Asymmetric Interplay Between K+ and Blocker and Atomistic Parameters From Physiological Experiments Quantify K+ Channel Blocker Release.

Modulating the activity of ion channels by blockers yields information on both the mode of drug action and on the biophysics of ion transport. Here we investigate the interplay between ions in the selectivity filter (SF) of K+ channels and the release kinetics of the blocker tetrapropylammonium in the model channel KcvNTS. A quantitative expression calculates blocker release rate constants directly from voltage-dependent ion occupation probabilities in the SF. The latter are obtained by a kinetic model of single-channel currents recorded in the absence of the blocker. The resulting model contains only two adjustable parameters of ion-blocker interaction and holds for both symmetric and asymmetric ionic conditions. This data-derived model is corroborated by 3D reference interaction site model (3D RISM) calculations on several model systems, which show that the K+ occupation probability is unaffected by the blocker, a direct consequence of the strength of the ion-carbonyl attraction in the SF, independent of the specific protein background. Hence, KcvNTS channel blocker release kinetics can be reduced to a small number of system-specific parameters. The pore-independent asymmetric interplay between K+ and blocker ions potentially allows for generalizing these results to similar potassium channels.

Distinct lipid bilayer compositions have general and protein-specific effects on K+ channel function.

It has become increasingly apparent that the lipid composition of cell membranes affects the function of transmembrane proteins such as ion channels. Here, we leverage the structural and functional diversity of small viral K+ channels to systematically examine the impact of bilayer composition on the pore module of single K+ channels. In vitro-synthesized channels were reconstituted into phosphatidylcholine bilayers ± cholesterol or anionic phospholipids (aPLs). Single-channel recordings revealed that a saturating concentration of 30% cholesterol had only minor and protein-specific effects on unitary conductance and gating. This indicates that channels have effective strategies for avoiding structural impacts of hydrophobic mismatches between proteins and the surrounding bilayer. In all seven channels tested, aPLs augmented the unitary conductance, suggesting that this is a general effect of negatively charged phospholipids on channel function. For one channel, we determined an effective half-maximal concentration of 15% phosphatidylserine, a value within the physiological range of aPL concentrations. The different sensitivity of two channel proteins to aPLs could be explained by the presence/absence of cationic amino acids at the interface between the lipid headgroups and the transmembrane domains. aPLs also affected gating in some channels, indicating that conductance and gating are uncoupled phenomena and that the impact of aPLs on gating is protein specific. In two channels, the latter can be explained by the altered orientation of the pore-lining transmembrane helix that prevents flipping of a phenylalanine side chain into the ion permeation pathway for long channel closings. Experiments with asymmetrical bilayers showed that this effect is leaflet specific and most effective in the inner leaflet, in which aPLs are normally present in plasma membranes. The data underscore a general positive effect of aPLs on the conductance of K+ channels and a potential interaction of their negative headgroup with cationic amino acids in their vicinity.

Extended beta distributions open the access to fast gating in bilayer experiments-assigning the voltage-dependent gating to the selectivity filter.

Lipid bilayers provide many benefits for ion channel recordings, such as control of membrane composition and transport molecules. However, they suffer from high membrane capacitance limiting the bandwidth and impeding analysis of fast gating. This can be overcome by fitting the deviations of the open-channel noise from the baseline noise by extended beta distributions. We demonstrate this analysis step-by-step by applying it to the example of viral K+  channels (Kcv), from the choice of the gating model through the fitting process, validation of the results, and what kinds of results can be obtained. These voltage sensor-less channels show profoundly voltage-dependent gating with dwell times in the closed state of about 50 µs. Mutations assign it to the selectivity filter.

A simple recipe for setting up the flux equations of cyclic and linear reaction schemes of ion transport with a high number of states: The arrow scheme.

The calculation of flux equations or current-voltage relationships in reaction kinetic models with a high number of states can be very cumbersome. Here, a recipe based on an arrow scheme is presented, which yields a straightforward access to the minimum form of the flux equations and the occupation probability of the involved states in cyclic and linear reaction schemes. This is extremely simple for cyclic schemes without branches. If branches are involved, the effort of setting up the equations is a little bit higher. However, also here a straightforward recipe making use of so-called reserve factors is provided for implementing the branches into the cyclic scheme, thus enabling also a simple treatment of such cases.

Effect of cytosolic pH on inward currents reveals structural characteristics of the proton transport cycle in the influenza A protein M2 in cell-free membrane patches of Xenopus oocytes.

Transport activity through the mutant D44A of the M2 proton channel from influenza virus A was measured in excised inside-out macro-patches of Xenopus laevis oocytes at cytosolic pH values of 5.5, 7.5 and 8.2. The current-voltage relationships reveal some peculiarities: 1. "Transinhibition", i.e., instead of an increase of unidirectional outward current with increasing cytosolic H(+) concentration, a decrease of unidirectional inward current was found. 2. Strong inward rectification. 3. Exponential rise of current with negative potentials. In order to interpret these findings in molecular terms, different kinetic models have been tested. The transinhibition basically results from a strong binding of H(+) to a site in the pore, presumably His37. This assumption alone already provides inward rectification and exponential rise of the IV curves. However, it results in poor global fits of the IV curves, i.e., good fits were only obtained for cytosolic pH of 8.2, but not for 7.5. Assuming an additional transport step as e.g. caused by a constriction zone at Val27 resulted in a negligible improvement. In contrast, good global fits for cytosolic pH of 7.5 and 8.2 were immediately obtained with a cyclic model. A "recycling step" implies that the protein undergoes conformational changes (assigned to Trp41 and Val27) during transport which have to be reset before the next proton can be transported. The global fit failed at the low currents at pHcyt = 5.5, as expected from the interference of putative transport of other ions besides H(+). Alternatively, a regulatory effect of acidic cytosolic pH may be assumed which strongly modifies the rate constants of the transport cycle.

Creation of a reactive oxygen species-insensitive Kcv channel.

The current of the minimal viral K(+) channel Kcv(PCBV-1) heterologously expressed in Xenopus oocytes is strongly inhibited by reactive oxygen species (ROS) like H(2)O(2). Possible targets for the ROS effect are two cysteines (C53 and C79) and four methionines (M1, M15, M23, and M26). The C53A/C79A and M23L/M26L double mutations maintained the same ROS sensitivity as the wild type. However, M15L as a single mutant or in combination with C53A/C79A and/or M23L/M26L caused a complete loss of sensitivity to H(2)O(2). These results indicate a prominent role of M15 at the cytosolic end of the outer transmembrane helix for gating of Kcv(PCBV-1). Furthermore, even though the channel lacks a canonical voltage sensor, it exhibits a weak voltage sensitivity, resulting in a slight activation in the millisecond range after a voltage step to negative potentials. The M15L mutation inverts this kinetics into an inactivation, underlining the critical role of this residue for gating. The negative slope of the I-V curves of M15L is the same as in the wild type, indicating that the selectivity filter is not involved.

Ca2+ block and flickering both contribute to the negative slope of the IV curve in BK channels.

Single-channel current-voltage (IV) curves of human large-conductance, voltage- and Ca(2+)-activated K(+) (BK) channels are quite linear in 150 mM KCl. In the presence of Ca(2+) and/or Mg(2+), they show a negative slope conductance at high positive potentials. This is generally explained by a Ca(2+)/Mg(2+) block as by Geng et al. (2013. J. Gen. Physiol. http://dx.doi.org/10.1085/jgp.201210955) in this issue. Here, we basically support this finding but add a refinement: the analysis of the open-channel noise by means of ß distributions reveals what would be found if measurements were done with an amplifier of sufficient temporal resolution (10 MHz), namely that the block by 2.5 mM Ca(2+) and 2.5 mM Mg(2+) per se would only cause a saturating curve up to +160 mV. Further bending down requires the involvement of a second process related to flickering in the microsecond range. This flickering is hardly affected by the presence or absence of Ca(2+)/Mg(2+). In contrast to the experiments reported here, previous experiments in BK channels (Schroeder and Hansen. 2007. J. Gen. Physiol. http://dx.doi.org/10.1085/jgp.200709802) showed saturating IV curves already in the absence of Ca(2+)/Mg(2+). The reason for this discrepancy could not be identified so far. However, the flickering component was very similar in the old and new experiments, regardless of the occurrence of noncanonical IV curves.

Modulation of enrofloxacin binding in OmpF by Mg2+ as revealed by the analysis of fast flickering single-porin current.

One major determinant of the efficacy of antibiotics on gram-negative bacteria is the passage through the outer membrane. During transport of the fluoroquinolone enrofloxacin through the trimeric outer membrane protein OmpF of Escherichia coli, the antibiotic interacts with two binding sites within the pore, thus partially blocking the ionic current. The modulation of one affinity site by Mg(2+) reveals further details of binding sites and binding kinetics. At positive membrane potentials, the slow blocking events induced by enrofloxacin in Mg(2+)-free media are converted to flickery sojourns at the highest apparent current level (all three pores flickering). This indicates weaker binding in the presence of Mg(2+). Analysis of the resulting amplitude histograms with ß distributions revealed the rate constants of blocking (k(OB)) and unblocking (k(BO)) in the range of 1,000 to 120,000 s(-1). As expected for a bimolecular reaction, k(OB) was proportional to blocker concentration and k(BO) independent of it. k(OB) was approximately three times lower for enrofloxacin coming from the cis side than from the trans side. The block was not complete, leading to a residual conductivity of the blocked state being ∼25% of that of the open state. Interpretation of the results has led to the following model: fast flickering as caused by interaction of Mg(2+) and enrofloxacin is related to the binding site at the trans side, whereas the cis site mediates slow blocking events which are also found without Mg(2+). The difference in the accessibility of the binding sites also explains the dependency of k(OB) on the side of enrofloxacin addition and yields a means of determining the most plausible orientation of OmpF in the bilayer. The voltage dependence suggests that the dipole of the antibiotic has to be adequately oriented to facilitate binding.

Fast and slow gating are inherent properties of the pore module of the K+ channel Kcv.

Kcv from the chlorella virus PBCV-1 is a viral protein that forms a tetrameric, functional K+ channel in heterologous systems. Kcv can serve as a model system to study and manipulate basic properties of the K+ channel pore because its minimalistic structure (94 amino acids) produces basic features of ion channels, such as selectivity, gating, and sensitivity to blockers. We present a characterization of Kcv properties at the single-channel level. In symmetric 100 mM K+, single-channel conductance is 114+/-11 pS. Two different voltage-dependent mechanisms are responsible for the gating of Kcv. "Fast" gating, analyzed by beta distributions, is responsible for the negative slope conductance in the single-channel current-voltage curve at extreme potentials, like in MaxiK potassium channels, and can be explained by depletion-aggravated instability of the filter region. The presence of a "slow" gating is revealed by the very low (in the order of 1-4%) mean open probability that is voltage dependent and underlies the time-dependent component of the macroscopic current.

Using a five-state model for fitting amplitude histograms from MaxiK channels: beta-distributions reveal more than expected.

Fast gating of ion channels with rate constants higher than the corner frequency of the recording set-up can be evaluated by fitting so-called beta distributions to measured amplitude histograms. Up to now, this was preferentially done for O-C Markov sub-models with one open and one closed state. Here, a fit of the amplitude histograms from MaxiK (BK) single-channel records was achieved with a five-state model with two open and three closed states including three open-close transitions with rate constants higher than the corner frequency (20 kHz) of the inevitable low-pass filter of the recording system. The numerical values of the rate constants of these transitions enabled a nearly one-to-one relationship between typical regions of the histograms and the reactions in the Markov model. These characteristic features are the width of the peak at the apparent single-channel current, the side slopes at the open and at the closed peak, and the depth of the valley between the two peaks. However, the simplex routine alone was incapable of finding the solution but could do so if guided by hand along a suggested strategy.

Interference of shot noise of open-channel current with analysis of fast gating: patchers do not (Yet) have to care.

Microsecond gating of ion channels can be evaluated by fitting beta distributions to amplitude histograms of measured time series. The shape of these histograms is determined not only by the rate constants of the gating process (in relation to the filter frequency) but also by baseline noise and shot noise, resulting from the stochastic nature of ion flow. Under normal temporal resolution, the small shot noise can be ignored. This simplification may no longer be legitimate when rate constants reach the range above 1 mus(-1). Here, the influence of shot noise is studied by means of simulated time series for several values of single-channel current of the fully open state and baseline noise. Under realistic optimal conditions (16 pA current, 1 pA noise, 50 kHz bandwidth), ignoring the shot noise leads to an underestimation of the rate constants above 1 mus(-1) by a factor of about 2.5. However, in that range, the scatter of the evaluated rate constants is at least of the same magnitude, obscuring the systematic error. The incorporation of shot noise into the analysis will become more important when amplifiers with significantly reduced noise become available.

Tl+-induced micros gating of current indicates instability of the MaxiK selectivity filter as caused by ion/pore interaction.

Patch clamp experiments on single MaxiK channels expressed in HEK293 cells were performed at high temporal resolution (50-kHz filter) in asymmetrical solutions containing 0, 25, 50, or 150 mM Tl+ on the luminal or cytosolic side with [K+] + [Tl+] = 150 mM and 150 mM K+ on the other side. Outward current in the presence of cytosolic Tl+ did not show fast gating behavior that was significantly different from that in the absence of Tl+. With luminal Tl+ and at membrane potentials more negative than -40 mV, the single-channel current showed a negative slope resistance concomitantly with a flickery block, resulting in an artificially reduced apparent single-channel current I(app). The analysis of the amplitude histograms by beta distributions enabled the estimation of the true single-channel current and the determination of the rate constants of a simple two-state O-C Markov model for the gating in the bursts. The voltage dependence of the gating ratio R = I(true)/I(app) = (k(CO) + k(OC))/k(CO) could be described by exponential functions with different characteristic voltages above or below 50 mM Tl(+). The true single-channel current I(true) decreased with Tl+ concentrations up to 50 mM and stayed constant thereafter. Different models were considered. The most likely ones related the exponential increase of the gating ratio to ion depletion at the luminal side of the selectivity filter, whereas the influence of [Tl+] on the characteristic voltage of these exponential functions and of the value of I(true) were determined by [Tl+] at the inner side of the selectivity filter or in the cavity.

Four-mode gating model of fast inactivation of sodium channel Nav1.2a.

Basic principles of the gating mechanisms of neuronal sodium channels, especially the fast inactivation process, were revealed by a quantitative analysis of the effects of the chemically irreversible modifying agent chloramine T. The compound is known to enhance the open probability of sodium channels by interfering with the inactivation process. The key for the deduction of structure-function relationships was obtained from the analysis of single-channel patch-clamp data, especially the finding that chloramine T-induced modification of inactivation occurred in four steps. These steps were termed modes 1-4 (four-mode gating model), and their temporal sequence was always the same. The kinetic analysis of single-channel traces with an improved two-dimensional dwell-time fit revealed the possible mechanism related to each mode. Similarities to the kinetics of the sodium channel mutant F1489Q led to the assignment of modes 1 and 2 to transient defects in the locking of the inactivation particle (hinged lid). In the third mode, the hinged lid was unable to lock permanently. Finally, in mode 4, the apparent single-channel current was reduced, which could be explained by fast gating, presumably related to the selectivity filter.

Saturation and microsecond gating of current indicate depletion-induced instability of the MaxiK selectivity filter.

Patch clamp experiments on single MaxiK channels expressed in HEK293 cells were performed with a high temporal resolution (50-kHz filter) in symmetrical solutions with 50, 150, or 400 mM KCl and 2.5 mM CaCl(2) and 2.5 mM MgCl(2). At membrane potentials >+100 mV, the single-channel current showed a negative slope resistance, concomitantly with a flickery block, which was not influenced by Ca(2+) or Mg(2+). The analysis of the amplitude histograms by beta distributions revealed that current in this voltage range was reduced by two effects: rate limitation at the cytosolic side of the pore and gating with rate constants 10-20-fold higher than the cutoff frequency of the filter (i.e., dwell times in the microsecond range). The data were analyzed in terms of a model that postulates a coupling between both effects; if the voltage over the selectivity filter withdraws ions from the cavity at a higher rate than that of refilling from the cytosol, the selectivity filter becomes instable because of ion depletion, and current is interrupted by the resulting flickering. The fit of the IV curves revealed a characteristic voltage of 35 mV. In contrast, the voltage dependence of the gating factor R, i.e., the ratio between true and apparent single-channel current, could be fitted by exponentials with a characteristic voltage of 60 mV, suggesting that only part of the transmembrane potential is felt by the flux through the selectivity filter.

Determination of DPPH Radical Oxidation Caused by Methanolic Extracts of Some Microalgal Species by Linear Regression Analysis of Spectrophotometric Measurements.

The demonstrated modified spectrophotometric method makes use of the 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical and its specific absorbance properties. Theabsorbance decreases when the radical is reduced by antioxidants. In contrast to otherinvestigations, the absorbance was measured at a wavelength of 550 nm. This wavelengthenabled the measurements of the stable free DPPH radical without interference frommicroalgal pigments. This approach was applied to methanolic microalgae extracts for twodifferent DPPH concentrations. The changes in absorbance measured vs. the concentrationof the methanolic extract resulted in curves with a linear decrease ending in a saturationregion. Linear regression analysis of the linear part of DPPH reduction versus extractconcentration enabled the determination of the microalgae's methanolic extractsantioxidative potentials which was independent to the employed DPPH concentrations. Theresulting slopes showed significant differences (6 - 34 µmol DPPH g-1 extractconcentration) between the single different species of microalgae (Anabaena sp.,Isochrysis galbana, Phaeodactylum tricornutum, Porphyridium purpureum, Synechocystissp. PCC6803) in their ability to reduce the DPPH radical. The independency of the signal on the DPPH concentration is a valuable advantage over the determination of the EC50 value.

A model for correcting the fluorescence signal from a free-falling depth profiler.

Measuring chlorophyll fluorescence at five different wavelengths provides the discrimination of four phytoplankton groups. Here the problems associated with a free-falling depth profiler for phytoplankton discrimination are considered. When F0, F, and Fm are determined sequentially in the same measuring cell, then the algae inside the cell have a different light history. It depends on their different locations in the cell as caused by the induction curve of chlorophyll fluorescence. Mathematical algorithms are developed which enable the calculation of the concentrations of individual phytoplankton groups from the integral fluorescence signal (averaged for 1s) for different velocities of the falling probe. The theory requires the knowledge of the fluorescence behaviour of phytoplankton in stationary suspensions. The predictions of the model are compared with measurements in flowing suspensions containing chlorophyta, cyanobacteria, cryptophyta and diatoms. The comparison shows the reliability of the algorithms. The application of the algorithms is indispensable for dark-adapted cells and is less important for light-adapted cells.

The power of two-dimensional dwell-time analysis for model discrimination, temporal resolution, multichannel analysis and level detection.

Two-dimensional (2D) dwell-time analysis of time series of single-channel patch-clamp current was improved by employing a Hinkley detector for jump detection, introducing a genetic fit algorithm, replacing maximum likelihood by a least square criterion, averaging over a field of 9 or 25 bins in the 2D plane and normalizing per measuring time, not per events. Using simulated time series for the generation of the "theoretical" 2D histograms from assumed Markov models enabled the incorporation of the measured filter response and noise. The effects of these improvements were tested with respect to the temporal resolution, accuracy of the determination of the rate constants of the Markov model, sensitivity to noise and requirement of open time and length of the time series. The 2D fit was better than the classical hidden Markov model (HMM) fit in all tested fields. The temporal resolution of the two most efficient algorithms, the 2D fit and the subsequent HMM/beta fit, enabled the determination of rate constants 10 times faster than the corner frequency of the low-pass filter. The 2D fit was much less sensitive to noise. The requirement of computing time is a problem of the 2D fit (100 times that of the HMM fit) but can now be handled by personal computers. The studies revealed a fringe benefit of 2D analysis: it can reveal the "true" single-channel current when the filter has reduced the apparent current level by averaging over undetected fast gating.