Effect of orientational order on the decay of the fluorescence anisotropy in membrane suspensions. Experimental verification on unilamellar vesicles and lipid/alpha-lactalbumin complexes

Various models for the analysis of time-dependent fluorescence anisotropy measurements were evaluated. The discussion was based on the analysis of pulsed experiments with 1,6-diphenyl-1,3,5-hexatriene embedded in small unilamellar vesicles of dimyristoylphosphatidylcholine or dipalmitoylphosphatidylcholine and in dimyristoylphosphatidylcholine/alpha-lactalbumin complexes. It was shown that a recently proposed model (Van der Meer, W., H. Pottel, W. Herreman, M. Ameloot, H. Hendrickx, H. Schröder, 1984, Biophys. J., 46:515-523) described the data better than did the earlier suggested cone model (Kinosita K., Jr., S. Kawato, and A. Ikegami, 1977, Biophys. J., 20:289-305). This permitted the use of the new model for the estimation of the second- and fourth-rank order parameters on nonoriented systems. The results indicated that a fraction of the probes was oriented perpendicularly to the preferred direction of the lipids. An increase of the rotational correlation times of the fluorescent probe and a higher order of its environment were detected after the interaction of alpha-lactalbumin with the dimyristoylphosphatidylcholine vesicles at acidic pH at 24.2 degrees C.     

Comments on the approximate solution of the diffusion equation: I

The approximation method of N. Rashevsky is discussed and reviewed. It is shown that in addition to theexplicit assumptions and approximations there is involved the assumption that the rate of metabolism is the same at every point in the cell and that theaverage rate of metabolism is different from zero. An expression is given for the error in the approximate method when the rate of metabolism is any function of the concentration. It is also shown that a solution in theform of that obtained by the approximate method is not possible if the generalized laws of diffusion are assumed to apply. A portion of this work was performed while the author was a research participant, Oak Ridge Institute of Nuclear Studies, assigned to the Mathematics Panel, Oak Ridge National Laboratory.     

Comments on the approximate solution of the diffusion equation: II

On the basis of a previous general formulation (Bull. Math. Biophysics,15, 21–29, 1953a) a discussion is given of the error in the approximation method of N. Rashevsky. This error, inherent in the method when the metabolic rate is different at each point in the cell, is discussed in detail and numerical values are presented for two particular cases: the rate proportional to the concentration and the rate a prescribed function of the spatial coordinates. It is shown that the formulation for the first case also applies to several other cases, that the error is negligible provided the rate is sufficiently small, and that the error is fairly sensitive to the cell size. If the rate depends upon the coordinatesalone a small rate is not sufficient to insure a negligible error. The relations between the exact method, the standard approximate method, an earlier approximate method (Physics,7 260, 1936), and a more recent refinement (Bull. Math. Biophysics,10, 201, 1948) of the standard method are discussed. This work was performed while the author was a research participant, Oak Ridge Institute of Nuclear Studies, assigned to the Mathematics Panel, Oak Ridge National Laboratory.     

On the wobbling-in-cone analysis of fluorescence anisotropy decay.

Interpretation of fluorescence anisotropy decay for the case of restricted rotational diffusion often requires a model. To investigate the extent of model dependence, two models are compared: a strict cone model, in which a fluorescent probe wobbles uniformly within a cone, and a Gaussian model, where the stationary distribution of the probe orientation is of a Gaussian type. For the same experimental anisotropy decay, analysis by the Gaussian model predicts a smaller value for the rate of wobbling motion than the strict cone analysis, but the difference is 35% at most; the cone angle obtained by the strict cone analysis agrees closely with the effective width of the Gaussian distribution. The results suggest that, when only two parameters (the rate and the angular range) are extracted from an experiment, the choice of a model is not crucial as long as the model contains the essential feature, e.g., the more-or-less conical restriction, of the motion under study. Model-independent analyses are also discussed.     

Enhanced biopotency of synthetic C3a analogues by membrane binding. A fluorescence anisotropy decay study.

The biological activity of oligopeptide analogues of C3a is markedly increased by N-terminal attachment of a hydrophobic group as, for instance, 9-fluorenylmethoxycarbonyl (Fmoc), either direct or via a flexible 6-aminohexanoyl (Ahx) spacer. This study presents evidence from fluorescence anisotropy decay measurements that the hydrophobic appendix mediates non-specific binding of the synthetic peptide analogues to phospholipid vesicles. According to quantitative considerations no alternative or additional rate-enhancing mechanisms other than surface diffusion are required to account for the gain in biopotency.     

Orientational order and rotational diffusion of the head group in the bilayer membrane. A nuclear magnetic resonance study.

An order parameter-based interpretation is applied to the temperature dependence of the deuterium magnetic resonance splittings and the anisotropic contribution to the chemical shift for 31P from the head groups of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC). It is shown that the rotational motion of the molecule about its long axis is not a free rotational motion as normally assumed, but instead a biased one. Changes in the degree of biasing appear to be primarily responsible for the variation of the NMR spectra with temperature. The degree of biasing is described by orientational order parameters. With the use of these order parameters, it is shown that the temperature dependence of the anisotropic contribution to the chemical shift for 31P can be predicted from that of the deuterium quadrupole splittings.     

Time-dependent decay and anisotropy of fluorescence from diphenylhexatriene embedded in the chloroplast thylakoid membrane

The hydrophobic fluorescent probe 1,6-diphenyl-1,3,5-hexatriene has been incorporated into the membranes of isolated thylakoids, separated granal and stromal lamellae and aqueous dispersions of extracted thylakoid galactolipids. Time-resolved fluorescence decays have been recorded on a nanosecond scale using single-photon counting in order to assess the motional properties of the probe. All the experimental systems used showed biphasic decay kinetics and the anisotropies of the decays have been interpreted in terms of a model for wobbling diffusion confined to a cone. The analysis has given information about dynamic and structural restraints of the lipid acyl chains. In the intact thylakoid membrane the degree of order of the fatty acid acyl chains is higher and their rate of motion slower than for isolated lipids. Even so, the dynamic and structural parameters indicate that the thylakoids can be considered as a relatively fluid membrane system when compared with many other biological membranes, a property which is probably required to facilitate efficient long-range diffusion of lipophilic mobile electron-transport components. It is suggested that the optimization of thylakoid fluidity is linked to regulation of the membrane protein/lipid ratio which is also likely to be responsible for the higher fluidity of stromal membranes relative to those of the grana.     

Time-resolved fluorescence studies of flavodoxin. Fluorescence decay and fluorescence anisotropy decay of tryptophan in Desulfovibrio flavodoxins

The time-resolved fluorescence characteristics of tryptophan in flavodoxin isolated from the sulfate-reducing bacteria Desulfovibrio vulgaris and Desulfovibrio gigas have been examined. By comparing the results of protein preparations of normal and FMN-depleted flavodoxin, radiationless energy transfer from tryptophan to FMN has been demonstrated. Since the crystal structure of the D. vulgaris flavodoxin is known, transfer rate constants from the two excited states ¹ L _a and ¹ L _b can be calculated for both tryptophan residues (Trp 60 and Trp 140). Residue Trp 60, which is very close to the flavin, transfers energy very rapidly to FMN, whereas the rate of energy transfer from the remote Trp 140 to FMN is much smaller. Both tryptophan residues have the indole rings oriented in such a way that transfer will preferentially take place from the ¹ L _a excited state. The fluorescence decay of all protein preparations turned out to be complex, the parameter values being dependent on the emission wavelength. Several decay curves were analyzed globally using a model in which tryptophan is involved in some nanosecond relaxation process. A relaxation time of about 2 ns was found for both D. gigas apo- and holoflavodoxin. The fluorescence anisotropy decay of both Desulfovibrio FMN-depleted flavodoxins is exponential, whereas that of the two holoproteins is clearly non-exponential. The anisotropy decay was analyzed using the same model as that applied for fluorescence decay. The tryptophan residues turned out to be immobilized in the protein. A time constant of a few nanoseconds results from energy transfer from tryptophan to flavin, at least for D. gigas flavodoxin. The single tryptophan residue in D. gigas flavodoxin occupies a position in the polypeptide chain remote from the flavin prosthetic group. Because of the close resemblance of steady-state and time-resolved fluorescence properties of tryptophan in both flavodoxins, the center to center distance between tryptophan and FMN in D. gigas flavodoxin is probably very similar to the distance between Trp 140 and FMN in D. vulgaris flavodoxin (i.e. 20 Å). Offprint requests to: A.J.W.G. Visser     

Time-dependent absorption anisotropy and rotational diffusion of proteins in membranes.

The decay of flash-induced absorption anisotropy, r(t), of a chromophore in a membrane protein is closely correlated with rotational diffusion of the protein in the membrane. We develop a theory of time-dependent absorption anisotropy which is applicable to both linear chromophores and planar chromophores which have two different absorption moments at right angles to one another. The theory treats two types of rotational diffusion of membrane proteins: one is rotation of the whole protein about the normal to the plane of the membrane, and the other is restricted wobbling of the whole or part of the protein molecule. In the former case, r(t) is determined by a rotational diffusion coefficient and an angle between the absorption moment(s) and the normal to the plane of the membrane. Rotation of rigid transmembrane proteins can be described by this treatment. In the latter case, r(t) is characterized by a wobbling diffusion coefficient and the degree of orientational constraint. This treatment may be applicable to independent wobbling of the hydrophilic part of membrane proteins. We further show that, for linear and circularly degenerate chromophores, the effect of the excitation flash intensity on r(t) can be accounted for by a constant scaling factor.     

Large-amplitude picosecond anisotropy decay of the intrinsic fluorescence of double-stranded DNA.

The conformational flexibility of the DNA double helix is of great interest because of its potential role in protein recognition, packaging into chromosomes, formation of photodefects, and interaction with drugs. Theory finds that DNA is very flexible; however, there is a scarcity of experimental results that examine intrinsic properties of the DNA bases for the inherent flexibility in solution. We have studied the dynamics of poly(dA).poly(dT) and (dA)20.(dT)20 in a 50 mM cacodylate, 0.1 M NaCl, pH 7 buffer by using the time-correlated picosecond fluorescence anisotropy of thymine selectively excited at 293 nm. For both nucleic acids, a large-amplitude biphasic decrease in the anisotropy is observed that has a very fast, large-amplitude component on the picosecond time scale and a slower, smaller-amplitude component on the nanosecond time scale. These modes are sensitive to sucrose concentration, and are greatly attenuated at 77% sucrose by volume. This observation suggests that motions of the bases make a significant contribution to the observed fluorescence depolarization (in the absence of sucrose). Measurements on the single-stranded systems poly(dT) and (dT)20 reveal a much smaller amplitude of the very fast depolarization mode. These observations are consistent with a mechanism that involves concerted motions in the interior of the double-stranded systems.     

Photobleaching recovery and anisotropy decay of green fluorescent protein GFP-S65T in solution and cells: cytoplasmic viscosity probed by green fluorescent protein translational and rotational diffusion.

The green fluorescent protein (GFP) was used as a noninvasive probe to quantify the rheological properties of cell cytoplasm. GFP mutant S65T was purified from recombinant bacteria for solution studies, and expressed in CHO cell cytoplasm. GFP-S65T was brightly fluorescent in solution (lambda ex 492 nm, lambda em 509 nm) with a lifetime of 2.9 ns and a rotational correlation time (tc) of 20 ns. Recovery of GFP fluorescence after photobleaching was complete with a half-time (t1/2) in aqueous saline of 30 +/- 2 ms (5-micron diameter spot), giving a diffusion coefficient of 8.7 x 10(-7) cm2/s. The t1/2 was proportional to solution viscosity and was dependent on spot diameter. In contrast to fluorescein. GFP photobleaching efficiency was not affected by solution O2 content, triplet state quenchers, singlet oxygen scavengers, and general radical quenchers. In solutions of higher viscosity, an additional, rapid GFP recovery process was detected and ascribed to reversible photobleaching. The t1/2 for reversible photobleaching was 1.5-5.5 ms (relative viscosity 5-250), was independent of spot diameter, and was unaffected by O2 or quenchers. In cell cytoplasm, time-resolved microfluorimetry indicated a GFP lifetime of 2.6 ns and a tc of 36 +/- 3 ns, giving a relative viscosity (cytoplasm versus water) of 1.5. Photobleaching recovery of GFP in cytoplasm was 82 +/- 2% complete with a t1/2 of 83 +/- 6 ms, giving a relative viscosity of 3.2. GFP translational diffusion increased 4.7-fold as cells swelled from a relative volume of 0.5 to 2. Taken together with measurements of GFP translation and rotation in aqueous dextran solutions, the data in cytoplasm support the view that the primary barrier to GFP diffusion is collisional interactions between GFP and macromolecular solutes.     

Effects of lateral diffusion on the fluorescence anisotropy in hexagonal lipid phases. I. Theory.

It is shown that fluorescence anisotropy from lipidlike probes in the hexagonal HII phase gives information of (a) orientational order parameters, (b) the wobbling diffusion constant, and (c) the hopping diffusion constant of the probe, DH, equals DL/R2, the lateral diffusion constant over the square of the radius of the hexagonal tubes. Here we consider only lipidlike probes having the absorption transition movement and/or the emission transition moment along the long axis of the molecule. Three models are introduced for analysis of time-resolved data: the "WOBHOP," the "reduced WOBHOP," and the "P2P4HOP" model. The fluorescence anisotropy in response to a very short excitation pulse in each of the three models is a constant plus a number of exponentials. The WOBHOP and reduced WOBHOP models have 3 and 2 exponentials, respectively, and both contain four fitting parameters: r0 (the fundamental anisotropy), (P2) (the second rank orientational order parameter), DW (the wobbling diffusion constant), and DH (the hopping diffusion constant). The P2P4HOP model has eight exponentials and five fitting parameters: the four parameters listed above and (P4) (the fourth rank orientational order parameter). Analysis of fluorescence anisotropy data in the hexagonal HII phase using one of these models allows for obtaining the hopping diffusion constant, and, if the lateral diffusion constant is known, the radius of the hexagonal tubes. Substitution of DH = 0 in each of the three models yields an expression for the fluorescence anisotropy that is used in the literature for lamellar (L alpha or L beta) phases. The fluorescence anisotropy in coexisting L alpha/HII phases is discussed.     

A new approximate whole boundary solution of the Lamm differential equation for the analysis of sedimentation velocity experiments

Sedimentation velocity is one of the best-suited physical methods for determining the size and shape of macromolecular substances or their complexes in the range from 1 to several thousand kDa. The moving boundary in sedimentation velocity runs can be described by the Lamm differential equation. Fitting of suitable model functions or solutions of the Lamm equation to the moving boundary is used to obtain directly sedimentation and diffusion coefficients, thus allowing quick determination of size, shape and other parameters of macromolecules. Here we present a new approximate whole boundary solution of the Lamm equation that simultaneously allows the specification of sedimentation and diffusion coefficients with deviations smaller than 1% from the expected values.     

Study of the rotational diffusion properties of peptides in solution

In this paper we examine the theory and method for obtaining rotational diffusion coefficients for peptides in dilute solution from ¹³C-nmr spin-lattice relaxation data. We show that even for the case of nearly equal observed relaxation times of chemically and magnetically nonequivalent alpha-carbons marked rotational anisotropy will be the usual case. We describe two interactive, minicomputer programs which are of general use in this type of work. The implications of this study on spectral density-based conformational determinations of peptides is discussed.     

Dynamics of melittin in water and membranes as determined by fluorescence anisotropy decay.

Fluorescence anisotropy decay measurements were performed on melittin in water and in membranes of dimyristoylphosphatidylcholine. The fluorescence of the single tryptophan residue of melittin and of a pyrene label attached to melittin was detected. In water, the slowest relaxation process in the anisotropy decay occurs with a relaxation time of 1.5 or 5.5 ns in the case of low or high ionic strength and corresponds to rotational diffusion of monomeric or tetrameric melittin. Superimposed on this slow process are fast processes in the subnanosecond range reflecting fluctuations of the fluorophores relative to the polypeptide backbone. In membranes, the fast relaxation processes are not much altered. A slow process with a relaxation time of 35 ns is observed and assigned to orientational fluctuations of the melittin helices in membranes.     

Effects of lateral diffusion on the fluorescence anisotropy in hexagonal lipid phases. II. An experimental study.

The polymorphic phase behavior of unsaturated phosphatidylethanolamine (PE)/diacylglycerol (DG) binary lipid mixtures was investigated by the use of time-resolved fluorescence anisotropy. Using a fluorescent lipid, 1-palmitoyl-2-[[2-[4-(6-phenyl-trans-1,3,5-hexatrienyl)phenylethyl] carbonyl]3-sn-phosphatidyl-choline (DPH-PC), the orientational order and rotational dynamics of the above lipid mixtures in the liquid crystalline lamellar (L alpha) and inverted hexagonal (HII) phases were studied. By employing a one-exponential model (Cheng, K.H. 1989: Biophys. J. 55:1025-1031) to fit the anisotropy decay data, abrupt decreases in the normalized initial anisotropy decay slope and the residual anisotropy of DPH-PC were observed at approximately 6-8% DG, signifying a L alpha/HII phase transition. Using our new theoretical WOBHOP and P2P4HOP models as described in a preceding paper (Van Der Meer, B.W., K.H. Cheng, and S.Y. Chen. 1990. Biophys. J. 58:000-000), two or more rotational correlation times were required to describe the anisotropy decay behavior of DPH-PC in the HII phase. These rotation correlation times were further related to the second and fourth rank order parameters, and the wobbling and hopping diffusion constants of the fluorescent probe in the highly curved lipid cylindrical tubes of the HII phase. The hopping diffusion constant (DH) equals the lateral diffusion constant (DL) divided by R2 (R = radius of the lipid cylindrical tubes). The value of DL was estimated by measuring the excimer formation rate of 1-palmitoyl-2-[10-(1-pyrenl)decanoyl] phosphatidyl choline (py-PC) in the same PE/DG mixtures. Upon comparing the values of DH and DL, the value of R was determined to be approximately 10-15 A, and agreed with that derived from x-ray diffraction (Tate, M.W., and S.M. Gruner, 1989, Biochemistry. 28:4245-4253; Rand, R.P., N.L. Fuller, S.M. Gruner, and V.A. Parsegian. 1990. Biochemistry. 29:76-87).     

Molecular dynamics of tryptophan in ribonuclease-T1. I. Simulation strategies and fluorescence anisotropy decay.

Molecular dynamics simulations of Ribonuclease-T1 (RNAse-T1) were performed using x-ray crystal coordinates for the enzyme and various simulation strategies. From each of the simulations, a predicted fluorescence anisotropy decay for the single-tryptophan residue was derived and compared with experimental values for the limiting anisotropy of this protein. Simulations conducted in vacuo demonstrated large displacements among some of the residues adjacent to the tryptophan side chain. As a consequence, the ring system rotates relatively unhindered through an angle far in excess of that implied by experimental data. In contrast, the explicit simulation of solvent within a stochastic boundary led to excellent agreement between simulation and experiment. In the case of RNAse-T1, the experimentally-determined limiting anisotropy is useful as a criterion of simulation accuracy in the vicinity of the tryptophan side chain.     

Subnanosecond polarized fluorescence photobleaching: rotational diffusion of acetylcholine receptors on developing muscle cells.

Polarized fluorescence recovery after photobleaching (PFRAP) is a technique for measuring the rate of rotational motion of biomolecules on living, nondeoxygenated cells with characteristic times previously ranging from milliseconds to many seconds. Although very broad, that time range excludes the possibility of quantitatively observing freely rotating membrane protein monomers that typically should have a characteristic decay time of only several microseconds. This report describes an extension of the PFRAP technique to a much shorter time scale. With this new system, PFRAP experiments can be conducted with sample time as short as 0.4 microseconds and detection of possible characteristic times of less than 2 microseconds. The system is tested on rhodamine-alpha-bungarotoxin-labeled acetylcholine receptors (AChRs) on myotubes grown in primary cultures of embryonic rat muscle, in both endogenously clustered and nonclustered regions of AChR distribution. It is found that approximately 40% of the AChRs in nonclustered regions undergoes rotational diffusion fast enough to possibly arise from unrestricted monomer Brownian motion. The AChRs in clusters, on the other hand, are almost immobile. The effects of rat embryonic brain extract (which contains AChR aggregating factors) on the myotube AChR were also examined by the fast PFRAP system. Brain extract is known to abolish the presence of endogenous clusters and to induce the formation of new clusters. It is found here that rotational diffusion of AChR in the extract-induced clusters is as slow as that in endogenous clusters on untreated cells but that rotational diffusion in the nonclustered regions of extract-treated myotubes remains rapid.     

Time-dependent phosphorescence anisotropy measurements of the slow rotational motions of proteins in viscous solution

A method of monitoring slow rotational motions of proteins from the decay of the intrinsic phosphorescence is described. The phosphorescence is excited with a 10-μsec pulse of vertically polarized light from an air gap lamp, and the anisotropy was computed as a function of time from the simultaneously detected vertically and horizontally polarized components of the emission. The approach is illustrated with time-dependent measurements of the anisotropy of the tryptophan phosphorescence of Staphylococcus aureus nuclease, bovine carbonic anhydrase, and liver alcohol dehydrogenase in glycerol-phosphate buffer between ?90 and ?70°C. The temperature- and molecular-weight dependence of the exponential decays in the anisotropy indicate that overall rotation of the proteins is at the origin of the depolarization. The potential of the approach as a probe of the slow rotational motions of proteins in membranes and other macromolecular complexes is stressed.