Piece Of Membrane Research Articles

Matrix metalloproteinase-9 and tensile strength of fetal membranes in uncomplicated labor

Objective: To analyze the relation between tensile strength and levels of matrix metalloproteinase-9, tissue inhibitor of metalloproteinase-1, and tissue inhibitor of metalloproteinase-2 at a number of sites in human fetal membranes. Methods: Tensile strengths of fetal membranes from five women who delivered vaginally at term were measured by the method of modified force application. A piece of membrane at each measured site was then dissected, and the levels of matrix metalloproteinase-9, tissue inhibitor of metalloproteinase-1, and tissue inhibitor of metalloproteinase-2 were measured by sandwich enzyme immunoassay. The relationship between tensile strength and enzyme levels was evaluated by Scheffé F test at a total of 81 sites on the five membranes. Results: The mean tensile strength of the membranes was 45.3 ± 19.8 (mean ± standard deviation) mmHg/0.3 mm 2 ( n = 81). When the measured sites were divided according to tensile strength into four groups (<25, 25–49, 50–74, and ≥75 mmHg/0.3 mm 2), the level of matrix metalloproteinase-9 (0.72 ± 0.82 nmol/g protein, n = 12) in the less than 25 mmHg/0.3 mm 2 group was significantly higher than the other groups (0.35 ± 0.22, 0.28 ± 0.15, and 0.15 ± 0.08 nmol/g protein; n = 39, 23, and 7, respectively). The significance level was still higher when the molar ratio of matrix metalloproteinase-9 to tissue inhibitor of metalloproteinase-1 was used for comparison. Conclusion: An increased molar ratio of matrix metalloproteinase-9 to tissue inhibitor of metalloproteinase-1 might be related to decreased tensile strength of human fetal membranes in uncomplicated labor.

Direct determination of selenoproteins in polyvinylidene difluoride membranes by electrothermal atomic absorption spectrometry.

A method for the direct determination of selenoproteins in plastic membranes after protein separation by gel electrophoresis was developed. Quantification was based on the determination of the selenium content of the proteins by electrothermal atomic absorption spectrometry (ET-AAS) after manual introduction of membrane pieces into the graphite furnace. The proteins were separated by sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) and subsequently transferred to a polyvinylidene difluoride (PVDF) membrane by semi-dry electroblotting. After staining the membrane, the protein bands were excised and chemical modifier was added on top of the excised membrane prior to atomic absorption measurement. Acceptable linearity was achieved in the range 2-10 ng Se, corresponding to selenium concentrations close to 1 mg/L, when aqueous solutions of selenomethionine standard as well as selenoprotein standard were applied to the membrane. A characteristic mass of 54 +/- 4 pg/0.0044 s was obtained for the selenoprotein standard. Protein transfer from polyacrylamide gel to the membrane was quantitative and no interferences were introduced. The method was used for identification of selenoprotein P after enrichment of the protein from human plasma.

Disintegration of Mg2+ -induced hexagonal assembly of an R-form lipopolysaccharide from Klebsiella pneumoniae by treatment with CaCl2.

R-form lipopolysaccharide (LPS) from Klebsiella pneumoniae strain LEN-111 (O3-: K1-), which was precipitated by the addition of 2 volumes of ethanol containing 10 mM MgCl2 for the purification process, ultrastructurally exhibited membrane pieces consisting of an ordered hexagonal lattice structure with a lattice constant of 14 to 15 nm. When the R-form LPS was suspended in 50 mM tris (hydroxymethyl) aminomethane buffer (at pH 8.5) containing 1 mM or higher concentrations of CaCl2 and kept at 4 C for 10 hr, the ordered hexagonal lattice structure of the R-form LPS was disintegrated and changed to an irregular rough, mesh-like structure. By treatment with CaCl2, the content of Mg in the LPS was markedly decreased, and conversely, the content of Ca was increased to a level depending upon the concentration of CaCl2. Results indicate that the addition of CaCl2 to suspensions of the Mg-bound R-form LPS result in a tighter binding of Ca2+ to the R-form LPS and the release of Mg2+ from the R-form LPS, and as a consequence, destroys the Mg2+ -induced ordered hexagonal lattice structure of the R-form LPS.

A simple, inexpensive method for teaching how membrane potentials are generated.

We have developed a simple laboratory exercise that uses an inexpensive dialysis membrane (molecular weight cutoff = 100) to illustrate the generation of membrane potentials (Vm) across plasma membranes of animal cells. A piece of membrane approximately 2.0 cm2 is mounted in an Ussing-like chamber. One chamber half is designated cytosol and the other half external. Chamber sidedness helps students relate their findings to those of real cells. As in real cells, outward directed K+ concentration gradients [high cytosolic K+ concentration ([K+]c) and low extracellular K+ concentration] generate cytosol electrically negative Vm with a slope of approximately -45 mV/decade change in [K+]c. The polarity of Vm reflects the outward flow of potassium ions because flow of the larger counterion, H2PO4-, is restricted to the pores in the membrane. A slope less than Nernstian (<59 mV/decade) suggests that the membrane is slightly permeable to H2PO4-. Importantly, this facilitates teaching the use of the Nernst equation to quantify the relationship between ion concentration ratios across membranes and magnitude of Vm. For example, students use their data and calculate a permeability ratio PK/PH2PO4 that corresponds to a slope of approximately 24% less than Nernstian. This calculation shows that Nernstian slopes are achieved only when permeability to the counterion is zero. Finally, students use the concept of membrane capacitance to calculate the number of ions that cross the membrane. They learn where these ions are located and why the bulk solutions conform to the principle of electroneutrality.

A Single-Sample Method for Determination of Carbohydrate and Protein Contents Glycoprotein Bands Separated by Sodium Dodecyl Sulfate– Polyacrylamide Gel Electrophoresis

A method is described for determination of carbohydrate and protein contents of glycoproteins separated by sodium dodecyl sulfate–polyacrylamide gel electrophoresis and then electroblotted onto polyvinylidene difluoride (PVDF) membranes. Blots were stained, and appropriate pieces of PVDF membranes were excised, destained, and subjected to sequential hydrolysis with 0.2 M trifluoroacetic acid (TFA) for 1 h at 80°C, then with 2 M TFA for 4 h at 100°C, and finally with 6 M HCl at 100°C for 24 h to release sialic acids, neutral sugars with hexosamines, and amino acids, respectively. In some instances preliminary methanolysis was used. Carbohydrates including sialic acids were quantitated by high pH anion exchange chromatography with pulsed amperometric detection. Protein content of the bands was determined as amino acids by the fluorescamine or ninhydrin method. In the calculation of results proper adjustments were made for small amounts of fucose released by hydrolysis with 0.2 M TFA at 80°C, and for partial degradation of protein during hydrolysis with 2 M TFA at 100°C. Recoveries of amino acids from hydrolysates of glycoproteins that had been electroblotted onto PVDF membranes equaled those of carbohydrates. This was possible because of preliminary hydrolysis of glycoproteins with TFA, as well as washing of wet, instead of dried, PVDF membranes after hydrolysis with 6 M HCl. The two modifications increased yields of amino acids by about 30%. The method was successfully applied to the determination of molar and weight percentage composition of human transferrin, band 3 protein, glycophorin A, and α1-acid glycoprotein. In each case the results obtained for directly hydrolyzed and electrophoresed/electroblotted glycoproteins were practically identical. We also determined the glucosamine content of band 4.1 protein of erythrocytes.

Absorption of visible spectrum radiation by the wing membranes of living pteropodid bats

The wing membranes of bats present a large surface area upon which radiation might be taken up, increasing heat load to the animals. This, combined with the high amount of heat produced during flight, has been advanced as one hypothesis explaining the fact that bats are almost exclusively nocturnal. The proportion of short-wave (visible) radiation absorbed by bat wing membrane has previously been measured at between 0.7 and 0.92. These measurements were made on pieces of membrane taken from the wings of dead, mainly insectivorous bats from temperate regions. Here we examined the amount of light transmitted through and reflected off the wing membranes of four species of live pteropodid bats. There were significant differences in wing reflection between species. At 0.68, the average proportion of light absorbed into the wing membranes was lower than previously reported. This might be because we worked with live animals or because ours were tropical bats which are routinely exposed to tropical sun when roosting. Variation in wing tension strongly affected light absorption. It was predicted that the relaxed state of wing membrane through part of the wing beat cycle would increase the absorption of light into the wings of day-flying bats. The proportion of light absorbed into wings was shown to be an important factor in the heat balance of hypothetical bats flying during the day. Our results raise the predicted temperature at which bats flying during the day might experience hyperthermia by approximately 2 degrees C and suggest that variation in albedo of wings between species may make some species more susceptible to overheating than others.

Eggshell Membrane Structure and Penetration by Salmonella Typhimurium

Eggshell membrane was removed from 10 broiler hatching eggs at approximately monthly intervals through the productive life of a commercial flock. A piece of membrane (2 by 2 cm) was used to cover an opening in an apparatus designed to test penetration by Salmonella Typhimurium. The membrane was placed between two chambers as the only means of liquid transfer. The chamber above the membrane was filled with a suspension of Salmonella Typhimurium cells. Sampling of the bottom chamber provided cultural evidence of the penetration by a marker strain of Salmonella Typhimurium. Samples were drawn at 15 min and at 1, 3, 5, 7, 12, 24, and 48 h. Following the cultural penetration experiment, the same pieces of membrane were removed and stained for microscopic examination. Membrane structure was examined with the use of a confocal laser scanning microscope. Each image consisted of a composite of eight 1-μm optical slices showing the fibers making up the outer surface of the membrane. These images were transferred to an image analysis software package that allowed the measurement of the interfiber area. No clear correlation could be made between the average size of all interfiber areas or the total interfiber area measured in the outer 8μm of the outer membrane and the ability of Salmonella Typhimurium to penetrate the same piece of eggshell membrane.

Membrane supports as the stationary phase in high-performance immunoaffinity chromatography.

The membrane with a composite of cellulose grafted with acrylic polymers formed by polymerizing a glycidyl methacrylate in the presence of dispersed cellulose fiber was prepared as the stationary phase; the column (40 x 4 mm i.d.) which was compatible with the HPLC instrument was packed with pieces of the cut membrane. Protein A and human IgG were immobilized on the membrane stationary phase. The column based on the membrane support provided us good reproducibility, high efficiency, and low back pressure. High-performance immunoaffinity chromatographic analysis of human IgG in serum and polyclonal antibody to human IgG raised in goat was performed within 2.5 min. The fast-speed immunoaffinity analysis was developed by increasing the flow rate of the mobile phase and decreasing the duration time for the switch of the mobile phase; an operation for immunoaffinity analysis of human IgG could be finished within 30 s.

An optical method for recording the activity of single transporters in membrane patches.

We have previously introduced an optical technique for recording the transport of fluorescent substrates by single membrane transporters. Referred to as optical single-transporter recording (OSTR), the method was restricted to cases in which membrane transporters occurred at extremely small densities, namely at one or a few transporters per cell. Here we describe the extension of OSCR from whole cells harbouring a small number of transporters to small membrane patches containing transporters at normal densities. A technique was developed for firmly attaching cells to isoporous filters, i.e. very thin transparent sheets containing homogeneous populations of cylindrical pores. The flux of fluorescent transport substrates across the tiny membrane pieces spanning the filter pores was measured by scanning microphotolysis, a combination of fluorescence microphotolysis and confocal laser scanning microscopy. The technique was tested by attaching erythrocytes to filters containing pores of 1.2, 2.0 or 3.0 microns diameter. After treating filter-attached erythrocyte membranes with streptolysin O, the transport of the fluorescent protein B-phycoerythrin through single streptolysin O pores was observed. From the flux data the functional radius of the streptolysin O pore was derived to be 12.5 +/- 0.9 nm, in very good agreement with previous electron microscopic estimates. The new technique features a number of unique properties: (i) the size of the membrane patch can be chosen within wide limits according to transporter density, (ii) transport can be recorded on many membrane patches in parallel, (iii) both influx and efflux may be analysed employing either photobleaching of fluorescent or photorelease of caged nonfluorescent substrates, (iv) two or more transport substrates may be monitored simultaneously. The new technique can be used, for instance, for analysing the activity of protein/particle pumps, a membrane transport domain not previously accessible to a single-transporter analysis.

Stimulation of Open Complex Formation by Nicks and Apurinic Sites Suggests a Role for Nucleation of DNA Melting in Escherichia coli Promoter Function

We report the effects of depurination and prenicking at various positions of the phage lambda prmup-1Delta265 promoter DNA on the rate of open complex formation. We have found that depurination and prenicking at positions around the -10 region strongly stimulated the rate of open complex formation. Since nicking and depurination are known to destabilize DNA helical structure, our observations indicate that the instability of the -10 region is important for open complex formation. We further infer that (i) the nucleation of DNA melting, which occurs during the isomerization from the closed complex into the open complex, contributes to the rate of open complex formation; (ii) the nucleation of melting occurs around the -10 region; and (iii) the propagation of DNA melting from the nucleation region is not rate-limiting. In addition, we have found that depurination at several positions inhibited open complex formation. We used dimethyl sulfate modification protection studies to show that most of the guanine bases that are among these positions are in contact with RNA polymerase in the open complex.

Amperometric biosensor for uric acid based on uricase-immobilized silk fibroin membrane

An amperometric urate sensor based on a uricase-immobilized silk fibroin membrane and an oxygen electrode in flow injection analysis are described in the present paper. The biosensor shows that recoveries of uric acid in human serum and urine are in the range of 94.2–102.6% and 92.5–97.9%, respectively. The relative standard deviations (RSDs) for repeatedly monitoring standard urate solution, human serum and urine are 2.37, 3.72 and 2.95%, respectively, based on 100 measurements. The urate sensor based on the uricase-immobilized membrane is capable of detecting 60–70 human serum samples per hour. Moreover, a piece of uricase-immobilized fibroin membrane used at the sensor could not only be stored for over 2 years, but also repeatedly monitored more than 1000 times for biosamples such as human serum or urine.

Ultrastructure of Extracellular Matrix Deposits Associated with Conidia of the Powdery Mildew Fungus Blumeria graminis F. Sp. Hordei

Small pieces of sterile dialysis membrane were touched to sporulating colonies of the powdery mildew fungus Blumeria graminis f. sp. hordei and either cryofixed within 5 s or incubated for 30 min or 2 h before cryofixation. Following freeze substitution and processing for study with transmission electron microscopy, thin sections of conidia on dialysis membrane were examined ultrastructurally. Each conidium was surrounded by a copious deposit of an extracellular matrix (ECM) material. ECM deposits developed as soon as conidia contacted membranes and persisted for the duration of the 2-h time period of this study. While only a thin layer of ECM was present between the central portion of the underside of each conidium and the underlying membrane, ECM filled the space between the curved conidium surface and the membrane and extended halfway or more up the surface of the conidium. The ECM spread out away from the conidium onto the membrane for a distance of up to 30 μm. Strands of ECM also extended up over some conidia. Most conidia were not in direct contact with their respective ECM deposits, and some were displaced totally from their deposits, which adhered closely to membranes. The Thiery stain for polysaccharides gave little if any staining of the ECM. Gold labeling for mannose residues in the matrix using Conconavilin A was negative.

Recovery of sulfuric acid from waste aluminum surface processing solution by diffusion dialysis

Diffusion dialysis with anionic ion exchange membranes was employed to recover sulfuric acid from the waste acid solution of aluminum surface processing plant. Experiments were conducted to examine the dialyzer performances under various operating conditions, including feed flow rates, sulfuric acid concentration in the feed solution, temperature and number of pieces of ion exchange membrane. Diffusion dialysis was found very efficient for this purpose. Based on the test results, optimum operating conditions of these variables were identified. Preliminary economic evaluation of the process indicated that diffusion dialysis is highly viable for sulfuric acid recovery due to its short payback period.

Monoclonal antibodies against human prostasomes.

The prostasomes are secreted into the gland ducts of the human prostate. At ejaculation, these native prostasomes are expelled with the secretions of the prostate and appear in the seminal plasma as seminal prostasomes, where they facilitate sperm function in various ways. We have designed methods for producing monoclonal anti-prostasome antibodies to be used for immunohistochemistry and sequencing analyses of the prostasomes. The immunogen applied was purified seminal prostasomes placed on small pieces of nitrocellulose membranes (prostasome blots) and deposited into the spleen of mice for immunization. For screening, both seminal and native prostasomes were used. We obtained antibodies which detected native prostasomes both in prostatic secretions and in paraffin sections of the prostate. The immunostaining demonstrated that all prostate epithelial cells contained prostasomes. They were located in the apical parts of the secretory cells and in the gland ducts, while the nuclei and the corpora amylacea were unstained. Using the methods described, monoclonal antibodies against native prostasomes were produced. In addition to their usefulness in structural and functional studies of prostasomes, specific monoclonal antibodies can be used to characterize prostasomes by sequencing analyses.

Oral microbiota and implant type membranes.

Candida albicans (Ca), Staphylococcus aureus (Sa), Streptococcus sanguis (Ss), Actinomyces naeslundii (An), Actinomyces odontolyticus (Ao), Porphyromona spp (P spp), Candida glabrata (Cg), Candida krusei (Ck), and Rhodotorula spp (R spp) were tested with equal pieces of biodegradable membranes. Membranes pretreated with saliva or clorhexidine and nontreated control membranes were tested in three different culture media containing 0.1 mL homologous suspension for each strain under study. Incubation was performed at 37 degrees C for 48 hours for aerobiosis and for five days for anaerobiosis. Macroscopy and microscopy were carried out. Membranes were removed, washed, and resuspended. Samples were sonicated, and the supernatant was disseminated on brain heart infusion broth or blood agar. Incubation was repeated, colony-forming unit counts were performed, and statistical analysis was carried out using analysis of variance transforming results to Log10 (x + 1), the highest interaction level was used to calculate standard error. Orthogonal contrast was used to compare the different microorganisms under study. Highest adhesion was found with Ca, Cg, Ck, Sa, and Ss. A sufficient quantity of Actinomyces could not be recovered from the membranes. Results with P spp were poor, confirming lower gram-negative adhesion. Replicate flasks with Ss and Ca were cultivated. Membranes were removed after washing and subjected to scanning electron microscopy, as were untreated control pieces. A cavelike surface was observed. Streptococcus sanguis adhering to the membranes showed extracellular projections. Candida and gram-positive cocci showed great recovery capacity.

Tubular-type pervaporation module with zeolite NaA membrane

Zeolite NaA membranes were prepared on the surfaces of porous tubular supports composed of mullite, α-alumina and/or cristobalite using the hydrothermal synthesis. The zeolite NaA crystals and the surface morphologies of the membranes were characterized by X-ray diffraction and SEM. EPMA analysis revealed that the zeolite composite membranes consisted of three layers — the zeolite layer, the intermediate layer and the mullite support. According to pervaporation measurements using H 2O EtOH mixture, the permselectivity increased in the alumina content of the substrate and reached a constant at >70 wt% Al 2O 3. Zeolite NaA membrane showed very high water-selective permeation through all the ethanol concentrations. The tubular-type module with ca. 0.5 m 2 membrane area was composed of 17 pieces of zeolite membrane using 65 wt% alumina content substrate, which has high pervaporation performance and can be purchased at a low price. The efficiency of the module on permeation rate increased in proportion to the feed flow rate and exhibited 100% at Reynolds number >80. Pervaporation flux and separation factor of the module for 5 wt% water/95 wt% ethanol mixture at 95°C was ca. 2.35 kg m −2 h −1 and was greater than 5 000, respectively.

A spot-PCR technique for the detection of phloem-limited grapevine viruses

Specific amplification of genomic fragments of grapevine trichovirus A (GVA), grapevine trichovirus B (GVB) and grapevine leafroll-associated closterovirus 3 (GLRaV3) was obtained by reverse transcription-PCR on total nucleic acid solubilized from small pieces of charged nylon membrane, on which a drop of crude infected grapevine sap was spotted (spot-PCR). A thermal treatment (95 ° for 10') of spotted sap in a buffered solution improved the release of viral template. Consistent amplification was obtained with three viruses from fragments of the same respective blots up to 1 month after spotting, while a detection threshold limit comparable with standard PCR techniques was found for this method. Duplex PCR (i.e. amplification of different viruses from a mixed-infected grapevine source) was also found to be effective, since GVA and GLRaV3 were amplified by a mixture of specific primers in the same reaction. This rapid and easy sampling technique, using leaf petioles to express crude sap, may have a wide field application for screening grapevine viruses.

Evaluation of nanofiltration membranes for filtration of paper mill total effluent

In the pulp and paper industry, membrane technology can be applied both in recycling of the valuable materials within the process, and in pollution control. A major challenge for membrane technology is purification of process water, so that it can be reused, for example, as shower water. The study is part of a project to develop a single-stage nanofiltration process for recirculation of paper mill water, and to reuse this water as shower water. Different membranes were used to treat effluent, which consisted of water from a thermomechanical pulp plant and paper machine. In the ultrafiltration experiments it was seen that the resulting permeates were practically free from highly conjugated lignin residuals, anionic trash and turbidity. The reductions in total carbon, chemical oxygen demand and inorganic matter were between 50% and 60%. Even better reductions were achieved from experiments with nanofiltration membranes. It was seen that the resulting permeates were totally free from turbidity, colour and anionic trash. Reductions of more than 80% were measured for chemical oxygen demand, total carbon and inorganic matter. Chloride ions were not well retained by NF membranes. The permeabilities of NF membranes were between 3 and 13 I/(M 2h bar), depending on the piece of membrane and the pretreatment of the membrane. The use of parallel spacers greatly decreased the reduction in the permeate flux during the filtration. Reductions in chloride ions were better using RO membranes, as expected. The reductions in chemical oxygen demand, total carbon and sugar were above 95% for filtration using RO membranes. The permeabilities of these membranes were below 2.5 l/(M 2h bar). Thus they are not suitable for industrial-scale filtration. The best membranes for treatment of the paper mill effluent used here were the Desal-5 and NF45 membranes. These had a low flux reduction of the pure water flux, stable permeate flux and good permeabilities. The reductions in the measured parameters were also acceptable.

Ultrastructure of conidia and conidium germination in the plant pathogenic fungus Alternaria cassiae

Transmission electron microscopy of plunge-frozen and freeze-substituted samples was used to examine germinating conidia of Alternaria cassiae, a plant pathogenic fungus used as a biological control agent for sicklepod (Cassia obtusifolia). Hydrated conidia on small pieces of dialysis membrane were incubated for 1, 2, or 3 h on the surface of corn meal agar prior to fixation. Conidia were large, darkly pigmented, and surrounded by a thick, two-layered wall. Each conidium was divided by transverse and longitudinal septa into multiple cells, a few of which sometimes appeared necrotic. Each septum tapered to a small central pore region with which Woronin bodies were associated. Each healthy cell of a conidium contained a typical complement of cellular organelles including multiple nuclei. With the exception of lipid bodies, all the various organelles were well preserved by plunge freezing and freeze substitution. Evidence of germ tube development was visible by 2 h post-incubation and well-developed germ tubes were present by 3 h. Two modes of germ tube development were observed. In the less common mode germ tubes developed inside conidia and grew internally through one or more adjacent cells before emerging from the conidium surface. Cells penetrated by internal germ tubes appeared necrotic. In the more common mode of germination, germ tubes developed directly from the conidium surface. Multiple germ tubes usually arose from each conidium and grew out in all directions. Germ tubes that contacted the underlying dialysis membrane continued to grow along its surface. Extracellular material was produced in association with developing germ tubes and coated the sides of germinated conidia and covered germ tubes growing along membranes. Key words: transmission electron microscopy, cryofixation, freeze substitution, germ tube development.

Large deviations of the average shapes of vesicles from equilibrium:Effects of thermal fluctuations in the presence of constraints

In the absence of external stresses, the surface area and the volume of a closed, flaccid lipid vesicle are practically constant. Thermal shape fluctuations of vesicles that are subject to these constraints recently have been shown to induce a shift of the average shapes away from the equilibrium (zero temperature) shapes. Since only the average shapes can be determined from observations by optical microscopy, it is important to establish the magnitude of their deviation from the well-studied equilibrium shapes. In this paper we develop a formalism to calculate this thermal shift, and we demonstrate that nonlinearities in the constraints may cause it to be unexpectedly large. Allowing for arbitrary shape deformations, we present numerical calculations revealing a logarithmic dependence of the thermal shift on the number of fluctuational degrees of freedom of the vesicle membrane or, equivalently, on the number of lipid molecules constituting the membrane. As a consequence, the surface area ('projected area') and, to a lesser extent, the volume ('projected volume') of the average shape are smaller than their true values. These numerical results are in general agreement with theoretical predictions that have been made so far only for pieces of flat membranes but not for closed lipid membranes subject to the constraints of both constant area and volume. Furthermore, we derive an expression for the correlation function of deviations from equilibrium including terms of the order of (${\mathrm{k}}_{\mathrm{B}}$ T${)}^{2}$ that involve the (quadratic) thermal shift. We demonstrate that these terms may actually exceed the commonly used leading term of the correlation function. This analysis suggests that the determination of the membrane bending modulus ${\mathrm{k}}_{\mathrm{c}}$ from observations of thermal vesicle shape fluctuations should be based on the variances rather than the correlation functions.