Imperfect space clamp permits electrotonic interactions between inhibitory and excitatory synaptic conductances, distorting voltage clamp recordings

The voltage clamp technique is frequently used to examine the strength and composition of synaptic input to neurons. Even accounting for imperfect voltage control of the entire cell membrane ("space clamp"), it is often assumed that currents measured at the soma are a proportional indicator of the postsynaptic conductance. Here, using NEURON simulation software to model somatic recordings from morphologically realistic neurons, we show that excitatory conductances recorded in voltage clamp mode are distorted significantly by neighboring inhibitory conductances, even when the postsynaptic membrane potential starts at the reversal potential of the inhibitory conductance. Analogous effects are observed when inhibitory postsynaptic currents are recorded at the reversal potential of the excitatory conductance. Escape potentials in poorly clamped dendrites reduce the amplitude of excitatory or inhibitory postsynaptic currents recorded at the reversal potential of the other conductance. In addition, unclamped postsynaptic inhibitory conductances linearize the recorded current-voltage relationship of excitatory inputs comprising AMPAR and NMDAR-mediated components, leading to significant underestimation of the relative contribution by NMDARs, which are particularly sensitive to small perturbations in membrane potential. Voltage clamp accuracy varies substantially between neurons and dendritic arbors of different morphology; as expected, more reliable recordings are obtained from dendrites near the soma, but up to 80% of the synaptic signal on thin, distant dendrites may be lost when postsynaptic interactions are present. These limitations of the voltage clamp technique may explain how postsynaptic effects on synaptic transmission could, in some cases, be attributed incorrectly to presynaptic mechanisms.     

Compensation for resistance in series with excitable membranes.

Extracellular resistance in series (Rs) with excitable membranes can give rise to significant voltage errors that distort the current records in voltage-clamped membranes. Electrical methods for measurement of and compensation for such resistances are described and evaluated. Measurement of Rs by the conventional voltage jump in response to a current step is accurate but the measurement of sine-wave admittance under voltage-clamp conditions is better, having about a fivefold improvement in resolution (+/- 0.1 omega cm2) over the conventional method. Conventional feedback of the membrane current signal to correct the Rs error signal leads to instability of the voltage clamp when approximately two-thirds of the error is corrected. We describe an active electronic bridge circuit that subtracts membrane capacitance from the total membrane current and allows full, yet stable, compensation for the voltage error due to ionic currents. Furthermore, this method provides not only fast and accurate control of the membrane potential in response to a command step, but also fast recovery following an abrupt change in the membrane conductance. Marked changes in the kinetics and amplitude of ionic currents resulting from full compensation for Rs are shown for several typical potential patterns.     

A numerical approach to ion channel modelling using whole-cell voltage-clamp recordings and a genetic algorithm

The activity of trans-membrane proteins such as ion channels is the essence of neuronal transmission. The currently most accurate method for determining ion channel kinetic mechanisms is single-channel recording and analysis. Yet, the limitations and complexities in interpreting single-channel recordings discourage many physiologists from using them. Here we show that a genetic search algorithm in combination with a gradient descent algorithm can be used to fit whole-cell voltage-clamp data to kinetic models with a high degree of accuracy. Previously, ion channel stimulation traces were analyzed one at a time, the results of these analyses being combined to produce a picture of channel kinetics. Here the entire set of traces from all stimulation protocols are analysed simultaneously. The algorithm was initially tested on simulated current traces produced by several Hodgkin-Huxley–like and Markov chain models of voltage-gated potassium and sodium channels. Currents were also produced by simulating levels of noise expected from actual patch recordings. Finally, the algorithm was used for finding the kinetic parameters of several voltage-gated sodium and potassium channels models by matching its results to data recorded from layer 5 pyramidal neurons of the rat cortex in the nucleated outside-out patch configuration. The minimization scheme gives electrophysiologists a tool for reproducing and simulating voltage-gated ion channel kinetics at the cellular level.     

Chloride channels in toad skin

A study of the voltage and time dependence of a transepithelial Cl- current in toad skin (Bufo bufo) by the voltage-clamp method leads to the conclusion that potential has a dual role for Cl- transport. One is to control the permeability of an apical membrane Cl-pathway, the other is to drive Cl- ions through this pathway. Experimental analysis of the gating kinetics is rendered difficult owing to a contamination of the gated currents by cellular ion redistribution currents. To obtain insight into the effects of accumulation-depletion currents on voltage clamp currents of epithelial membranes, a mathematical model of the epithelium has been developed for computer analysis. By assuming that the apical membrane Cl- permeability is governed by a single gating variable (Hodgkin-Huxley kinetics), the model predicts fairly well steady-state current-voltage curves, the time course of current activations from a closed state, and the dependence of unidirectional fluxes on potential. Other predictions of the model do not agree with experimental findings, and it is suggested that the gating kinetics are governed by rate coefficients that also depend on the holding potential. Evidence is presented that Cl- transport through open channels does not obey the constant-field equation.     

Electrophysiological properties of macrophages

Electrophysiological studies indicate that the macrophage can display at least two different K conductances, a Ca-mediated K conductance and an inward rectifying K conductance, as well as an electrogenic Na+-K+ pump. Spontaneous hyperpolarizations associated with a Ca-mediated K permeability have been noted in all types of macrophages studied. Similar membrane hyperpolarizations can be elicited by a variety of stimuli that presumably increase intracellular calcium. These include mechanical and electrical stimulation as well as exposure to endotoxin-activated serum, chemotactic peptides, and the Ca ionophore A23187. Recent patch clamp studies on macrophages demonstrated channel activity that probably corresponds to currents through the inward rectifying K conductance previously described with current clamp techniques. With the advent of the patch clamp, this and other conductances can be effectively examined by using both whole-cell voltage clamp and patch recordings in a variety of different macrophages, including small freshly isolated cells.     

Ion conductances related to development of repetitive firing in mouse retinal ganglion neurons in situ

ABSTRACT: In the retina, the ability to encode graded depolarizations into spike trains of variable frequency appears to be a specific property of retinal ganglion neurons (RGNs). To deduce the developmental changes in ion conductances underlying the transition from single to repetitive firing, patch-clamp recordings were performed in the isolated mouse retina between embryonic day 15 (E15) and postnatal day 5 (P5). Immature neurons of the E15 retina were selected according to their capacity to generate voltage-activated Na+ currents (I(Na)(v)). Identification of P5 RGNs was based on retrograde labeling, visualization of the axon, or the amplitude of I(Na)(v). At E15, half of the cells were excitable but none of them generated more than one spike. At P5, all cells were excitable and a majority discharged in tonic fashion. Ion conductances subserving maintenance of repetitive discharge were identified at P5 by exposure to low extracellular Ca2+, Cd2+, and charybdotoxin, all of which suppressed repetitive discharge. omega-Conotoxin GVIA and nifedipine had no effect. We compared passive membrane properties and a variety of voltage-activated ion channels at E15 and P5. It was found that the density of high voltage-activated (HVA) Ca2+ currents increased in parallel with the development of repetitive firing, while the density of Ni2+-sensitive low voltage-activated (LVA) Ca2+ currents decreased. Changes in density and activation kinetics of tetrodotoxin-sensitive Na+ currents paralleled changes in firing thresholds and size of action potentials, but seemed to be unrelated to maintenance of repetitive firing. Densities of A-type K+ currents and delayed rectifier currents did not change. The results suggest that HVA Ca2+ channels, and among them a toxin-resistant subtype, are specifically engaged in activation of Ca2+-sensitive K+ conductance and thereby account for frequency coding in postnatal RGNs.     

Transfer properties of neuronal dendrites with tonically activated conductances

The somatopetal current transfer was studied in the mathematical models of a reconstructed brainstem motoneuron with tonically activated excitatory synaptic inputs uniformly distributed over dendritic arborization. The soma and axon provided a constant passive leak. The extrasynaptic dendritic membrane was either passive or active (of a Hodgkin-Huxley type). The longitudinal membrane current density (per unit path length) was used as an estimate of the current transfer effectiveness of different dendritic paths. Introduction of a steady uniform voltage-independent conductance per unit membrane area simulated such a synaptic activation. This actions always produced a spatially inhomogeneous membrane depolarization decaying from the distal dendritic tips toward the soma. The reason for such an inhomogeneity was the preponderance of somatopetal over somatofugal input conductance at every site in the dendrites with sealed distal ends and a leaky somatic end. In active dendrites, partial voltage-dependent extrasynaptic conductances followed this depolarization according to their activation-inactivation kinetics. The greater the local depolarization, the greater the contribution of the non-inactivating potassium conductance to the total membrane conductance. The contribution of the inactivated sodium conductance was one order of magnitude smaller. Correspondingly, the effective equilibrium potential of the total transmembrane current became spatially inhomogeneous and shifted to the potassium equilibrium potential. In the passive dendrites, the equilibrium potential remained spatially homogeneous. Inhomogeneities of the dendritic geometry (abrupt change in the diameter and, especially, asymmetrical branching) caused characteristic perturbations in the voltage gradient, so that the path profiles of the voltage, conductances, and currents diverged. This indicated a geometry-induced separation of the dendritic paths in their transfer effectiveness. Active dendrites of the same geometry were less effective than passive ones due to the effect of the potassium conductance associated with the hyperpolarizing equilibrium potential.     

Multiple-state model of ionic channel in reproducing the time course of electrophysiological events.

BACKGROUND: The predictions of the Hodgkin-Huxley model do not accurately fit all the measurements of voltage-clamp currents, gating charge and single-channel currents. There are many quantitative differences between the predicted and measured characteristics of the sodium and potassium channels. For example, the two-state gate model has exponential onset kinetics, whereas the sodium and potassium conductances show S-shaped activation and the sodium conductance shows an exponential inactivation. In this paper we shall examine a more general channel model that can more faithfully represent the measured properties of ionic channels in the membrane of the excitable cell. METHODS: The model is based on the generalisation of the notion of a channel with a discrete set of states. Each state has state attributes such as the state conductance, state ionic current and state gating charge. These variables can have quite different waveforms in time, in contrast with a two-state gate channel model, in which all have the same waveforms. RESULTS: The kinetics of all variables are equivalent: gating and ionic currents give equivalent information about channel kinetics; both the equilibrium values of the current and the time constants are functions of membrane potential. The results are in almost perfect concordance with the experimental data regarding the characteristics of nerve impulse. CONCLUSIONS: The expected values of the gating charge and the ionic conductance are weighted sums of the state occupancy probabilities, but the weights differ: for the expected value of the gating charge the weights are the state gating charges and for the expected value of the ionic conductance the weights are the state conductances. Since these weights are different, the expected values of the gating charge and the ionic conductance will differ.     

Early development of voltage-dependent sodium currents in cultured mouse spinal cord neurons

Spinal cord neurons were dissociated from 13-day embryonic mice and grown in culture for 1-28 days. Sodium currents of neurons in culture for 1-2 days were compared with those in culture for 2-4 weeks, using the whole-cell voltage clamp method. Rapid neurite outgrowth created space clamp limitations so that unclamped neuritic sodium action potentials prevented accurate analysis of sodium current properties. Therefore neurons were bathed in sodium-free solution and brief puffs of sodium were delivered to the cell soma so that only somatic sodium currents were recorded. Sodium currents of neurons at 1-2 days in culture had voltage-dependent activation and inactivation characteristic of these channels, both in mature cultured spinal neurons and in other preparations. However, the estimated channel density on the soma of neurons 1-2 days in culture was less than two channels per micron2. Since the available sodium conductance (as measured by action potential rise rates) increases during development of spinal cord neurons in culture (Westbrook and Brenneman, 1984), we suggest that changes in channel density and/or distribution, rather than in channel kinetics, may underlie the increase in sodium conductance.     

Estimating and eliminating junctional current in coupled cell populations by leak subtraction. A computational study

The quantitative characterization of ion channel properties in pancreatic β-cells under typical patch clamp conditions can be questioned because of the unreconciled differences in experimental conditions and observed behavior between microelectrode recordings of membrane potential in intact islets of Langerhans and patch recordings of single cells. Complex bursting is reliably observed in islets but not in isolated cells under patch clamp conditions. E. Rojas et al. (J. Membrane Biol. 143:65–77, 1995) have attempted to circumvent these incompatibilities by measuring currents in β-cells in intact islets by voltage-clamping with intracellular microelectrodes (150–250 MΩ tip resistance). The major potential pitfall is that β-cells within the islet are electrically coupled, and contaminating coupling currents must be subtracted from current measurements, just as linear leak currents are typically subtracted. To characterize the conditions under which such coupling current subtraction is valid, we have conducted a computational study of a model islet. Assuming that the impaled cell is well clamped, we calculate the native and coupling components of the observed current. Our simulations illustrate that coupling can be reliably subtracted when neighbor cells' potentials are constant or vary only slowly (e.g., during their silent phases) but not when they vary rapidly (e.g., during their active phases). We also show how to estimate coupling conductances in the intact islet from measurements of coupling currents.     

Conductances contributing to the action potential of Sternopygus electrocytes

In Sternopygus macrurus, electrocyte action potential duration determines the electric organ discharge pulse duration. Since the electric organ discharge is a sexually-dimorphic behavior under the control of steroid hormones, and because electrocyte action potential durations can range from 3–14 ms, the electrocytes provide a unique opportunity to study how sex steroids regulate membrane excitability. In this study, the voltage-sensitive ionic currents of electrocytes were identified under current- and voltage-clamp as a prelude to further studies on their regulation by sex steroid hormones.Bath application of TTX completely abolished the spike and eliminated an inward current under voltage clamp, indicating that the action potential is due primarily to a sodium current. Calcium-free saline had no effect on spike waveform or voltage-clamp currents, indicating that neither calcium nor calcium-dependent currents contribute to the action potential. Application of potassium channel blocking agents, such as tetraethylammonium and cesium ions, caused changes in the spike which, together with voltage-clamp results, indicate the presence of two potassium currents: an inward rectifier and a classical delayed rectifier. In addition, these cells have a large, presumably voltage-insensitive, chloride current. Differences in one or more of these currents could be responsible for the range of action potential durations found in these cells and for the steroid-mediated changes in spike duration.Abbreviations EOD electric organ discharge - VC voltage clamp - CC current clamp - AP action potential - VI/IV voltage-current/current-voltage     

A new algorithm for voltage clamp by iteration: A learning control of a nonlinear neuronal system

Voltage-clamp of excitable membrane allows the measurement of membrane currents associated with electrical potential changes across the membrane. However, it has been impossible in practice to apply the conventional analog feedback voltageclamp circuits to single electrode voltage clamping in central neurons. The reason for this is that the feedback system becomes unstable because of the positive feedback required for compensation of capacitative loss through the wall of the microelectrode. Park et al. (1981) proposed a new iterative technique to solve this problem. It requires that the potential to be clamped repeats itself with little or no change. The amount of current needed to clamp the membrane potential is not determined at once, but in a step-wise, trial and error fashion in the course of a set of repetitions. Since the feedback loop is open in real time, the system has great stability, and this advantage can be exploited in single electrode preparations. The computation algorithm which calculates the current waveform based on the voltage deviation during the last trial is the central part of the iterative voltage-clamp system. In this paper, we propose a new algorithm, which has several theoretical and practical advantages over the original one proposed by Park et al. First, two parameters used in the new algorithm are predetermined by a current-clamp experiment. Second, the speed of convergence of the new algorithm is faster than that of the Park's original algorithm. This was shown by computer simulation of iterative voltage clamp of artificial membrane following Hodgkin-Huxley equations for squid axon membrane and Rall's compartment model for a neuron with dendrites. Finally, we offer proof that the new algorithm is certain to converge for the general cases of voltage-clamp experiments with active membrane properties, synaptic membranes, etc. Consequently, the new algorithm for iterative voltage clamp is very suitable for single electrode voltage clamp in the central neurons. The new algorithm has been successfully applied to voltage-clamp experiments on rubrospinal neurons of cats (Tsukahara, Murakami, Kawato, Oda, and Etoh, in preparation).     

Corrections for space-clamp errors in measured parameters of voltage-dependent conductances in a cylindrical neurite

The ability to correct parameters of voltage-gated conductances measured under poor spatial control by point voltage clamp could rescue much flawed experimental data. We explore a strategy for correcting errors in experiments that employs a full-trace approach to parameter determination. Simulated soma voltage-clamp runs are made on a model neuron with a single voltage-gated, Hodgkin-Huxley channel type distributed uniformly along an elongate process. Estimates for both kinetic and I(V) parameters are obtained by fitting a form of the Hodgkin-Huxley equations to the complete time course of leak-subtracted current curves. The fitted parameters are used to determine how much correction in each parameter is needed to regenerate the set actually belonging to the channel. Corrections are generated for a range of neurite lengths, conductance densities, and channel characteristics.     

Excitatory responses of trigeminal neurons to substance P suggest involvement in sensory transmission

Responses to substance P application were studied with intracellular recording techniques in in vitro preparations of trigeminal root ganglion neurons of guinea pigs. Perfusion of substance P in micromolar concentrations markedly depolarized neurons and reduced their input conductances. Also, the threshold for spikes evoked by injections of depolarizing current pulses was decreased. Single electrode voltage-clamp recordings showed that substance P increased inward, and decreased outward currents evoked by hyperpolarizing voltage steps from holding potentials near rest. Depolarizing responses to substance P were attenuated in Na+-deficient solutions. The excitatory actions of this endogenous peptide on the perikarya of primary sensory neurons give rise to the possibility of physiological actions of substance P at multiple sites in the trigeminal system.     

Voltage clamping with single microelectrodes: comparison of the discontinuous mode and continuous mode using the Axoclamp 2A amplifier

The voltage clamp technique is a powerful method for studying the physiology of excitable membrane. This technique has made possible the determination of ionic responses generated by activation of either receptor-mediated or voltage-dependent processes. The development of the whole-cell, 'tight-seal' voltage clamp method has allowed the analysis and examination of membrane physiology at the single cell level. The method allows the characterization of voltage-dependent ionic conductances both at the macroscopic (whole-cell) and at the microscopic (unitary conductance or single channel) level in cells less than 10 micron in diameter, a feat difficult to achieve with 'conventional' fine-tipped micropipettes. In this paper, several methologies used for culturing neuronal and non-neuronal cells in the laboratory are described. A comparison between the two modes of voltage clamp using blunt-tipped 'patch'-microelectrodes, the switching (discontinuous) and the non-switching (continuous) modes, of the Axoclamp-2A amplifier is made. Some results on membrane currents obtained from neuronal and non-neuronal cells using the single electrode whole-cell 'tight-seal' voltage clamp is illustrated. The possible existence of two inactivating K+ currents, one dependent on Ca++ the other is not, is discussed.     

Measurement of nonuniform current densities and current kinetics in Aplysia neurons using a large patch method

A large patch electrode was used to measure local currents from the cell bodies of Aplysia neurons that were voltage-clamped by a two-microelectrode method. Patch currents recorded at the soma cap, antipodal to the origin of the axon, and whole-cell currents were recorded simultaneously and normalized to membrane capacitance. The patch electrode could be reused and moved to different locations which allowed currents from adjacent patches on a single cell to be compared. The results show that the current density at the soma cap is smaller than the average current density in the cell body for three components of membrane current: the inward Na current (INa), the delayed outward current (Iout), and the transient outward current (IA). Of these three classes of ionic currents, IA is found to reach the highest relative density at the soma cap. Current density varies between adjacent patches on the same cell, suggesting that ion channels occur in clusters. The kinetics of Iout, and on rare occasions IA, were also found to vary between patches. Possible sources of error inherent to this combination of voltage clamp techniques were identified and the maximum amplitudes of the errors estimated. Procedures necessary to reduce errors to acceptable levels are described in an appendix.     

Non-Stationary Fluctuation Analysis of Macroscopic Gap Junction Channel Records

Non-stationary fluctuation analysis was applied to macroscopic records of junctional currents arising from homotypic Cx37 and Cx43 gap junction channels expressed in RIN cells. The data were analyzed by a modification of existing analytical methods that takes endemic uncoupling into account. The results are consistent with both channels having open probabilities ranging from 0.7 to near unity for low transjunctional voltages. The analysis also yielded estimates of single-channel conductances for the two channel types similar to those seen in single-channel recordings. The results presented here show that fluctuation analysis can be used to extract single-channel gap junctional conductances from macroscopic double whole-cell recordings. These results also constitute empirically determined estimates of the open probability that are not model-dependent.     

What we talk about when we talk about capacitance measured with the voltage-clamp step method

Capacitance is a fundamental neuronal property. One common way to measure capacitance is to deliver a small voltage-clamp step that is long enough for the clamp current to come to steady state, and then to divide the integrated transient charge by the voltage-clamp step size. In an isopotential neuron, this method is known to measure the total cell capacitance. However, in a cell that is not isopotential, this measures only a fraction of the total capacitance. This has generally been thought of as measuring the capacitance of the ??well-clamped?? part of the membrane, but the exact meaning of this has been unclear. Here, we show that the capacitance measured in this way is a weighted sum of the total capacitance, where the weight for a given small patch of membrane is determined by the voltage deflection at that patch, as a fraction of the voltage-clamp step size. This quantifies precisely what it means to measure the capacitance of the ??well-clamped?? part of the neuron. Furthermore, it reveals that the voltage-clamp step method measures a well-defined quantity, one that may be more useful than the total cell capacitance for normalizing conductances measured in voltage-clamp in nonisopotential cells.     

Voltage-sensitive calcium currents and their role in regulating phrenic motoneuron electrical excitability during the perinatal period

This study examined the ontogeny of voltage-sensitive calcium conductances in rat phrenic motoneurons (PMNs) and their role in regulating electrical excitability during the perinatal period. Specifically, we studied the period spanning from embryonic day (E)16 through postnatal day (P)1, when PMNs undergo fundamental transformation in their morphology, passive properties, ionic channel composition, synaptic inputs, and electrical excitability. Low voltage-activated (LVA) and high voltage-activated (HVA) conductances were measured using whole cell patch recordings utilizing a cervical slice-phrenic nerve preparation from perinatal rats. Changes between E16 and P0-1 included the following: an approximately 2-fold increase in the density of total calcium conductances, an approximately 2-fold decrease in the density of LVA calcium conductances, and an approximately 3-fold increase in the density of HVA conductances. The elevated expression of T-type calcium channels during the embryonic period lengthened the action potential and enhanced electrical excitability as evidenced by a hyperpolarization-evoked rebound depolarization. The reduction of LVA current density coupled to the presence of a hyperpolarizing outward A-type potassium current had a critical effect in diminishing the rebound depolarization in neonatal PMNs. The increase in HVA current density was concomitant with the emergence of a calcium-dependent "hump-like" afterdepolarization (ADP) and burst-like firing. Neonatal PMNs develop a prominent medium-duration afterhyperpolarization (mAHP) as the result of coupling between N-type calcium channels and small conductance, calcium-activated potassium channels. These data demonstrate that changes in calcium channel expression contribute to the maturation of PMN electrophysiological properties during the time from the commencement of fetal inspiratory drive to the onset of continuous breathing at birth.     

Discontinuous single electrode voltage-clamp measurements: assessment of clamp accuracy in Vicia faba guard cells

The use of a discontinuous single electrode voltage-clamp (dSEVC) offers an attractive alternative to the patch-clamp technique, since whole-cell measurements can be performed with a single sharp electrode. Comparison of current-voltage relations, however, revealed a weaker voltage dependence of channels measured with the dSEVC compared to patch clamp. The accuracy of the dSEVC was tested on Vicia faba guard cells impaled with double-barrelled electrodes. The actual clamp potential was measured independently of the dSEVC, at the second barrel. The weaker voltage dependence of ion channels appeared to be due to an overestimation of the clamp potential by the dSEVC. The deviation between the intended and actual clamp potential showed a linear relationship with the injected current; on average a 126 mV deviation was found for a clamp current of 1 nA. The deviation was probably caused by a slow settling capacity at the electrode, not compensated by the dSEVC amplifier. It is concluded that the dSEVC method in its current state is only suited for the study of small ion conductances in plant cells.