Measuring and Overcoming Limits of the Saffman-Delbrück Model for Soap Film Viscosities

We observe tracer particles diffusing in soap films to measure the two-dimensional (2D) viscous properties of the films. Saffman-Delbrück type models relate the single-particle diffusivity to parameters of the film (such as thickness h) for thin films, but the relation breaks down for thicker films. Notably, the diffusivity is faster than expected for thicker films, with the crossover at h/d = 5.2 ± 0.9 using the tracer particle diameter d. This indicates a crossover from purely 2D diffusion to diffusion that is more three-dimensional. We demonstrate that measuring the correlations of particle pairs as a function of their separation overcomes the limitations of the Saffman-Delbrück model and allows one to measure the viscosity of a soap film for any thickness.     

Lateral Diffusion of Membrane Proteins: Consequences of Hydrophobic Mismatch and Lipid Composition

Biological membranes are composed of a large number lipid species differing in hydrophobic length, degree of saturation, and charge and size of the headgroup. We now present data on the effect of hydrocarbon chain length of the lipids and headgroup composition on the lateral mobility of the proteins in model membranes. The trimeric glutamate transporter (GltT) and the monomeric lactose transporter (LacY) were reconstituted in giant unilamellar vesicles composed of unsaturated phosphocholine lipids of varying acyl chain length (14-22 carbon atoms) and various ratios of DOPE/DOPG/DOPC lipids. The lateral mobility of the proteins and of a fluorescent lipid analog was determined as a function of the hydrophobic thickness of the bilayer (h) and lipid composition, using fluorescence correlation spectroscopy. The diffusion coefficient of LacY decreased with increasing thickness of the bilayer, in accordance with the continuum hydrodynamic model of Saffman-Delbrück. For GltT, the mobility had its maximum at diC18:1 PC, which is close to the hydrophobic thickness of the bilayer in vivo. The lateral mobility decreased linearly with the concentration of DOPE but was not affected by the fraction of anionic lipids from DOPG. The addition of DOPG and DOPE did not affect the activity of GltT. We conclude that the hydrophobic thickness of the bilayer is a major determinant of molecule diffusion in membranes, but protein-specific properties may lead to deviations from the Saffman-Delbrück model.     

Lateral diffusion in an archipelago. Dependence on tracer size.

In a pure fluid-phase lipid, the dependence of the lateral diffusion coefficient on the size of the diffusing particle may be obtained from the Saffman-Delbrück equation or the free-volume model. When diffusion is obstructed by immobile proteins or domains of gel-phase lipids, the obstacles yield an additional contribution to the size dependence. Here this contribution is examined using Monte Carlo calculations. For random point and hexagonal obstacles, the diffusion coefficient depends strongly on the size of the diffusing particle, but for fractal obstacles--cluster-cluster aggregates and multicenter diffusion-limited aggregates--the diffusion coefficient is independent of the size of the diffusing particle. The reason is that fractals have no characteristic length scale, so a tracer sees on average the same obstructions, regardless of its size. The fractal geometry of the excluded area for tracers of various sizes is examined. Percolation thresholds are evaluated for a variety of obstacles to determine how the threshold depends on tracer size and to compare the thresholds for compact and extended obstacles.     

Effect of Microvilli on Lateral Diffusion Measurements Made by the Fluorescence Photobleaching Recovery Technique

To consider the effect of surface microvilli on measurements of lateral diffusion by fluorescence photobleaching recovery, we have measured the diffusion of the lipid probe 3,3′-dihexadecyl indocarbocyanine iodide on the villated main body and unvillated budding polar body of unfertilized mouse eggs. On the main body we found D = (6.41 ± 0.62) × 10^-9 cm²/s with (77.0 ± 2.1)% recovery, and on the budding polar body we found D = (7.05 ± 0.75) × 10^-9 cm²/s with (84.7 ± 1.3)% recovery. We thus find only slight differences in diffusion in the two regions.     

THE ELECTRIC RESISTANCE AND CAPACITY OF BLOOD FOR FREQUENCIES BETWEEN 800 AND 4? MILLION CYCLES

1. The variation of the experimental values (R (ω)), (C (ω)) of the resistance and capacity of blood for increasing frequencies is approximately represented by the equation: See PDF for Equation in which R _o and C _o are the resistance and capacity of the blood at low frequency and See PDF for Equation is the resistance of the blood at infinite frequency. Formulæ (1) and (2) are derived by considering the blood as equivalent to the system shown in the diagram (a) of Fig. 1. 2. By the application of formula (1) to our experimental data the value of R(∞) can be extrapolated with high accuracy. R(∞) represents the resistance) which would have been obtained at low frequency, if the membranes around the corpuscles could have been removed. 3. The specific resistance of the corpuscle interior can be calculated by equation (5), using experimental values for R(∞), for the volume concentration of the blood and for the specific resistance of the serum. 4. The specific resistance of the interior of the red corpuscle of the calf is found to be 3.5 ± 10 per cent times the specific resistance of the serum.     

Stereo- and Regioselective Hydroxylation of α-Ionone by Streptomyces Strains

A total of 215 Streptomyces strains were screened for their capacity to regio- and stereoselectively hydroxylate β- and/or α-ionone to the respective 3-hydroxy derivatives. With β-ionone as the substrate, 15 strains showed little conversion to 4-hydroxy- and none showed conversion to the 3-hydroxy product as desired. Among these 15 Streptomyces strains, S. fradiae Tü 27, S. arenae Tü 495, S. griseus ATCC 13273, S. violaceoniger Tü 38, and S. antibioticus Tü 4 and Tü 46 converted α-ionone to 3-hydroxy-α-ionone with significantly higher hydroxylation activity compared to that of β-ionone. Hydroxylation of racemic α-ionone [(6R)-(−)/(6S)-(+)] resulted in the exclusive formation of only the two enantiomers (3R,6R)- and (3S,6S)-hydroxy-α-ionone. Thus, the enzymatic hydroxylation of α-ionone by the Streptomyces strains tested proceeds with both high regio- and stereoselectivity.     

Influence of the long-chain/short-chain amphiphile ratio on lateral diffusion of PEG-lipid in magnetically aligned lipid bilayers as measured via pulsed-field-gradient NMR

Lateral diffusion measurements of polyethylene glycol(PEG)-lipid incorporated into magnetically aligned lipid bilayers, composed of dimyristoyl phosphatidylcholine (DMPC) plus dihexanoyl phosphatidylcholine (DHPC) plus 1 mol % (relative to DMPC) dimyristoyl phosphatidylethanolamine-n-[methoxy(polyethylene glycol)-2000] (DMPE-PEG 2000), were performed using stimulated-echo pulsed-field-gradient proton (¹H) nuclear magnetic resonance spectroscopy. The DMPE-PEG 2000 (1 mol %, 35°C) lateral diffusion coefficient D varied directly with the mole fraction of DMPC, X_DMPC = q/(1+q) where q = DMPC/DHPC molar ratio, decreasing progressively from D = 1.65 × 10⁻¹¹ m² s⁻¹ at q ≈ 4.7 to D = 0.65 × 10⁻¹¹ m² s⁻¹ at q ≈ 2.5. Possible sources of this dependence, including orientational disorder, obstruction, and PEG-lipid sequestration, were simulated using, respectively, a diffusion-in-a-cone model, percolation theory, and a two-phase PEG distribution model. Orientational disorder alone was not capable of reproducing the observations, but in combination with either obstruction or PEG-lipid two-phase distribution models did so satisfactorily. A combination of all three models yielded the most reasonable fit to the observed dependence of lateral diffusion on q. These same effects would be expected to influence lateral diffusion of any bilayer-associating species in such systems.     

Diffusion of insulin-like growth factor-I and ribonuclease through fibrin gels

A fluorescence-based method for simultaneously determining the diffusion coefficients of two proteins is described, and the diffusion coefficient of insulin-like growth factor (IGF-I) and ribonuclease (RNase) in a 0.27% fibrin hydrogel is reported. The method is based on two-color imaging of the relaxation of the protein concentration field with time and comparing the results with a transport model. The gel is confined in a thin (200 μm) capillary and the protein is labeled with a fluorescent dye. The experimentally determined diffusion coefficient of RNase (D = 1.21 × 10⁻⁶ cm²/s) agrees with literature values for dilute gels and bulk aqueous solutions, thus indicating the gel and the dye had a negligible effect on diffusion. The experimental diffusion coefficient of IGF-I (D = 1.59 × 10⁻⁶ cm²/s), in the absence of binding to the fibrin matrix, is consistent with the dimensions of the molecule known from x-ray crystallography and a correlation between D and molecular weight based on 14 other proteins. The experimental method developed here holds promise for determining molecular transport properties of biomolecules under a variety of conditions, for example, when the molecule adsorbs to the gel or is convected through the gel by fluid transport.     

Diffusion Coefficients of Endogenous Cytosolic Proteins from Rabbit Skinned Muscle Fibers

Efflux time courses of endogenous cytosolic proteins were obtained from rabbit psoas muscle fibers skinned in oil and transferred to physiological salt solution. Proteins were separated by gel electrophoresis and compared to load-matched standards for quantitative analysis. A radial diffusion model incorporating the dissociation and dissipation of supramolecular complexes accounts for an initial lag and subsequent efflux of glycolytic and glycogenolytic enzymes. The model includes terms representing protein crowding, myofilament lattice hindrance, and binding to the cytomatrix. Optimization algorithms returned estimates of the apparent diffusion coefficients, D(r,t), that were very low at the onset of diffusion (∼10⁻¹⁰ cm² s⁻¹) but increased with time as cytosolic protein density, which was initially high, decreased. D(r,t) at later times ranged from 2.11 × 10⁻⁷ cm² s⁻¹ (parvalbumin) to 0.20 × 10⁻⁷ cm² s⁻¹ (phosphofructose kinase), values that are 3.6- to 12.3-fold lower than those predicted in bulk water. The low initial values are consistent with the presence of complexes in situ; the higher later values are consistent with molecular sieving and transient binding of dissociated proteins. Channeling of metabolic intermediates via enzyme complexes may enhance production of adenosine triphosphate at rates beyond that possible with randomly and/or sparsely distributed enzymes, thereby matching supply with demand.     

Detection of Diffusion Heterogeneity in Single Particle Tracking Trajectories Using a Hidden Markov Model with Measurement Noise Propagation

We develop a Bayesian analysis framework to detect heterogeneity in the diffusive behaviour of single particle trajectories on cells, implementing model selection to classify trajectories as either consistent with Brownian motion or with a two-state (diffusion coefficient) switching model. The incorporation of localisation accuracy is essential, as otherwise false detection of switching within a trajectory was observed and diffusion coefficient estimates were inflated. Since our analysis is on a single trajectory basis, we are able to examine heterogeneity between trajectories in a quantitative manner. Applying our method to the lymphocyte function-associated antigen 1 (LFA-1) receptor tagged with latex beads (4 s trajectories at 1000 frames s⁻¹), both intra- and inter-trajectory heterogeneity were detected; 12–26% of trajectories display clear switching between diffusive states dependent on condition, whilst the inter-trajectory variability is highly structured with the diffusion coefficients being related by D ₁ = 0.68D ₀ − 1.5 × 10⁴ nm² s⁻¹, suggestive that on these time scales we are detecting switching due to a single process. Further, the inter-trajectory variability of the diffusion coefficient estimates (1.6 × 10² − 2.6 × 10⁵ nm² s⁻¹) is very much larger than the measurement uncertainty within trajectories, suggesting that LFA-1 aggregation and cytoskeletal interactions are significantly affecting mobility, whilst the timescales of these processes are distinctly different giving rise to inter- and intra-trajectory variability. There is also an ‘immobile’ state (defined as D < 3.0 × 10³ nm² s⁻¹) that is rarely involved in switching, immobility occurring with the highest frequency (47%) under T cell activation (phorbol-12-myristate-13-acetate (PMA) treatment) with enhanced cytoskeletal attachment (calpain inhibition). Such ‘immobile’ states frequently display slow linear drift, potentially reflecting binding to a dynamic actin cortex. Our methods allow significantly more information to be extracted from individual trajectories (ultimately limited by time resolution and time-series length), and allow statistical comparisons between trajectories thereby quantifying inter-trajectory heterogeneity. Such methods will be highly informative for the construction and fitting of molecule mobility models within membranes incorporating aggregation, binding to the cytoskeleton, or traversing membrane microdomains.     

Determination of Thermal Inactivation Kinetics of Hepatitis A Virus in Blue Mussel (Mytilus edulis) Homogenate

Hepatitis A virus (HAV) is a food-borne enteric virus responsible for outbreaks of hepatitis associated with shellfish consumption. The objectives of this study were to determine the thermal inactivation behavior of HAV in blue mussels, to compare the first-order and Weibull models to describe the data, to calculate Arrhenius activation energy for each model, and to evaluate model efficiency by using selected statistical criteria. The times required to reduce the population by 1 log cycle (D-values) calculated from the first-order model (50 to 72°C) ranged from 1.07 to 54.17 min for HAV. Using the Weibull model, the times required to destroy 1 log unit (t_{D = 1}) of HAV at the same temperatures were 1.57 to 37.91 min. At 72°C, the treatment times required to achieve a 6-log reduction were 7.49 min for the first-order model and 8.47 min for the Weibull model. The z-values (changes in temperature required for a 90% change in the log D-values) calculated for HAV were 15.88 ± 3.97°C (R², 0.94) with the Weibull model and 12.97 ± 0.59°C (R², 0.93) with the first-order model. The calculated activation energies for the first-order model and the Weibull model were 165 and 153 kJ/mol, respectively. The results revealed that the Weibull model was more appropriate for representing the thermal inactivation behavior of HAV in blue mussels. Correct understanding of the thermal inactivation behavior of HAV could allow precise determination of the thermal process conditions to prevent food-borne viral outbreaks associated with the consumption of contaminated mussels.     

A Quantitative Study of Cellular Rheotropism

Sparsely sowed, hence independent Botrytis spores, which are fixed to the wall of a laminar flow chamber, tend to germinate downstream. For a velocity, v_∞, one cell radius from the wall, of 0.1 to 1000 μ/second, this tendency, expressed as a percentage of perfect orientation, approximates 9 · log (10 v_∞). Indirect proof is given that this rheotropic response is mediated by the convection across each cell of a diffusible stimulator emitted by it. Analysis of the response indicates that this stimulator has a diffusion constant of the order of 10^-7 cm²/second and thus is macromolecular, and a half-life of the order of 10 seconds and thus a radius of action in a stagnant medium of about one cell diameter. The rate of germination falls so slowly with increasing flow rate as to indicate a much lower sensitivity of the rate than of the localization of growth to this stimulator's concentration.     

Diffusion of a soluble protein,photoactivatable GFP,through a sensory cilium

Transport of proteins to and from cilia is crucial for normal cell function and survival, and interruption of transport has been implicated in degenerative and neoplastic diseases. It has been hypothesized that the ciliary axoneme and structures adjacent to and including the basal bodies of cilia impose selective barriers to the movement of proteins into and out of the cilium. To examine this hypothesis, using confocal and multiphoton microscopy we determined the mobility of the highly soluble photoactivatable green fluorescent protein (PAGFP) in the connecting cilium (CC) of live Xenopus retinal rod photoreceptors, and in the contiguous subcellular compartments bridged by the CC, the inner segment (IS) and the outer segment (OS). The estimated axial diffusion coefficients are D_CC = 2.8 ± 0.3, D_IS = 5.2 ± 0.6, and D_OS = 0.079 ± 0.009 µm² s⁻¹. The results establish that the CC does not pose a major barrier to protein diffusion within the rod cell. However, the results also reveal that axial diffusion in each of the rod’s compartments is substantially retarded relative to aqueous solution: the axial diffusion of PAGFP was retarded ∼18-, 32- and 1,000-fold in the IS, CC, and OS, respectively, with ∼20-fold of the reduction in the OS attributable to tortuosity imposed by the lamellar disc membranes. Previous investigation of PAGFP diffusion in passed, spherical Chinese hamster ovary cells yielded D_CHO = 20 µm² s⁻¹, and estimating cytoplasmic viscosity as D_aq/D_CHO = 4.5, the residual 3- to 10-fold reduction in PAGFP diffusion is ascribed to sub-optical resolution structures in the IS, CC, and OS compartments.     

Chloride Transport in Porous Lipid Bilayer Membranes

This paper describes dissipative Cl_- transport in "porous" lipid bilayer membranes, i.e., cholesterol-containing membranes exposed to 1–3 x 10^-7 M amphotericin B. P_DCl (cm·s^-1), the diffusional permeability coefficient for Cl^-, estimated from unidirectional ³⁶Cl^- fluxes at zero volume flow, varied linearly with the membrane conductance (Gm, Ω^-1·cm^-2) when the contributions of unstirred layers to the resistance to tracer diffusion were relatively small with respect to the membranes; in 0.05 M NaCl, P_DCl was 1.36 x 10^-4 cm·s^-1 when Gm was 0.02 Ω^-1·cm^-2. Net chloride fluxes were measured either in the presence of imposed concentration gradients or electrical potential differences. Under both sets of conditions: the values of P_DCl computed from zero volume flow experiments described net chloride fluxes; the net chloride fluxes accounted for ~90–95% of the membrane current density; and, the chloride flux ratio conformed to the Ussing independence relationship. Thus, it is likely that Cl^- traversed aqueous pores in these anion-permselective membranes via a simple diffusion process. The zero current membrane potentials measured when the aqueous phases contained asymmetrical NaCl solutions could be expressed in terms of the Goldman-Hodgkin-Katz constant field equation, assuming that the P_DNa/P_DCl ratio was 0.05. In symmetrical salt solutions, the current-voltage properties of these membranes were linear; in asymmetrical NaCl solutions, the membranes exhibited electrical rectification consistent with constant-field theory. It seems likely that the space charge density in these porous membranes is sufficiently low that the potential gradient within the membranes is approximately linear; and, that the pores are not electrically neutral, presumably because the Debye length within the membrane phase approximates the membrane thickness.     

Self Crowding of Globular Proteins Studied by Small-Angle X-Ray Scattering

Small-angle x-ray scattering (SAXS) was used to study the behavior of equine metmyoglobin (Mb) and bovine pancreatic trypsin inhibitor (BPTI) at concentrations up to 0.4 and 0.15 g/mL, respectively, in solutions also containing 50% D₂O and 1 M urea. For both proteins, significant effects because of interference between x-rays scattered by different molecules (interparticle interference) were observed, indicating nonideal behavior at high concentrations. The experimental data were analyzed by comparison of the observed scattering profiles with those predicted by crystal structures of the proteins and a hard-sphere fluid model used to represent steric exclusion effects. The Mb scattering data were well fit by the hard-sphere model using a sphere radius of 18 Å, only slightly smaller than that estimated from the three-dimensional structure (20 Å). In contrast, the scattering profiles for BPTI in phosphate buffer displayed substantially less pronounced interparticle interference than predicted by the hard-sphere model and the radius estimated from the known structure of the protein (15 Å). Replacing the phosphate buffer with 3-(N-morpolino)propane sulfonic acid (MOPS) led to increased interparticle interference, consistent with a larger effective radius and suggesting that phosphate ions may mediate attractive intermolecular interactions, as observed in some BPTI crystal structures, without the formation of stable oligomers. The scattering data were also used to estimate second virial coefficients for the two proteins: 2.0 ×10^-4 cm³mol/g² for Mb in phosphate buffer, 1.6 ×10^-4 cm³mol/g² for BPTI in phosphate buffer and 9.2 ×10^-4 cm³mol/g² for BPTI in MOPS. The results indicate that the behavior of Mb, which is nearly isoelectric under the conditions used, is well described by the hard-sphere model, but that of BPTI is considerably more complex and is likely influenced by both repulsive and attractive electrostatic interactions. The hard-sphere model may be a generally useful tool for the analysis of small-angle scattering data from concentrated macromolecular solutions.     

Translational Diffusion of Macromolecule-sized Solutes in Cytoplasm and Nucleus

Fluorescence recovery after photobleaching (FRAP) was used to quantify the translational diffusion of microinjected FITC-dextrans and Ficolls in the cytoplasm and nucleus of MDCK epithelial cells and Swiss 3T3 fibroblasts. Absolute diffusion coefficients (D) were measured using a microsecond-resolution FRAP apparatus and solution standards. In aqueous media (viscosity 1 cP), D for the FITC-dextrans decreased from 75 to 8.4 × 10⁻⁷ cm²/s with increasing dextran size (4–2,000 kD). D in cytoplasm relative to that in water (D/D_o) was 0.26 ± 0.01 (MDCK) and 0.27 ± 0.01 (fibroblasts), and independent of FITC-dextran and Ficoll size (gyration radii [R_G] 40–300 Å). The fraction of mobile FITC-dextran molecules (f_mob), determined by the extent of fluorescence recovery after spot photobleaching, was >0.75 for R_G < 200 Å, but decreased to <0.5 for R_G > 300 Å. The independence of D/D_o on FITC-dextran and Ficoll size does not support the concept of solute “sieving” (size-dependent diffusion) in cytoplasm. Photobleaching measurements using different spot diameters (1.5–4 μm) gave similar D/D_o, indicating that microcompartments, if present, are of submicron size. Measurements of D/D_o and f_mob in concentrated dextran solutions, as well as in swollen and shrunken cells, suggested that the low f_mob for very large macromolecules might be related to restrictions imposed by immobile obstacles (such as microcompartments) or to anomalous diffusion (such as percolation). In nucleus, D/D_o was 0.25 ± 0.02 (MDCK) and 0.27 ± 0.03 (fibroblasts), and independent of solute size (R_G 40–300 Å). Our results indicate relatively free and rapid diffusion of macromolecule-sized solutes up to approximately 500 kD in cytoplasm and nucleus.     

Physical Properties of Lipid Monolayers on Alkylated Planar Glass Surfaces

A method for transferring a lipid monolayer from an air-water interface to an alkylated glass slide is described. Specific antibodies bind tightly to lipid haptens contained in these monolayers on the glass slides. We conclude that the polar head groups of the lipids face the aqueous phase. A monolayer containing a fluorescent lipid was used to show that the monolayer is homogeneous as observed with an epifluorescence microscope. A periodic pattern photobleaching technique was used to measure the lateral diffusion of this fluorescent lipid probe in monolayers composed of dipalmitoyl phosphatidylcholine and dimyristoyl phosphatidylcholine. Different regions of the pressure-area isotherms of the monolayers at the air-water interface can be correlated with the diffusion of the fluorescent probe molecules on the monolayer-coated glass slide. Monolayers derived from the so-called “solid-condensed” state of a monolayer at the air-water interface showed a very low probe diffusion coefficient in this monolayer when placed on a glass slide, D ≤ 10^-10 cm²/s. Monolayers derived from the “liquid condensed/liquid expanded” (LC/LE) region of the monolayer isotherms at the air-water interface showed rapid diffusion (D > 10^-8 cm²/s) when these same monolayers were observed on an alkylated glass slide. The monolayers attached to the glass slide appear to be homogeneous when derived from monolayers in the LC/LE region of monolayers at the air-water interface. There is no major variation of the diffusion coefficient of a fluorescent lipid probe when this diffusion is measured on a lipid monolayer on a glass slide, for monolayers derived from various regions of the LC/LE monolayers at the air-water interface. This is consistent with the view that the LC/LE region is most likely a single fluid phase. Monolayers supported on a planar glass substrate are of much potential interest for biophysical and biochemical studies of the interactions between model membranes and cellular membranes, and for physical chemical studies relating the properties of lipid monolayers to the properties of lipid bilayers.     

Transient Phases of the Isometric Tetanus in Frog's Striated Muscle

In an isometric tetanus in frog's sartorius muscle tension approaches the plateau exponentially with rate constant α. α a depends on sarcomere length, s, and temperature, T, according to the Arrhenius equation See PDF for Equation for temperatures between 1 and 20°C and for sarcomere lengths 2.0–2.8 µm. The energy of activation, E, does not vary significantly with s; E = 13.9 ± 2.4 kcal/mole. A(s) decreases monotonically with s; A(2.1 µm) is about three times greater than A(2.8 µm). Late in relaxation active tension approaches zero exponentially with rate constant r. r decreases exponentially with increasing duration of tetanus, D, from r₀ in a twitch to r_∞ for large D. The rate constant for decrease of r with D increases with s and with T. r₀ and r_∞ obey the Arrhenius equation and decrease with increasing s.     

Detection of Hindered Rotations of 1,6-Diphenyl-1,3,5-Hexatriene in Lipid Bilayers by Differential Polarized Phase Fluorometry

Differential polarized phase fluorometry has been used to investigate the depolarizing motions of 1,6-diphenyl-1,3,5-hexatriene (DPH) in the isotropic solvent propylene glycol and in lipid bilayers of dimyristoyl-L-α-phosphatidylcholine (DMPC), dipalmitoyl-L-α-phosphatidylcholine (DPPC), and other phosphatidylcholines. Differential phase fluorometry is the measurement of differences in the phase angles between the parallel and perpendicular components of the fluorescence emission of a sample excited with sinusoidally modulated light. The maximum value of the tangent of the phase angle (tan Δ_max) is known to be a function of the isotropy of the depolarizing motions. For DPH in propylene glycol the maximum tangent is observed at 18°C, and this tangent value corresponds precisely with the value expected for an isotropic rotator. Additionally, the rotational rates determined by steady-state polarization measurements are in precise agreement with the differential phase measurements. These results indicate that differential phase fluorometry provides a reliable measure of the probe's rotational rate under conditions where these rotations are isotropic and unhindered.

Rotational rates of DPH obtained from steady-state polarization and differential phase measurements do not agree when this probe is placed in lipid bilayers. The temperature profile of the tan Δ measurements of DPH in DMPC and DPPC bilayers is characterized by a rapid increase of tan Δ at the transition temperature (T_c), followed by a gradual decline in tan Δ at temperatures above T_c. The observed tanΔ_max values are only 62 and 43% of the theoretical maximum. This defect in tanΔ_max is too large to be explained by any degree of rotational anisotropy. However, these defects are explicable by a new theory that describes the tan Δ values under conditions where the probe's rotational motions are restricted to a limiting anisotropy value, r_∞. Theoretical calculations using this new theory indicate that the temperature dependence of the depolarizing motions of DPH in these saturated bilayers could be explained by a rapid increase in its rotational rate (R) at the transition temperature, coupled with a simultaneous decrease in r_∞ at this same temperature. The sensitivity of the tan Δ values to both R and r_∞ indicates that differential phase fluorometry will provide a method to describe more completely the depolarizing motion of probes in lipid bilayers.

     

Diffusion of Single Cardiac Ryanodine Receptors in Lipid Bilayers Is Decreased by Annexin 12

Diffusion of cardiac ryanodine receptors (RyR2) in lipid bilayers was characterized. RyR2 location was monitored by imaging fluo-3 fluorescence due to Ca²⁺ flux through RyR2 channels or fluorescence from RyR2 conjugated with Alexa 488 or containing green fluorescent protein. Single channel currents were recorded to ensure that functional channels were studied. RyR2 exhibited an apparent diffusion coefficient (D_RyR) of 1.2 × 10⁻⁸ cm² s⁻¹ and a mean path length of 5.0 μm. Optimal use of optical methods for analysis of RyR2 channel function requires that RyR2 diffusion be limited. Therefore, we tested the effect of annexin 12, which interacts with anionic phospholipids in a Ca²⁺-dependent manner. Addition of annexin 12 (0.25–4.0 μM) to the trans side of bilayers containing an 80:20 ratio of phosphatidylethanolamine/phosphatidylserine decreased RyR2 diffusion in a concentration-dependent manner. Annexin 12 (2 μM) decreased the apparent D_RyR 683-fold from 1.2–10⁻⁸ to 1.8 × 10⁻¹¹ cm² s⁻¹ and the mean path length 10-fold from 5.0 to 0.5 μm without obvious changes in the conductance of the native bilayer or in activation of RyR2 channels by Ca²⁺ or suramin. Thus, annexin 12 may provide a useful tool for optimizing optical analysis of RyR2 channels in lipid bilayers.