A new interpretation of flux ratio exponents using statistical rate theory

By viewing permeation as a three-step process (movements between the bulk intracellular medium and the channel, within the channel, and between the channel and the extracellular bulk medium), and describing each step in the process with a statistical rate theory (SRT) approach, we can envisage different permeation scenarios which consider whether movements across certain interfaces can be approximated to be at equilibrium. A new interpretation of the flux ratio exponent is presented and its value can be used to predict whether the rate-limiting region occurs within the channel or at the interface. By considering saturation profiles, estimates for SRT exchange rates can be obtained, and a comparison with the more well-known Eyring rate theory is provided. Received: 27 May 1998 / Revised version: 9 December 1998 / Accepted: 9 December 1998     

Evaluation of transport pathways for Na+ across frog skin epithelium by means of presteady-state flux ratio

Summary A method is described that makes it possible to separate the sodium fluxes through the isolated frog skin into sets characteristic of the cellular and the paracellular pathway, respectively. If there are two significant pathways for the ion, and if they differ with respect to flux ratio as well as mean passage time, the flux ratios for the individual pathways can be obtained from a set of inward and outward tracer fluxes, covering the time from the addition of the tracers until the achievement of constant fluxes in both directions.Deceased, formerly Department of Ophthalmology, College of Physicians and Surgeons, Columbia University, New York, New York 10032.     

Amendments to the theory underlying Ussing chamber data of chloride ion secretion after bacterial enterotoxin exposure

Bacterial enterotoxins may cause life-threatening diarrhoeal fluid loss in part because they stimulate enterocytes to secrete fluid into the small intestine as well as preventing normal fluid uptake. Abnormal chloride ion secretion is believed to provide the osmotic driving force for the inappropriate fluid movement. Evidence for enhanced chloride secretion consists of isotopic flux measurements in Ussing chambers, the standard apparatus for permeation studies. Flux from the lumen of the intestine is assumed to be determined solely by absorptive processes and flux towards the lumen solely by secretory processes. Bacterial enterotoxin increased flux towards the lumen is taken as an evidence of enhanced secretion. Examination of the flux equation solutions shows that the existing theoretical treatment of the Ussing chamber consists of the super-imposition of two contradictory unidirectional models. In contrast, the present analysis shows that a measured 'unidirectional' flux contains information both about absorptive and secretory processes, regardless of which flux is measured. Reciprocity is predicted for the fluxes, as decreases in the absorptive processes will cause increases in apparent secretory flux. Data from the literature show that mucosal-to-serosal chloride ion flux in rabbit ileum after exposure to secretagogues correlates inversely and highly significantly (r=0.74, n=17, p<0.001) with increases in serosal-to-mucosal chloride ion flux. As a category of evidence, flux data do not provide conclusive evidence of enhanced chloride secretion after exposure to enterotoxins, since an apparently enhanced serosal-to-mucosal flux would also be noted after inhibition of the mucosal-to-serosal flux. As interruption of absorptive processes can be misinterpreted as enhanced secretion in the Ussing chamber, this is a serious deficiency in the evidence for direct enterotoxin enhancement of the intestinal chloride ion channel as a basis for diarrhoeal disease.     

Salinity-induced ion flux patterns from the excised roots of <Emphasis Type="Italic">Arabidopsis sos</Emphasis> mutants

The SOS signal-transduction pathway is known to be important for ion homeostasis and salt tolerance in plants. However, there is a lack of in planta electrophysiological data about how the changes in signalling and ion transport activity are integrated at the cellular and tissue level. In this study, using the non-invasive ion flux MIFE technique, we compared net K⁺, H⁺ and Na⁺ fluxes from elongation and mature root zones of Arabidopsis wild type Columbia and sos mutants. Our results can be summarised as follows: (1) SOS mutations affect the function of the entire root, not just the root apex; (2) SOS signalling pathway is highly branched; (3) Na⁺ effects on SOS1 may by-pass the SOS2/SOS3 complex in the root apex; (4) SOS mutation affects H⁺ transport even in the absence of salt stress; (5) SOS1 mutation affects intracellular K⁺ homeostasis with a plasma membrane depolarisation-activated outward-rectifying K⁺ channel being a likely target; (6) H⁺ pump also may be a target of SOS signalling. We provide an improved model of SOS signalling and discuss physiological mechanisms underlying salt stress perception and signalling in plants. Our work shows that in planta studies are essential for understanding the functional genomics of plant salt tolerance.     

Establishment of an in Vitro Model of the Human Placental Barrier by Placenta Slice Culture and Ussing Chamber

Aggregation occurs through hydrophobic interactions when a polypeptide chain refolds in non-native states or when genetic variants of biologically active proteins assume inappropriate conformations, as observed in the case of dysfunctional serpins. Here, using the molecular chaperone BiP from bovine liver microsomes, we characterized the hydrophobic nature of the peptide segment which is considered to be a site required for aggregation among a non-inhibitory serpin ovalbumin in a heat-denatured state. Screening of the peptide scan for binding of BiP showed that BiP-binding sites are mostly buried in the folded ovalbumin. When ovalbumin was heat-denatured, the denatured protein was recognized by the antibody that reacts with the hydrophobic surface of the amino-terminal segment of ovalbumin. This antibody significantly suppressed the binding of BiP to denatured ovalbumin. BiP also bound the immobilized peptide in an ATP-dependent manner and the peptide stimulated the ATPase activity of BiP with a K _m of 165 μM and a V _max of 0.4 nmol/min per milligram. Measurement of surface plasmon resonance showed that the peptide had a K _d of 0.52 μM by BiP, lower than that for RCMLA (K _d=1.1 μM) and even lower than that of the peptide P10K, PLSRTLSVAAKK, (K _d=21 μM). These results demonstrate that the aggregation-prone site on heat-denatured ovalbumin has almost the same hydrophobic nature of interacting with the molecular chaperone BiP as the conventionally known peptides that bind to the Escherichia coli chaperone DnaK.     

A comparative tool for the validity of rate kinetics in ion channels by Onsager reciprocity theorem

The precise form of the rate constant functions of ion channels is very crucial for reproducing the electrophysiological behavior. Therefore, how well they account for experimental data plays an important role in the behavior of the model. In this study, we derive kinetic coefficients of activation and inactivation gates in ion channels by Onsager reciprocity theorem for an ensemble of gating particles, and propose that the obtained kinetic coefficients can be used as a comparative tool for the empirical validity of fitted rate constant functions to experimental data. We also illustrate its applicability based on the activation and inactivation kinetics of T-type calcium channel in thalamic relay neurons. We show that the shape of the steady-state curve by itself seems to be a poor indicator of the functional form of the rate functions, but the time constant curves reflect considerable variation depending on the particular form of the rate functions, and that the kinetic coefficients related to the time constants provide a powerful tool to determine the empirical validity of the fitted rate constants.     

Statistical properties of ion channel records. Part II: estimation from the macroscopic current

Macroscopic ion channel current is the summation of the stochastic records of individual channel currents and therefore relates to their statistical properties. As a consequence of this relationship, it may be possible to derive certain statistical properties of single channel records or even generate some estimates of the records themselves from the macroscopic current when the direct measurement of single channel currents is not applicable. We present a procedure for generating the single channel records of an ion channel from its macroscopic current when the stochastic process of channel gating has the following two properties: (I) the open duration is independent of the time of opening event and has a single exponential probability density function (pdf), (II) all the channels have the same probability to open at time t. The application of this procedure is considered for cases where direct measurement of single channel records is difficult or impossible. First, the probability density function (pdf) of opening events, a statistical property of single channel records, is derived from the normalized macroscopic current and mean channel open duration. Second, it is shown that under the conditions (I) and (II), a non-stationary Markov model can represent the stochastic process of channel gating. Third, the non-stationary Markov model is calibrated using the results of the first step. The non-stationary formulation increases the model ability to generate a variety of different single channel records compared to common stationary Markov models. The model is then used to generate single channel records and to obtain other statistical properties of the records. Experimental single channel records of inactivating BK potassium channels are used to evaluate how accurately this procedure reconstructs measured single channel sweeps.     

Single channel gating events in tracer flux experiments. III. acetylcholine receptor-controlled Li+ efflux from sealed Torpedo marmorata membrane fragments

Filter assay measurements of Li+ efflux from acetylcholine receptor-containing vesicular Torpedo marmorata membrane fragments (microsacs) are presented. Techniques are introduced for: (a) inducing a complete emptying of the Li+ content of all microsacs containing one or more functionally intact receptors, and (b) for determining the distribution of internal volumes of the microsacs using filtration with membrane filters of different pore sizes. The flux amplitudes resulting for acetylcholine receptor-controlled Li+ efflux, when receptors are inhibited by alpha-bungarotoxin or inactivated by a neuroactivator-induced desensitization process, were measured. Amplitude analysis was used to determine characteristic parameters of the microsacs that may vary with the technique of preparation (e.g., the distribution in size and receptor content), as well as the mean single channel flux amplitude contribution (e-kt)infinity, which represents the mean reduction of the Li+ content of a microsac due to efflux from a single receptor-controlled channel closing due to inhibition or inactivation of the receptor. The ratio keff/ki was found to lie in the range 0.1 less than keff/ki less than 0.5, where keff and ki are, respectively, the rate constant for Li+-Na+ exchange flux and for the slow inactivation reaction mode of the acetylcholine receptor induced by carbamoylcholine at high concentrations.     

Regulation of the photosynthetic capacity of primary bean leaves by the red:far-red ratio and photosynthetic photon flux density of incident light

The main objective of the present work was to examine the effects of the red:far-red ratio (R:FR) prevailing during leaf development on the photosynthetic capacity of mature leaves. Plants of Phaseolus vulgaris L. cv. Balin de Albenga were grown from time of emergence in a controlled environment room, 25 ± 3°C, 12-h photoperiod, with different light treatments:a) high photosynthetic photon flux density (PPFD) = 800 μmol m⁻¹ s⁻¹+ high R:FR= 1.3;b) low PPFD= 300 μmol m⁻² s⁻¹+ high R:FR= 1.3; c) high PPFD=800 μmol m⁻² s⁻¹+ low R:FR= 0.7; d) low PPFD= 300 μmol m⁻²s⁻¹+ low R:FR=0.7. With an R:FR ratio of 1.3, a decrease in irradiance during leaf growth reduced photosynthesis when measured at moderate to high PPFD; but when measured at low PPFD, leaves expanded under low irradiance actually had photosynthesis rates higher than those of leaves grown in high irradiance. A low R:FR ratio during development reduced the photosynthetic capacity of the leaves. In leaves expanded under R:FR = 0.7 and high irradiance photosynthesis was reduced by 42 to 89%, depending on the PPFD at which measurements were made, whereas for leaves developed at R:FR = 0.7 and low irradiance photosynthesis decreased by 21 to 24%, compared to leaves under R:FR = 1.3 and similar irradiance. The reduced photosynthetic capacity under R:FR = 0.7 and high irradiance. In natural environments, leaves may experience low R:FR conditions temporarily during their development, and this may affect their future photosynthetic capacity in full sunlight.     

Statistical properties of ion channel records. Part I: relationship to the macroscopic current

Macroscopic ion channel current can be derived by summation of the stochastic records of individual channel currents. In this paper, we present two probability density functions of single channel records that can uniquely determine the macroscopic current regardless of other statistical properties of records or the stochastic model of channel gating (presented often with stationary Markov models). We show that H(t), probability density function of channel opening events (introduced explicitly in this paper), and D(t), probability density function of the open duration (sometimes has named dwell time distribution as well), determine the normalized macroscopic current, G(t), through G(t) = P(t) - H(t) * Q(t) where P(t) is the cumulative density function of H(t), Q(t) is the cumulative density function of D(t), * is the symbol of convolution integral and G(t) is the macroscopic current divided by the amplitude of single channel current and the number of single channel sweeps. Compared to other equations for the macroscopic current, here the macroscopic current is expressed only in terms of the statistical properties of single channel current and not the stochastic model of ion channel gating or a conditioned form of macroscopic current. Single channel currents of an inactivating BK channel were used to validate this relationship experimentally too. In this paper, we used median filters as they can remove the unwanted noise without smoothing the transitions between open and closed states (compare to low pass filters). This filtering leads to more accurate measurement of transition times and less amount of missed events.     

Molecular regions underlying the activation of low- and high-voltage activating calcium channels

We have studied two aspects of calcium channel activation. First, we investigated the molecular regions that are important in determining differences in activation between low- and high-voltage activated channels. For this, we made chimeras between the low-voltage activating Ca_V3.1 channel and the high-voltage activating Ca_V1.2 channel. Chimeras were expressed in oocytes, and calcium channel currents recorded by voltage clamp. For domain I, we found that the molecular region that is important in determining the voltage dependence of activation comprises the pore regions S5-P as well as P-S6, but surprisingly not the voltage sensor S1–S4 region, which might have been expected to play a major part. By contrast, the smaller, but still significant, modulating effects of domain II on activation properties were due to effects involving both S1–S4 and S5–S6 but not the I/II linker. Second, during channel activation we studied movement of the S4 segment in domain I of one of the chimeras, using cysteine-scanning mutagenesis. The reagent parachloromercuribenzensulfonate inhibited currents for mutants V263, A265, L266 and A268, but not for F269 and V271, and voltage dependence of inhibition for residue V263 indicated S4 movement, which occurred before channel opening. The data indicate movement outwards upon depolarisation so as to expose amino acids up to residue 268 in S4.Junying Li and Louisa Stevens contributed equally to this work.     

The roles of intracellular regions in the activation of voltage-dependent potassium channels

The involvement of the transmembrane regions S2, S3 and S4 in the activation of potassium channels by depolarization has been well clarified. However, a role of the intracellular regions in channel function is emerging. Here we review recent evidence for the roles of intracellular regions in the functioning of members of two families of channels. The Kv2.1 potassium channel, a member of the voltage activated Kv family, has long intracellular regions. By mutagenesis studies and expression in oocytes, we identify residues in both the N- and C-terminal regions that contribute to determining activation kinetics of this channel. It seems that the C-terminus wraps around the N-terminus and interacts with it functionally. The voltage-activated ether-a-go-go (eag) channels also have long intracellular regions. Despite considerable homology, eag1 and eag2 channels display different activation kinetics. By making chimeras between these channels and again expressing in oocytes, we show that residues in both the N-terminal region and the membrane-spanning region are involved in determining these differences in activation kinetics. The intracellular N- and C-terminal regions are likely to continue to prove fertile regions in future investigations into the functioning of ion channels.Presented at the Biophysical Society Meeting on Ion channels—from structure to disease held in May 2003, Rennes, France     

Determination of the electromotive force of active sodium transport in frog skin epithelium (Rana temporaria) from presteady-state flux ratio experiments

Summary The presteady-state influxes and effluxes of sodium across frog skin epithelium have been determined as a function of time while all electrophysiological parameters were maintained constant. The fluxes measured were resolved in the fractions which have passed a pathway through the cells and those that have used a paracellular pathway. The procedure is based on the theory that all presteady-state flux ratios have to be equal to the steady-state flux ratio if only one pathway is involved. The flux ratios for the transcellular route were used to calculate the electromotive force of the sodium pump. The calculation hinges on the assumptions (a) that both influx and efflux have to pass through the sodium pump and (b) that single file diffusion of sodium is not taking place anywhere along the path. The validity of both assumptions is discussed. Our calculated values for the electromotive force of the sodium pumpE _Na ^a vary between 146 and 200 mV, which is in agreement with the energy of the ATP/ADP system. There is a distinct indication that, as the electrochemical gradient for sodium opposing the transport is being increased, the emf increases towards an asymptotic value around 200 mV. The relation between the value ofE _Na ^a and the cellular phosphorylation potential for ATP is discussed.     

Brownian dynamics study of flux ratios in sodium channels

Measurements of unidirectional fluxes in ion channels provide one of the experimental methods for studying the steps involved in ion permeation in biological pores. Conventionally, the number of ions in the pore is inferred by fitting the ratio of inward and outward currents to an exponential function with an adjustable parameter known as the flux ratio exponent. Here we investigate the relationship between the number of ions in the pore and the flux ratio exponent in a model sodium channel under a range of conditions. Brownian dynamics simulations enable us to count the precise number of ions in the channel and at the same time measure the currents flowing across the pore in both directions. We show here that the values of the flux ratio exponent n′ ranges between 1 and 3 and is highly dependent on the ionic concentrations in which measurements are made. This is a consequence of the fact that both inward and outward currents are susceptible to saturation with increasing concentration. These results indicate that measurements of the flux ratio exponent cannot be directly related to the number of ions in the pore and that interpretation of such experimental measurements requires careful consideration of the conditions in which the study is made.     

若尔盖高原沼泽湿地N_2O排放通量研究

应用静态箱/气相色谱法,测定了若尔盖高原沼泽N2O排放能量,测定期为该地植物生长期,即2004年4 月末至10月初。结果表明,若尔盖高原沼泽湿地N2O排放通量平均值为0.010 mg·m-2h-1,最大值为0.079 mg·m-2h-1, 最小值为-0.051mg·m-2h-1。高峰排放期为5月,最低排放期为地表水深最大的6月。沼泽湿地N2O排放通量季节变化与沼泽湿地水深呈负相关关系。沼泽湿地N2O排放通量日变化与大气温度呈正相关关系,排放高值出现在午后。若尔盖高原沼泽湿地在植物生长期的年排放总量约为0.159Gg·a-1。     

Extracellular proton sensing of the rat gustatory cyclic nucleotide-gated channel

Elevations of the intracellular levels of cyclic nucleotides appear to cause the cation influx through gustatory cyclic nucleotide-gated (CNGgust) channels expressed in taste cells. Although changes in the oral pH may directly regulate the activity of the CNGgust channel, the mechanism of pH-dependent control of the channel is not understood. In the present study, we combined the whole-cell patch-clamp recording and the site-directed mutagenesis to investigate the effect of extracellular pH on the ion permeation through CNGgust channels expressed in HEK293 cells. Extracellular acidification strongly inhibited ion permeation through open CNGgust channels. Mutation of Glu(289) remarkably attenuated the pH-dependence of the channel, suggesting that Glu(289) in the pore-forming region is a major proton acceptor site. However, the mutant E289A-CNGgust channel possesses the other residual protonation/deprotonation site. The channel activity, tightly regulated by pH(o) and [cNMP](i), suggests the involvement of its pH(o)-dependent ion permeation in taste signal transduction events.     

Ion permeation of pores in model membranes: selectivity,fluctuations and the role of surface charge

Fluctuation of surface charge on pore walls provides a realistic, additional mechanism for generating fluctuation of ionic current and ionic selectivity in narrow pores.     

Flux ratio of valinomycin-mediated K+ fluxes across the human red cell membrane in the presence of the protonophore CCCP

Summary The ratio of valinomycin-mediated unidirectional K⁺ fluxes across the human red cell membrane, has been determined in the presence of the protonophore carbonylcyanidem-chlorophenylhydrazone, CCCP, using the K⁺ net efflux and⁴²K influx. The driving force for the net efflux (V _m –E _K ⁺) has been calculated from the membrane potential, estimated by the CCCP-mediated proton distribution and the Nernst potential for potassium ions across the membrane. An apparent driving potential for the K⁺ net efflux has been calculated from the K⁺ flux ratio, determined in experiments where the valinomycin and CCCP concentrations were varied systematically. This apparent driving force, in conjunction with the actual driving force calculated on basis of the CCCP estimated membrane potential, is used to calculate a flux ratio exponent, which represents an estimate of the deviation of valinomycin-mediated K⁺ transport from unrestricted electrodiffusion, when protonophore is present.In the present work, the flux ratio exponent is found to be 0.90 when the CCCP concentration is 5.0 m and above, while the exponent decreases to about 0.50 when no CCCP is present. The influence of CCCP upon the rate constants in the valinomycin transport cycle is discussed. The significance of this result is that red cell membrane potentials are overestimated, when calculated from valinomycin-mediated potassium isotope fluxes, using a constant field equation.