1/f Membrane noise generated by diffusion processes in unstirred solution layers

A mathematical treatment is given for 1/f noise observed in the ion transport through membranes. It is shown that this noise can be generated by current or voltage fluctuations which occur after step changes of the membrane permeability. Due to diffusion polarization in the unstirred solution layers near the membrane these fluctuations exhibit a 1/t time course which produces noise with a 1/f frequency dependence. The spectral density of 1/f noise is calculated for porous membranes with random switches between a finite and zero pore permeability. A wide frequency range and a magnitude of 1/f noise are obtained which are compatible with experimental data of 1/f noise reported for nerve membranes.Supported by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 38 Membranforschung.     

1/f-Noise of Open Bacterial Porin Channels

General diffusion pores and specific porin channels from outer membranes of gram-negative bacteria were reconstituted into lipid bilayer membranes. The current noise of the channels was investigated for the different porins in the open state and in the ligand-induced closed state using fast Fourier transformation. The open channel noise exhibited 1/f-noise for frequencies up to 200 Hz. The 1/f-noise was investigated using the Hooge formula (Hooge, Phys. Lett. 29A: 139–140 (1969)), and the Hooge parameter α was calculated for all bacterial porins used in this study. The 1/f-noise was in part caused by slow inactivation and activation of porin channels. However, when care was taken that during the noise measurement no opening or closing of porin channels occurred, the Hooge Parameter α was a meaningful number for a given channel. A linear relationship was observed between α and the single-channel conductance, g, of the different porins. This linear relation between single-channel conductance and the Hooge parameter α could be qualitatively explained by assuming that the passing of an ion through a bacterial porin channel is—to a certain extent—influenced by nonlinear effects between channel wall and passing ion. Received: 8 May 1996/Revised: 27 January 1997     

Current noise of a protein-selective biological nanopore

1/f current noise is ubiquitous in protein pores, porins, and channels. We have previously shown that a protein-selective biological nanopore with an external protein receptor can function as a 1/f noise generator when a high-affinity protein ligand is reversibly captured by the receptor. Here, we demonstrate that the binding affinity and concentration of the ligand are key determinants for the nature of current noise. For example, 1/f was absent when a protein ligand was reversibly captured at a much lower concentration than its equilibrium dissociation constant against the receptor. Furthermore, we also analyzed the composite current noise that resulted from mixtures of low-affinity and high-affinity ligands against the same receptor. This study highlights the significance of protein recognition events in the current noise fluctuations across biological membranes.     

Noise analysis of the K+ current through the apical membrane ofNecturus gallbladder

Summary Current noise power spectra of the voltage-clamped (V=0)Necturus gallbladder, exposed to NaCl-Ringer's on both sides contained a relaxation noise component, which overlapped with a 1/f noise component, with being about 2. Substitution of all Na⁺ by K⁺ on either the serosal or mucosal side increased the relaxation as well as the 1/f noise component considerably. InNecturus gallbladder both noise components are reduced by addition of 10mm 2,4,6-triaminopyrimidine (TAP) or 5mm of tetraethylammonium (TEA⁺) added to ification of the mucosal solution to pH 5 and lower. Fivemm of tetraethylammonium (TEA⁺) added to the mucosal solution, abolished K⁺ relaxation noise and decreased the 1/f noise component. Applying a Cs⁺ concentration gradient across the epithelium did not yield relaxation noise. However, if Rb⁺ was substituted for all Na⁺ on one side, a Lorentzian noise component appeared in the spectrum. Its plateau was smaller than with KCl-Ringer's on the respective side. These data confirm the existence of fluctuating K⁺ channels in the apical membrane of theNecturus gallbladder. Furthermore it can be concluded that these channels have the permeability sequence K⁺>Rb⁺>Sc⁺. The inhibition of the fluctuations by mucosal acidification indicates the existence of acidic sites in the channel. The single-channel conductance was estimated to be between 6.5 and 40 pS.     

Osmotic water permeability of plasma and vacuolar membranes in protoplasts II. Theoretical basis

Water permeability of the plasma membrane (PM) and the vacuolar membrane (VM) is important for intracellular and transcellular water movement in plants, because mature plant cells have large central vacuoles. We have developed a new method for measuring the osmotic water permeability of the PM and VM (P _f1 and P _f2, respectively) in individual plant cells. Here, the theoretical basis and procedure of the method are discussed. Protoplasts isolated from higher plant tissues are used to measure P _f1 and P _f2. Because of the semi-permeability (selective permeability) of cellular membranes, protoplasts swell or shrink under hypotonic or hypertonic conditions. A theoretical three-compartment model is presented for simulating time-dependent volume changes in the vacuolar and cytoplasmic spaces in a protoplast during osmotic excursions. The model describes the theoretical relationships between P _f1, P _f2 and the bulk osmotic water permeability of protoplasts (P _f(bulk)). The procedure for measuring the osmotic water permeability is: (1) P _f(bulk) is calculated from the time when half of the total change in protoplast volume is completed, by assuming that the protoplast has a single barrier to water movement across it (two-compartment model); (2) P _f2 of vacuoles isolated from protoplasts is obtained in the same manner; and (3) P _f1 is determined from P _f(bulk) and P _f2 according to the three-compartment model. The theoretical relationship between P _fl (m s⁻¹) and L _Pl (hydraulic conductivity, l=1, 2) (m s⁻¹ Pa⁻¹) is also discussed. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorised users. Tsuneo Kuwagata and Mari Murai-Hatano contributed equally to the paper.     

Osmotic water permeability of plasma and vacuolar membranes in protoplasts I. High osmotic water permeability in radish ( Raphanus sativus ) root cells as measured by a new method

Intra- and transcellular water movements in plants are regulated by the water permeability of the plasma membrane (PM) and vacuolar membrane (VM) in plant cells. In the present study, we investigated the osmotic water permeability of both PM (P _f1) and VM (P _f2), as well as the bulk osmotic water permeability of a protoplast (P _f(bulk)) isolated from radish (Raphanus sativus) roots. The values of P _f(bulk) and P _f2 were determined from the swelling/shrinking rate of protoplasts and isolated vacuoles under hypo- or hypertonic conditions. In order to minimize the effect of unstirred layer, we monitored dropping or rising protoplasts (vacuoles) in sorbitol solutions as they swelled or shrunk. P _f1 was calculated from P _f(bulk) and P _f2 by using the ‘three-compartment model’, which describes the theoretical relationship between P _f1, P _f2 and P _f(bulk) (Kuwagata and Murai-Hatano in J Plant Res, 2007). The time-dependent changes in the volume of protoplasts and isolated vacuoles fitted well to the theoretical curves, and solute permeation of PM and VM was able to be neglected for measuring the osmotic water permeability. High osmotic water permeability of more than 500 μm s⁻¹, indicating high activity of aquaporins (water channels), was observed in both PM and VM in radish root cells. This method has the advantage that P _f1 and P _f2 can be measured accurately in individual higher plant cells. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users. It includes four appendices, four tables and two figures. Mari Murai-Hatano and Tsuneo Kuwagata contributed equally to the paper. An erratum to this article is available at .     

Osmotic water permeabilities of brush border and basolateral membrane vesicles from rat renal cortex and small intestine

Summary The osmotic water permeabilityP _f of brush border (BBM) and basolateral (BLM) membrane vesicles from rat small intestine and renal cortex was studied by means of stopped-flow spectrophotometry. Scattered light intensity was used to follow vesicular volume changes upon osmotic perturbation with hypertonic mannitol solutions. A theoretical analysis of the relationship of scattered light intensity and vesicular volume justified a simple exponential approximation of the change in scattered light intensity. The rate constants extracted from fits to an exponential function were proportional to the final medium osmolarity as predicted by theory. For intestinal membranes, computer analysis of optical responses fitted well with a single-exponential treatment. For renal membranes a double-exponential treatment was needed, implying two distinct vesicle populations.P _f values for BBM and BLM preparations of small intestine were equal and amount to 60 m/sec. For renal preparations,P _f values amount to 600 m/sec for the fast component, BBM as well as BLM, and to 50 (BBM) and 99 (BLM) m/sec for the slow component. The apparent activation energy for water permeation in intestinal membranes was 13.3±0.6 and in renal membranes, 1.0±0.3 kCal/mole, between 25 and 35°C. The mercurial sulfhydryl reagentpCMBS inhibited completely and reversibly the highP _f value in renal brush border preparations. These observations suggest that in intestinal membranes water moves through the lipid matrix but that in renal plasma membranes water channels may be involved. From the highP _f values of renal membrane vesicles a transcellular water permeability for proximal tubules can be calculated which amounts to 1 cm/sec. This value allows for an entirely transcellular route for water flow during volume reabsorption.     

Diffusion and 1/f noise

Summary The noise associated with ion transport through porous membranes is considered as a diffusion process. This is confirmed experimentally by measuring the noise spectra associated with pores of known dimension. It is then shown that one dimensional diffusion through pores of variable length can produce approximate 1/f noise spectra, if the distribution of lengths is proportional to (length)^–1.     

Purification and characterization of a calcium-dependent protein kinase from beetroot plasma membranes

Several calcium-dependent protein kinases (CDPKs) are located in plant plasma membranes where they phosphorylate enzymes and transporters, like the H⁺-ATPase and water channels, thereby regulating their activities. In order to determine which kinases phosphorylate the H⁺-ATPase, a calcium-dependent kinase was purified from beetroot (Beta vulgaris L.) plasma membranes by anion-exchange chromatography, centrifugation in glycerol gradients and hydrophobic interaction chromatography. The kinetic parameters of this kinase were determined (V _max: 3.5 μmol mg⁻¹ min⁻¹, K _m for ATP: 67 μM, K _m for syntide 2: 15 μM). The kinase showed an optimum pH of 6.8 and a marked dependence on low-micromolar Ca²⁺ concentrations (K _d : 0.77 μM). During the purification procedure, a 63-kDa protein with an isoelectric point of 4.7 was enriched. However, this protein was shown not to be a kinase by mass spectrometry. Kinase activity gels showed that a 50-kDa protein could be responsible for most of the activity in purified kinase preparations. This protein was confirmed to be a CDPK by mass spectrometry, possibly the red beet ortholog of rice CDPK2 and Arabidopsis thaliana CPK9, both found associated with membranes. This kinase was able to phosphorylate purified H⁺-ATPase in a Ca²⁺-dependent manner.Electronic Supplementary Material Supplementary material is available to authorised users in the online version of this article at .     

Differences among the cell wall galactomannans from Aspergillus wentii and Chaetosartorya chrysella and that of Aspergillus fumigatus

The alkali extractable and water-soluble cell wall polysaccharides F1SS from Aspergillus wentii and Chaetosartorya chrysella have been studied by methylation analysis, 1D- and 2D-NMR, and MALDI-TOF analysis. Their structures are almost identical, corresponding to the following repeating unit: [→ 3)-β-D-Galf-(1 → 5)-β-D-Galf-(1 →] _n → mannan core. The structure of this galactofuranose side chain differs from that found in the pathogenic fungus Aspergillus fumigatus, in other Aspergillii and members of Trichocomaceae: [→ 5)-β-D-Galf-(1 →] _n → mannan core. The mannan cores have also been investigated, and are constituted by a (1 → 6)-α-mannan backbone, substituted at positions 2 by chains from 1 to 7 residues of (1 → 2) linked α-mannopyranoses. Published in 2004. This revised version was published online in July 2006 with corrections to the Cover Date.     

The effects of detergents DDM and β-OG on the singlet excited state lifetime of the chlorophyll a in cytochrome b6f complex from spinach chloroplasts

The singlet excited state lifetime of the chlorophyll a (Chi a) in cytochrome b6f (Cyt b6f) complex was reported to be shorter than that of free Chl a in methanol, but the value was different for Cyt b6f complexes from different sources (～200 and ～600 ps are the two measured results). The present study demonstrated that the singiet excited state lifetime is associated with the detergents n-dodecyl-β-D-maltoside (DDM) and n-octyl-β-D-glucopyranoside (β-OG), but has nothing to do with the different sources of Cyt b6f complexes. Compared with the Cyt b6f dissolved in β-OG, the Cyt b6f in DDM had a lower fluorescence yield, a lower photodegradation rate of Chl a, and a shorter lifetime of Chl a excited state. In short, the singlet excited state lifetime, ～200 ps, of the Chl a in Cyt b6f complex in DDM is closer to the true in vivo.     

Noise analysis and relaxation experiments of transport of hydrophobic anions across lipid membranes at equilibrium and nonequilibrium

Under equilibrium and nonequilibnum steady-stale conditions the spectral intensity of current noise S_J(f) generated by the transport of hydrophobic unions across lipid bilayer membranes was investigated. The experimental results were compared with different reaction models S_J(f) showed a characteristic increase proportional to f² between frequency-independent tails at low and high frequencies. This gradient was found to be independent of applied voltage which indicates the contribution of a single voltage-dependent reaction step of ion translocation across the membrane From the shape of S_J(f) at low frequencies the rate constant of ion desorption from the membrane into the aqueous phase could be estimated. Unambiguous evidence for the application of a general model, which includes the coupling of slow ion diffusion in the aqueous phase to ion adsorption/desorption at the membrane interface, could not be obtained from the low-frequency shape of S_J(f). The shot noise of this ion transport determines the amplitude of S_J(f) at high frequencies which decreases with increasing voltage applied. Analysis of voltage-jump current-relaxation experiments and of current noise carried cut on one membrane yielded significant differences of the derived ion partition coefficient. This deviation is qualitatively described on the basis of incomplete reaction steps.     

Osmotic water permeabilities of human placental microvillous and basal membranes

Summary Literature data suggest that water accumulation by the human fetus is driven by osmotic gradients of small solutes. However, the existence of such gradients has not been supported by prior measurements. Attempts to estimate the size of the gradient necessary to drive net water movement have been seriously hampered by the lack of permeability data for the syncytiotrophoblast membranes. Stopped-flow light scattering techniques were employed to measure the osmotic water permeability (P _f )of microvillous (MVM) and basal membrane (BM) vesicles isolated from human term placenta. At 37°C, the P _f was determined to be 1.9±0.06 × 10^+–3 cm/sec for MVM and 3.1±0.20 × 10^+–3 cm/sec for BM (mean ±SD, n = 6). At 23°C, P _f was reduced to 0.7±0.04 × 10^+–3 cm/sec in MVM and 1.6±0.05 × 10^+–3 cm/sec in BM. These P _f values are comparable to those observed in membranes where water has been shown to permeate via a lipid diffusive mechanism. Arrhenius plots of P _f over the range 20–40°C were linear, with activation energies of 13.6 ± 0.6 kcal/mol for MVM and 12.9±1.0 kcal/mol for BM. Water permeation was not affected by mercurial sulfhydryl agents and glucose transport inhibitors. These data clearly suggest that water movement across human syncytiotrophoblast membranes occurs by a lipid diffusion pathway. As noted in several other epithelial tissues, the basal membrane has a higher water permeability than the microvillous membrane. It is speculated that water accumulation by the human fetus could be driven by a solute gradient small enough to be within the error of osmolarity measurements.We thank the staff of the labor and delivery ward at University of San Francisco Medical Center for help in obtaining placental tissue. This work was supported by NIH grant HD 26392. Dr. Jansson was supported by the Sweden-America Foundation, The Swedish Society of Medicine, The Swedish Society for Medical Research, and the Swedish Medical Research Council.     

Excess electrical noise during current flow through porous membranes separating ionic solutions

Summary Spectral analysis of electrical noise from various artificial membrane systems suggests that excess noise of anf ^–n spectral form, wheren is approximately unity, is not primarily a bulk phenomenon simply dependent on the number of charge carriers. Measurements from aqueous and nonaqueous electrolytic resistors, comprised of several different ionic species, show only flat power density spectra under applied currents, even at extreme dilutions. Excess noise off ^–n form is observed under applied d-c current in single pore membranes, as previously reported, but is also seen in multipore and polymer mesh membranes. Calculations based on single pore membrane noise data are in significant variance with the bulk charge carrier model proposed by Hooge. These observations suggest that such excess noise occurs in conjunction with anisotropic constraints to ion flow.1 Fishman, H. M., Moore, L. E., Poussart, D. J. M. 1975. Potassium ion conduction noise in squid axon membrane.J. Membrane Biol. (Submitted for publication).     

Bifurcation Analysis of Genetically Engineered Pacemaking in Mammalian Heart

Genetically engineered pacemaking in ventricular cells has been achieved by down-regulation of the time independent inward rectifying current (I _K1), or insertion of the hyperpolarisation-activated funny current (I _f). We analyse the membrane system (i.e. ionic concentrations clamped) of an epicardial Luo-Rudy dynamic cell model using continuation algorithms with the maximum conductance () of I _K1 and I _f as bifurcation parameters. Pacemaker activity can be induced either via Hopf or homoclinic bifurcations. As _K1 is decreased by ≈74%, autorhythmicity emerged via a homoclinic bifurcation, i.e., the periodicity first appear with infinitely large periods. In contrast, the insertion of _f induced periodicity via a subcritical Hopf bifurcation at _f≈ 0.25 mSμF⁻¹. Stable autorhythmic action potentials occurred at _f > 0.329 mSμF⁻¹.     

Cytochrome b 6 f complex: Dynamic molecular organization,function and acclimation

The cytochrome b ₆ f complex occupies a central position in photosynthetic electron transport and proton translocation by linking PS II to PS I in linear electron flow from water to NADP⁺, and around PS I for cyclic electron flow. Cytochrome b ₆ f complexes are uniquely located in three membrane domains: the appressed granal membranes, the non-appressed stroma thylakoids and end grana membranes, and also the non-appressed grana margins, in contrast to the marked lateral heterogeneity of the localization of all other thylakoid multiprotein complexes. In addition to its vital role in vectorial electron transfer and proton translocation across the membrane, cytochrome b ₆ f complex is also involved in the regulation of balanced light excitation energy distribution between the photosystems, since its redox state governs the activation of LHC II kinase (the kinase that phosphorylates the mobile peripheral fraction of the chlorophyll a/b-proteins of LHC II of PS II). Hence, cytochrome b ₆ f complex is the molecular link in the interactive co-regulation of light-harvesting and electron transfer.The importance of a highly dynamic, yet flexible organization of the thylakoid membranes of plants and green algae has been highlighted by the exciting discovery that a lateral reorganization of some cytochrome b ₆ f complexes occurs in the state transition mechanism both in vivo and in vitro (Vallon et al. 1991). The lateral redistribution of phosphorylated LHC II from stacked granal membrane regions is accompanied by a concomitant movement of some cytochrome b ₆ f complexes from the granal membranes out to the PS I-containing stroma thylakoids. Thus, the dynamic movement of cytochrome b ₆ f complex as a multiprotein complex is a molecular mechanism for short-term adaptation to changing light conditions. With the concept of different membrane domains for linear and cyclic electron flow gaining credence, it is thought that linear electron flow occurs in the granal compartments and cyclic electron flow is localised in the stroma thylakoids at non-limiting irradiances. It is postulated that dynamic lateral reversible redistribution of some cytochrome b ₆ f complexes are part of the molecular mechanism involved in the regulation of linear electron transfer (ATP and NADPH) and cyclic electron flow (ATP only). Finally, the molecular significance of the marked regulation of cytochrome b ₆ f complexes for long-term regulation and optimization of photosynthetic function under varying environmental conditions, particularly light acclimation, is discussed.Abbreviations Chl chlorophyll - cyt cytochrome - PS Photosystem     

Using eggshell membranes as a non-invasive tool to investigate the source of nutrients in avian eggs

Development of minimally invasive techniques to collect nutritional information from free-living birds is desirable for both ethical and conservation reasons. Here, we explore the utility of waterfowl eggshell membranes to determine the nutrient source of egg formation by using stable isotope ratios. We compared δ¹³C and δ¹⁵N of membranes from complete king eider (Somateria spectabilis) eggs to membranes of hatched or depredated eggs of the same clutch remaining after incubation. Despite large variation among membranes (δ¹³C: −26 to −14‰) we found a highly predictable relationship between δ¹³C of complete egg membranes and remaining (hatched or depredated) membranes from the same clutch. We did not find a consistent change in either δ¹³C or δ¹⁵N of eggshell membranes during incubation. We suggest that isotope ratios of membranes can be used to determine the source of exogenous nutrients for egg production in income breeders, and that membranes may offer a clutch-specific reference point for dietary nutrients (‘income endpoint’) in isotopic mixing models quantifying nutrient allocation in capital or mixed-strategy breeders.     

On the mode of integration of plastid-encoded components of the cytochrome bf complex into thylakoid membranes

Four distinct integration/translocation routes into/across thylakoid membranes have recently been deduced for nuclear-encoded polypeptides of the photosynthetic membrane. Corresponding information for the plastid-encoded protein complement is lacking. We have investigated this aspect with in-organello assays employing chimeric constructs generated with codon-correct cassettes for genes of plastid-encoded thylakoid proteins, and appropriate transit peptides from six nuclear genes, representing three targeting classes, as a strategy. The three major plastid-encoded components of the cytochrome b ₆  f complex, namely pre-apocytochrome f, (including apocytochrome f, and pre-apocytochrome f lacking the C-terminal transmembrane segment), cytochrome b ₆ , and subunit IV, which differ in the number of their transmembrane segments, were studied. Import into chloroplasts could be observed in all instances but with relatively low efficiency. Thylakoid integration can occurr post-translationally, but only components with secretory/secretory pathway (SEC)-route-specific epitopes were correctly assembled with the cytochrome complex, or competed with this process. Inhibitor studies were consistent with these findings. Imported cytochrome b ₆ and subunit IV operated with uncleaved targeting signals for thylakoid integration. The corresponding determinant for cytochrome f is its signal peptide; its C-terminal hydrophobic segment did not, or did not appreciably, contribute to this process. The N-termini of cytochrome b ₆ and subunit IV appear to reside on the same (lumenal) side of the membrane, consistent with the currently favored four-helix model for the cytochrome, but in disagreement with the topography proposed for both components. The impact of the findings for protein routing, including for applied approaches such as compartment-alien transformation, is discussed. Received: 18 September 1996 / Accepted: 15 October 1996     

Singlet oxygen formation and chlorophyll a triplet excited state deactivation in the cytochrome b6f complex from Bryopsis?corticulans

We have attempted to investigate the correlation between the detergent-perturbed structural integrity of the Cyt b ₆ f complex from the marine green alga Bryopsis corticulans and its photo-protective properties, for which the nonionic detergents n-octyl-β-d-glucopyranoside (β-OG) and n-dodecyl-β-d-maltoside (β-DM), respectively, were used for the preparation of Cyt b ₆ f, and the singlet oxygen (¹O₂*) production as well as the triplet excited-state chlorophyll a (³Chl a*) formation and deactivation were examined by spectroscopic means. Near-infrared luminescence of ¹O₂ * (~1,270 nm) on photo-irradiation was detected for the β-OG preparation where the complex is mainly in oligomeric state, but not for the β-DM one in which the complex exists in dimeric form. Under anaerobic condition, photo-excitation of Chl a in the β-DM preparation generated ³Chl a* with a lower quantum yield of Φ_T ~ 0.02 and a longer lifetime of ~600 μs with respect to those as in the case of β-OG preparation, Φ_T ~ 0.12 and 200–300 μs. These results prove that the enzymatically active and intact Cyt b ₆ f complex on photo-excitation tends to produce little ³Chl a* or ¹O₂ *, which implies that the pigment–protein assembly of Cyt b ₆ f complex per se is crucial for photo-protection. F. Ma and X.-B. Chen contributed equally to this work.     

1/f noise in black lipid membranes induced by ionic channels formed by chemically dimerized gramicidin A

Summary The noise behavior of lipid bilayer membranes, doped with a chemically dimerized gramicidin A, was investigated. In contrast to normal gramicidin A, which generates a Lorentzian type power spectrum due to the formation and disappearance of conducting dimers, the current power spectrum densityS _m (f) obtained with this gramicidin A derivative showed over several orders of magnitude a clear 1/f behavior. The intensity of this 1/f component was analyzed as a function of the membrane-applied voltage, membrane resistance, electrolyte concentration, and composition. The relationship between the meansquare fluctuation in current and the membrane current mean value was found to follow Hooge's equation, i.e., I ²=I _m ² /N f whereN is the number of channels and is a constant equal to 1.0×10^–2. It is suggested that a 1/f type noise was observed because the chemically dimerized form of gramicidin A produces long lasting cation selective channels.