Noise analysis and performance comparison of low current measurement systems for biomedical applications.

In this paper, we report on the noise analysis of low current measurement systems for biomedical applications and their fundamental limits. We analyzed resistive feedback, capacitive feedback and current amplifier circuits for low current measurement systems. Detailed noise analysis for different biomedical applications are presented and matched with measurement data using a 0.5-µm fabrication process. Based on the theoretical analysis and the corresponding measurement results, the capacitive feedback system provides better noise performance for the measurement of low current than the others. The capacitive feedback circuit is capable of measuring 750 fA RMS at a 10 kHz sampling rate, whereas the resistive feedback provides 4 pA and the current conveyor provides 600 pA at the same bandwidth. This paper provides design guidelines to maximize the performance of low current measuring system for biomedical instrumentation and to provide the best performance available with CMOS technologies.

Noise models and cryo-EM drift correction with a direct-electron camera.

Blurring due to specimen-holder drift is a common occurrence in cryo-EM images. Cameras employing active-pixel sensors are capable of high frame rates such that a single low-dose exposure can be acquired as a series of frames. In this paper we consider the possibility of tracking and compensating for overall drift in typical single-particle specimens through the analysis of frame sequences. A problem that arises in tracking through cross-correlation of frames obtained with the DE-12 camera from Direct Electron LLC is the presence of "hot-pixel noise". This random pattern of bright pixels is highly correlated among frames. We show how a model of this noise can be employed to greatly reduce its effects. A filter function is derived that optimizes the tracking of image shifts by cross-correlation, and we demonstrate the tracking of specimen drift in typical cryo-EM specimens.

An integrated patch-clamp potentiostat with electrode compensation.

We present the first fully integrated implementation of a patch-clamp measurement system with series-access resistance and parasitic capacitive compensation capability. The system was implemented in a 0.5- mum silicon-on-sapphire process and is capable of recording cell membrane currents up to plusmn20 nA, with an rms noise of 5 pA at 10-kHz bandwidth. The system can compensate for the capacitance and resistance of the electrode, up to 20 pF and up to 70% of the series-access resistance, respectively. The die size is 1150 by 700 mum. The power consumption is 300 muW at 3.3 V. The integrated patch-clamp system will be used to fabricate high-throughput planar patch-clamp systems.

Applying hidden Markov models to the analysis of single ion channel activity.

Hidden Markov models have recently been used to model single ion channel currents as recorded with the patch clamp technique from cell membranes. The estimation of hidden Markov models parameters using the forward-backward and Baum-Welch algorithms can be performed at signal to noise ratios that are too low for conventional single channel kinetic analysis; however, the application of these algorithms relies on the assumptions that the background noise be white and that the underlying state transitions occur at discrete times. To address these issues, we present an "H-noise" algorithm that accounts for correlated background noise and the randomness of sampling relative to transitions. We also discuss three issues that arise in the practical application of the algorithm in analyzing single channel data. First, we describe a digital inverse filter that removes the effects of the analog antialiasing filter and yields a sharp frequency roll-off. This enhances the performance while reducing the computational intensity of the algorithm. Second, the data may be contaminated with baseline drifts or deterministic interferences such as 60-Hz pickup. We propose an extension of previous results to consider baseline drift. Finally, we describe the extension of the algorithm to multiple data sets.

Hidden Markov model analysis of intermediate gating steps associated with the pore gate of shaker potassium channels.

Cooperativity among the four subunits helps give rise to the remarkable voltage sensitivity of Shaker potassium channels, whose open probability changes tenfold for a 5-mV change in membrane potential. The cooperativity in these channels is thought to arise from a concerted structural transition as the final step in opening the channel. Recordings of single-channel ionic currents from certain other channel types, as well as our previous recordings from T442S mutant Shaker channels, however, display intermediate conductance levels in addition to the fully open and closed states. These sublevels might represent stepwise, rather than concerted, transitions in the final steps of channel activation. Here, we report a similar fine structure in the closing transitions of Shaker channels lacking the mutation. Describing the deactivation time course with hidden Markov models, we find that two subconductance levels are rapidly traversed during most closing transitions of chimeric, high conductance Shaker channels. The lifetimes of these levels are voltage-dependent, with maximal values of 52 and 22 micros at -100 mV, and the voltage dependences of transitions among these states suggest that they arise from equivalent conformational changes occurring in individual subunits. At least one subconductance level is found to be traversed in normal conductance Shaker channels. We speculate that voltage-dependent conformational changes in the subunits give rise to changes in a "pore gate" associated with the selectivity filter region of the channel, producing the subconductance states. As a control for the hidden Markov analysis, we applied the same procedures to recordings of the recovery from N-type inactivation in Shaker channels. These transitions are found to be instantaneous in comparison.

Potassium channel mechanics.

What is the moving part that switches an ion channel's current on and off? In this issue of Neuron del Camino and Yellen (2001) exploit scanning cysteine mutagenesis and sulfhydryl reagents to show that the intracellular end of the S6 helices forms a mechanical gate for the Shaker potassium channel.

Spherical reconstruction: a method for structure determination of membrane proteins from cryo-EM images.

We propose a new method for single-particle reconstruction, which should be generally applicable to structure determination for membrane proteins. After reconstitution into a small spherical vesicle, a membrane protein takes a particular orientation relative to the membrane normal, and its position in the projected image of the vesicle directly defines two of its three Euler angles of orientation. The spherical constraint imposed by the vesicle effectively reduces the dimensionality of the alignment search from 5 to 3 and simplifies the detection of the particle. Projection images of particles in vesicles collectively take all possible orientations and therefore cover the whole Fourier space. Analysis of images of vesicles in ice showed that the vesicle density is well described by a simple model for membrane electron scattering density. In fitting this model we found that osmotically swollen vesicles remain nearly spherical through the freezing process. These results satisfy the basic experimental requirements for spherical reconstruction. A computer simulation of particles in vesicles showed that this method provides good estimates of the two Euler angles and thus may improve single-particle reconstruction and extend it to smaller membrane proteins.

Electrostatics and the gating pore of Shaker potassium channels.

Various experiments have suggested that the S4 segment in voltage-dependent Na(+) and K(+) channels is in contact with a solvent-accessible cavity. We explore the consequences of the existence of such a cavity through the electrostatic effects on the gating currents of Shaker K(+) channels under conditions of reduced ionic strength S. We observe that approximately 10-fold reductions of intracellular S produce reductions of the measured gating charge of approximately 10%. These effects continue at even lower values of S. The reduction of gating charge when S is reduced by 10-fold at the extracellular surface is much smaller (approximately 2%). Shifts of the Q(V) curve because of a reduced S are small (<10 mV in size), which is consistent with very little fixed surface charge. Continuum electrostatic calculations show that the S effects on gating charge can be explained by the alteration of the local potential in an intracellular conical cavity of 20-24-A depth and 12-A aperture, and a smaller extracellular cavity of 3-A depth and the same aperture. In this case, the attenuation of the membrane potential at low S leads to reduction of the apparent gating charge. We suggest that this cavity is made by a bundle of transmembrane helices, and that the gating charge movement occurs by translocation of charged residues across a thin septum of approximately 3-7 A thickness.

Functional reconstitution and characterization of recombinant human alpha 1-glycine receptors.

By utilizing a baculoviral expression system described previously (Cascio, M., Schoppa, N. E., Grodzicki, R. L., Sigworth, F. J., and Fox, R. O. (1993) J. Biol. Chem. 268, 22135-22142), functional recombinant homomeric human alpha(1)-glycine receptors (GlyR) were overexpressed in insect cell culture, solubilized, purified, and reconstituted into lipid vesicles via gel filtration. Reconstituted GlyR channels were observed to retain native-like activity in single channel recordings of planar bilayers and in flux assays of small unilamellar vesicles, providing evidence that the recombinant homomeric receptor may be functionally reconstituted. This reconstitution is significant in that it indicates that the overexpressed homomeric receptor is an appropriate substrate for subsequent biophysical characterization aimed at the general elucidation of structure-function. Circular dichroism spectroscopy of reconstituted GlyR indicated a low alpha-helical content and a significant fraction of polyproline structure. The small fraction of observed alpha-helix is insufficient to accommodate the four helical transmembrane domains proposed in models for this receptor. By inference, other members of the homologous ligand-gated channel superfamily, which include the ionotropic gamma-aminobutyric acid, acetylcholine, and serotonin receptors, may also be erroneously modeled, and alternate models should be considered.

Voltage sensitivity and gating charge in Shaker and Shab family potassium channels.

The members of the voltage-dependent potassium channel family subserve a variety of functions and are expected to have voltage sensors with different sensitivities. The Shaker channel of Drosophila, which underlies a transient potassium current, has a high voltage sensitivity that is conferred by a large gating charge movement, approximately 13 elementary charges. A Shaker subunit's primary voltage-sensing (S4) region has seven positively charged residues. The Shab channel and its homologue Kv2.1 both carry a delayed-rectifier current, and their subunits have only five positively charged residues in S4; they would be expected to have smaller gating-charge movements and voltage sensitivities. We have characterized the gating currents and single-channel behavior of Shab channels and have estimated the charge movement in Shaker, Shab, and their rat homologues Kv1.1 and Kv2.1 by measuring the voltage dependence of open probability at very negative voltages and comparing this with the charge-voltage relationships. We find that Shab has a relatively small gating charge, approximately 7.5 e(o). Surprisingly, the corresponding mammalian delayed rectifier Kv2.1, which has the same complement of charged residues in the S2, S3, and S4 segments, has a gating charge of 12.5 e(o), essentially equal to that of Shaker and Kv1.1. Evidence for very strong coupling between charge movement and channel opening is seen in two channel types, with the probability of voltage-independent channel openings measured to be below 10(-9) in Shaker and below 4 x 10(-8) in Kv2.1.

Two-microelectrode voltage clamp of Xenopus oocytes: voltage errors and compensation for local current flow.

Oocytes from Xenopus laevis are commonly used as an expression system for ion channel proteins. The most common method for their electrophysiological investigation is the two-microelectrode voltage clamp technique. The quality of voltage clamp recordings obtained with this technique is poor when membrane currents are large and when rapid charging of the membrane is desired. Detailed mathematical modeling of the experimental setup shows that the reasons for this weak performance are the electrical properties of the oocytes and the geometry of the setup. We measured the cytosolic conductivity to be approximately 5 times lower than that of the typical bath solution, and the specific membrane capacitance to be approximately 6 times higher than that of a simple lipid bilayer. The diameter of oocytes is typically approximately 1 mm, whereas the penetration depth of the microelectrodes is limited to approximately 100 microm. This eccentric current injection, in combination with the large time constants caused by the low conductivity and the high capacitance, yields large deviations from isopotentiality that decay slowly with time constants of up to 150 micros. The inhomogeneity of the membrane potential can be greatly reduced by introducing an additional, extracellular current-passing electrode. The geometrical and electrical parameters of the setup are optimized and initial experiments show that this method should allow for faster and more uniform control of membrane potential.

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.

A maximum-likelihood approach to single-particle image refinement.

The alignment of single-particle images fails at low signal-to-noise ratios and small particle sizes, because noise produces false peaks in the cross-correlation function used for alignment. A maximum-likelihood approach to the two-dimensional alignment problem is described which allows the underlying structure to be estimated from large data sets of very noisy images. Instead of finding the optimum alignment for each image, the algorithm forms a weighted sum over all possible in-plane rotations and translations of the image. The weighting factors, which are the probabilities of the image transformations, are computed as the exponential of a cross-correlation function. Simulated data sets were constructed and processed by the algorithm. The results demonstrate a greatly reduced sensitivity to the choice of a starting reference, and the ability to recover structures from large data sets having very low signal-to-noise ratios.

Intermediate conductances during deactivation of heteromultimeric Shaker potassium channels.

A previous study of the T442S mutant Shaker channel revealed activation-coupled subconductance levels that apparently represent kinetic intermediates in channel activation (Zheng, J., and F.J. Sigworth. 1997. J. Gen. Physiol. 110:101-117). We have now extended the study to heteromultimeric channels consisting of various numbers of mutant subunits as well as channels without mutant subunits, all in the background of a chimeric Shaker channel having increased conductance. It has been found that activation-coupled sublevels exist in all these channel types, and are traversed in at least 80% of all deactivation time courses. In symmetric K+ solutions, the currents in the two sublevels have a linear voltage dependence, being 23-44% and 54-70% of the fully open conductance. Sublevels in different channel types share similar voltage dependence of the mean lifetime and similar ion selectivity properties. However, the mean lifetime of each current level depends approximately geometrically on the number of mutant subunits in the channel, becoming shorter in channels having fewer mutant subunits. Each mutant subunit appears to stabilize all of the conducting states by approximately 0.5 kcal/mol. Consistent with previous results in the mutant channel, sublevels in channels with two or no mutant subunits also showed ion selectivities that differ from that of the fully open level, having relatively higher K+ than Rb+ conductances. A model is presented in which Shaker channels have two coupled activation gates, one associated with the selectivity filter and a second associated with the S6 helix bundle.

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.

Activation of Shaker potassium channels. II. Kinetics of the V2 mutant channel.

This second of three papers, in which we functionally characterize activation gating in Shaker potassium channels, focuses on the properties of a mutant channel (called V2), in which the leucine at position 382 (in the Shaker B sequence) is mutated to valine. The general properties of V2's ionic and gating currents are consistent with changes in late gating transitions, in particular, with V2 disrupting the positively cooperative gating process of the normally activating wild type (WT) channel. An analysis of forward and backward rate constants, analogous to that used for WT in the previous paper, indicates that V2 causes little change in the rates for most of the transitions in the activation path, but causes large changes in the backward rates of the final two transitions. Single channel data indicate that the V2 mutation causes moderate changes in the rates of transitions to states that are not in the activation path, but little change in the rates from these states. V2's data also yield insights into the general properties of the activation gating process that could not be readily obtained from the WT channel, including evidence that intermediate transitions have rapid backward rates, and an estimate of a total charge 2 e0 for the final two transitions. Taken together, these data will help constrain an activation gating model in the third paper of this series, while also providing an explanation for V2's effects.

Activation of Shaker potassium channels. III. An activation gating model for wild-type and V2 mutant channels.

A functional kinetic model is developed to describe the activation gating process of the Shaker potassium channel. The modeling in this paper is constrained by measurements described in the preceding two papers, including macroscopic ionic and gating currents and single channel ionic currents. These data were obtained from the normally activating wild-type channel as well as a mutant channel V2, in which the leucine at position 382 has been mutated to a valine. Different classes of models that incorporate Shaker's symmetrical tetrameric structure are systematically examined. Many simple gating models are clearly inadequate, but a model that can account for all of the qualitative features of the data has the channel open after its four subunits undergo three transitions in sequence, and two final transitions that reflect the concerted action of the four subunits. In this model, which we call Scheme 3+2', the channel can also close to several states that are not part of the activation path. Channel opening involves a large total charge movement (10.8 e0), which is distributed among a large number of small steps each with rather small charge movements (between 0.6 and 1.05 e0). The final two transitions are different from earlier steps by having slow backward rates. These steps confer a cooperative mechanism of channel opening at Shaker's activation voltages. In the context of Scheme 3+2', significant effects of the V2 mutation are limited to the backward rates of the final two transitions, implying that L382 plays an important role in the conformational stability of the final two states.

Selectivity changes during activation of mutant Shaker potassium channels.

Mutations of the pore-region residue T442 in Shaker channels result in large effects on channel kinetics. We studied mutations at this position in the backgrounds of NH2-terminal-truncated Shaker H4 and a Shaker -NGK2 chimeric channel having high conductance (Lopez, G.A., Y.N. Jan, and L.Y. Jan. 1994. Nature (Lond.). 367: 179-182). While mutations of T442 to C, D, H, V, or Y resulted in undetectable expression in Xenopus oocytes, S and G mutants yielded functional channels having deactivation time constants and channel open times two to three orders of magnitude longer than those of the parental channel. Activation time courses at depolarized potentials were unaffected by the mutations, as were first-latency distributions in the T442S chimeric channel. The mutant channels show two subconductance levels, 37 and 70% of full conductance. From single-channel analysis, we concluded that channels always pass through the larger subconductance state on the way to and from the open state. The smaller subconductance state is traversed in approximately 40% of activation time courses. These states apparently represent kinetic intermediates in channel gating having voltage-dependent transitions with apparent charge movements of approximately 1.6 e0. The fully open T442S chimeric channel has the conductance sequence Rb+ > NH4+ > K+. The opposite conductance sequence, K+ > NH4+ > Rb+, is observed in each of the subconductance states, with the smaller subconductance state discriminating most strongly against Rb+.

Enhanced closed-state inactivation in a mutant Shaker K+ channel.

Many mutations that shift the voltage dependence of activation in Shaker channels cause a parallel shift of inactivation. The I2 mutation (L382I in the Shaker B sequence) is an exception, causing a 45 mV activation shift with only a 9 mV shift of inactivation midpoint relative to the wildtype (WT) channel. We compare the behavior of WT and I2 Shaker 29-4 channels in macropatch recordings from Xenopus oocytes. The behavior of WT channels can be described by both simple and detailed kinetic models which assume that inactivation proceeds only from the open state. The behavior of I2 channels requires that they inactivate from closed states as well, a property characteristic of voltage-gated sodium channels. A detailed "multiple-state inactivation" model is presented that describes both activation and inactivation of I2 channels. The results are consistent with the view that residue L382 is associated with the receptor for the inactivation particles in Shaker channels.