Vesicle Orientation Research Articles

Analytical solutions and classification of vesicle motion and deformation in shear flow: Uncovering new tank-treading modes.

Using a small deformation approach, a fractional ordinary differential system is proposed to investigate the motion and deformation of a vesicle in shear flow. Closed analytical expressions of the orientation angle and the ellipticity of the vesicle contour (shape deformation) are provided. Three different motions are identified, the classical tank-treading state, and two new types of motions, namely, the over-damped tank-treading mode, in which the vesicle's orientation angle ψ and its shape deformation R tend more slowly toward equilibrium, and the under-damped tank-treading mode, in which ψ oscillates all the time along the flow direction with decreasing amplitude, while R starts making a breathing motion and then tends to an attractive amplitude. The implications of our findings extend widely within the field of fluid dynamics, revealing the potential for further advancements and applications in understanding complex fluid systems.

In Vivo Fast Nonlinear Microscopy Reveals Impairment of Fast Axonal Transport Induced by Molecular Motor Imbalances in the Brain of Zebrafish Larvae.

Cargo transport by molecular motors along microtubules is essential for the function of eukaryotic cells, in particular neurons in which axonal transport defects constitute the early pathological features of neurodegenerative diseases. Mainly studied in motor and sensory neurons, axonal transport is still difficult to characterize in neurons of the brain in absence of appropriate in vivo tools. Here, we measured fast axonal transport by tracing the second harmonic generation (SHG) signal of potassium titanyl phosphate (KTP) nanocrystals (nanoKTP) endocytosed by brain neurons of zebrafish (Zf) larvae. Thanks to the optical translucency of Zf larvae and to the perfect photostability of nanoKTP SHG, we achieved a high scanning speed of 20 frames (of ≈90 μm × 60 μm size) per second in Zf brain. We focused our study on endolysosomal vesicle transport in axons of known polarization, separately analyzing kinesin and dynein motor-driven displacements. To validate our assay, we used either loss-of-function mutations of dynein or kinesin 1 or the dynein inhibitor dynapyrazole and quantified several transport parameters. We successfully demonstrated that dynapyrazole reduces the nanoKTP mobile fraction and retrograde run length consistently, while the retrograde run length increased in kinesin 1 mutants. Taking advantage of nanoKTP SHG directional emission, we also quantified fluctuations of vesicle orientation. Thus, by combining endocytosis of nanocrystals having a nonlinear response, fast two-photon microscopy, and high-throughput analysis, we are able to finely monitor fast axonal transport in vivo in the brain of a vertebrate and reveal subtle axonal transport alterations. The high spatiotemporal resolution achieved in our model may be relevant to precisely investigate axonal transport impairment associated with disease models.

Effect of ac electric field on the dynamics of a vesicle under shear flow in the small deformation regime.

Vesicles or biological cells under simultaneous shear and electric field can be encountered in dielectrophoretic devices or designs used for continuous flow electrofusion or electroporation. In this work, the dynamics of a vesicle subjected to simultaneous shear and uniform alternating current (ac) electric field is investigated in the small deformation limit. The coupled equations for vesicle orientation and shape evolution are derived theoretically, and the resulting nonlinear equations are handled numerically to generate relevant phase diagrams that demonstrate the effect of electrical parameters on the different dynamical regimes such as tank treading (TT), vacillating breathing (VB) [called trembling (TR) in this work], and tumbling (TU). It is found that while the electric Mason number (Mn), which represents the relative strength of the electrical forces to the shear forces, promotes the TT regime, the response itself is found to be sensitive to the applied frequency as well as the conductivity ratio. While higher outer conductivity promotes orientation along the flow axis, orientation along the electric field is favored when the inner conductivity is higher. Similarly a switch of orientation from the direction of the electric field to the direction of flow is possible by a mere change of frequency when the outer conductivity is higher. Interestingly, in some cases, a coupling between electric field-induced deformation and shear can result in the system admitting an intermediate TU regime while attaining the TT regime at high Mn. The results could enable designing better dielectrophoretic devices wherein the residence time as well as the dynamical states of the vesicular suspension can be controlled as per the application.

Rheological properties of a vesicle suspension.

The rheological behavior of a dilute suspension of vesicles in linear shear flow at a finite concentration is analytically examined. In the quasispherical limit, two coupled nonlinear equations that describe the vesicle orientation in the flow and its shape evolution were derived [Phys. Rev. Lett. 96, 028104 (2006)PRLTAO0031-900710.1103/PhysRevLett.96.028104] and serve here as a starting point. Of special interest is to provide, for the first time, an exact analytical prediction of the time-dependent effective viscosity η_{eff} and normal stress differences N_{1} and N_{2}. Our results shed light on the effect of the viscosity ratio λ (defined as the inner over the outer fluid viscosities) as the main controlling parameter. It is shown that η_{eff},N_{1}, and N_{2} either tend to a steady state or describe a periodic time-dependent rheological response, previously reported numerically and experimentally. In particular, the shear viscosity minimum and the cusp singularities of η_{eff},N_{1}, and N_{2} at the tumbling threshold are brought to light. We also report on rheology properties for an arbitrary linear flow. We were able to obtain a constitutive law in a closed form relating the stress tensor to the strain rate tensor. It is found that the resulting constitutive markedly contrasts with classical laws known for other complex fluids, such as emulsions, capsule suspensions, and dilute polymer solutions (Oldroyd B model). We highlight the main differences between our law and classical laws.

Development of a fluorescence-based assay for drug interactions with human Multidrug Resistance Related Protein (MRP2; ABCC2) in MDCKII-MRP2 membrane vesicles

Purpose To establish a fluorescence-based assay for drug interactions with the ABC-export-protein MRP2 (ABCC2). Methods Apical membrane vesicles were isolated by differential centrifugation from polarized MDCKII cells and MDCKII cells transfected with human MRP2. Vesicle fractions were characterized by electron microscopy, determination of the marker enzyme alkaline phosphatase and Western blot analysis of MRP2. Vesicle orientation was determined by measurement of 5′-nucleotidase activity in the absence and in the presence of detergents. To assess MRP2 activity, the uptake of the fluorescent MRP2-substrate 5-(6)-carboxy-2′,7′-dichlorofluorescein (CDF) was determined in the absence and in the presence of other compounds potentially interacting with MRP2. Results Apical membrane vesicles could be isolated from cells in considerable purity as indicated by electron microscopy, enrichment of alkaline phosphatase and high enrichment of MRP2 in vesicles of MDCKII-MRP2 cells. About half of the vesicles showed “inside-out” orientation. CDF was taken up into the membrane vesicles in a time- and concentration-dependent manner following a Michaelis–Menten type of kinetics with a K M of 39 μM and a V max of 465.3 fmol/(mg protein × min). Thereby, uptake into vesicles from transfected cells was significantly higher than uptake into vesicles from control cells. Presence of known MRP2-substrates/inhibitors in the incubation medium decreased CDF uptake into the vesicles in a concentration-dependent manner, whereas nonsubstrates/inhibitors had no effect. Conclusions This CDF-based uptake assay can be used as a rapid and sensitive screening system to assess drug interactions with human MRP2 and therefore represents a useful tool in compound profiling.

Vesicles under simple shear flow: Elucidating the role of relevant control parameters

The dynamics of vesicles under shear flow are carefully analyzed in the regime of a small vesicle excess area relative to a sphere. This regime corresponds to the quasispherical limit, for which several groups have analytically extracted simple nonlinear differential equations. Under shear flow, vesicles are known to exhibit three types of motion: (i) tank-treading (TT): the vesicle assumes a steady inclination angle with respect to the flow direction, while its membrane undergoes a tank-treading motion, (ii) tumbling (TB), and (iii) vacillating-breathing (VB): the vesicle main axis oscillates about the flow direction, whereas the overall shape undergoes a breathinglike motion. The region of existence for each regime depends on material and control parameters. The whole set of parameters can be cast into three dimensionless control parameters: (i) the viscosity ratio between the internal and external fluid, lambda , (ii) the excess area relative to a sphere (this parameter measures the degree of the vesicle deflation), Delta , and (iii) the capillary number (the ratio between the vesicle relaxation time toward its equilibrium shape after cessation of the flow and the flow time scale, which is the inverse shear rate), Ca. Recent studies [Danker, Phys. Rev. E 76, 041905 (2007)] have focused on the shape of the phase diagram (representing the TT, TB, and VB regimes in the Ca-lambda plane). In this paper, the physical quantities are analyzed in detail and attention is brought to features that are essential for future experimental studies. It is shown that the boundaries delimiting different dynamical regimes (TT, TB, and VB) in parameter space depend on the three dimensionless control parameters, in contrast with a recent study [V. V. Lebedev, Phys. Rev. Lett. 99, 218101 (2007)] where it is claimed that only two parameters are relevant. Consideration of the amplitude of oscillation (of the vesicle orientation angle and its shape deformation) in the VB mode reveals an even more significant dependence on the three parameters. It is also shown that the inclination angle in the TT regime significantly depends on the shear rate (Ca), which runs contrary to common belief. Finally, we show that the TB and VB periods are quite insensitive to Ca, in marked contrast with a recent study [H. Noguchi and G. Gompper, Phys. Rev. Lett. 98, 128103 (2007)].

On coupling between the orientation and the shape of a vesicle under a shear flow

A simple 2D model of deformable vesicles tumbling in a shear under flow is introduced in order to account for the main qualitative features observed experimentally as shear rates are increased. The simplicity of the model allows for a full analytical tractability while retaining the essential physical ingredients. The model reveals that the main axes of the vesicle undergo oscillations which are coupled to the vesicle orientation in the flow. The model reproduces and sheds light on the main novel features reported in recent experiments [M. Mader et al., Eur. Phys. J. E. 19, 389 (2006)], namely that both coefficients A and B that enter the Keller-Skalak equation, d psi/dt = A+B cos(2 psi) (psi is the vesicle orientation angle in the shear flow), undergo a collapse upon increasing shear rate.

Shear-driven release of a bud from a multicomponent vesicle

The authors study the response of a multicomponent budded vesicle to an imposed shear flow using dissipative particle dynamics. Under certain circumstances, phase separation in the vesicle membrane leads to the formation of a minority domain which deforms into a nearly spherical bud in order to reduce its interfacial energy. The authors show that an imposed shear force has a varying effect on the vesicle, tending either to separate the bud from the vesicle or to stretch the bud open, depending on the vesicle orientation. The authors examine the interplay of membrane bending rigidity, line tension, and shear in determining the behavior of the vesicle. With the appropriate design, vesicles can be made to release buds in a controlled manner in response to shear. The authors outline a regime in which bud release is favorable.

Vacillating Breathing and Tumbling of Vesicles under Shear Flow

The dynamics of vesicles under a shear flow are analyzed analytically in the small deformation regime. We derive two coupled nonlinear equations which describe the vesicle orientation in the flow and its shape evolution. A new type of motion is found, namely, a "vacillating-breathing" mode: the vesicle orientation undergoes an oscillation around the flow direction, while the shape executes breathing dynamics. This solution coexists with tumbling. Moreover, we provide an explicit expression for the tumbling threshold. A rheological law for a dilute vesicle suspension is outlined.

Na+ transport, H+ concentration gradient dissipation, and system A amino acid transporter activity in purified microvillous plasma membrane isolated from first-trimester human placenta: Comparison with the term microvillous membrane

Our purpose was to isolate microvillous plasma membrane from first-trimester placenta and to measure its transport properties with regard to Na+, H+, and a neutral amino acid. Microvillous membrane was isolated from first-trimester (10 to 13 weeks) and term (38 to 42 weeks) placenta and the purity determined. Uptake of 22Na+ was measured in the presence of an outwardly directly H+ gradient in the presence or absence of amiloride (0.5 mmol/L). The rate of dissipation of an H+ concentration gradient was determined with the H(+)-sensitive fluorescent probe 2',7'-bis(carboxyethyl)-5(6)-carboxyfluorescein. 14C-methylaminoisobutyric acid uptake was measured in the presence and absence of an inwardly directed Na+ gradient. Purity, vesicle volume, vesicle orientation, and electron micrographic appearance of the first-trimester membranes were similar to those obtained from term placenta, but vesicle protein recovery was lower. Amiloride-sensitive Na+ uptake and Na(+)-dependent 14C-methylaminoisobutyric acid uptake was threefold to fourfold lower by first-trimester than by term membranes. The rate of H+ concentration gradient dissipation was greater in the former. The first-trimester microvillous membrane has similar general characteristics to that from term placenta, but its transport activity is quite different.

Measurement of sarcolemmal vesicle orientation by beta-adrenergic receptor binding

To assess the orientation (inside-out vs. outside-out) of purified cardiac sarcolemmal vesicles, we developed a new method utilizing the known outward-facing binding site of the β-adrenergic receptor. We compared the binding of the lipid-insoluble ligand 3H-CGP-12177, which binds to β-adrenergic receptors on outside-out sarcolemmal vesicles only, to the binding of the lipid soluble ligand 125I-iodocyanopindolol, which binds to β-adrenergic receptors in sarcolemmal vesicles of either orientation. The ratio of CGP to ICYP binding is equal to the fraction of outside-out sarcolemmal vesicles. Sidedness measurements by β-adrenergic receptor-binding showed similar mean values but less scatter than sidedness assessments by measurement of 3H-ouabain-binding or Na +, K +-ATPase activity in the presence or absence of membrane permeabilizing agents.

Isolation of plasma membrane fractions from green wheat leaves by free‐flow electrophoresis or two‐phase partition alone or in combination

Plasma membrane vesicles were isolated from shoots of light‐grown wheat seedlings by preparative free‐flow electrophoresis, aqueous polymer two‐phase partition or both. Plasma membrane vesicles were identified from staining of thin sections prepared for electron microscopy with phosphotungstic acid at low pH. The orientation of the plasma membrane vesicles was determined from latency and trypsin sensitivity of K+ Mg2+ATPase and of glucan synthase II, and concanavalin A‐peroxidase binding and membrane asymmetry visualized by electron microscopy. The K+Mg2+ATPase and of glucan synthase II activities of plasma membrane fractions isolated by two‐phase partition were latent and trypsin resistant. The vesicles bound concanavalin A‐peroxidase strongly and exhibited a cytoplasmic side‐in morphology. These fractions of cytoplasmic side‐in vesicles were less than 10% contaminated by cytoplasmic side‐out vesicles. By free‐flow electrophoresis, two populations of vesicles which stained with phosphotungstic acid at low pH, designated D and E, were obtained. The vesicle population with the lower electrophoretic mobility, fraction E, contained plasma membrane vesicles with properties similar to those of the plasma membrane vesicles obtained after two‐phase partition. The phosphotungstic‐reactive vesicles with greater electrophoretic mobility, fraction D, were concanavalin A unreactive with the cytoplasmic membrane leaflet outwards. Less than 50% of the K+Mg2+‐ATPase activity of this fraction was latent and trypsin sensitive. The vesicles of fraction D appeared to be preferentially cytoplasmic side‐out. The electrophoretic mobilities of cytoplasmic side‐out (non‐latent glucan synthase II activity) and cytoplasmic side‐in (latent glncan synthase II activity) plasma membrane vesicles isolated from a frozen and thawed wheat plasma membrane fraction, corresponded with the mobilities of fraction D and E, respectively, again showing that the plasma membrane vesicles with the lesser electrophoretic mobility were cytoplasmic side‐in. The cytoplasmic side‐in and cytoplasmic side‐out vesicles therefore showed opposite eletrophoretic mobilities compared with a previous free‐flow electrophoretic separation of soybean plasma membranes. The majorities of the plasma membrane vesicles of both fractions D and E entered the upper phase upon two‐phase partition with the phase composition used for purification of wheat plasma membranes. Thus, neither electrophoretic mobility nor phase partitioning characteristics can be used as the only criteria for assignment of vesicle orientation.

Simultaneous preparation of paired, syncytial, microvillous and basal membranes from human placenta

A method for the simultaneous preparation of microvillous and basal membrane vesicles from human placental syncytiotrophoblast is described. Mg 2+-aggregated basal membranes are separated from microvillous membranes by low-speed centrifugation after initial homogenization and centrifugation steps. Microvillous membranes (MVM) are obtained from the low speed supernatant while basal membranes (BM) contained in the Mg 2+-aggregated material are resuspended and further purified on a sucrose step gradient. MVM and BM prepared by this method were enriched 20-fold and 11-fold as determined by the membrane marker enzymes, alkaline phosphatase (MVM) and adenylate cyclase (BM). There was minimal cross-contamination of the two isolated plasma membrane fractions and the yields obtained were 26% (MVM) and 21% (BM) compared to the initial homogenate. The MVM and BM fractions were free from contamination by mitochondrial or lysosomal membranes and showed only minor contamination by microsomal membranes. The two membrane fractions were also tested for the presence of non-syncytial plasma membranes by electrophoretic immunoblotting. Contamination of both MVM and BM by fibroblast, endothelial, macrophage and cytotrophoblast plasma membranes amounted to less than 15% of the total membrane protein as determined by immunoblotting. Vesicle orientation, determined from the latency of specific concanavalin A binding, was 88 ± 4% right-side out for MVM and 73 ± 12% right-side out for BM. This simple preparative procedure produces a high yield of both MVM and BM from human placenta. The analytical data demonstrates that ‘paired’ MVM and BM fractions derived from the same placental tissue have a high purity in terms not only of contamination by intracellular membranes, but also in terms of contamination by non-syncytial plasma membranes.

Effects of storage methods of fetal calf serum on the development of mouse embryos

A membrane fraction prepared by freeze-thawing envelope vesicles from Halobacterium halobium exhibits menadione-dependent NADH dehydrogenase activity (EC 1.6.9.9.3). The activity is “unmasked” by Triton X-100. Activity in freeze-thawed membrane preparations is more firmly membrane-bound than in sonicated vesicle preparations. Affinity for NADH is higher than in untreated vesicles and pyridine adenine dinucleotide specificity is the same. The data indicate that freeze-thawing causes reintegration of an adsorbed, extrinsic form of the dehydrogenase to yield an intrinsic, more native-like form of the enzyme. It is concluded that the extrinsic NADH dehydrogenase activity in vesicle preparations is not directly related to vesicle orientation.

Effect of detergents on the H +-ATPase activity of inside-out and right-side-out plant plasma membrane vesicles

In search for a detergent to be used to assess the sidedness of plant plasma membrane vesicles by enzyme latency we tested the effect of 42 detergents on the ATPase activity of right-side-out and inside-out plasma membrane vesicles from sugar beet leaves. Most of the detergents seemed to inactivate the ATPase in addition to disrupting the permeability barrier to ATP. These were two main exceptions, namely long chain polyoxyethylene acyl ethers, such as detergents of the Brij series and Lubrol WX, and long chain lysophospholipids. These two types of detergents permeabilized the membranes at low concentrations and did not inhibit the ATPase at higher concentrations. Unmasking of latent active sites seemed to explain the activation of the plasma membrane H +-ATPase produced by long chain polyoxyethylene acyl ethers. These detergents should therefore be ideal for determination of vesicle orientation based on ATPase latency. By contrast, long chain lysophospholipids were found to be highly specific activators of the enzyme. In addition, long chain fatty acids were found to strongly inhibit ATP-dependent proton accumulation in the vesicles without inhibiting ATP hydrolysis. This uncoupling effect of the fatty acids could be abolished by the addition of fatty acid-free bovine serum albumin (BSA). Similarly, the proton transport capacity of ageing vesicles could be restored by addition of BSA. The latter findings may explain why isolated plasma membranes so often exhibit increased permeability to protons on ageing.

Determination of brush border membrane vesicle orientation using monoclonal antibodies recognizing extracytoplasmic and cytoplasmic domains of neutral endopeptidase-24.11

A method for determination of the orientation and integrity of brush border membrane vesicles is described. The method takes advantage of the availability of two monoclonal antibodies, 23B11 and 2B12, which recognize a cytoplasmic and an extracytoplasmic domain, respectively, of the neutral endopeptidase-24.11. Specific binding of the antibodies to intact kidney brush border vesicles or to vesicles permeabilized by digitonin is detected by fluorescence using an anti-mouse immunoglobulin G-fluorescein isothiocyanate conjugate. The method allows discrimination between right side out, inside out, and unsealed vesicles. It requires limited amounts of material and can be completed the day of the brush border vesicle preparation. Application to rabbit kidney brush border membranes freshly prepared led to values of 89, 8, and 3% for right side out, inside out, and unsealed vesicles, respectively. Storage at low temperature was associated with a marked increase in the proportion of unsealed vesicles.

Decreased transport in renal basolateral membrane vesicles from hypertaurinuric mice

Basolateral membrane vesicles were prepared from mouse kidney by use of a Percoll density gradient method. The preparation was enriched ninefold in Na+-K+-ATPase with minimal contamination by other cellular membranes. The basolateral membranes were a mixture of sealed inside-out and right-side-out vesicles (30%) and leaky vesicles or sheets (70%). Taurine uptake into basolateral membrane vesicles was osmotically sensitive, sodium dependent, temperature sensitive, inhibited by beta-alanine, and saturable (apparent Km, 360 microM; Vmax, 25.4 pmol.mg protein-1.15 s-1), indicating transport by a carrier-mediated process. The function of this transporter was examined in an inbred mouse strain, C57BL/6J, which has selective hypertaurinuria, presumably a result of decreased basolateral membrane permeability to taurine [Rozen et al., Am. J. Physiol. 244 (Renal Fluid Electrolyte Physiol. 13): F150-F155, 1983]. The sodium-dependent component of taurine uptake was significantly lower in C57BL/6J vesicles relative to control (C3H/HeJ strain): 2.9 +/- 0.7 vs. 9.4 +/- 0.3 (SE) pmol.mg protein-1.15 s-1, respectively; P less than 0.001. The interstrain difference in uptake was specific for taurine and could not be ascribed to differences in vesicle purification, integrity, orientation, or size. These findings indicate that the renal basolateral membrane is the site of a transport defect, which explains decreased net taurine reabsorption in vivo in the C57BL/6J strain, and corroborate earlier observations in the renal cortical slice preparation.

Trypsin digestion for determining orientation of ATPase in Halobacterium saccharovorum membrane vesicles.

Membranes prepared by low pressure disruption of cells exhibited no ATPase activity in the absence of Triton X-100, although 43% of the total menadione reductase activity was detected. Trypsin digestion reduced menadione reductase activity by 45% whereas ATPase activity was not affected. Disruption of the membrane fraction at higher pressure solubilized about 45% of the ATPase activity. The soluble activity was still enhanced by Triton X-100, suggesting that the detergent, besides disrupting membrane vesicles, also activated the ATPase. The discrepancy in localization of menadione reductase and ATPase activities raised questions regarding the reliability of using a single marker enzyme as an indicator of vesicle orientation.

Orientation of synaptic plasma membrane vesicles containing calcium pump and sodium-calcium exchange activities

Sidedness of synaptic plasma membrane vesicles isolated from brain synaptosomes has been assessed by two distinct experimental approaches: first, analysis of (Na + + K +)-ATPase, Mg 2+-ATPase, and (Ca 2+ + Mg 2+)-ATPase activities before and after permeabilization of vesicles; second, analysis of Ca 2+ fluxes via the Na +/Ca 2+ exchanger, before and after modification of an imposed Na + gradient by penetrating or nonpenetrating Na + channel-modifying drugs. 0.05% saponin, which completely permeabilizes the vesicles, increases digitoxigenin-sensitive (Na + + K +)-ATPase, basal Mg 2+-ATPase, and (Ca 2+ + Mg 2+)-ATPase activities by 51.0, 47.4, and 83.6%, respectively. Saponin increases only the V max of the latter activity, the K m for Ca 2+ (0.13 μM; the same as that for Ca 2+-pumping) being unaltered by saponin. An increment of 20.5% in the V max of (Ca 2+ + Mg 2+)-ATPase activity with 10 μM A23187, reveals that the enzyme activity in nonpermeabilized vesicles is limited by the formation of a Ca 2+ gradient. Thus, the saponin-induced increment in (Ca 2+ + Mg 2+)-ATPase due only to exposure of occluded sites (as opposed to Ca 2+ gradient dissipation) is actually 52%, which is similar to values for both other ATPases, and suggests that 32–35% of plasma membranes exist in an inverted orientation. Vesicle orientation was independently assessed by the differential actions of tetrodotoxin (a membrane impermeant blocker) and veratridine (a membrane permeant agonist) on Na +-channel opening measured indirectly by dissipation of an imposed Na + gradient utilized to drive a large 45Ca 2+ accumulation via the Na +/Ca 2+ exchanger. Tetrodotoxin reverses 35–44% of veratridine-mediated Na + gradient-dissipation, the relative membrane-permeability of the two channel modifiers, suggesting that 56–65% of sealed vesicles are inverted. The concurrence of these two independent measurements of vesicle orientation reinforces their validity.

On the dielectrically observable consequences of the diffusional motions of lipids and proteins in membranes. 1. Theory and overview.

A system consisting of any array of cylindrical, polytopic membrane proteins (or protein complexes) possessed of a permanent dipole moment and immersed in a closed, spherical phospholipid bilayer sheet is considered. It is assumed that rotation of the protein (complex) in a plane normal to the membrane, if occurring, is restricted by viscous drag alone. Lateral diffusion is assumed either to be free and random or to be partially constrained by barriers of an unspecified nature. The dielectric relaxation times calculated for membrane protein rotation in a suspension of vesicles of the above type are much longer than those observed with globular proteins in aqueous solution, and fall in the mid-to-high audio frequency range. If the long range lateral diffusion of (charged) membrane protein complexes is essentially unrestricted, as in the "fluid mosaic" membrane model, dielectric relaxation times for lateral motions will lie, except in the case of the very smallest vesicles, in the sub-audio (ELF) range. If, in contrast, the lateral diffusion of membrane protein complexes is partially restricted by "barriers" or "long-range" interactions (of unspecified nature), significant dielectric dispersions may be expected in both audio- and radio-frequency ranges, the critical (characteristic) frequencies depending upon the average distance moved before a barrier is encountered. Similar analyses are given for rotational and translational motions of phospholipids. At very low frequencies, a dispersion due to vesicle orientation might in principle also be observed; the dielectrically observable extent of this rotation will depend, inter alia, upon the charge mobility and disposition of the membrane protein complexes, as well as, of course, on the viscosity of the aqueous phase. The role of electroosmotic interactions between double layer ions (and water dipoles) and proteins raised above the membrane surface is considered. In some cases, it seems likely that such interactions serve to raise the dielectric increment, relative to that which might otherwise have been expected, of dispersions due to protein motions in membranes. Depending upon the tortuosity of the ion-relaxation pathways, such a relaxation mechanism might lead to almost any characteristic frequency, and, even in the absence of protein/lipid motions, would cause dielectric spectra to be much broader than one might expect from a simple, macroscopic treatment.