Mechanotransduction by Membrane Proteins: The speed of the hair cell mechanotransducer channel revealed by fluctuation analysis

Although mechanoelectrical transducer (MET) channels have been extensively studied, uncertainty persists about their molecular architecture and single-channel conductance. We made electrical measurements from mouse cochlear outer hair cells (OHCs) to reexamine the MET channel conductance comparing two different methods. Analysis of fluctuations in the macroscopic currents showed that the channel conductance in apical OHCs determined from nonstationary noise analysis was about half that of single-channel events recorded after tip link destruction. We hypothesized that this difference reflects a bandwidth limitation in the noise analysis, which we tested by simulations of stochastic fluctuations in modeled channels. Modeling indicated that the unitary conductance depended on the relative values of the channel activation time constant and the applied low-pass filter frequency. The modeling enabled the activation time constant of the channel to be estimated for the first time, yielding a value of only a few microseconds. We found that the channel conductance, assayed with both noise and recording of single-channel events, was reduced by a third in a new deafness mutant, Tmc1 p.D528N. Our results indicate that noise analysis is likely to underestimate MET channel amplitude, which is better characterized from recordings of single-channel events.     

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.     

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 μs⁻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 μs⁻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.     

Recruiting RyRs to Open in a Ca2+ Release Unit: Single-RyR Gating Properties Make RyR Group Dynamics

In cardiac myocytes, clusters of type-2 ryanodine receptors (RyR2s) release Ca²⁺ from the sarcoplasmic reticulum (SR) via a positive feedback mechanism in which fluxed Ca²⁺ activates nearby RyRs. Although the general principles of this are understood, less is known about how single-RyR gating properties define the RyR group dynamics in an array of many channels. Here, we examine this using simulations with three models of RyR gating that have identical open probabilities: the commonly used two-state Markov gating model, one that utilizes multiple exponentials to fit single-channel open time (OT) and closed time (CT) distributions, and an extension of this multiexponential model that also includes experimentally measured correlations between single-channel OTs and CTs. The simulations of RyR clusters that utilize the multiexponential gating model produce infrequent Ca²⁺ release events with relatively few open RyRs. Ca²⁺ release events become even smaller when OT/CT correlations are included. This occurs because the correlations produce a small but consistent bias against recruiting more RyRs to open during the middle of a Ca²⁺ release event, between the initiation and termination phases (which are unaltered compared to the uncorrelated simulations). In comparison, the two-state model produces frequent, large, and long Ca²⁺ release events because it had a recruitment bias in favor of opening more RyRs. This difference stems from the two-state model’s single-RyR OT and CT distributions being qualitatively different from the experimental ones. Thus, the details of single-RyR gating can profoundly affect SR Ca²⁺ release even if open probability and mean OTs and CTs are identical. We also show that Ca²⁺ release events can terminate spontaneously without any reduction in SR [Ca²⁺], luminal regulation, Ca²⁺-dependent inactivation, or physical coupling between RyRs when Ca²⁺ flux is below a threshold value. This supports and extends the pernicious attrition/induction decay hypothesis that SR Ca²⁺ release events terminate below a threshold Ca²⁺ flux.     

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.     

K-current fluctuations in inward-rectifying channels of frog skeletal muscle

Summary K currents and K-current fluctuations were recorded in inwardly rectifying K channels of frog skeletal muscle under voltage-clamp conditions. External application of 0.2 to 10mm Cs reduces the inward mean K current but produces a distinct increase of the spectral density of K-current fluctuations. The additional fluctuations arise from the random blocking by Cs ions. From the variance of current fluctuations, the steady-state current and the probability of the open unblocked channel an effective single-channel conductance ^* was calculated. ^* strongly depends on the external Cs concentration (7.8 pS at 0.2mm Cs, 2.1 pS at 10mm Cs). This dependence is interpreted in terms of a two-step blocking process: (1) a fast exchange of Cs ions between the external solution and a first binding site inside the channel which leads to the Cs-modulated effective single-channel conductance, and (2) a slow Cs binding to a second site deeper in the channel which produces the observed current fluctuations. With this hypothesis we obtained a real single-channel conductance of 10 pS and a real density ofn4 inwardly rectifying channels per m² of muscle surface area.     

Single-Channel Properties of IKs Potassium Channels

Expressed in Xenopus oocytes, KvLQT1 channel subunits yield a small, rapidly activating, voltage- dependent potassium conductance. When coexpressed with the minK gene product, a slowly activating and much larger potassium current results. Using fluctuation analysis and single-channel recordings, we have studied the currents formed by human KvLQT1 subunits alone and in conjunction with human or rat minK subunits. With low external K⁺, the single-channel conductances of these three channel types are estimated to be 0.7, 4.5, and 6.5 pS, respectively, based on noise analysis at 20 kHz bandwidth of currents at +50 mV. Power spectra computed over the range 0.1 Hz–20 kHz show a weak frequency dependence, consistent with current interruptions occurring on a broad range of time scales. The broad spectrum causes the apparent single-channel current value to depend on the bandwidth of the recording, and is mirrored in very “flickery” single-channel events of the channels from coexpressed KvLQT1 and human minK subunits. The increase in macroscopic current due to the presence of the minK subunit is accounted for by the increased apparent single-channel conductance it confers on the expressed channels. The rat minK subunit also confers the property that the outward single-channel current is increased by external potassium ions.     

Activation of Shaker Potassium Channels : I. Characterization of Voltage-dependent Transitions

The conformational changes associated with activation gating in Shaker potassium channels are functionally characterized in patch-clamp recordings made from Xenopus laevis oocytes expressing Shaker channels with fast inactivation removed. Estimates of the forward and backward rates for transitions are obtained by fitting exponentials to macroscopic ionic and gating current relaxations at voltage extremes, where we assume that transitions are unidirectional. The assignment of different rates is facilitated by using voltage protocols that incorporate prepulses to preload channels into different distributions of states, yielding test currents that reflect different subsets of transitions. These data yield direct estimates of the rate constants and partial charges associated with three forward and three backward transitions, as well as estimates of the partial charges associated with other transitions. The partial charges correspond to an average charge movement of 0.5 e₀ during each transition in the activation process. This value implies that activation gating involves a large number of transitions to account for the total gating charge displacement of 13 e₀. The characterization of the gating transitions here forms the basis for constraining a detailed gating model to be described in a subsequent paper of this series.     

Quantal charge redistributions accompanying the structural transitions of sodium channels

Asymmetric displacement currents, I _g , associated with the gating of nerve sodium channels have been recorded in cell-attached macropatches of Xenopus laevis oocytes injected with exogenous mRNA coding for rat-brain-II sodium channels. The I _g properties were found to be similar to those of gating currents previously observed in native nerve preparations. I _g fluctuations were measured in order to ascertain the discreteness of the conformational changes which precede the channel opening. The autocorrelation of the fluctuations is consistent with a shot-like character of the elementary I _g contributions. The variance of the fluctuations indicates that most of the gating-charge movement that accompanies the activation of a single sodium channel occurs in 2 to 3 brief packets, each carrying an equivalent of about 2.3 electron charges.     

Monte Carlo uncertainty analysis of dose estimates in radiochromic film dosimetry with single-channel and multichannel algorithms

PurposeTo provide a multi-stage model to calculate uncertainty in radiochromic film dosimetry with Monte-Carlo techniques. This new approach is applied to single-channel and multichannel algorithms.Material and methodsTwo lots of Gafchromic EBT3 are exposed in two different Varian linacs. They are read with an EPSON V800 flatbed scanner. The Monte-Carlo techniques in uncertainty analysis provide a numerical representation of the probability density functions of the output magnitudes. From this numerical representation, traditional parameters of uncertainty analysis as the standard deviations and bias are calculated. Moreover, these numerical representations are used to investigate the shape of the probability density functions of the output magnitudes. Also, another calibration film is read in four EPSON scanners (two V800 and two 10000XL) and the uncertainty analysis is carried out with the four images.ResultsThe dose estimates of single-channel and multichannel algorithms show a Gaussian behavior and low bias. The multichannel algorithms lead to less uncertainty in the final dose estimates when the EPSON V800 is employed as reading device. In the case of the EPSON 10000XL, the single-channel algorithms provide less uncertainty in the dose estimates for doses higher than four Gy.ConclusionA multi-stage model has been presented. With the aid of this model and the use of the Monte-Carlo techniques, the uncertainty of dose estimates for single-channel and multichannel algorithms are estimated. The application of the model together with Monte-Carlo techniques leads to a complete characterization of the uncertainties in radiochromic film dosimetry.     

Biophysical characterization of OprB,a glucose-inducible porin ofPseudomonas aeruginosa

OprB, a glucose-inducible porin ofP. aeruginosa, was characterized by black lipid bilayer analysis and circular dichroism spectroscopy. Black lipid bilayer analysis of OprB revealed a single-channel conductance of 25 pS, the presence of a glucose binding site with aK _s for glucose of 380 ± 40 mM, and the formation of channels with a strong selection for anions. Analysis ofP. aeruginosa OprB circular dichroism spectra revealed a high sheet content (40%) which is within the range of that determined for other porins. Values obtained from black lipid bilayer analysis were compared to those previously obtained for OprB ofP. putida [Saravolacet al. (1991).J. Bacteriol. 173, 4970–4976] and indicated extensive similarities in the single-channel conductance and glucose-binding properties of these two porins. Immunological and amino terminal sequence analysis revealed a high degree of homology. Of the first 14 amino terminal residues, 12 were identical. A major difference between the two porins was found in their ion selectivity. WhereasP. aeruginosa OprB is anion selective,P. putida OprB and other carbohydrate selective porins are known to be cation selective.     

Molecular Dynamics Simulations With First Order Coupling to a Bath of Constant Chemical Potential

Abstract

In molecular dynamics simulations the temperature or pressure can be controlled by applying a weak first-order coupling to a bath of constant temperature or pressure. This weak coupling technique to control system properties using a first-order relaxation equation is analyzed from a statistical mechanics point of view. It is shown, how the weak coupling scheme can be generalized and applied to a bath of contstant chemical potential. The presented method, to which in the following will be referred to as chemical potential weak coupling, is applied and tested on a Lennard-Jones fluid. The thermodynamic quantities known from the literature are accuratly reproduced.

The temperature and chemical potential weak coupling methods aim to sample the canonical and grand canonical ensembles respectively. By analyzing the fluctuations in energy and number of particles, the tight relation between the ensembles and the distributions obtained from the weak coupling simulations is demonstrated. The influence of the choice of the coupling parameters on the quality of the approximation of the ensemble distribution is discussed.     

Recent advances in maximum entropy biasing techniques for molecular dynamics

ABSTRACT

This review describes recent advances by the authors and others on the topic of incorporating experimental data into molecular simulations through maximum entropy methods. Methods which incorporate experimental data improve accuracy in molecular simulation by minimally modifying the thermodynamic ensemble. This is especially important where force fields are approximate, such as when employing coarse-grain models, or where high accuracy is required, such as when attempting to mimic a multiscale self-assembly process. The authors review here the experiment directed simulation (EDS) and experiment directed metadynamics (EDM) methods that allow matching averages and distributions in simulations, respectively. Important system-specific considerations are discussed such as using enhanced sampling simultaneously, the role of pressure, treating uncertainty, and implementations of these methods. Recent examples of EDS and EDM are reviewed including applications to ab initio molecular dynamics of water, incorporating environmental fluctuations inside of a macromolecular protein complex, improving RNA force fields, and the combination of enhanced sampling with minimal biasing to model peptides     

A Combined 2D-NMR and Molecular Dynamics Analysis of the Structure of the Actinomycin D: d(ATGCAT)2 Complex

Abstract

We present a comparative analysis of an NMR experiment and molecular and harmonic dynamics simulations of an actinomycin D: d(ATGCAT)₂ complex. A comparison of NOE measurements and 1/R⁶ weighted proton-proton distances confirm the general correctness of the Actinomycin D-DNA model proposed by Sobell. There are, however, some substantial differences between the proton-proton distances inferred from the NOE results and the molecular and harmonic dynamics simulations. The remaining discrepancies could either come from contributions of other conformations to the average properties of the complex or from uncertainties in the NMR distance analysis. An analysis of the molecular dynamics helix properties, sugar puckers, hydrogen bonding, rms fluctuations and torsional properties are qualitatively consistent with those from previous simulations, but the presence of an intercalated drug leads to some new structural and dynamical features.     

Charges in the Cytoplasmic Pore Control Intrinsic Inward Rectification and Single-Channel Properties in Kir1.1 and Kir2.1 Channels

An E224G mutation of the Kir2.1 channel generates intrinsic inward rectification and single-channel fluctuations in the absence of intracellular blockers. In this study, we showed that positively charged residues H226, R228 and R260, near site 224, regulated the intrinsic inward rectification and single-channel properties of the E224G mutant. By carrying out systematic mutations, we found that the charge effect on the intrinsic inward rectification and single-channel conductance is consistent with a long-range electrostatic mechanism. A Kir1.1 channel where the site equivalent to E224 in the Kir2.1 channel is a glycine residue does not show inward rectification or single-channel fluctuations. The G223K and N259R mutations of the Kir1.1 channel induced intrinsic inward rectification and reduced the single-channel conductance but did not generate large open-channel fluctuations. Substituting the cytoplasmic pore of the E224G mutant into the Kir1.1 channel induced open-channel fluctuations and intrinsic inward rectification. The single-channel conductance of the E224G mutant showed inward rectification. Also, a voltage-dependent gating mechanism decreased open probability during depolarization and contributed to the intrinsic inward rectification in the E224G mutant. In addition to an electrostatic effect, a close interaction of K⁺ with channel pore may be required for generating open-channel fluctuations in the E224G mutant.     

Allosteric Effects of Permeating Cations on Gating Currents during K+ Channel Deactivation

K⁺ channel gating currents are usually measured in the absence of permeating ions, when a common feature of channel closing is a rising phase of off-gating current and slow subsequent decay. Current models of gating invoke a concerted rearrangement of subunits just before the open state to explain this very slow charge return from opening potentials. We have measured gating currents from the voltage-gated K⁺ channel, Kv1.5, highly overexpressed in human embryonic kidney cells. In the presence of permeating K⁺ or Cs⁺, we show, by comparison with data obtained in the absence of permeant ions, that there is a rapid return of charge after depolarizations. Measurement of off-gating currents on repolarization before and after K⁺ dialysis from cells allowed a comparison of off-gating current amplitudes and time course in the same cells. Parallel experiments utilizing the low permeability of Cs⁺ through Kv1.5 revealed similar rapid charge return during measurements of off-gating currents at E_Cs. Such effects could not be reproduced in a nonconducting mutant (W472F) of Kv1.5, in which, by definition, ion permeation was macroscopically absent. This preservation of a fast kinetic structure of off-gating currents on return from potentials at which channels open suggests an allosteric modulation by permeant cations. This may arise from a direct action on a slow step late in the activation pathway, or via a retardation in the rate of C-type inactivation. The activation energy barrier for K⁺ channel closing is reduced, which may be important during repetitive action potential spiking where ion channels characteristically undergo continuous cyclical activation and deactivation.     

The nicotinic acetylcholine receptor: from molecular model to single-channel conductance

The nicotinic acetylcholine receptor (nAChR) is the archetypal ligand-gated ion channel. A model of the α7 homopentameric nAChR is described in which the pore-lining M2 helix bundle is treated atomistically and the remainder of the molecule is treated as a “low resolution” cylinder. The surface charge on the cylinder is derived from the distribution of charged amino acids in the amino acid sequence (excluding the M2 segments). This model is explored in terms of its predicted single-channel properties. Based on electrostatic potential profiles derived from the model, the one-dimensional Poisson-Nernst-Planck equation is used to calculate single-channel current/voltage curves. The predicted single-channel conductance is three times higher (ca. 150 pS) than that measured experimentally, and the predicted ion selectivity agrees with the observed cation selectivity of nAChR. Molecular dynamics (MD) simulations are used to estimate the self-diffusion coefficients (D) of water molecules within the channel. In the narrowest region of the pore, D is reduced ca. threefold relative to that of bulk water. Assuming that the diffusion of ions scales with that of water, this yields a revised prediction of the single-channel conductance (ca. 50 pS) in good agreement with the experimental value. We conclude that combining atomistic (MD) and continuum electrostatics calculations is a promising approach to bridging the gap between structure and physiology of ion channels. Received: 2 August 1999 / Revised version: 5 November 1999 / Accepted: 9 November 1999     

A beam model for focused proton pencil beams

IntroductionWe present a beam model for Monte Carlo simulations of the IBA pencil beam scanning dedicated nozzle installed at the Skandion Clinic. Within the nozzle, apart from entrance and exit windows and the two ion chambers, the beam traverses vacuum, allowing for a beam that is convergent downstream of the nozzle exit.Materials and methodsWe model the angular, spatial and energy distributions of the beam phase space at the nozzle exit with single Gaussians, controlled by seven energy dependent parameters. The parameters were determined from measured profiles and depth dose distributions. Verification of the beam model was done by comparing measured and GATE acquired relative dose distributions, using plan specific log files from the machine to specify beam spot positions and energy.ResultsGATE-based simulations with the acquired beam model could accurately reproduce the measured data. The gamma index analysis comparing simulated and measured dose distributions resulted in >95% global gamma index pass rates (3%/2 mm) for all depths.ConclusionThe developed beam model was found to be sufficiently accurate for use with GATE e.g. for applications in quality assurance (QA) or patient motion studies with the IBA pencil beam scanning dedicated nozzles.     

Patch-clamp studies in human macrophages: Single-channel and whole-cell characterization of two K+ conductances

Summary Human peripheral blood monocytes cultured for varying periods of time were studied using whole-cell and single-channel patch-clamp recording techniques. Whole-cell recordings revealed both an outward K current activating at potentials >20 mV and an inwardly rectifying K current present at potentials negative to –60 mV. Tail currents elicited by voltage steps that activated outward current reversed nearE _K, indicating that the outward current was due to a K conductance. TheI–V curve for the macroscopic outward current was similar to the mean single-channelI–V curve for the large conductance (240 pS in symmetrical K) calcium-activated K channel present in these cells. TEA and charybdotoxin blocked the whole-cell outward current and the single-channel current. Excised and cell-attached single-channel data showed that calcium-activated K channels were absent in freshly isolated monocytes but were present in >85% of patches from macrophages cultured for >7 days. Only 35% of the human macrophages cultured for >7 days exhibited whole-cell inward currents. The inward current was blocked by external barium and increased when [K] _o increased. Inward-rectifying single-channel currents with a conductance of 28 pS were present in cells exhibiting inward whole-cell currents. These single-channel currents are similar to those described in detail in J774.1 cells (L.C. McKinney & E.K. Gallin,J. Membrane Biol. 103:41–53, 1988).