Capacitance compensation and bridge balance adjustment in intracellular recording from dendritic neurons

Small Size of Recorded Neuronal Structures Confines the Accuracy in Direct Axonal Voltage Measurements

Patch-clamp instruments including amplifier circuits and pipettes affect the recorded voltage signals. We hypothesized that realistic and complete in silico representation of recording instruments together with detailed morphology and biophysics of small recorded structures will reveal signal distortions and provide a tool that predicts native, instrument-free electrical signals from distorted voltage recordings. Therefore, we built a model that was verified by small axonal recordings. The model accurately recreated actual action potential (AP) measurements with typical recording artefacts and predicted the native electrical behavior. The simulations verified that recording instruments substantially filter voltage recordings. Moreover, we revealed that instrumentation directly interferes with local signal generation depending on the size of the recorded structures, which complicates the interpretation of recordings from smaller structures, such as axons. However, our model offers a straightforward approach that predicts the native waveforms of fast voltage signals and the underlying conductances even from the smallest neuronal structures.

Long-term, multisite, parallel, in-cell recording and stimulation by an array of extracellular microelectrodes

Here we report on the development of a novel neuroelectronic interface consisting of an array of noninvasive gold-mushroom-shaped microelectrodes (gMmicroEs) that practically provide intracellular recordings and stimulation of many individual neurons, while the electrodes maintain an extracellular position. The development of this interface allows simultaneous, multisite, long-term recordings of action potentials and subthreshold potentials with matching quality and signal-to-noise ratio of conventional intracellular sharp glass microelectrodes or patch electrodes. We refer to the novel approach as "in-cell recording and stimulation by extracellular electrodes" to differentiate it from the classical intracellular recording and stimulation methods. This novel technique is expected to revolutionize the analysis of neuronal networks in relations to learning, information storage and can be used to develop novel drugs as well as high fidelity neural prosthetics and brain-machine systems.

Causes of transient instabilities in the dynamic clamp

The dynamic clamp is a widely used method for integrating mathematical models with electrophysiological experiments. This method involves measuring the membrane voltage of a cell, using it to solve computational models of ion channel dynamics in real-time, and injecting the calculated current(s) back into the cell. Limitations of this technique include those associated with single electrode current clamping and the sampling effects caused by the dynamic clamp. In this study, we show that the combination of these limitations causes transient instabilities under certain conditions. Through physical experiments and simulations, we show that dynamic clamp instability is directly related to the sampling delay and the maximum simulated conductance being injected. It is exaggerated by insufficient electrode series resistance and capacitance compensation. Increasing the sampling rate of the dynamic clamp system increases dynamic clamp stability; however, this improvement, is constrained by how well the electrode series resistance and capacitance are compensated. At present, dynamic clamp sampling rates are justified solely on the temporal dynamics of the models being simulated; here we show that faster rates increase the stable range of operation for the dynamic clamp system. In addition, we show that commonly accepted levels of resistance compensation nevertheless significantly compromise the stability of a dynamic clamp system.

Estimation of the Electrical Parameters of Spinal Motoneurons Using Impedance Measurements

Electrical parameters of spinal motoneurons were estimated by optimizing the parameters of motoneuron models to match experimentally determined impedance functions with those of the models. The model was described by soma area, somatic and dendritic membrane resistivities, and the diameter of an equivalent dendritic cable having a standard profile. The impedance functions of motoneurons and optimized models usually differed (rms error) by <2% of input resistance. Consistent estimates for most parameters were obtained from repeated impedance determinations in individual motoneurons; estimates of dendritic resistivity were most variable. The few cells that could not be fit well had reduced impedance phase lag consistent with dendritic penetrations. Most fits were improved by inclusion of a voltage-dependent conductance GV with time constant τV. A uniformly distributed GV with τV >5 ms provided a better fit for most cells. The magnitude of this conductance decreased with depolarization. Impedance functions of other cells were adequately fit by a passive model or by a model with a somatic GV and τV <5 ms. Most of these neurons (7/8) had resting potentials positive to −60 mV. The electrotonic parameters ρ, τ, and L, estimated from model parameters, were consistent with published distributions. Most motoneuron parameters obtained in somatic shunt and sigmoidal models were well correlated, and parameters were moderately affected by changes in dendritic profile. These results demonstrate the utility and limitations of impedance measurements for estimating motoneuron parameters and suggest that voltage-dependent conductances are a substantial component of resting electrical properties.

Correction of conductance measurements in non-space-clamped structures: 1. Voltage-gated K+ channels

To understand functions of a single neuron, such as propagation and generation of synaptic or action potentials, a detailed description of the kinetics and distribution of the underlying ionic conductances is essential. In voltage-clamp experiments, incomplete space clamp distorts the recorded currents, rendering accurate analysis impossible. Here, we present a simple numerical algorithm that corrects such distortions. The method performs a stepwise approximation of the conductance density at the site of a local voltage clamp. This is achieved by estimating membrane conductances in a simulation that yields simulated clamp currents, which are then fitted to the distorted recordings from the non-space-clamped structure, relying on accurately reconstructed cell morphology and experimentally determined passive properties. The method enabled accurate retrieval of the local densities, kinetics, and density gradients of somatic and dendritic channels. Neither the addition of noise nor variation of passive parameters significantly reduced the performance of the correction algorithm. The correction method was applied to two-electrode voltage-clamp recordings of K(+) currents from the apical dendrite of layer 5 neocortical pyramidal neurons. The generality and robustness of the algorithm make it a useful tool for voltage-clamp analysis of voltage-gated currents in structures of any morphology that is amenable to the voltage-clamp technique.

Firing properties and electrotonic structure of Xenopus larval spinal neurons

Whole cell voltage- and current-clamp measurements were done on intact Xenopus laevis larval spinal neurons at developmental stages 42-47. Firing patterns and electrotonic properties of putative interneurons from the dorsal and ventral medial regions of the spinal cord at myotome levels 4-6 were measured in isolated spinal cord preparations. Passive electrotonic parameters were determined with internal cesium sulfate solutions as well as in the presence of active potassium conductances. Step-clamp stimuli were combined with white-noise frequency domain measurements to determine both linear and nonlinear responses at different membrane potential levels. Comparison of analytic and compartmental dendritic models provided a way to determine the number of compartments needed to describe the dendritic structure. The electrotonic structure of putative interneurons was correlated with their firing behavior such that highly accommodating neurons (Type B) had relatively larger dendritic areas and lower electrotonic lengths compared with neurons that showed sustained action potential firing in response to a constant current (Type A). Type A neurons had a wide range of dendritic areas and potassium conductances that were activated at membrane potentials more negative than observed in Type B neurons. The differences in the potassium conductances were in part responsible for a much greater rectification in the steady-state current voltage (I-V curve) of the strongly accommodating neurons compared with repetitively firing cells. The average values of the passive electrotonic parameters found for Rall Type A and B neurons were c(soma) = 3.3 and 2.6 pF, g(soma) = 187 and 38 pS, L = 0.36 and 0.21, and A = 3.3 and 6.5 for soma capacitance, soma conductance, electrotonic length, and the ratio of the dendritic to somatic areas, respectively. Thus these experiments suggest that there is a correlation between the electrotonic structure and the excitability properties elicited from the somatic region.

NMDA-induced dendritic oscillations during a soma voltage clamp of chick spinal neurons

An investigation of dendritic membrane properties was performed by whole-cell patch measurements of the biophysical properties of intact chick spinal neurons that are involved in rhythmogenesis. A whole-cell voltage clamp of the somatic membrane was used to block NMDA-induced voltage oscillations from the cell body, thus partially isolating the intrinsic oscillatory properties of dendritic membranes from those of the soma. An experimental approach was developed that takes into account the complexity of the dendritic tree in an environment as normal as possible, without the need for cell isolation or slice preparations. A computational study of the experimentally determined model showed that excitatory amino acid receptors on dendrites can dynamically control the electrotonic length of the dendrites through the activation of negative slope conductances. These experiments demonstrate the presence of NMDA receptors on the dendrites and that they induce intrinsic oscillations when the synaptic input from other cells is significantly reduced.

Two electrophysiologically distinct types of granule cells in epileptic human hippocampus

We investigated the electrophysiology of morphologically identified human granule cells with conventional current-clamp recordings. Slices were prepared from 14 human epileptic sclerotic hippocampi. Granule cells appeared to have a diverse electrophysiology. Each cell was distinguished by the shape of the afterhyperpolarization following single action potentials. Two types could be discerned: type I afterhyperpolarizations were monophasic and brief (typically 10-40 ms), whilst type II afterhyperpolarizations were biphasic and long (typically 50-100 ms). The two types also differed in their repetitive firing behaviour and action potential morphology: type I cells had significantly weaker spike frequency adaptation, lower action potential amplitude and smaller action potential upstroke/downstroke ratio. Thus, the firing pattern of type I cells resembled that of rodent dentate interneurons. In contrast, the corresponding parameters of type II cells were comparable to rodent dentate granule cells. Despite the distinct firing patterns, membrane properties were not different. The two types of cells also differed in their synaptic responses to stimulation of the perforant path. At strong suprathreshold stimulation intensity, type I cells always generated multiple action potentials, whereas type II cells usually spiked once only. Slow inhibitory postsynaptic potentials were not detected in type I neurons, but were easily identified in type II neurons. Extracellular recordings of perforant path-evoked field potentials in the cell layer confirmed that the majority of granule cells showed multiple discharges even when we recorded simultaneously from a type II cell that generated one action potential only. The morphology of both types of cells was characteristic of what has been described for primate dentate granule cells. Based on comparisons with previous studies on rodent and human granule cells, we tentatively hypothesize that: (i) the majority of granule cells from sclerotic hippocampus display an hyperexcitable epileptogenic electrophysiology; (ii) there is a subset of granule cells whose electrophysiology is preserved and is more comparable to granule cells from non-epileptic hippocampus.

Experimental analysis of the method of 'peeling' exponentials for measuring passive electrical properties of mammalian motoneurons

Trigeminal motoneurons of the guinea pig brain stem slice preparation were studied using intracellular recording techniques. The voltage response to a 100-ms constant-current pulse was studied and a population of cells was found which did not exhibit sag or overshoot of their voltage response to a pulse of hyperpolarizing current of < 1 nA but did exhibit both phenomena when a current pulse of > 1 nA was used. The sag and overshoot observed with large-current pulses were reduced or blocked when 4 mM CsCl was added to the bathing solution. This observation supports the hypothesis that these phenomena were due to the voltage- and time-dependent activation of the Q-current. The method of peeling exponentials was then used to correct raw voltage data from cells in which the Q-current was present. The mean membrane time constant was within 1% and the mean input resistance was within 2% of the means for these parameters when measured in these same cells under conditions in which the Q-current was absent. We conclude from these experiments that the method of peeling exponentials is valid for obtaining estimates of the membrane time constant and input resistance from cells that exhibit sag and overshoot due to voltage- and time-dependent changes in the magnitude of the Q-current.

The effect of neuronal growth on synaptic integration

The way in which the dimensions of neurons change during postembryonic development has important effects on their electrotonic structures. Theoretically, only one mode of growth can conserve the electrotonic structures of growing neurons without employing changes in membrane electrical properties. If the dendritic diameters of a neuron increase as the square of the increase in dendritic lengths, then the neuron's electrotonic structure is conserved. We call this special mode of allometric growth "isoelectrotonic growth." In this study we compared the developmental changes in morphology of two identified invertebrate neurons with theoretical growth curves. We found that a cricket neuron, MGI, grows isoelectrotonically and thereby preserves its electrotonic properties. In contrast, the crayfish neuron, LG, grows in nearly isometric manner resulting in an increase in its electrotonic length.

Solutions for transients in arbitrarily branching cables: III. Voltage clamp problems

Branched cable voltage recording and voltage clamp analytical solutions derived in two previous papers are used to explore practical issues concerning voltage clamp. Single exponentials can be fitted reasonably well to the decay phase of clamped synaptic currents, although they contain many underlying components. The effective time constant depends on the fit interval. The smoothing effects on synaptic clamp currents of dendritic cables and series resistance are explored with a single cylinder + soma model, for inputs with different time courses. "Soma" and "cable" charging currents cannot be separated easily when the soma is much smaller than the dendrites. Subtractive soma capacitance compensation and series resistance compensation are discussed. In a hippocampal CA1 pyramidal neurone model, voltage control at most dendritic sites is extremely poor. Parameter dependencies are illustrated. The effects of series resistance compound those of dendritic cables and depend on the "effective capacitance" of the cell. Plausible combinations of parameters can cause order-of-magnitude distortions to clamp current waveform measures of simulated Schaeffer collateral inputs. These voltage clamp problems are unlikely to be solved by the use of switch clamp methods.

Tuberal supraoptic neurons--II. Electrotonic properties

The electrotonic properties of tuberal supraoptic neurons were studied from conventional intracellular recordings made in the hypothalamo-neurohypophysial explant in vitro. The cable parameters electrotonic dendritic length, and the dendritic to somatic conductance ratio, were estimated using the slopes and intercepts of the first two peeled exponentials of the voltage transients generated by current steps. The estimations were made assuming an equivalent cylinder model consisting of a soma and an attached, lumped dendrite of finite length. An equalizing time constant was resolved in 12 of 17 neurons, allowing calculation of both cable parameters. In only one of these 12 was it necessary to assume a somatic shunt to account for the data. The average value of the dendritic electrotonic length was 1.02, and that of the dendritic to somatic conductance ratio, 4.11. In the remaining five neurons, an equalizing time constant could not be peeled and consequently the dendritic cable parameters could not be estimated. The average input resistance of these 12 neurons was 162 M omega and the average membrane time constant was 11.86 ms. Principal Components Analysis revealed that the variance of input resistance and time constant was largely explained by one factor, while that of dendritic electrotonic length and the dendritic to somatic conductance ratio was explained by a separate, independent factor, suggesting a separation of electrical and morphological parameters, respectively. In addition, the variability of the data indicates that considerable differences in the morphology and specific membrane resistivity exist across supraoptic neurons. An analysis of spontaneously occurring postsynaptic potentials revealed that the shapes of these potentials could not be explained simply by assuming that they were determined by their passive decay from some point along the equivalent cable to the soma. In conclusion, dendrites make a significant and previously unappreciated contribution to the electrotonic behavior of supraoptic neurons. These electrotonic properties are similar to those of many other, morphologically diverse, central nervous system neurons.