 in the mutants. We suggest that the E_a activation barrier in the Pr* S₁ excited state might correspond to the D‐ring (C19) carbonyl – H290 hydrogen bond or possibly to the hindrance caused by the C13¹/C17¹ methyl groups of the C and D rings. The critical role of the tyrosine hydroxyl group can be at the prelumi‐R bifurcation point to optimize the yield of the photoprocess and energy storage in the form of lumi‐R for subsequent rearrangement processes culminating in Pfr formation.     

Reorientational Motions of the D96N and T46V/D96N Mutants of Bacteriorhodopsin in the Purple Membrane

Abstract— The reorientational motions of the D96N and T46V/D96N mutants of bacteriorhodopsin in purple membrane have been investigated by time-resolved linear dichroism measurements. The reorientations in the early stages of the photocycle are identical to those observed in wild-type bacteriorhodopsin: anisotropics of photocycle intermediates in both D96N and T46V/D96N are r_K= 0.38±0.01, r_L= 0.35±0.01, r_M= 0.35±0.01. The anisotropy of the initial state, r_BR, exhibits decays to zero in D96N and to negative values in T46V/D96N on the time scale of tens of milliseconds. This anisotropy decay can be explained by a model that involves the motion of unexcited or spectator proteins adjacent to a photocycling protein. The amplitude and time constants of spectator reorientational motion are similar to those that have been observed in the wild type. Contributions from the anisotropy of the N-state were detected in measurements of the T46V/D96N mutant, in which a large N-state population accumulates. The value of r_N is estimated to be 0.30±0.05 in T46V/D96N.