Transport Parameters in a Porous Cellulose Acetate Membrane

The transport parameters of a cellulose acetate membrane prepared from a mixture of cellulose acetate, formamide, and acetone, 25:25:50 by weight, were studied. The membrane consists of a thin, porous layer, the skin, in series with a thick, highly porous layer, the coarse support. In the skin the diffusional permeability coefficient, ω, of a number of small amides and alcohols depends critically upon the partition coefficient, K_s, the size of the molecule, and the apparent hydrogen-bonding ability, N_s, of the solute. These observations are in general agreement with our earlier conclusions on the properties of nonporous membranes. On the other hand, the corrected reflection coefficient, σ', is not a very sensitive function of either N_s or K_s taken separately. The correlation between σ' and molecular diameter is reasonably good; however, it is much improved when both N_s and K_s are taken into consideration. Isotope interaction was also studied in the present preparation and was found to provide only a small (5–8%) contribution to the diffusional permeability coefficient of ethylene glycol. The contribution of solute-water friction was found to be less than 24% of the total solute friction.     

Effect of Geometrical and Chemical Constraints on Water Flux across Artificial Membranes

Studies have been made on the temperature dependence of both the hydraulic conductivity, L_p, and the THO diffusion coefficient, ω, for a series of cellulose acetate membranes (CA) of varying porosity. A similar study was also made of a much less polar cellulose triacetate membrane (CTA). The apparent activation energies, E_a, for diffusion across CA membranes vary with porosity, being 7.8 kcal/mole for the nonporous membrane and 5.5 kcal/mole for the most porous one. E_a for diffusion across the less polar CTA membrane is smaller than E_a for the CA membrane of equivalent porosity. Classical viscous flow, in which the hydraulic conductivity is inversely related to bulk water viscosity, has been demonstrated across membranes with very small equivalent pores. Water-membrane interactions, which depend upon both chemical and geometrical factors are of particular importance in diffusion. The implication of these findings for the interpretation of water permeability experiments across biological membranes is discussed.     

A Physical Interpretation of the Phenomenological Coefficients of Membrane Permeability

A "translation" of the phenomenological permeability coefficients into friction and distribution coefficients amenable to physical interpretation is presented. Expressions are obtained for the solute permeability coefficient ω and the reflection coefficient σ for both non-electrolytic and electrolytic permeants. An analysis of the coefficients is given for loose membranes as well as for dense natural membranes where transport may go through capillaries or by solution in the lipoid parts of the membrane. Water diffusion and filtration and the relation between these and capillary pore radius of the membrane are discussed. For the permeation of ions through the charged membranes equations are developed for the case of zero electrical current in the membrane. The correlation of σ with ω and L_p for electrolytes resembles that for non-electrolytes. In this case ω and σ depend markedly on ion concentration and on the charge density of the membrane. The reflection coefficient may assume negative values indicating anomalous osmosis. An analysis of the phenomena of anomalous osmosis was carried out for the model of Teorell and Meyer and Sievers and the results agree with the experimental data of Loeb and of Grim and Sollner. A set of equations and reference curves are presented for the evaluation of ω and σ in the transport of polyvalent ions through charged membranes.     

The Water and Nonelectrolyte Permeability Induced in Thin Lipid Membranes by the Polyene Antibiotics Nystatin and Amphotericin B

Nystatin and amphotericin B increase the permeability of thin (<100 A) lipid membranes to ions, water, and nonelectrolytes. Water and nonelectrolyte permeability increase linearly with membrane conductance (i.e., ion permeability). In the unmodified membrane, the osmotic permeability coefficient, P_f, is equal to the tagged water permeability coefficient, (P_d)_w; in the nystatin- or amphotericin B-treated membrane, P_f/(P_d)_w ≈ 3. The unmodified membrane is virtually impermeable to small hydrophilic solutes, such as urea, ethylene glycol, and glycerol; the nystatin- or amphotericin B-treated membrane displays a graded permeability to these solutes on the basis of size. This graded permeability is manifest both in the tracer permeabilities, P_d, and in the reflection coefficients, σ (Table I). The "cutoff" in permeability occurs with molecules about the size of glucose (Stokes-Einstein radius 4 A). We conclude that nystatin and amphotericin B create aqueous pores in thin lipid membranes; the effective radius of these pores is approximately 4 A. There is a marked similarity between the permeability of a nystatin- or amphotericin B-treated membrane to water and small hydrophilic solutes and the permeability of the human red cell membrane to these same molecules.     

An analysis of unstirred layers in series with "tight" and "porous" lipid bilayer membranes

The present experiments were designed to evaluate the effective thickness of the unstirred layers in series with native and porous (i.e., in the presence of amphotericin B) lipid bilayer membranes and, concomitantly, the respective contributions of membranes and unstirred layers to the observed resistances to the diffusion of water and nonelectrolytes between aqueous phases. The method depended on measuring the tracer permeability coefficients for the diffusion of water and nonelectrolytes (P_DDi, cm sec^-1) when the aqueous phase viscosity (η) was increased with solutes having a unity reflection coefficient, such as sucrose or dextran. The effective thickness of the unstirred layers (α^t, cm) and the true, or membrane, permeability coefficients for diffusion of water and nonelectrolytes (P_mmi, cm sec^-1) were computed from, respectively, the slope and intercept of the linear regression of 1/P_DDi on η. In both the native and porous membranes, α^t was approximately 110 x 10^-4 cm. The ratio of P_f, the osmotic water permeability coefficient (cm sec^-1) to P_mmH2O was 1.22 in the native membranes and 3.75 in the porous membranes. For the latter, the effective pore radius, computed from Poiseuille's law, was approximately 5.6 A. A comparison of P_mmi and P_DDi, indicated that the porous membranes accounted for 16, 25, and 66% of the total resistance to the diffusion of, respectively, H₂O, urea, and glycerol, while the remainder was referable to the unstirred layers.     

Simple Uniaxial and Uniform Biaxial Deformation of Nearly Isotropic Incompressible Tissues

A method is developed for analyzing in a unified manner both uniaxial and uniform biaxial strain data obtained from nearly isotropic tissues. The formulation is a direct application of nonlinear elasticity theory pertaining to large deformations. The general relation between Eulerian stress (σ) and extension ratio (λ) in soft isotropic elastic bodies undergoing uniform deformation takes the simple form: σ = ((λ³ - 1)/λ) f(λ), where f(λ) must be determined for each material. The extension ratio may be either greater than 1.0 (uniaxial elongation), or lie between zero and 1.0 (uniform biaxial extension). Simple analytical functions for f(λ) are most readily found for each tissue by plotting all data as (λ³ - 1)/λσ vs. λ. Of those tissues investigated in this way (dog pericardium and pleura, and cat mesentery and dura), all but pleura could be adequately described by a parabola: 1/f(λ) = 1/k{[(λ_M - λ)(λ - λ_m)]/[λ_M - λ_m}. In these instances, three material constants per tissue (K, λ_M, λ_m) served to predict approximately the stresses attained during both small and large deformations, in strips and sheets alike. It was further found that the uniaxial strain asymptote (λ_M) was linearly related to the biaxial strain asymptote (Λ_M), thus effectively reducing the number of constants by one.     

Frequency-resolved intramolecular excimer fluorescence study of lipid bilayer and nonbilayer phases

Frequency-domain fluorescence intensity decays of the intramolecular excimer forming (DipyPE) in a fully hydrated dioleoyl-phosphatidylethanolamine (DOPE) suspension have been measured at the monomer (395 nm) and excimer (475 nm) emissions and at different temperatures (0-30°C). A classical Birks (two-state) and a new three-state kinetics models were used to analyze the frequency-domain data. The three-state model allowed us to resolve various intramolecular dynamics parameters of DipyPE in the host DOPE suspension. Those parameters are the excimer association (K_dm) and dissociation (K_md) rate constants, effective concentration (C), and lateral diffusion rate (f) of the pyrene moieties in the DipyPE. In contrast, only CK_dm and K_md were determined based on the two-state model. We observed that K_dm declined while C increased abruptly at ∼12°C, the known thermotropic lamellar liquid crystalline-to-inverted hexagonal (L_α-H_II) phase transition temperature of DOPE. No abrupt changes in K_md and f were observed at all temperatures. We concluded that the rotation of the lipid acyl chains is hindered and the free volume available for the lipid terminal methyl ends is reduced as the lipid membrane enters the highly curved H_II phase from the planar L_α phase.     

The Arabidopsis COBRA Protein Facilitates Cellulose Crystallization at the Plasma Membrane

Mutations in the Arabidopsis COBRA gene lead to defects in cellulose synthesis but the function of COBRA is unknown. Here we present evidence that COBRA localizes to discrete particles in the plasma membrane and is sensitive to inhibitors of cellulose synthesis, suggesting that COBRA and the cellulose synthase complex reside in close proximity on the plasma membrane. Live-cell imaging of cellulose synthesis indicated that, once initiated, cellulose synthesis appeared to proceed normally in the cobra mutant. Using isothermal calorimetry, COBRA was found to bind individual β1–4-linked glucan chains with a K_D of 3.2 μm. Competition assays suggests that COBRA binds individual β1–4-linked glucan chains with higher affinity than crystalline cellulose. Solid-state nuclear magnetic resonance studies of the cell wall of the cobra mutant also indicated that, in addition to decreases in cellulose amount, the properties of the cellulose fibrils and other cell wall polymers differed from wild type by being less crystalline and having an increased number of reducing ends. We interpret the available evidence as suggesting that COBRA facilitates cellulose crystallization from the emerging β1–4-glucan chains by acting as a “polysaccharide chaperone.”     

Mathematical analysis of the dependence of cell potential on external potassium in corn roots

The K⁺ dependence of normal (ψ) and diffusion (ψ_D) potentials in corn roots [Zea mays L., hybrid (A619 × Oh43) × A632] was determined experimentally and analyzed with respect to the parameter ξ [defined as exp (F ψ/RT)]. In the presence of 10 micromolar carbonyl cyanide p-trifluoromethoxyphenylhydrazone (FCCP), ψ behaved as expected of a diffusion potential. Based upon the assumptions (a) that FCCP did not change any term of the Goldman-Hodgkin-Katz equation, and (b) that total potential was functionally the algebraic sum of ψ_D and ψ_P (the deviation from ψ_D due to an electrogenic system), ψ_P was found to be a complex function of external potassium and to have a minimum value of 0.69 millimolar K ion activity outside the cell. Analysis of ψ allowed us to develop an equation which predicts a complicated K⁺ dependence of ψ such as that found by Mertz and Higinbotham (Membrane Transport in Plants and Plant Organelles. Springer-Verlag 1974).     

Cross-Correlation Functions for a Neuronal Model

Cross-correlation functions, R_XY(t,τ), are obtained for a neuron model which is characterized by constant threshold θ, by resetting to resting level after an output, and by membrane potential U(t) which results from linear summation of excitatory postsynaptic potentials h(t). The results show that: (1) Near time lag τ = 0, R_XY(t,τ) = f_U [θ-h(τ), t + τ] {h′(τ) + E_U [u′(t + τ)]} for positive values of this quantity, where f_U(u,t) is the probability density function of U(t) and E_U [u′(t + τ)] is the mean value function of U′(t + τ). (2) Minima may appear in R_XY(t,τ) for a neuron subjected only to excitation. (3) For large τ, R_XY(t,τ) is given approximately by the convolution of the input autocorrelation function with the functional of point (1). (4) R_XY(t,τ) is a biased estimator of the shape of h(t), generally over-estimating both its time to peak and its rise time.     

Material Studies of Lipid Vesicles in the Lα and Lα-Gel Coexistence Regimes

In this work, we utilize micropipette aspiration and fluorescence imaging to examine the material properties of lipid vesicles made from mixtures of palmitoyloleoylphosphocholine (POPC) and dipalmitoylphosphatidylcholine (DPPC). At elevated temperatures/low DPPC fractions, these lipids are in a miscible liquid crystalline (L_α) state, whereas at lower temperatures/higher DPPC fractions they phase-separate into L_α and gel phases. We show that the elastic modulus, K, and critical tension, τ_c, of L_α vesicles are independent of DPPC fraction. However, as the sample temperature is increased from 15°C to 45°C, we measure decreases in both K and τ_c of 20% and 50%, respectively. The elasticity change is likely driven by a change in interfacial tension. We describe the reduction in critical tension using a simple model of thermally activated membrane pores. Vesicles with two-phase coexistence exhibit material properties that differ from L_α vesicles including critical tensions that are 20–40% lower. Fluorescence imaging of phase coexistent POPC/DPPC vesicles shows that the DPPC-rich domains exist in an extended network structure that exhibits characteristics of a solid. This gel network explains many of the unusual material properties of two-phase membranes.     

Membrane Permeability: Generalization of the Reflection Coefficient Method of Describing Volume and Solute Flows

The reflection coefficient method for describing volume and solute fluxes through membranes is generalized to take into account the nonideality of the solutions bathing the membrane and/or multicomponent systems. The reflection coefficient of the impermeable species in these systems is less than unity by a coefficient γ. The reflection coefficient obtained solely from the volume flow equation, σ^v, will always be less than the reflection coefficient obtained from the solute flow equation, σ^8v. These two coefficients are related by σ^8v = σ^v + γ.     

Corynebacterium glutamicum Is Equipped with Four Secondary Carriers for Compatible Solutes: Identification, Sequencing, and Characterization of the Proline/Ectoine Uptake System, ProP, and the Ectoine/Proline/Glycine Betaine Carrier, EctP

Gram-positive soil bacterium Corynebacterium glutamicum uses the compatible solutes glycine betaine, proline, and ectoine for protection against hyperosmotic shock. Osmoregulated glycine betaine carrier BetP and proline permease PutP have been previously characterized; we have identified and characterized two additional osmoregulated secondary transporters for compatible solutes in C. glutamicum, namely, the proline/ectoine carrier, ProP, and the ectoine/glycine betaine/proline carrier, EctP. A ΔbetP ΔputP ΔproP ΔectP mutant was unable to respond to hyperosmotic stress, indicating that no additional uptake system for these compatible solutes is present. Osmoregulated ProP consists of 504 residues and preferred proline (K_m, 48 μM) to ectoine (K_m, 132 μM). The proP gene could not be expressed from its own promoter in C. glutamicum; however, expression was observed in Escherichia coli. ProP belongs to the major facilitator superfamily, whereas EctP, together with the betaine carrier, BetP, is a member of a newly established subfamily of the sodium/solute symporter superfamily. The constitutively expressed ectP codes for a 615-residue transporter. EctP preferred ectoine (K_m, 63 μM) to betaine (K_m, 333 μM) and proline (K_m, 1,200 μM). Its activity was regulated by the external osmolality. The related betaine transporter, BetP, could be activated directly by altering the membrane state with local anesthetics, but this was not the case for EctP. Furthermore, the onset of osmotic activation was virtually instantaneous for BetP, whereas it took about 10 s for EctP.     

Kinetics of Butyrate, Acetate, and Hydrogen Metabolism in a Thermophilic, Anaerobic, Butyrate-Degrading Triculture

Kinetics of butyrate, acetate, and hydrogen metabolism were determined with butyrate-limited, chemostat-grown tricultures of a thermophilic butyrate-utilizing bacterium together with Methanobacterium thermoautotrophicum and the TAM organism, a thermophilic acetate-utilizing methanogenic rod. Kinetic parameters were determined from progress curves fitted to the integrated form of the Michaelis-Menten equation. The apparent half-saturation constants, K_m, for butyrate, acetate, and dissolved hydrogen were 76 μM, 0.4 mM, and 8.5 μM, respectively. Butyrate and hydrogen were metabolized to a concentration of less than 1 μM, whereas acetate uptake usually ceased at a concentration of 25 to 75 μM, indicating a threshold level for acetate uptake. No significant differences in K_m values for butyrate degradation were found between chemostat- and batch-grown tricultures, although the maximum growth rate was somewhat higher in the batch cultures in which the medium was supplemented with yeast extract. Acetate utilization was found to be the rate-limiting reaction for complete degradation of butyrate to methane and carbon dioxide in continuous culture. Increasing the dilution rate resulted in a gradual accumulation of acetate. The results explain the low concentrations of butyrate and hydrogen normally found during anaerobic digestion and the observation that acetate is the first volatile fatty acid to accumulate upon a decrease in retention time or increase in organic loading of a digestor.     

Electrostatic Changes in Lycopersicon esculentum Root Plasma Membrane Resulting from Salt Stress

Salinity-induced alterations in tomato (Lypersicon esculentum Mill. cv Heinz 1350) root plasma membrane properties were studied and characterized using a membrane vesicle system. Equivalent rates of MgATP-dependent H⁺-transport activity were measured by quinacrine fluorescence (ΔpH) in plasma membrane vesicles isolated from control or salt-stressed (75 millimolar salt) tomato roots. However, when bis-[3-phenyl-5-oxoisoxazol-4-yl] pentamethine was used to measure MgATP-dependent membrane potential (ΔΨ) formation, salt-stressed vesicles displayed a 50% greater initial quench rate and a 30% greater steady state quench than control vesicles. This differential probe response suggested a difference in surface properties between control and salt-stressed membranes. Fluorescence titration of vesicles with the surface potential probe, 8-anilino-1-napthalenesulphonic acid (ANS) provided dissociation constants (K_d) of 120 and 76 micromolar for dye binding to control and salt-stressed vesicles, respectively. Membrane surface potentials (Ψ_o) of−26.0 and −13.7 millivolts were calculated for control and salt-stressed membrane vesicles from the measured K_d values and the calculated intrinsic affinity constant, K_i. The concentration of cations and anions at the surface of control and salt-stressed membranes was estimated using Ψ_o values and the Boltzmann equation. The observed difference in membrane surface electrostatic properties was consistent with the measured differences in K⁺-stimulated kinetics of ATPase activity between control and salt-stressed vesicles and by the differential ability of Cl⁻ ions to stimulate H⁺-transport activity. Salinity-induced changes in plasma membrane electrostatic properties may influence ion transport across the plasma membrane.     

Water permeability of thin lipid membranes

The osmotic permeability coefficient, P_f, and the tagged water permeability coefficient, P_d, were determined for thin (<100 A) lipid membranes formed from ox brain lipids plus DL-α-tocopherol; their value of approximately 1 x 10^-3 cm/sec is within the range reported for plasma membranes. It was established that P_f = P_d. Other reports that P_f > P_d can be attributed to the presence of unstirred layers in the experimental determination of P_d. Thus, there is no evidence for the existence of aqueous pores in these thin phospholipid membranes. The adsorption onto the membrane of a protein that lowers its electrical resistance by a factor of 10³ was found not to affect its water permeability; however, glucose and sucrose were found to interact with the membrane to modify P_f. Possible mechanisms of water transport across these films are discussed, together with the implications of data obtained on these structures for plasma membranes.     

Quantifying Interactions of a Membrane Protein Embedded in a Lipid Nanodisc using Fluorescence Correlation Spectroscopy

Using fluorescence correlation spectroscopy, we measured a dissociation constant of 20 nM between EGFP-labeled LcrV from Yersinia pestis and its cognate membrane-bound protein YopB inserted into a lipid nanodisc. The combination of fluorescence correlation spectroscopy and nanodisc technologies provides a powerful approach to accurately measure binding constants of interactions between membrane bound and soluble proteins in solution. Straightforward sample preparation, acquisition, and analysis procedures make this combined technology attractive for accurately measuring binding kinetics for this important class of protein-protein interactions.Interactions involving membrane proteins are integral to a multitude of cellular processes, including signal transduction, energy production and conversion, cell adhesion, and foreign molecule identification. More than half of all pharmaceutical drugs target membrane proteins, further illustrating their importance in human health (1). Due to this, there is a continuing high demand for methods that can screen, validate, and quantify interactions involving membrane proteins. Unfortunately, the quantitative techniques available to characterize protein-protein interactions are most often directed toward soluble proteins, and are often difficult to apply to membrane proteins (2). Recently, advances in lipid nanodisc technologies, often referred to as reconstituted high-density lipoproteins, have enabled biophysical and biochemical studies of solubilized membrane proteins. The nativelike lipid environment of nanodiscs maintains protein functionality, opening a realm of possibilities in analyzing membrane protein function and dynamics in solution (3).Nanodiscs are discoidal cell membrane mimetics that are 8–20 nm in diameter, consisting of a lipid bilayer stabilized by two peripheral apolipoprotein A-I proteins (4). These particles provide an excellent alternative to traditional lipid-based platforms (e.g., liposomes) for membrane protein solubilization and interrogation. The diameter of nanodisc can be engineered to accommodate different-sized membrane proteins by varying lipid composition. As such, nanodiscs represent an important platform for expression, isolation, and study of functional membrane proteins and the multiprotein complexes they form. Several groups have successfully reconstituted a variety of membrane proteins, including bacteriorhodopsin (5), G-protein coupled receptors (6), and cytochrome P450 (7) to name a few. To produce solubilized, discrete membrane proteins, we utilized a cell-free expression approach to embed membrane proteins directly into nanodiscs formed in situ. This approach allows for enhanced purification and rapid labeling of proteins of interest where traditional approaches are unsuccessful (8). Fluorescence correlation spectroscopy (FCS) analysis coupled with nanodisc technology has been successfully used to monitor small ligand binding interactions with membrane proteins (6,8) and to measure lipid-protein interactions at the single molecule level (9). Here, we show that FCS can be used to measure interactions between soluble proteins and cognate membrane proteins inserted into nanodiscs produced using cell-free expression methodologies.FCS uses correlation analysis of fluorescence arising from randomly diffusing molecules to measure diffusion constants, and hence hydrodynamic radii, of species in solution. Diffusion times measured by FCS are inversely proportional to diffusion constants. A shift to slower diffusion time indicates an increase in the hydrodynamic radius due to binding. Due to this size sensitivity, FCS has been proposed repeatedly as a method to quantify molecular interactions in solution (10). However, an important difficulty in FCS arises when characterizing interactions between two proteins of similar size. The diffusion time is inversely proportional to the cube root of the molecular mass τ_D ∼ M^−1/3. Doubling the mass results in only a factor-of-1.3 increase in diffusion time, but a factor of 1.6 is required to resolve two species (11). As we demonstrate, this difficulty is overcome by using FCS to measure the interactions between labeled soluble proteins and membrane proteins supported within a nanodisc. The much larger size of the membrane protein-nanodisc complex (Fig. 1 A) relative to most soluble proteins provides the necessary differential in diffusion times to easily resolve bound and free species by FCS.Open in a separate windowFigure 1(A) Model of YopB (blue) inserted into a 10-nm nanodisc with cognate protein LcrV (red) labeled with EGFP (green). The molecular masses used in this model are: LcrV (35 kDa), EGFP (27 kDa), YopB (42 kDa, monomer), and nanodisc-YopB complex (258 kDa). The small LcrV binds to the much larger YopB-nanodisc complex, resulting in a significant shift in the autocorrelation curves to longer diffusion times. (B) Hypothetical autocorrelation curves expected for a series of titration experiments measured using FCS. Increased binding is measured as an increase in diffusion time. For intermediate binding, diffusion components are detectable as illustrated (red, green, and blue curves). To see this figure in color, go online.Binding kinetics are readily measured using FCS by titrating increasing amounts of unlabeled cognate protein, resulting in a series of autocorrelation curves similar to those modeled in a hypothetical example in Fig. 1 B. For 0% binding (black curve), only the labeled soluble protein is present, producing a single component correlation curve with a diffusion time of 0.1 ms. On the autocorrelation curve with a single component, the diffusion time is the time at which the autocorrelation amplitude decreases by half. For 100% binding (cyan curve), the amount of nanodisc with inserted membrane protein is well above the dissociation constant so that all available soluble protein is bound.Again, a single component correlation curve is found, but now with a longer diffusion time (10 ms in this hypothetical example). Intermediate cases have two components, corresponding to free and bound protein. The relative amplitudes of the components obtained by fitting to two component models in these cases can be used to obtain a binding curve. For binding interactions, the amount of ligand in the free and bound state can be separated by their diffusion time and quantified as a function of concentration. The fraction of bound protein is calculated by fitting the correlation to two components. The first component f₀(τ) is the correlation of the free protein. The second component g₀(τ) is the correlation when the protein is bound. The total correlation function ish(τ) = αf₀(τ) + βg₀(τ), (1)where f₀(τ) = 1/(1 + τ/τ_f) and g₀(τ) = 1/(1 + τ/τ_b). The values α and β are, respectively, the amplitudes of the correlation function for free and bound protein, with the corresponding diffusion times τ_f and τ_b. The ratio F = β/(α + β) gives the fraction bound.We investigated by FCS the interaction of two Yersinia pestis proteins: soluble EGFP-labeled LcrV and membrane-bound YopB (Fig. 1 A). YopB is an effector protein involved in host cell invasion and disarming the cell’s defense. Although the structure of YopB is largely unknown, it is thought to exist as a dimer (12). Delivery of YopB to the host cell is regulated by the Type III secretion system (T3SS) (i.e., injectisome). The needle tip of the injectisome contains the LcrV protein. When Y. pestis comes in contact with a cell membrane, the injectisome forms a pore through the membrane to facilitate the diffusion of effector proteins into the host cell. Multiple lines of evidence suggest that pores are formed only through the direct interaction of YopB with LcrV (13).The FCS diffusion times of free LcrV (τ_f; Fig. 2 A, black curve) and fully bound LcrV (τ_b; [YopB] = 10 μM) were found to be 140 and 630 μs, respectively. Because no measurable change in diffusion time was detected above [YopB] = 1 μM (Fig. 2, green curve), LcrV was assumed to be completely bound at [YopB] = 10 μM. The diffusion times of free and bound LcrV were determined by fitting the autocorrelation curves to a one-component model (χ² ∼ 1 for each diffusion time). These diffusion times correspond to average hydrodynamic radii of 2.5 nm for free LcrV and 11.1 nm for the LcrV + YopB-nanodisc complex, as calculated by the Einstein-Stokes equation. No significant change in diffusion time was detected when LcrV was incubated with 2 μM of nanodiscs lacking the YopB protein (Fig. 2 A, gray curve), suggesting that LcrV alone is unable to interact directly with a lipid bilayer.Open in a separate windowFigure 2(A) FCS autocorrelation curves of 1 nM EGFP-labeled LcrV protein in the absence and presence of YopB at increasing concentrations. The diffusion time of freely diffusing LcrV is τ_D,free = 140 s (black curve). At [YopB] = 1 μM where LcrV is completely bound, the FCS curve is dominated by a single component (green curve). The autocorrelation curves at intermediate concentrations (in particular [YopB] = 25 and 50 nM, blue and cyan curves) contain contributions from two diffusing components. A control experiment was performed with 2 μM of nanodisc lacking the YopB protein (gray curve). No significant change in diffusion time was detected. (B) The fraction of bound LcrV as a function of YopB concentration (log scale). This fraction is calculated by fitting the FCS curves shown in Fig. 2A with Eq. 1. The dissociation constant extracted is K_d = 20.45 ± 2.0 nM. Error bars represent an average over six FCS measurements. To see this figure in color, go online.To extract the dissociation constant (K_D), a titration was performed over a range of YopB concentrations (10 pM to 1 μM), obtained by varying the concentration of YopB-nanodisc complexed. Having determined the values of the diffusion times for free (τ_f) and bound (τ_b) protein, we fitted the autocorrelation curves to a two-species correlation function with Eq. 1. The brightness per LcrV molecule was between 2170 and 2280 photons/(s × molecule) for the entire titration, validating the use of Eq. 1. The only varying parameters were the correlation amplitudes α (free protein) and β (bound protein). Intermediate binding was observed between 10 and 100 nM, because two correlation components are resolved. At [YopB] = 50 nM (cyan curve), the ratio β/α was 1.5, indicating that more than half of LcrV was bound. For the two-component model in these intermediate cases, the χ² value was between 1 and 1.3, indicating a good fit. In contrast, fitting the data to a one-component model resulted in a poor fit (χ² > 7), justifying the use of the two-species model. Binding curves were fitted to the equation y = x/(K_D + x), where y is the fraction of bound LcrV, x is the YopB concentration, and K_d the dissociation constant.Fitting this model with a least-squares algorithm (Fig. 2 B), we extracted K_d = 20.5 ± 2.0 nM. To quantify the statistical error, three measurements were recorded for 2 min, and the entire titration was repeated. Importantly, these data provide not only a quantitative binding affinity for the YopB-LcrV interaction, but support the hypothesis that LcrV requires direct interaction with YopB, not just a lipid bilayer, to promote pore formation.In conclusion, the coupling of FCS with nanodisc technology provides a facile yet powerful tool to quantitatively measure interactions involving membrane proteins in solution. FCS can simultaneously detect the presence of both free and bound species without the need for surface immobilization of the cognate proteins. Cell-free coexpression of both membrane protein and apolipoprotein components in the presence of lipids is a facile methodology for producing functional, soluble, nanodisc-supported membrane proteins. Labeling the soluble cognate proteins with EGFP provides a simple path to obtaining fluorescent, single-labeled proteins compatible with FCS. The combination of FCS with nanodisc technology presented here provides not only new key data for modeling the invasion process of Y. pestis, but can also be generalized to study interactions between most other soluble and membrane proteins. Such methods have been lacking, yet are critical for understanding interaction networks, e.g., signal transduction cascades.See the Supporting Material for additional detail on the methodology used.     

A study of lipid bilayer membrane stability using precise measurements of specific capacitance

A method is described for measuring the specific capacitance (C_m) of lipid bilayer membranes with an estimated experimental error of only 1%. The gross capacitance was measured with an AC Wheatstone bridge and a photographic technique was used to determine the area of thin membrane. The results of measurements on oxidized cholesterol-decane membranes formed in 1 × 10^-2 M KCl show that C_m depends upon temperature, voltage, time, and the age of the bulk membrane solutions. For a freshly thinned membrane (from 5 week old solution), C_m increases exponentially from an initial value of 0.432 ±0.021 (SD) μF/cm² with a time constant of ~15 min. A 100 mv potential applied across the membrane for 10-20 min prior to making measurements eliminated this time dependence and produced final-state membranes. C_m of final-state membranes depends upon applied voltage (V_a) and obeys the equation C_m = C₀ + βV_a² where V_a V_DC + V^rms_AC. C₀ and β depend upon temperature; C₀ decreases linearly with temperature while β increases linearly. At 20°C, C₀ = 0.559 ±0.01 (SD) μF/cm² and β = 0.0123 ±0.0036 (SD) (μF/cm²)/(mv²) and at 34°C, C₀ = 0.472 ±0.01 and β = 0.0382 ±0.0039. These variations in C_m are interpreted as resulting from thickness changes. The possibility that they result from diffuse layer and/or membrane dielectric phenomena is discussed and found to be unlikely. The results are discussed in terms of membrane stability by constructing hypothetical potential energy vs. thickness curves.     

The influence of external potassium on the inactivation of sodium currents in the giant axon of the squid, Loligo pealei

Isolated giant axons were voltage-clamped in seawater solutions having constant sodium concentrations of 230 mM and variable potassium concentrations of from zero to 210 mM. The inactivation of the initial transient membrane current normally carried by Na⁺ was studied by measuring the Hodgkin-Huxley h parameter as a function of time. It was found that h reaches a steady-state value within 30 msec in all solutions. The values of h _∞, τ_h, α_h,and β_h as functions of membrane potential were determined for various [K _o]. The steady-state values of the h parameter were found to be inversely related, while the time constant, τ_h, was directly related to external K⁺ concentration. While the absolute magnitude as well as the slopes of the h _∞ vs. membrane potential curves were altered by varying external K⁺, only the magnitude and not the shape of the corresponding τ_h curves was altered. Values of the two rate constants, α_h and β_h, were calculated from h_∞ and τ_h values. α_h is inversely related to [K_o] while β_h is directly related to [K_o] for hyperpolarizing membrane potentials and is independent of [K_o] for depolarizing membrane potentials. Hodgkin-Huxley equations relating α_h and β_h to E_m were rewritten so as to account for the observed effects of [K_o]. It is concluded that external potassium ions have an inactivating effect on the initial transient membrane conductance which cannot be explained solely on the basis of potassium membrane depolarization.     

Biochemistry of Suberization: Incorporation of [1-C]Oleic Acid and [1-C]Acetate into the Aliphatic Components of Suberin in Potato Tuber Disks (Solanum tuberosum)

Biosynthesis of the aliphatic components of suberin was studied in suberizing potato (Solanum tuberosum) slices with [1-¹⁴C]oleic acid and [1-¹⁴C]acetate as precursors. In 4-day aged tissue, [1-¹⁴C]oleic acid was incorporated into an insoluble residue, which, upon hydrogenolysis (LiA1H₄), released the label into chloroform-soluble products. Radio thin layer and gas chromatographic analyses of these products showed that ¹⁴C was contained exclusively in octadecenol and octadecene-1, 18-diol. OsO₄ treatment and periodate cleavage of the resulting tetraol showed that the labeled diol was octadec-9-ene-1, 18-diol, the product expected from the two major components of suberin, namely 18-hydroxyoleic acid and the corresponding dicarboxylic acid. Aged potato slices also incorporated [1-¹⁴C]acetate into an insoluble material. Hydrogenolysis followed by radio chromatographic analyses of the products showed that ¹⁴C was contained in alkanols and alkane-α,ω-diols. In the former fraction, a substantial proportion of the label was contained in aliphatic chains longer than C₂₀, which are known to be common constituents of suberin. In the labeled diol fraction, the major component was octadec-9-ene-1,18-diol, with smaller quantities of saturated C₁₆, C₁₈, C₂₀, C₂₂, and C₂₄-α,ω-diols. Soluble lipids derived from [1-¹⁴C]acetate in the aged tissue also contained labeled very long acids from C₂₀ to C₂₈, as well as C₂₂ and C₂₄ alcohols, but no labeled ω-hydroxy acids or dicarboxylic acids were detected. Label was also found in n-alkanes isolated from the soluble lipids, and the distribution of label among them was consistent with the composition of n-alkanes found in the wound periderm of this tissue; C₂₁ and C₂₃ were the major components with lesser amounts of C₁₉ and C₂₅. The amount of ¹⁴C incorporated into these bifunctional monomers in 0-, 2-, 4-, 6-, and 8-day aged tissue were 0, 1.5, 2.5, 0.8, and 0.3% of the applied [1-¹⁴C]oleic acid, respectively. Incorporation of [1-¹⁴C]acetate into the insoluble residue was low up to the 3rd day of aging, rapid during the next 4 days of aging, and subsequently the rate decreased. These changes in the rates of incorporation of exogenous oleic acid and acetate reflected the development of diffusion resistance of the tissue surface to water vapor. As the tissue aged, increasing amounts of the [1-¹⁴C]acetate were incorporated into longer aliphatic chains of the residue and the soluble lipids, but no changes in the distribution of radioactivity among the α-ω-diols were obvious. The above results demonstrated that aging potato slices constitute a convenient system with which to study the biochemistry of suberization.