Rotational and translational dynamics of lysozyme in water-glycerol solution

In this paper, we report a study of the effect of solvent viscosity on both translational and rotational dynamics of a simple model protein: the egg white lysozyme. For this, we investigated the dynamical properties of lysozyme in mixtures water–glycerol by means of parallel measurements of photon correlation spectroscopy (PCS) and dielectric spectroscopy at radiofrequencies (DS). In the framework of the Debye–Stokes–Einstein theory, the translational and rotational coefficients allow an estimation of hydrodynamic radius of the protein. A decoupling between translational and rotational dynamics, observed as a different estimation of hydrodynamic radius, is reported in the literature for some systems. In order to ascertain if this effect is present also in our sample, we performed PCS and DS measurements on lysozyme–water–glycerol solutions. The content of glycerol was in the range of 0–70% w/w, with a solvent viscosity from 0.9 to about 10 cpoise, and the protein concentration was up to 20 mg ml⁻¹. The average sizes of lysozyme, obtained by the two methods, are remarkably different at high protein concentrations. However, the values of hydrodynamic radius extrapolated to infinite dilution are coincident and independent of glycerol. These results indicate that the diffusive behavior of lysozyme in the water–glycerol mixture is coherent with the Debye–Stokes–Einstein hydrodynamic model.     

Imaging translational and rotational diffusion of single anisotropic nanoparticles with planar illumination microscopy

Here we demonstrated a simple yet powerful method, planar illumination microscopy, to directly track the rotational and translational diffusion dynamics of individual anisotropic nanoparticles in solution and living cells. By illuminating gold nanorods (GNRs) with two orthogonal sheets of light and resolving the polarized scattering signal with a birefringent crystal, we readily achieved three-dimensional angular resolving capability for single GNRs in noisy surroundings. The rotational dynamics of individual GNRs dispersed in glycerol/water mixtures with different chemical modification were tracked, and the measured rotational diffusion coefficient was well fitted to a previously reported theoretical model (Torre, J. G. d. l.; Martinez, M. C. L. Macromolecules 1987, 20, 661-666; Tirado, M. M.; Torre, J. G. d. l. J. Chem. Phys. 1980, 73, 1986-1993). In addition, the translational and rotational movements of individual GNRs transported by kinesin motor protein on microtubules inside living cells were directly imaged. Compared to its motion in free solution, a GNR attached to motor-protein did not rotate significantly while moving forward. Our method can be further generalized to allow determination of three-dimensional orientation of single dipoles using many different illumination modes.     

Negative thixotropy of solutions of partially hydrolyzed polyacrylamide

We found that the character of negative thixotropy of partially hydrolyzed polyacrylamide in aqueous glycerol strongly depends on polymer concentration, glycerol content and shear rate applied. At low polymer and glycerol concentrations, shear stress and viscosity slowly increased during shearing to a limiting value. In addition to this behavior, a steep increase in shear stress as well as normal stress followed by their pronounced oscillations occurred at higher concentrations of both components and at higher shear rates. Similarly to the negative thixotropic effect in solutions of other polymers in organic solvents, the hydrodynamic conditions in which the effects set in seem to be controlled by the shear stress acting in the flowing solution; initial kinetics of the effect depends on solvent viscosity and shear stress applied. To explain the influence of the glycerol content and degree of ionization of the polymer on the minimum shear stress at which the effect sets in, a decisive role of intermolecular electrostatic repulsions in association of the polymer molecules in shear field is assumed.     

Rotational and Translational Dynamics of Ras Proteins upon Binding to Model Membrane Systems

Plasma-membrane-associated Ras proteins typically control signal transduction processes. As nanoclustering and membrane viscosity sensing provide plausible signaling mechanisms, determination of the rotational and translational dynamics of membrane-bound Ras isoforms can help to link their dynamic mobility to their function. Herein, by using time-resolved fluorescence anisotropy and correlation spectroscopic measurements, we obtain the rotational-correlation time and the translational diffusion coefficient of lipidated boron-dipyrromethene-labeled Ras, both in bulk Ras and upon membrane binding. The results show that the second lipidation motif of N-Ras triggers dimer formation in bulk solution, whereas K-Ras4B is monomeric. Upon membrane binding, an essentially free rotation of the G-domain is observed, along with a high lateral mobility; the latter is essentially limited by the viscosity of the membrane and by lipid-mediated electrostatic interactions. This high diffusional mobility warrants rapid recognition–binding sequences in the membrane-bound state, thereby facilitating efficient interactions between the Ras proteins and scaffolding or effector proteins. The lipid-like rapid lateral diffusion observed here complies with in vivo data.     

Reversible Photobleaching of Fluorescein Conjugates in Air-Saturated Viscous Solutions: Singlet and Triplet State Quenching by Tryptophan

Abstract— Fluorescence recovery after photobleaching (FRAP) measurements on air-saturated aqueous solutions of fluorescein made viscous with glycerol or sucrose revealed a rapid component of fluorescence recovery with exponential time constants of 30-120 μs at viscosities of 15-300 cP. The rapid recovery process was not related to fluorophore translational diffusion and was insensitive to fluorophore concentration and the additive used to increase solution viscosity. At constant viscosity, the rate of reversible photobleaching recovery increased 2.5-fold in an O₂- vs N₂-saturated solution. The relative efficiency of reversible-to-irreversible photobleaching decreased with increasing photobleaching time and/or beam intensity. Reversible photobleaching was also detected for conjugates of fluorescein with dextrans and proteins in viscous media. In screening triplet state quenchers that might influence the reversible recovery, it was found that tryptophan enhanced the rate of reversible photobleaching recovery (two-fold increase at 8 m M ) and quenched the fluorescein singlet state (Stern-Volmer constant, 12 M ⁻¹). Analysis of fluorescein lifetimes and photobleaching parameters for a series of fluorescein-labeled proteins with different numbers of tryptophans were also carried out. The results provide evidence for an oxygen-dependent, reversible photobleaching mechanism for the fluorescein chromophore involving triplet state relaxation. The identification of reversible fluorescein photobleaching has important implications for FRAP measurements of rapid solute diffusion in biological systems.     

Strukturviskosität von verdünnten Lösungen von Biopolymeren

The importance of the rheological behaviour of solutions of macromolecules is briefly evaluated. The viscosity of the solutions depends on concentration, shear rate and time of shear, this relation being determined by the structure of the dissolved molecules. In dilute solutions shear dependence of viscosity is very frequently caused by the preferential orientation of anisotropic molecules. In such a case the particle dimensions can be calculated from the true limiting viscosity number, an anisotropy factor, the rotational diffusion constant and the effective particle density. These numbers can be derived from the flow curve, which has been extrapolated to zero concentration. It is necessary to measure the flow curve at shear gradients, which are sufficiently low to allow for an extrapolation to vanishing shear rate. By comparing the experimental flow curve with a choice of theoretical ones, the rotational diffusion constant and the anisotropy factor (axial ratio) can be found. From the limiting viscosity number and the axial ratio, the particle density can be calculated.     

Comparison of photophysical properties of the hemicyanine dyes in ionic and nonionic solvents

The fluorescence properties of 4-[4-(dimethylamino)styryl]-1-n-alkylpyridinium bromide (hemicyanine) dissolved in solvents of different polarities and viscosities (methanol, ethylene glycol, tetra-ethylene glycol, glycerol, benzyl alcohol, pyridine, and two ionic liquids, 1-butyl-3-methylimidazolium tetrafluoroborate, [BMIM]BF4, and 1-butyl-3-methylimidazolium hexafluorophosphate, [BMIM]PF6) were investigated. Significant increase in the fluorescence quantum yield and the fluorescence decay lifetime was observed with the increase in the viscosity of the solvent medium. It is because the intramolecular rotational motion of the molecule becomes more difficult in viscous liquid, which leads to a decrease in the nonradiative decay processes. The fluorescence quantum yields for all of the solutions followed a semiempirical law that depends only on the solvent viscosity. The correlation function C(t) was obtained for each solution by joining fluorescence decay curves measured at different wavelengths. From the fitted results of C(t), we observed the distinctive feature unique to the ionic liquids, in which the correlation functions for ionic liquid solutions are fitted to be biphasic, while they are monophasic for other solvents. The fluorescence maximum of hemicyanine dissolved in these ionic liquids red-shifted following the increase in the excitation wavelength.     

Effects of translational and rotational diffusion on the association in kinetic model of nucleation

Kinetics of an association and dissociation of single elements with the effects of translational and rotational diffusion and angular limitations is discussed. Separated clusters embedded in a solution of orientable single elements are considered.Steady-state positional and angular distribution of single elements is calculated from the equation of translational-rotational diffusion and the boundary conditions proposed for orientation-limited association. Although spherical orientable elements are assumed, the model can be used for non-spherical particles with aspect ratios close to unity.Diffusion-limited rate constants of association and dissociation are proposed which depend on translational and rotational diffusion constants of single elements, the tolerance angle of the association, and the cluster size.Effective concentration of single elements and effective rate constants are expressed by the equilibrium and diffusion-limited rate constants. Effects of finite diffusion rates and finite tolerance angle are discussed.The equations of the kinetic model of nucleation are modified due to the diffusion-limited rate of the association.     

1H NMR relaxation in glycerol solutions of nitroxide radicals: effects of translational and rotational dynamics

(1)H spin-lattice relaxation rates in glycerol solutions of selected nitroxide radicals at temperatures between 200 K and 400 K were measured at 15 MHz and 25 MHz. The frequency and temperature conditions were chosen in such a way that the relaxation rates go through their maximum values and are affected by neither the electron spin relaxation nor the electron-nitrogen nucleus hyperfine coupling, so that the focus could be put on the mechanisms of motion. By comparison with (1)H spin-lattice relaxation results for pure glycerol, it has been demonstrated that the inter-molecular electron spin-proton spin dipole-dipole interactions are affected not only by relative translational motion of the solvent and solute molecules, but also by their rotational dynamics as the interacting spins are displaced from the molecular centers; the eccentricity effects are usually not taken into account. The (1)H relaxation data have been decomposed into translational and rotational contributions and their relative importance as a function of frequency and temperature discussed in detail. It has been demonstrated that neglecting the rotational effects on the inter-molecular interactions leads to non-realistic conclusions regarding the translational dynamics of the paramagnetic molecules.     

Effects of diffusion-controlled association in kinetic model of crystal nucleation in external orienting field

Translational and rotational diffusion equation of orientable single elements in external orienting potential field is used to discuss effective rate of association and dissociation during cluster growth. First and second harmonic terms of orientation-dependent potential energy of single elements are taken into consideration. Tolerance angle accounting for orientational limitations for association is introduced.Effective rate of association of single elements is derived with first-order correction for the effects of orienting potential. Net rate of cluster growth depends on orientation in the field, and it is controlled by longrange diffusion (rotational and translational) of single elements. Influence of diffusion is higher, the narrower the tolerance angle and the faster the association.At slow association, long-range diffusion does not influence the process, the growth of a cluster is controlled by thermodynamic, orientation-dependent potential of the species involved in the process.Effective rate constants of association and dissociation, as well as effective concentration of single elements are derived as functions of orientation angle in the field.The Fokker-Planck equation is proposed for the distribution of cluster size in external orienting potential, with the effects of finite translational and rotational diffusion of single elements, for the case of non-polar clusters.     

Dynamics of 4-benzylamino-7-nitrobenzofurazan in the 1-propanol/water binary solvent system. Evidence for composition-dependent solvent organization

We report on the fluorescence lifetime and rotational diffusion dynamics of 4-benzylamino-7-nitrobenzofurazan (BBD) in a series of 1-propanol/water binary solvent systems. The fluorescence lifetime of BBD increases monotonically with increasing 1-propanol concentration. The rotational diffusion dynamics of BBD also vary with solution 1-propanol content, but this variation is not monotonic. Comparison of the BBD rotational diffusion time constant to solution viscosity and 1-propanol composition reveals the presence of a solution composition dependence of solvent-solute interactions, with a relative decrease in solvent-solute interaction strength for solvent system compositions where the 1-propanol/water azeotrope is known to exist. These data point collectively to the existence of microscopic heterogeneity in these binary solvent systems.     

Characterization of globular protein solutions by dynamic light scattering, electrophoretic mobility, and viscosity measurements

In this work, physicochemical properties of two globular proteinsbovine serum albumin (BSA) having a molecular weight of 67 kDa and human serum albumin (HSA) having a molecular weight of 69 kDawere characterized. The bulk characteristics of these proteins involved the diffusion coefficient (hydrodynamic radius), electrophoretic mobility, and dynamic viscosity as a function of protein solution concentration for various pH values. The hydrodynamic radius data suggested an association of protein molecules, most probably forming compact dimers. Using the hydrodynamic diameter and the electropheretic mobility data allowed the determination of the number of uncompensated (electrokinetic) charges on protein surfaces. The electrophoretic mobility data were converted to zeta potential values, which allowed one to determine the isoelectric point (iep) of these proteins. It was found to be at pH 5.1 for both proteins, in accordance with previous experimental data and theoretical estimations derived from amino acid composition and p K values. To determine further the stability of protein solutions, dynamic viscosity measurements were carried out as a function of their bulk volume concentration for various pH values. The intrinsic viscosity derived from these measurements was interpreted in terms of the Brenner model, which is applicable to hard spheroidal particles. It was found that the experimental values of the intrinsic viscosity of these proteins were in good agreement with this model when assuming protein dimensions of 9.5 x 5 x 5 nm3 (prolate spheroid). The possibility of forming linear aggregates of association degree higher than 2 was excluded by these measurements. It was concluded that the combination of dynamic viscosity and dynamic light scattering can be exploited as a convenient tool for detecting not only the onset of protein aggregation in suspensions but also the form and composition of these aggregates.     

Coiled to diffuse: brownian motion of a helical bacterium

We employ real-time three-dimensional confocal microscopy to follow the Brownian motion of a fixed helically shaped Leptospira interrogans (LI) bacterium. We extract from our measurements the translational and the rotational diffusion coefficients of this bacterium. A simple theoretical model is suggested, perfectly reproducing the experimental diffusion coefficients, with no tunable parameters. An older theoretical model, where edge effects are neglected, dramatically underestimates the observed rates of translation. Interestingly, the coiling of LI increases its rotational diffusion coefficient by a factor of 5, compared to a (hypothetical) rectified bacterium of the same contour length. Moreover, the translational diffusion coefficients would have decreased by a factor of ～1.5, if LI were rectified. This suggests that the spiral shape of the spirochaete bacteria, in addition to being employed for their active twisting motion, may also increase the ability of these bacteria to explore the surrounding fluid by passive Brownian diffusion.     

Rotational diffusion of fluorescein family markers in solutions of human serum albumin

Rotational diffusion of fluorescein family nanomarkers (initial fluorescein and its halogenated derivatives, eosin and erythrosine) in solutions of human serum albumin (HSA) was studied at various pH values. In solutions of HSA, the degree of fluorescence polarization, rotational relaxation time, and Einstein radius of nanomarkers are larger and the rotational diffusion coefficient of nanomarkers smaller than in solutions without the protein. An increase in the electronegativity of atoms in the structural formulas of nanomarkers increases the degree of polarization of their fluorescence, decreases the coefficient of their rotational diffusion, and increases rotational relaxation time and the effective Einstein radius.     

Denaturation of human serum albumin under the action of cetyltrimethylammonium bromide according to fluorescence polarization data of protein

Denaturation of human serum albumin (HSA) under the action of cationic detergent cetyltrimethylammonium bromide (CTAB) is studied at different pH values by estimating the rotational diffusion of protein via fluorescence polarization. The degree of polarization of HSA tryptophan fluorescence, the rotational relaxation time, the rotational diffusion coefficient and the effective Einstein radius of the HSA molecules in solutions with different CTAB concentrations at different pH values are determined. The obtained rotational diffusion parameters of the HSA molecules show that under the action of CTAB, HSA denaturation has a one-stage character and proceeds more intensely and effectively at pH values higher than the pI value of protein (4.7).     

Mobility of Green Fluorescent Protein in Hydrogel‐Based Drug‐Delivery Systems Studied by Anisotropy and Fluorescence Recovery After Photobleaching

Modified hydroxyethyl starch is photo‐crosslinked in the presence of a green fluorescent protein (GFP) (mTagGFP) to obtain loaded hydrogels as model for a drug‐delivery system. An important factor for the protein release is the crosslinking density since a dense network should lead to hindered diffusion. To obtain information on the rotational and translational diffusion of GFP in the hydrogel, mTagGFP is analyzed by fluorescence anisotropy and fluorescence recovery after photo‐bleaching experiments using two‐photon excitation. The mTagGFP shows a viscosity‐retarded rotational and strongly hindered translational diffusion, depending on the polymer concentration. A comparison of anisotropy studies with mTagGFP‐loaded microparticles and hydrogel disks allows the polymer concentration to be determined for the microparticles, which has been previously unknown.

     

A revised quantum chemistry-based potential for poly(ethylene oxide) and its oligomers in aqueous solution

We have conducted a high-level quantum chemistry study of the interactions of 1,2-dimethoxyethane (DME) with water for complexes representing both hydrophilic and hydrophobic hydration. It was found that our previous quantum chemistry-based force field for poly(ethylene oxide) (PEO) and its oligomers in aqueous solution did a poor job in describing the hydrophobic binding of water to the ether, consistent with our recent calculations of the excess free energy and entropy of hydration of DME. Our original force field was revised to more accurately reproduce the interaction of water with the carboneous portions of DME. Molecular dynamics simulations of aqueous DME solutions using the revised quantum chemistry-based potential yielded good agreement with experiment for excess free energy, enthalpy, and volume as well as excess solution viscosity and the self-diffusion of water. Comparison with our original potential revealed that the relatively hydrophobic ether-water interactions in the new potential strongly reduced the favorable excess free energy and enthalpy but have relatively little influence on the excess entropy for dilute DME solutions. Other properties of DME and PEO solutions including conformational populations and dynamics, solution viscosity, hydrogen bonding, water translational and rotational diffusion and neutron structure factor as a function of solution composition were found to be largely unchanged from those obtained using the original potential.     

Influence of medium viscosity on photophysical properties of kynurenic acid and kynurenine yellow

Dependences of the fluorescence and triplet state quantum yields of kynurenic acid (1) and kynurenine yellow (2) in water—glycerol mixtures on medium viscosity have been studied. The main channel of the singlet excited state decay of compound 1 is the intersystem crossing, which rate weakly depends on the viscosity; only a small (approximately 1.5-fold) increase in the fluorescence yield was found for this compound with the increase of the solution viscosity from 0.84 cP (aqueous solution) to 78 cP (86% glycerol). The deactivation of the S₁ state of compound 2 is caused mainly by the internal conversion, and a noticeable increase of the fluorescence yield (approximately 3-fold), as well as the change in the photolysis product yields, was observed with the increasing percentage of glycerol in the mixture. The triplet state quantum yields for compounds 1 and 2 remained unchanged with the variation of the glycerol content in the mixture.     

The decay of the fluorescence anisotropy of tryptophan residues in fungal lipase fromHumicola lanuginosa

Pulse nanosecond fluorescence anisotropy decay has been used to study the mobility of tryptophan residues within fungal lipase fromHumicola lanuginosa. The decay of emission anisotropy of protein in native, inhibited and mutated form has been investigated in buffered water and 50% v/v glycerol solutions. The rotational motions of the lipase were analyzed in terms of two different kinetic models. It was found that the fluorescence emission anisotropy decay can best be desribed with two rotational correlation times: 0.63 and 5.45 ns in water and 0.98 and 10.70 ns and in 50% v/v glycerol solution. Using the same experimental conditions the decay of inhibited and mutatedH. lanuginosa lipase showed a similar biexponential character. These results are interpreted in terms of local or segmental motion arising from a mass of about 1083 daltons which corresponds to the ‘lid’-helix fragment of the enzyme.     

Quantitating the dynamics of NBD hexanoic acid in homogeneous solution and in solutions containing unilamellar vesicles

We report here on the motional and fluorescence lifetime dynamics of the chromophore NBDHA (6-(N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)hexanoic acid) in neat solvents and in aqueous solutions containing unilamellar vesicles of varying composition. We measure the transient response of this chromophore by time-correlated single-photon counting, using one- and two-photon excitation to resolve the Cartesian components of the rotational diffusion constant, D. Our experimental data for NBDHA in selected solvents of varying viscosity demonstrate that one- and two-photon excitation probe different components of the rotational diffusion constant and that this chromophore reorients as a prolate rotor with an aspect ratio of approximately 2. For NBDHA in aqueous solutions containing unilamellar vesicles of varying composition, we recover the same reorientation behavior regardless of vesicle composition. Fluorescence lifetime and steady-state fluorescence data show the chromophore to reside in a polar environment that is different from neat water. We understand these data in the context of the chromophore residing in close proximity to the unilamellar vesicle polar headgroups in all cases.