Site-specific ion occupation in the selectivity filter causes voltage-dependent gating in a viral K+ channel.

Many potassium channels show voltage-dependent gating without a dedicated voltage sensor domain. This is not fully understood yet, but often explained by voltage-induced changes of ion occupation in the five distinct K+ binding sites in the selectivity filter. To better understand this mechanism of filter gating we measured the single-channel current and the rate constant of sub-millisecond channel closure of the viral K+ channel KcvNTS for a wide range of voltages and symmetric and asymmetric K+ concentrations in planar lipid membranes. A model-based analysis employed a global fit of all experimental data, i.e., using a common set of parameters for current and channel closure under all conditions. Three different established models of ion permeation and various relationships between ion occupation and gating were tested. Only one of the models described the data adequately. It revealed that the most extracellular binding site (S0) in the selectivity filter functions as the voltage sensor for the rate constant of channel closure. The ion occupation outside of S0 modulates its dependence on K+ concentration. The analysis uncovers an important role of changes in protein flexibility in mediating the effect from the sensor to the gate.

Strengths and limits of Beta distributions as a means of reconstructing the true single-channel current in patch clamp time series with fast gating.

Single-channel current seems to be one of the most obvious characteristics of ion transport. But in some cases, its determination is more complex than anticipated at first glance. Problems arise from fast gating in time series of patch-clamp current, which can lead to a reduced apparent (measured) single-channel current. Reduction is caused by undetected averaging over closed and open intervals in the anti-aliasing filter. Here it is shown that fitting the measured amplitude histograms by Beta distributions is an efficient tool of reconstructing the true current level from measured data. This approach becomes even more powerful when it is applied to amplitude distributions-per-level. Simulated time series are employed to show that the error sum is a good guideline for finding the correct current level. Furthermore, they show that a Markov model smaller than the one used for gating analysis can be used for current determination (mostly O-C, i.e., open-closed). This increases the reliability of the Beta fit. The knowledge of the true current level is not only important for the understanding of the biophysical properties of the channel. It is also a prerequisite for the correct determination of the rate constants of gating. The approach is applied to measured data. The examples reveal the limits of the analysis imposed by the signal-to-noise ratio and the shape of the amplitude distribution. One application shows that the negative slope of the I-V curve of the human MaxiK channel expressed in HEK293 cells is caused by fast gating.

A subsequent fit of time series and amplitude histogram of patch-clamp records reveals rate constants up to 1 per microsecond.

Fast gating in time series of patch-clamp current demands powerful tools to reveal the rate constants of the adequate Hidden Markov model. Here, two approaches are presented to improve the temporal resolution of the direct fit of the time series. First, the prediction algorithm is extended to include intermediate currents between the nominal levels as caused by the anti-aliasing filter. This approach can reveal rate constants that are about 4 times higher than the corner frequency of the anti-aliasing filter. However, this approach is restricted to time series with very low noise. Second, the direct fit of the time series is combined with a beta fit, i.e., a fit of the deviations of the amplitude histogram from the Gaussian distribution. Since the "theoretical" amplitude histograms for higher-order Bessel filters cannot be calculated by analytical tools, they are generated from simulated time series. In a first approach, a simultaneous fit of the time series and of the Beta fit is tested. This simultaneous fit, however, inherits the drawbacks of both approaches, not the benefits. More successful is a subsequent fit: The fit of the time series yields a set of rate constants. The subsequent Beta fit uses the slow rate constants of the fit of the time series as fixed parameters and the optimization algorithm is restricted to the fast ones. The efficiency of this approach is illustrated by means of time series obtained from simulation and from the dominant K+ channel in Chara. This shows that temporal resolution can reach the microsecond range.

Effect of CO2 supply on formation of reactive oxygen species in Arabidopsis thaliana.

Light-induced generation of reactive oxygen species (ROS) in 2-week-old leaves of Arabidopsis thaliana was studied by means of the ROS-sensitive dyes nitroblue tetrazolium (NBT) and 5-(and-6)-carboxy-2',7'-dichlorodihydrofluorescein diacetate (DCF-DA). Superposition of pictures of chlorophyll fluorescence and DCF fluorescence indicated that the origin of ROS was in the chloroplasts. Experiments were done with zero, 0.1, or 10 mM NaHCO3 in the infiltration medium. Energy quenching in photosystem II was higher under low CO2 concentrations as measured by chlorophyll fluorescence. DCF fluorescence showed that CO2 deficiency led to an increase of ROS generation. In contrast, the photosystem II inhibitor 3-(3,4-dichlorophenyl)-1,1-dimethylurea reduced the light-induced increase of DCF fluorescence. This indicates that ROS production does not primarily result from over-reduction of photosystem II as caused by impeding electron flow in the electron transfer chain. More likely, it is an effect of diverting electron flux normally aimed at carboxylation in the Calvin cycle to other sinks more prone to the generation of toxic radicals. There was no significant effect of salicyl hydroxamate (a blocker of the alternative oxidase), showing that the mitochondrial electron transfer chain seems to play a minor role as already indicated by the superposition of chlorophyll and DCF fluorescence.

Light-induced decrease in DCF fluorescence of wheat leaves in the presence of salicyl hydroxamate.

5-(and-6)-Carboxy-2',7'-dichlorodihydrofluorescein diacetate (DCF-DA), a permeative indicator of oxidative stress, was loaded into dissected leaves of wheat in order to monitor the temporal development of reactive oxygen species. DCF fluorescence was found to be constant under dark conditions. Upon loading the leaves with salicyl hydroxamate, a blocker of the alternative oxidase, DCF fluorescence linearly increased in the dark. This indicates a function of alternative oxidase in preventing reactive oxygen radicals in the mitochondria. Upon illumination, the DCF signal decreased within 5 min. As illuminated chloroplasts would increase the load of reactive oxygen species, the observed decrease cannot be assigned to the production of reactive oxygen species in the chloroplasts. Three different putative mechanisms are considered which all assign an important role to light-induced delivery of NAD(P)H: (1) direct quenching of DCF fluorescence by light-generated NAD(P)H, (2) light-stimulated activation of scavenging enzymes, or (3) redirection of mitochondrial electron fluxes as caused by the delivery of excess redox equivalents (NADH) from the chloroplasts.

Distributions-per-level: a means of testing level detectors and models of patch-clamp data.

Level or jump detectors generate the reconstructed time series from a noisy record of patch-clamp current. The reconstructed time series is used to create dwell-time histograms for the kinetic analysis of the Markov model of the investigated ion channel. It is shown here that some additional lines in the software of such a detector can provide a powerful new means of patch-clamp analysis. For each current level that can be recognized by the detector, an array is declared. The new software assigns every data point of the original time series to the array that belongs to the actual state of the detector. From the data sets in these arrays distributions-per-level are generated. Simulated and experimental time series analyzed by Hinkley detectors are used to demonstrate the benefits of these distributions-per-level. First, they can serve as a test of the reliability of jump and level detectors. Second, they can reveal beta distributions as resulting from fast gating that would usually be hidden in the overall amplitude histogram. Probably the most valuable feature is that the malfunctions of the Hinkley detectors turn out to depend on the Markov model of the ion channel. Thus, the errors revealed by the distributions-per-level can be used to distinguish between different putative Markov models of the measured time series.

A reduced model of the fluorescence from the cyanobacterial photosynthetic apparatus designed for the in situ detection of cyanobacteria.

Fluorometric determination of the chlorophyll (Chl) content of cyanobacteria is impeded by the unique structure of their photosynthetic apparatus, i.e., the phycobilisomes (PBSs) in the light-harvesting antennae. The problems are caused by the variations in the ratio of the pigment PC to Chl a resulting from adaptation to varying environmental conditions. In order to include cyanobacteria in fluorometric analysis of algae, a simplified energy distribution model describing energy pathways in the cyanobacterial photosynthetic apparatus was conceptualized. Two sets of mathematical equations were derived from this model and tested. Fluorescence of cyanobacteria was measured with a new fluorometer at seven excitation wavelength ranges and at three detection channels (650, 685 and 720 nm) in vivo. By employing a new fit procedure, we were able to correct for variations in the cyanobacterial fluorescence excitation spectra and to account for other phytoplankton signals. The effect of energy-state transitions on the PC fluorescence emission of PBSs was documented. The additional use of the PC fluorescence signal in combination with our recently developed mathematical approach for phytoplankton analysis based on Chl fluorescence spectroscopy allows a more detailed study of cyanobacteria and other phytoplankton in vivo and in situ.

Gating models of the anomalous mole-fraction effect of single-channel current in Chara.

The dependence of single-channel current on the Tl+/K+ mole fraction exhibiting a minimum at [Tl+]/[K+] of about 1:15 is proportional to open probability in bursts. Five models are suggested to explain modulation of gating by the Tl+/K+ ratio. Three models start from a channel with 4 identical subunits, each with an allosteric binding site for K+ or Tl+. In the first model, ion binding is directly observable as a transition from one Markov state to another. This model can explain the dependence of the apparent single-channel current on Tl+ concentrations. However, the predicted linear dependence on ion concentrations of the apparent rate constants was not observed in measurements in 25 or 250 mM KNO3 and 250 mM Tl NO3. The second model can overcome this problem by introducing saturation kinetics for ion binding. In the third model, gating is caused by inherent vibrations of the protein, and the rate constants of the related transitions depend on the occupation of the allosteric sites. The fourth model is based on the foot-in-the-door approach with the essential feature that two K+ ions in the selectivity filter are necessary to keep the pore radius suitable for K+ ions. The fifth model is also a foot-in-the-door model, but non-Markovian because, similar to model 3, it is assumed that the conformation of the protein (and thus the rate constants of the Markov model of the time series) depends on the force exerted by the temporal average over the states of a Markov model of ion occupation. These ions may reside in the pore itself or outside.

A new level detector for ion channel analysis.

The algorithm proposed here for automatic level detection in noisy time series of patch-clamp current is based on the detection of jump-free sections in the time series. The detector moves along the time series and uses a chi(2) test for the detection of jumps. When a jump is detected, the mean value, the variance and the length of the preceding jump-free section are stored. A Student's t-test was employed for the assignment of detected jump-free sections to discrete levels of the Markov model and for rejection of all sections with multiple assignments. The choice of the two significance levels is based on a 3-D diagram displaying the average number of detected levels from several time series vs. the significance levels of jump detection and of level assignment. The correct one is selected out of several plateaus with integer number of levels by means of the criterion of minimum scatter or other plausibility considerations. The test has been applied to simulated data obtained from a 2-state model and a 5-state aggregated Markov model, and the influences of SNR and of gating frequency are shown. Finally, the performance of the level detector is compared with a fit-by-eye and with a fit of the amplitude histogram by a sum of gaussians. At high noise, the fit of amplitude histograms failed, whereas the other two approaches were about equal.

A chi(2) test for model determination and sublevel detection in ion channel analysis.

A chi(2) test is proposed that provides a means of discriminating between different Markov models used for the description of a measured (patch clamp) time series. It is based on a test statistic constructed from the measured and the predicted number of transitions between the current levels. With a certain probability, this test statistic is below a threshold if the model with a reduced number of degrees of freedom is compatible with the data. A second criterion is provided by the dependence of the test statistic on the number of data points. For data generated by the alternative model it increases linearly. The applicability of this test for verifying and rejecting models is illustrated by means of time series generated by two distinct channels with different conductances and by time series generated by one channel with two conductance levels. For noisy data, a noise correction is proposed, which eliminates noise-induced false jumps that would interfere with the test. It is shown that the test can also be extended to aggregated Markov models.

A fluorometric method for the differentiation of algal populations in vivo and in situ.

Fingerprints of excitation spectra of chlorophyll (Chl) fluorescence can be used to differentiate 'spectral groups' of microalgae in vivo and in situ in, for example, vertical profiles within a few seconds. The investigated spectral groups of algae (green group, Chlorophyta; blue, Cyanobacteria; brown, Heterokontophyta, Haptophyta, Dinophyta; mixed, Cryptophyta) are each characterised by a specific composition of photosynthetic antenna pigments and, consequently, by a specific excitation spectrum of the Chl fluorescence. Particularly relevant are Chl a, Chl c, phycocyanobilin, phycoerythrobilin, fucoxanthin and peridinin. A laboratory-based instrument and a submersible instrument were constructed containing light-emitting diodes to excite Chl fluorescence in five distinct wavelength ranges. Norm spectra were determined for the four spectral algal groups (several species per group). Using these norm spectra and the actual five-point excitation spectrum of a water sample, a separate estimate of the respective Chl concentration is rapidly obtained for each algal group. The results of dilution experiments are presented. In vivo and in situ measurements are compared with results obtained by HPLC analysis. Depth profiles of the distribution of spectral algal groups taken over a time period of few seconds are shown. The method for algae differentiation described here opens up new research areas, monitoring and supervision tasks related to photosynthetic primary production in aquatic environments.

Bundle sheath cells of small veins in maize leaves are the location of uptake from the xylem.

Rb(+) as a tracer for K(+) was used to test the hypothesis that uptake of K(+) from xylem vessels of small veins into the symplast of maize leaves occurs at the xylem/bundle sheath cell interface. 22.5 min after immersing cut leaves into 20 mM RbCl+1 mM KCl, Rb(+) appeared in the cells of the leaves. Sections of these leaves were freeze-dried. In cryo-thin sections (5 microm), (85)Rb(+) and (41)K(+) content was determined by laser microprobe mass analysis with a large resolution of about 1 microm. Determining the ratio of (85)Rb(+) to (41)K(+) in the cell walls and cytosols of bundle sheath cells, mesophyll cells, and in the cells between the xylem elements resulted in the following picture: In small veins, Rb(+) entered the symplast directly at the xylem/bundle sheath cell interface.

The anomalous mole fraction effect in Chara: gating at the edge of temporal resolution.

The anomalous mole fraction effect (AMFE) of the K(+) channel in excised patches of the tonoplast of Chara showed a minimum of apparent open-channel current at 20 mM Tl(+) and 230 mM K(+). Time series obtained at a sampling rate of 100 kHz (filter 25 kHz) were analyzed by three methods to find out whether the AMFE results from an effect on gating or on the conductivity of the open state. Fitting the amplitude histograms by a superposition of gaussians showed a broadening in the presence of Tl(+). Dwell-time analysis based on an O-O-C-C-C model failed to evaluate rate constants above the filter frequency. Thus, the absence of any reduction of apparent open-channel current in time series simulated with the evaluated rate constants could not be taken as evidence against the hypothesis of gating. Finally, a direct fit of the measured time series using five different 5-state Hidden Markov models revealed that the presence of Tl(+) changed the rate constants in such a way that the number of transitions into the short-lived open state (30 micros) increased strongly compared to those in the absence of Tl(+). These models explain 25% reduction of apparent single-channel current amplitude through a rapid gating mechanism.

Different pH-dependences of K+ channel activity in bundle sheath and mesophyll cells of maize leaves.

The isolation of bundle sheath protoplasts from leaves of Zea mays L. for patch clamp whole-cell experiments presents special problems caused by the suberin layer surrounding these cells. These problems were overcome by the isolation technique described here. Two different types of whole-cell response were found: a small response caused by MB-1 (maize bundle sheath conductance type 1) which was instantaneously activated, and another caused by MB-2 (maize bundle sheath conductance type 2) consisting of an instantaneous response (maize bundle sheath K+ instantaneous current type 2; MB-KI2) similar to but stronger than the current through MB-1 plus a small time-dependent outward rectifying component (maize bundle sheath activated outward rectifying current; MB-AOR) with voltage-dependent delayed activation. The occurrence of MB-AOR was often accompanied by a smaller contribution from an inward rectifying channel at negative potentials. Activation of MB-2 required ATP. It is suggested that MB-1 and MB-2 are related to bundle sheath cells with and without direct contact with the xylem vessels. In mesophyll cells, only one type of response caused by MM-2 (maize mesophyll conductance type 2) was found with an instantaneous (maize mesophyll K+ instantaneous current type 2, MM-KI2) and a voltage-dependent delayed component (maize mesophyll activated outward rectifying current, MM-AOR). The most striking difference between bundle sheath and mesophyll cells was the pH dependence of K+ uptake. At pH 7.2, uptake of K+ by MB-2 was identical to that by MM-2 over the whole voltage range. However, acidification stimulated K+ conductance in bundle sheath cells, whereas a decrease was found for MM-2. At pH 6.15, the bundle sheath channel MB-2 had more than a 10-fold higher K+ uptake at positive and negative potentials than MM-2. The channel MB-1, too, was stimulated by low pH. This seems to indicate a putative role for MB-1 and MB-2 in charge balance during uptake of nutrients via cotransport from the xylem into the symplasm.

Fluorescence clamp: A direct measure of fluxes into and out of the antenna pool of Photosystem II.

Fluorescence clamp (FC) is a method of directly measuring the fluxes out of Photosystem II antenna. This is achieved by a feed-back loop which controls the light intensity of light emitting diodes in order to keep the amplitude of modulated chlorophyll fluorescence constant, and by taking the intensity or the current fed into the light emitting diodes as a measure of the fluxes. Saturating flashes serve to distinguish between fluxes into thermal deactivation and into the photosynthetic electron transfer chain (ETC). As FC is only active in the light period of the measuring light, the background signal (induced by actinic light) is compensated by a second feed-back loop in the dark period of the measuring light. Equations are provided for the interpretation of the FC signals. This includes the quenching parameters of chlorophyll fluorescence, the flux into the electron transfer chain and the redox state of Q(A). Experiments are presented which show that traditional fluorescence (LC) and FC measurements yield the same results. However, the FC method provides a better presentation of fluxes as the scaling factor (flux/signal) is constant for all states of Photosystem II. This leads to a simpler analysis of quenching mechanisms. Examples are given which show that the co-existing quenching mechanisms with different effects on photochemical and non-photochemical fluxes can be better identified by FC rather than by LC.

Temperature sensing by plants: the primary characteristics of signal perception and calcium response.

Cold elicits an immediate rise in the cytosolic free calcium concentration ([Ca2+]c) of plant cells. We have studied the concerted action of the three underlying mechanisms, namely sensing, sensitisation and desensitisation, which become important when plants in the field are subjected to changes in temperature. We applied different regimes of temperature changes with well-defined cooling rates to intact roots of Arabidopsis thaliana expressing the calcium-indicator, aequorin. Our results indicate that temperature sensing is mainly dependent on the cooling rate, dT/dt, whereas the absolute temperature T is of less importance. Arabidopsis roots were found to be sensitive to cooling rates of less than dT/dt = 0.01 degrees C/s. However, at cooling rates below 0.003 degrees C/s (i.e. cooling 10 degrees C in 1 h) there is no detectable [Ca2+]c response at all. At low temperature, the sensitivity of the plant cold-detection system is increased. This in turn produces greater cooling-induced [Ca2+]c elevations. Prolonged or repeated cold treatment attenuates the [Ca2+]c responses to subsequent episodes of cooling.

Low-pH-mediated elevations in cytosolic calcium are inhibited by aluminium: a potential mechanism for aluminium toxicity.

Aluminium, the most abundant metal in the earth's crust, is highly toxic to most plant species. One of the prevailing dogmas is that aluminium exerts this effect by disrupting cellular calcium homeostasis. However, recent research gives strongly conflicting results: aluminium was shown to provoke either an increase or a decrease in cytosolic free calcium concentration ([Ca2+]c). To solve this question, we have adopted a novel approach: [Ca2+]c measurements in intact plant roots as opposed to isolated cells, and the correlative measurements of intracellular and external pH. The results obtained show that plant roots respond to low external pH by a sustained elevation in [Ca2+]c. In the presence of aluminium, this pH-mediated elevation in [Ca2+]c does not occur, therefore any potential calcium-mediated protection against low pH is likely to be irreversibly inhibited. The severity of the inhibitory effect of aluminium on [Ca2+]c depends on the concentration of external calcium, thus perhaps explaining why the effects of aluminium toxicity are ameliorated in calcium-rich soils. It seems possible that a primary toxic effect of aluminium might be to impair calcium-mediated plant defence responses against low pH.

Repetitive Ca2+ spikes in a unicellular green alga.

Cytosolic Ca2+ activity ([Ca2+]cy) and membrane potential were measured simultaneously in the unicellular green alga Eremosphaera viridis. Steady state [Ca2+]cy was about 160 nM. A 'light-off' stimulus induced a transient elevation of [Ca2+]cy ([Ca2+]cy spike) in parallel with a transient hyperpolarization of the plasma membrane. Caffeine and Sr2+, known to release Ca2+ from intracellular stores in animal cells, induced repetitive [Ca2+]cy spikes in Eremosphaera which were always accompanied by parallel repetitive transient hyperpolarizations. These transient hyperpolarizations could be used as an indicator for [Ca2+]cy spikes. Repetitive [Ca2+]cy spikes in Eremosphaera were similar to repetitive [Ca2+]cy spikes in excitable animal cells. The mechanisms underlying these [Ca2+]cy oscillations seem to be comparable in animal and plant cells.

Gating and permeation models of plant channels.

Models of different level are applied to plant membrane transport. For the evaluation of I/V curves, models based on enzyme kinetics, limitation by diffusion and the ion well are described. Physical models of ion-ion interaction deal with the Woodhull model, the multi-site single-file ion pore, the ion-ion ion-water interaction model and the effect of screening. The discussion of channel gating starts with pre-patch evidence of gating and the biological importance of gating. State models play a dominant role in the analysis of patch clamp records. Gating may strongly interfere with permeation models. With respect to this, the limits of temporal resolution are of great importance. The effects of Na(+) and Tl(+) are examples of the influence of fast gating on modelling and the problems of its detection. The highest level of modelling is achieved when the knowledge about the structure of channels is employed for the modelling of gating. Major topics in this field are blockade by ions and phosphorylation.

Estimation of kinetic rate constants from multi-channel recordings by a direct fit of the time series.

The maximum-likelihood technique for the direct estimation of rate constants from the measured patch clamp current is extended to the analysis of multi-channel recordings, including channels with subconductance levels. The algorithm utilizes a simplified approach for the calculation of the matrix exponentials of the probability matrix from the rate constants of the Markov model of the involved channel(s) by making use of the Kronecker sum and product. The extension to multi-channel analysis is tested by the application to simulated data. For these tests, three different channel models were selected: a two-state model, a three-state model with two open states of different conductance, and a three-state model with two closed states. For the simulations, time series of these models were calculated from the related first-order, finite-state, continuous-time Markov processes. Blue background noise was added, and the signals were filtered by a digital filter similar to the anti-aliasing low-pass. The tests showed that the fit algorithm revealed good estimates of the original rate constants from time series of simulated records with up to four independent and identical channels even in the case of signal-to-noise ratios being as low as 2. The number of channels in a record can be determined from the dependence of the likelihood on channel number. For large enough data sets, it takes on a maximum when the assumed channel number is equal to the "true" channel number.