Electrotonic parameters of rat dentate granule cells measured using short current pulses and HRP staining

A novel theoretical framework for simultaneous measurement of excitatory and inhibitory conductances

The firing of neurons throughout the brain is determined by the precise relations between excitatory and inhibitory inputs, and disruption of their balance underlies many psychiatric diseases. Whether or not these inputs covary over time or between repeated stimuli remains unclear due to the lack of experimental methods for measuring both inputs simultaneously. We developed a new analytical framework for instantaneous and simultaneous measurements of both the excitatory and inhibitory neuronal inputs during a single trial under current clamp recording. This can be achieved by injecting a current composed of two high frequency sinusoidal components followed by analytical extraction of the conductances. We demonstrate the ability of this method to measure both inputs in a single trial under realistic recording constraints and from morphologically realistic CA1 pyramidal model cells. Future experimental implementation of our new method will facilitate the understanding of fundamental questions about the health and disease of the nervous system.

Most neurons in the brain receive synaptic inputs from both excitatory and inhibitory neurons. Together, these inputs determine neuronal activity: excitatory synapses shift the electrical potential across the membrane towards the threshold for generation of action potentials, whereas inhibitory synapses lower this potential away from the threshold. Action potentials are the rapid electrochemical signals that transmit information to other neurons and they are critical for the information processing abilities of the brain.

Although there are many ways to measure either excitatory or inhibitory inputs, these methods have been unable to measure both at the same time. Measuring both inputs together is essential towards understanding how neurons integrate information. We developed a new analytical method to measure excitatory and inhibitory inputs at the same time from the voltage response to injection of an alternating current into a neuron. We describe the foundation of this new method and find that it works in biologically realistic simulations of neurons. By using this technique in real neurons, scientists could investigate basic principles of information processing in the healthy and diseased brain.

A computational approach for the inverse problem of neuronal conductances determination

The derivation by Alan Hodgkin and Andrew Huxley of their famous neuronal conductance model relied on experimental data gathered using the squid giant axon. However, the experimental determination of conductances of neurons is difficult, in particular under the presence of spatial and temporal heterogeneities, and it is also reasonable to expect variations between species or even between different types of neurons of the same species.We tackle the inverse problem of determining, given voltage data, conductances with non-uniform distribution in the simpler setting of a passive cable equation, both in a single or branched neurons. To do so, we consider the minimal error iteration, a computational technique used to solve inverse problems. We provide several numerical results showing that the method is able to provide reasonable approximations for the conductances, given enough information on the voltages, even for noisy data.

Computational models of dentate gyrus with epilepsy-induced morphological alterations in granule cells

Temporal lobe epilepsy provokes a number of different morphological alterations in granule cells of the hippocampus dentate gyrus. These alterations may be associated with the hyperactivity and hypersynchrony found in the epileptic dentate gyrus, and their study requires the use of different kinds of approaches including computational modeling. Conductance-based models of both normal and epilepsy-induced morphologically altered granule cells have been used in the construction of network models of dentate gyrus to study the effects of these alterations on epilepsy. Here, we review these models and discuss their contributions to the understanding of the association between alterations in neuronal morphology and epilepsy in the dentate gyrus.

Determining a distributed parameter in a neural cable model via a boundary control method

Dendrites of nerve cells have membranes with spatially distributed densities of ionic channels and hence non-uniform conductances. These conductances are usually represented as constant parameters in neural models because of the difficulty in experimentally estimating them locally. In this paper we investigate the inverse problem of recovering a single spatially distributed conductance parameter in a one-dimensional diffusion (cable) equation through a new use of a boundary control method. We also outline how our methodology can be extended to cable theory on finite tree graphs. The reconstruction is unique.

A simple method for characterizing passive and active neuronal properties: application to striatal neurons

The study of active and passive neuronal dynamics usually relies on a sophisticated array of electrophysiological, staining and pharmacological techniques. We describe here a simple complementary method that recovers many findings of these more complex methods but relies only on a basic patch-clamp recording approach. Somatic short and long current pulses were applied in vitro to striatal medium spiny (MS) and fast spiking (FS) neurons from juvenile rats. The passive dynamics were quantified by fitting two-compartment models to the short current pulse data. Lumped conductances for the active dynamics were then found by compensating this fitted passive dynamics within the current-voltage relationship from the long current pulse data. These estimated passive and active properties were consistent with previous more complex estimations of the neuron properties, supporting the approach. Relationships within the MS and FS neuron types were also evident, including a graduation of MS neuron properties consistent with recent findings about D1 and D2 dopamine receptor expression. Application of the method to simulated neuron data supported the hypothesis that it gives reasonable estimates of membrane properties and gross morphology. Therefore detailed information about the biophysics can be gained from this simple approach, which is useful for both classification of neuron type and biophysical modelling. Furthermore, because these methods rely upon no manipulations to the cell other than patch clamping, they are ideally suited to in vivo electrophysiology.

Subthreshold dendritic signal processing and coincidence detection in dentate gyrus granule cells

Although dendritic signal processing has been extensively investigated in hippocampal pyramidal cells, only little is known about dendritic integration of synaptic potentials in dentate gyrus granule cells, the first stage in the hippocampal trisynaptic circuit. Here we combined dual whole-cell patch-clamp recordings with high-resolution two-photon microscopy to obtain detailed passive cable models of hippocampal granule cells from adult mice. Passive cable properties were determined by direct fitting of the compartmental model to the experimentally measured voltage responses to short and long current pulses. The data are best fit by a cable model with homogenously distributed parameters, including an average specific membrane resistance (R(m)) of 38.0 kohms cm2, a membrane capacitance (C(m)) of 1.0 microF cm(-2), and an intracellular resistivity (R(i)) of 194 ohms cm. Computational analysis shows that signal propagation from somata into dendrites is more efficient in granule cells compared with CA1 pyramidal cells for both steady-state and sinusoidal voltage waveforms up to the gamma frequency range (f50% of 74 Hz). Similarly, distal synaptic inputs from entorhinal fibers can efficiently depolarize the somatic membrane of granule cells. Furthermore, the time course of distal dendritic synaptic potentials is remarkably fast, and temporal summation is restricted to a narrow time window in the range of approximately 10 ms attributable to the rapid dendritic charge redistribution during transient voltage signals. Therefore, the structure of the granule cell dendritic tree may be critically important for precise dendritic signal processing and coincidence detection during hippocampus-dependent memory formation and retrieval.

Factors mediating powerful voltage attenuation along CA1 pyramidal neuron dendrites

We performed simultaneous patch-electrode recordings from the soma and apical dendrite of CA1 pyramidal neurons in hippocampal slices, in order to determine the degree of voltage attenuation along CA1 dendrites. Fifty per cent attenuation of steady-state somatic voltage changes occurred at a distance of 238 microm from the soma in control and 409 microm after blocking the hyperpolarization-activated (H) conductance. The morphology of three neurons was reconstructed and used to generate computer models, which were adjusted to fit the somatic and dendritic voltage responses. These models identify several factors contributing to the voltage attenuation along CA1 dendrites, including high axial cytoplasmic resistivity, low membrane resistivity, and large H conductance. In most cells the resting membrane conductances, including the H conductances, were larger in the dendrites than the soma. Simulations suggest that synaptic potentials attenuate enormously as they propagate from the dendrite to the soma, with greater than 100-fold attenuation for synapses on many small, distal dendrites. A prediction of this powerful EPSP attenuation is that distal synaptic inputs are likely only to be effective in the presence of conductance scaling, dendritic excitability, or both.

A distributed parameter identification problem in neuronal cable theory models

Dendritic and axonal processes of nerve cells, along with the soma itself, have membranes with spatially distributed densities of ionic channels of various kinds. These ionic channels play a major role in characterizing the types of excitable responses expected of the cell type. These densities are usually represented as constant parameters in neural models because of the difficulty in experimentally estimating them. However, through microelectrode measurements and selective ion staining techniques, it is known that ion channels are non-uniformly spatially distributed. This paper presents a non-optimization approach to recovering a single spatially non-uniform ion density through use of temporal data that can be gotten from recording microelectrode measurements at the ends of a neural fiber segment of interest. The numerical approach is first applied to a linear cable model and a transformed version of the linear model that has closed-form solutions. Then the numerical method is shown to be applicable to non-linear nerve models by showing it can recover the potassium conductance in the Morris-Lecar model for barnacle muscle, and recover the spine density in a continuous dendritic spine model by Baer and Rinzel.

Spontaneous Waves in the Dentate Gyrus of Slices From the Ventral Hippocampus

Spontaneous negative-going potentials occurring at an average frequency of 0.7 Hz were recorded from the dentate gyrus of slices prepared from the temporal hippocampus of young adult rats. These events (here termed “dentate waves”) in several respects resembled the dentate spikes described for freely moving rats during immobile behaviors and slow-wave sleep. Action potentials were observed on the descending portion of the in vitro waves and, as expected from this, whole cell recordings established that the waves were composed of depolarizing currents. Dentate waves appeared to be locally generated within the granule cell layer and were greatly reduced by antagonists of AMPA-type glutamate receptors or by lesions to the entorhinal cortex. Simultaneous recordings indicated that the waves were often synchronized in the inner and outer blades of the dentate gyrus. Knife cuts through the perforant path and the commissural/associational system did not eliminate synchronization, leaving electrotonic propagation via gap junctions as its probable cause. In accord with this, cuts that separated the two blades of the dentate eliminated synchronization between them, and a compound that inhibits gap junctions reduced wave activity. Dentate waves were regularly accompanied by sharp waves in field CA3 and were reduced in size by the acetylcholinesterase inhibitor, physostigmine. It is hypothesized that dentate waves occur when spontaneous glutamate release from dentate afferents produces action potentials in neighboring granule cells that then summate electrotonically into a population event; once initiated, the waves propagate, again electrotonically, and thereby engage a significant portion of the granule cell population.

Distance-dependent modifiable threshold for action potential back-propagation in hippocampal dendrites

In hippocampal CA1 pyramidal neurons, action potentials generated in the axon back-propagate in a decremental fashion into the dendritic tree where they affect synaptic integration and synaptic plasticity. The amplitude of back-propagating action potentials (b-APs) is controlled by various biological factors, including membrane potential (Vm). We report that, at any dendritic location (x), the transition from weak (small-amplitude b-APs) to strong (large-amplitude b-APs) back-propagation occurs when Vm crosses a threshold potential, x. When Vm > x, back-propagation is strong (mostly active). Conversely, when Vm < x, back-propagation is weak (mostly passive). x varies linearly with the distance (x) from the soma. Close to the soma, x << resting membrane potential (RMP) and a strong hyperpolarization of the membrane is necessary to switch back-propagation from strong to weak. In the distal dendrites, x >> RMP and a strong depolarization is necessary to switch back-propagation from weak to strong. At approximately 260 micrometer from the soma, 260 approximately RMP, suggesting that in this dendritic region back-propagation starts to switch from strong to weak. x depends on the availability or state of Na+ and K+ channels. Partial blockade or phosphorylation of K+ channels decreases x and thereby increases the portion of the dendritic tree experiencing strong back-propagation. Partial blockade or inactivation of Na+ channels has the opposite effect. We conclude that x is a parameter that captures the onset of the transition from weak to strong back-propagation. Its modification may alter dendritic function under physiological and pathological conditions by changing how far large action potentials back-propagate in the dendritic tree.

Detailed passive cable models of layer 2/3 pyramidal cells in rat visual cortex at different temperatures

We present detailed passive cable models of layer 2/3 pyramidal cells based on somatic voltage transients in response to brief current pulses at physiological and room temperatures and demonstrate how cooling alters the shape of postsynaptic responses. Whole cell recordings were made from cells in visual cortical slices from 20- to 22-day-old rats. The cells were filled with biocytin and morphologies were reconstructed from three cells which were representative of the full range of physiological responses. These formed the basis for electrotonic models with four electrical variables, namely membrane capacitance (C(m)), membrane resistivity (R(m)), cytoplasmic resistivity (R(i)) and a somatic shunt conductance (G(sh)). Simpler models, with a single value for R(m) and no G(sh), did not fit the data adequately. Optimal parameter values were derived by simulating the responses to somatic current pulses, varying the parameters to give the best match to the experimental recordings. G(sh) and R(m) were badly constrained. In contrast, the total membrane conductance (G(tot)) was well constrained, and its reciprocal correlated closely with the slowest membrane time constant (tau(0)). The models showed close agreement for C(m) and R(i) (ranges at 36 degrees C: 0.78-0.94 microF cm(-2) and 140-170 Omegacm), but a larger range for G(tot) (7.2-18.4 nS). Cooling produced consistent effects in all three model cells; C(m) remained constant (Q(10) = 0.96), R(i) increased (Q(10) = 0.80), whilst G(tot) dropped (Q(10) = 1.98). In terms of whole cell physiology, the predominant effect of cooling is to dramatically lengthen the decay of transient voltage shifts. Simulations suggest that this markedly increases the temporal summation of postsynaptic potentials and we demonstrate this effect in the responses of layer 2/3 cells to tetanic extracellular stimulation in layer 4.

An estimator for the electrotonic size of neurons independent of charge equalization time constants

Electrotonic properties are important aspects of neuronal function but have been difficult to estimate without accurate morphological reconstruction. The complexity of the branching dendritic cables often gives charging curves composed of a very large number of exponential functions, making it difficult to distinguish the time constants that are needed for electrotonic estimates. We describe an estimator P for the electrotonic size of neurons based on simple measures from voltage and current clamp recordings that does not rely on the higher rank exponential components of the response. Our estimator gives a bounded scale for the electrotonic size of the cell and can be used for categorization and comparison when morphology is not available.

Dendritic attenuation of synaptic potentials in the CA1 region of rat hippocampal slices detected with an optical method

We directly measured fast excitatory postsynaptic potentials (EPSPs) along the dendrites of hippocampal CA1 pyramidal neurons by employing an optical method to study how synaptic potentials spread along the dendrites. Rat hippocampal slices were stained with a fluorescent voltage-sensitive dye JPW1114 and optical signals were monitored with a 16 x 16 photodiode array system. A stimulating electrode was placed either at stratum lacunosum moleculare to activate perforant fibers that make synaptic contacts to the distal apical dendrites or at stratum oriens to induce EPSPs at the basal dendrites of CA1 pyramidal cells. CNQX-sensitive components of the optical signals, which were assumed to be population EPSPs, were isolated. Propagation and attenuation of the CNQX components were successfully observed with the optical method. At the cell body layer, the peak of the CNQX-sensitive component was delayed by 17.08 +/- 1.64 ms from the input sites. Additionally we performed a simulation study to estimate the passive membrane parameters of the apical dendrites. Estimated apparent specific internal axial resistance (Ri) following stratum lacunosum moleculare stimulation was 76.0 +/- 4.2 Omega.cm and apparent specific membrane resistance (Rm) was 27.8 +/- 2.1 kOmega.cm2 (assuming the specific membrane capacitance of dendrites Cm = 1.6 microF/cm2). These values are comparable to those previously reported. When synaptic inputs were applied at stratum oriens, these apparent passive membrane parameters were different (high Ri and low Rm), suggesting that nonuniform dendritic membrane conductance or voltage-dependent conductances which are active near the resting potential may contribute to the measured passive membrane properties.

Development of glycinergic synaptic transmission to rat brain stem motoneurons

Using an in vitro rat brain stem slice preparation, we examined the postnatal changes in glycinergic inhibitory postsynaptic currents (IPSCs) and passive membrane properties that underlie a developmental change in inhibitory postsynaptic potentials (IPSPs) recorded in hypoglossal motoneurons (HMs). Motoneurons were placed in three age groups: neonate (P0-3), intermediate (P5-8), and juvenile (P10-18). During the first two postnatal weeks, the decay time course of both unitary evoked IPSCs [mean decay time constant, taudecay = 17.0 +/- 1.6 (SE) ms in neonates and 5.5 +/- 0.4 ms in juveniles] and spontaneous miniature IPSCs (taudecay = 14.2 +/- 2.4 ms in neonates and 6.3 +/- 0.7 ms in juveniles) became faster. As glycine uptake does not influence IPSC time course at any postnatal age, this change most likely results from a developmental alteration in glycine receptor (GlyR) subunit composition. We found that expression of fetal (alpha2) GlyR subunit mRNA decreased, whereas expression of adult (alpha1) GlyR subunit mRNA increased postnatally. Single GlyR-channels recorded in outside-out patches excised from neonate motoneurons had longer mean burst durations than those from juveniles (18.3 vs. 11.1 ms). Concurrently, HM input resistance (RN) and membrane time constant (taum) decreased (RN from 153 +/- 12 MOmega to 63 +/- 7 MOmega and taum from 21.5 +/- 2.7 ms to 9.1 +/- 1.0 ms, neonates and juveniles, respectively), and the time course of unitary evoked IPSPs also became faster (taudecay = 22.4 +/- 1.8 and 7.7 +/- 0.9 ms, neonates vs. juveniles, respectively). Simulated synaptic currents were used to probe more closely the interaction between IPSC time course and taum, and these simulations demonstrated that IPSP duration was reduced as a consequence of postnatal changes in both the kinetics of the underlying GlyR channel and the membrane properties that transform the IPSC into a postsynaptic potential. Additionally, gramicidin perforated-patch recordings of glycine-evoked currents reveal a postnatal change in reversal potential, which is shifted from -37 to -73 mV during this same period. Glycinergic PSPs are therefore depolarizing and prolonged in neonate HMs and become faster and hyperpolarizing during the first two postnatal weeks.

Determinants of voltage attenuation in neocortical pyramidal neuron dendrites

How effectively synaptic and regenerative potentials propagate within neurons depends critically on the membrane properties and intracellular resistivity of the dendritic tree. These properties therefore are important determinants of neuronal function. Here we use simultaneous whole-cell patch-pipette recordings from the soma and apical dendrite of neocortical layer 5 pyramidal neurons to directly measure voltage attenuation in cortical neurons. When combined with morphologically realistic compartmental models of the same cells, the data suggest that the intracellular resistivity of neocortical pyramidal neurons is relatively low ( approximately 70 to 100 Omegacm), but that voltage attenuation is substantial because of nonuniformly distributed resting conductances present at a higher density in the distal apical dendrites. These conductances, which were largely blocked by bath application of CsCl (5 mM), significantly increased steady-state voltage attenuation and decreased EPSP integral and peak in a manner that depended on the location of the synapse. Together these findings suggest that nonuniformly distributed Cs-sensitive and -insensitive resting conductances generate a "leaky" apical dendrite, which differentially influences the integration of spatially segregated synaptic inputs.

Morphology and electrophysiology of dentate granule cells in the rhesus monkey: comparison with the rat

The morphologic and electrophysiologic properties of dentate granule cells in the young adult rhesus monkey (Macaca mulatta) were examined for the first time with whole-cell patch clamp recordings and intracellular biocytin filling in in vitro hippocampal slice preparations. Data from monkeys were compared with data generated in an identical manner from adult Sprague-Dawley rats. Intracellularly filled monkey and rat granule cells were identical in numerous morphologic parameters, including area of somata, total dendritic length, dendritic spread, segment number and length, and branching pattern. The single statistically significant difference in morphology was the vertical extent of the dendritic tree (distance from soma to fissure), which was 20% greater in the monkey. The passive membrane properties (resting membrane potential, input resistance, and membrane time constant) measured under current clamp conditions were virtually identical. The thresholds and amplitudes of action potentials were the same, but significant differences were seen in the kinetics of single action potentials. Monkey granule cell action potentials were significantly longer in duration (with slower rise and fall times) than action potentials in rat cells. These differences were likely due to a much smaller fast after hyperpolarization in the monkey as compared with the rat cells. Thus, with the exception of action potential properties, the principal finding of this study is that there is significant conservation of both form and function in dentate granule cells in these two species, despite the enormous phylogenetic separation. This suggests that granule cell properties may be extremely stable across diverse mammalian species.

Tonic synaptic inhibition modulates neuronal output pattern and spatiotemporal synaptic integration

Irregular firing patterns are observed in most central neurons in vivo, but their origin is controversial. Here, we show that two types of inhibitory neurons in the cerebellar cortex fire spontaneously and regularly in the absence of synaptic input but generate an irregular firing pattern in the presence of tonic synaptic inhibition. Paired recordings between synaptically connected neurons revealed that single action potentials in inhibitory interneurons cause highly variable delays in action potential firing in their postsynaptic cells. Activity in single and multiple inhibitory interneurons also significantly reduces postsynaptic membrane time constant and input resistance. These findings suggest that the time window for synaptic integration is a dynamic variable modulated by the level of tonic inhibition, and that rate coding and temporal coding strategies may be used in parallel in the same cell type.

Subthreshold oscillations and resonant behavior: two manifestations of the same mechanism

The ability to generate subthreshold membrane potential oscillations in neurons from the inferior olive nucleus has been attributed to the electrical properties of these neurons, as well as to the properties of the network. In the present in vitro study we quantitatively characterized both intrinsic membrane and network properties that are directly involved in the oscillatory activity of olivary neurons in the guinea-pig. We also implemented an alternating current analysis to explore the resonance behavior of these neurons and to compare the resonant properties with the properties of the oscillatory activity. Spectral analysis, used for the quantitative characterization of the oscillatory activity under various experimental conditions, revealed that the pattern of the oscillatory activity is network specific rather than cell specific. These results are in agreement with the hypothesis that the oscillatory activity of olivary neurons is generated by a network of electrically coupled neurons. Using alternating current analysis, we found that impedance-frequency curves of olivary neurons demonstrate a peak impedance (resonance) at a frequency between 3 and 10 Hz, which corresponds to the frequency of the spontaneous oscillations. Like the spontaneous oscillations, this peak is tetrodotoxin insensitive, unaffected by K+ channel blockers and almost completely blocked in the presence of Ni2+ in the physiological solution. Increasing the temperature increases the resonance frequency, as well as the frequency of the spontaneous oscillations. These results show that the resonant behavior of individual neurons is the basis of the oscillatory behavior of the network and that resonance can serve as a lumped parameter which encodes the oscillatory tendency of a neuron.

Contribution of voltage-dependent potassium channels to the somatic shunt in neck motoneurons of the cat

The specific membrane resistivity of motoneurons at or near the soma (Rms) is much lower than the specific membrane resistivity of the dendritic tree (Rmd). The goal of the present experiments was to investigate the contribution of tonically active voltage-dependent potassium channels at or near the soma to the low Rms. These channels were blocked with the use of intracellular injections of cesium. Input resistance (RN), Rms/Rmd, a conductance representing voltage-dependent potassium channels on the soma, GK, and a conductance attributed to damage caused by electrode impalement, GDa, were estimated from voltage responses to a step of current. The effect of intracellular injections of cesium on electrotonic structure was determined with the use of two strategies: 1) a population analysis that compared data from two groups of motoneurons, those recorded with potassium acetate electrodes (control group) and those recorded with cesium acetate electrodes after the motoneurons were loaded with cesium; and 2) an analysis of changes in electrotonic structure that occurred over the course of multiple injections of cesium or during similar periods of time in control cells. RN of control and cesium-loaded motoneurons was similar. Over the course of the recordings, RN of control cells usually increased and this increase was associated with a hyperpolarization. In contrast, increases in RN after successive injections of cesium were closely linked to a depolarization. At corresponding membrane potentials, Rms/Rmd of cesium-loaded motoneurons was greater than Rms/Rmd of control motoneurons. Over the course of cesium injections, Rms/Rmd increased and the membrane potential depolarized. In contrast, increases in Rms/Rmd observed during the course of recordings from control cells were associated with a hyperpolarization. Compared with control cells at corresponding membrane potentials, GK was less in cesium-loaded cells. Increases in GK that occurred over the course of recordings in control cells were closely coupled to a depolarization. In cesium-loaded cells, GK usually decreased as the cell depolarized during the injections. In control cells, increases in GDa that occurred during the recording period were closely coupled to a depolarization. In contrast, changes in GDa that occurred during cesium injections were not related to the change in membrane potential and did not explain the corresponding changes in Rms/Rmd and membrane potential. The results of this study indicate that voltage-dependent potassium channels contribute to the somatic shunt (low Rms) in neck motoneurons and provide a voltage-dependent mechanism for the dynamic regulation of motoneuron electrotonic properties.

Nonlinear parameter estimation by weighted linear associative memory with nonzero interception

The method of linear associative memory (LAM) has recently been applied in nonlinear parameter estimation. In the method of LAM, a model response, nonlinear with respect to the parameters, is approximated linearly by a matrix, which maps inversely from a response vector to a parameter vector. This matrix is determined from a set of initial training parameter vectors and their response vectors according to a given cost function, and can be updated recursively and adaptively with a pair of newly generated parameter-response vector. The advantage of LAM is that it can yield good estimation of the true parameter from a given observed response even if the initial training parameter vectors are far from the true values. In a previous paper, we have significantly improved the LAM method by introducing a weighted linear associative memory (WLAM) approach for nonlinear parameter estimation. In the WLAM approach, the contribution of each pair of parameter-response vector to the cost function is weighted in a way such that if a response vector is closer to the observed one then its pair plays more important role in the cost function. However, in both LAM and WLAM, the linear association is introduced with zero interceptions, which would not give an exact association even if the model function is linear and so will affect the efficiency of the estimations. In this paper, we construct a theory which introduces a linear association memory with a nonzero interception (WLAMB). The results of our estimation tests on two quite different models, Van der Pol equation and somatic shunt cable model, suggest that WLAMB can still significantly improve on WLAM.

On the analytic solution of electrotonic spread in branched passive dendritic trees

From the classical work of Rall it is known that the spread of electric potential in a passive dendritic tree may be obtained by expressing the initial conditions as a linear combination of a set of trigonometric eigenfunctions, each decaying with the associated time constant. It is shown here that in order to evaluate the permissible parameters in these eigenfunctions one may formulate the boundary conditions at all the junctions and endings of the dendritic tree as a set of homogeneous linear equations in which the parameters in the eigenfunctions are the unknowns. These equations have a nontrivial solution if the relevant determinant vanishes, a condition that permits the evaluation of the various parameters, thus providing an analytic approach to the expression of the eigenfunctions as well as the decay time constants. The above approach is illustrated by application to a dendritic tree that has a parent segments and two generations of offspring segments, without any restrictions as to the relative diameters or lengths of the various segments in the tree. General properties of the tree may be readily derived, like the variation of the eigenvalues on scaling of the lengths or diameters of all the segments. A few special cases with specified dimensions of the various segments are derived from the general case. In the case of a dendritic tree that fulfills the "equivalent cylinder" conditions, all of the eigenvalues and eigenfunctions of the tree may be determined by the proposed method, including those that do not apply to the equivalent cylinder. The orthogonality properties of the eigenfunctions are discussed.

Evidence of a sensory processing unit in the mammalian macula

We cut serial sections through the medial part of the rat vestibular macula for transmission electron microscopic (TEM) examination, computer-assisted 3-D reconstruction, and compartmental modeling. The ultrastructural research showed that many primary vestibular neurons have an unmyelinated segment, often branched, that extends between the heminode (putative site of the spike initiation zone) and the expanded terminal(s) (calyx, calyces). These segments, termed the neuron branches, and the calyces frequently have spine-like processes of various dimensions with bouton endings that morphologically are afferent, efferent, or reciprocal to other macular neural elements. The major questions posed by this study were whether small details of morphology, such as the size and location of neuronal processes or synapses, could influence the output of a vestibular afferent, and whether a knowledge of morphological details could guide the selection of values for simulation parameters. The conclusions from our simulations are (1) values of 5.0 k omega cm2 for membrane resistivity and 1.0 nS for synaptic conductance yield simulations that best match published physiological results; (2) process morphology has little effect on orthodromic spread of depolarization from the head (bouton) to the spike initiation zone (SIZ); (3) process morphology has no effect on antidromic spread of depolarization to the process head; (4) synapses do not sum linearly; (5) synapses are electrically close to the SIZ; and (6) all whole-cell simulations should be run with an active SIZ.

Nonlinear parameter estimation by linear association: application to a five-parameter passive neuron model

Linear associative memories (LAM) have been intensely used in the areas of pattern recognition and parallel processing for the past two decades. Application of LAM to nonlinear parameter estimation, however, has only been recently attempted. The process consists in converting the nonlinear function in the parameters into a set of linear algebraic equations. The nature of the linearized system and the factors influencing the accuracy of the parameter estimates have not yet been fully investigated. In this paper, LAM is applied to a nonlinear five-parameter model of the neuron. Ill-conditioning, which is often exhibited in LAM, is treated with the method of regularization as well as by the singular value decomposition (SVD). Simulation results indicate that the parameters estimated by LAM exhibit a remarkable robustness against additive white noise in comparison with the classical gradient optimization technique. Moreover, it is shown that regularization can be superior to SVD under certain conditions. Our results suggest that LAM can be used both as a noise reduction technique and as a stand-alone nonlinear parameter estimation algorithm. The comparison between LAM and a gradient technique show that, for this estimation problem, the LAM method can give more reliable estimates. Further improvements in estimation quality may still be achieved by the use of other forms of regularizing functions.

Dendritic attenuation of synaptic potentials and currents: the role of passive membrane properties

The dendritic trees of neurons are structurally and functionally complex integrative units receiving thousands of synaptic inputs that have excitatory and inhibitory, fast and slow, and electrical and biochemical effects. The pattern of activation of these synaptic inputs determines if the neuron will fire an action potential at any given point in time and how it will respond to similar inputs in the future. Two critical factors affect the integrative function of dendrites: the distribution of voltage-gated ion channels in the dendritic tree and the passive electrical properties, or 'electrotonic structure', upon which these active channels are superimposed. The authors review recent data from patch-clamp recordings that provide new estimates of the passive membrane properties of hippocampal neurons, and show, with examples, how these properties affect the shaping and attenuation of synaptic potentials as they propagate in the dendrites, as well as how they affect the measurement of current from synapses located in the dendrites. Voltage-gated channels might influence the measurement of 'passive' membrane properties and, reciprocally, passive membrane properties might affect the activation of voltage-gated channels in dendrites.

Pyramidal neurons in layer 5 of the rat visual cortex. II. Development of electrophysiological properties

Two major classes of pyramidal neurons can be distinguished in layer 5 of the adult rat visual cortex. Cells of the "thick/tufted" type have stout apical dendrites with terminal tufts, and most of them project to the superior colliculus (Larkman and Mason: J Neurosci 10:407, '90; Kasper et al.: J Comp Neurol, this issue, 339:459-474). "Slender/untufted" cells have thinner apical trunks with no obvious terminal tufts, and a substantial proportion of them project to the contralateral visual cortex. These two types also differ in their intrinsic electrophysiological features. In this study we describe the postnatal maturation of the electrophysiological and synaptic properties of layer 5 pyramidal neurons and relate these findings to the morphological development and divergence of the two cell types. Living slices were prepared from the visual cortex of rats aged between postnatal day 3 (P3) and young adults and maintained in vitro. Stable intracellular impalements were obtained from a total of 63 pyramidal cells of layer 5 at various ages, which were injected with biocytin so that morphological and electrophysiological data could be obtained from the same cell. Before P15, injection of a single cell sometimes stained a cluster of neurons of similar morphology, probably as a result of dye coupling. The incidence of such clustering and the number of neurons within each cluster decreased with age. There was no obvious difference in electrophysiological properties between cells in clusters and age-matched, noncoupled neurons. From P5, the apical dendrites of neurons could easily be classified as "thick/tufted" or "slender/untufted." On average, the resting potential became more negative, and membrane time constant and input resistance decreased with age. Electrophysiological differences between the "thick/tufted" and "slender/untufted" cell types did not become apparent until the third postnatal week, after which the "thick/tufted" cells on average had lower input resistances and slightly faster time constants than "slender/untufted" cells. The current-voltage relations of the neurons became progressively more nonlinear during maturation, with both rapid inward rectification and time-dependent rectification or "sag" becoming more prominent. There were also changes in the amplitude and waveform of action potentials, which generally approached adult values by 3 weeks of age. Action potential threshold became more negative, both in absolute terms and relative to the resting membrane potential. Action potentials became larger in peak amplitude and of shorter duration, with both rise and fall times decreasing progressively during development.(ABSTRACT TRUNCATED AT 400 WORDS)

Pyramidal neurons in layer 5 of the rat visual cortex. I. Correlation among cell morphology, intrinsic electrophysiological properties, and axon targets

Previous work has established two structure/function correlations for pyramidal neurons of layer 5 of the primary visual cortex of the rat. First, cells projecting to the superior colliculus have thick apical dendrites with a florid terminal arborization in layer 1, whereas those projecting to the visual cortex of the opposite hemisphere have thinner apical dendrites that terminate below layer 1, without a terminal tuft (e.g., Hallman et al.: J Comp Neurol 272:149, '90). Second, intracellular recording combined with dye injection has revealed two classes of cells: the first has a thick, tufted apical dendrite and fires a distinctive initial burst of two or more impulses, of virtually fixed, short interspike interval, in response to current injection; and the other, with a slender apical dendrite lacking a terminal tuft, tends to have a longer membrane time constant and higher input resistance, and does not fire characteristic bursts (e.g., Larkman and Mason: J Neurosci 10:1407, '90). The present study combined intracellular recording in isolated slices of rat visual cortex and injection of carboxyfluorescein, to reveal soma-dendritic morphology, with prior injection of rhodamine-conjugated microspheres into the superior colliculus or contralateral visual cortex to label neurons according to the target of their axons. This permitted a complete correlation of morphology, intrinsic electrophysiological properties, and identity of the projection target for individual pyramidal cells. Neurons retrogradely labeled from the opposite visual cortex were found in all layers except layer 1 while those labeled from the superior colliculus lay exclusively in layer 5. Within layer 5 interhemispheric cells were more concentrated in the lower half of the layer but extensively overlapped the distribution of corticotectal cells. Every cell studied that projected to the superior colliculus was of the bursting type and had a thick apical dendrite with a terminal tuft. Every cell in this study projecting to the opposite visual cortex was a "nonburster" and had a slender apical dendrite with fewer oblique branches that ended without a terminal tuft, usually in the upper part of layer 2/3. Interhemispheric cells also had rounder, less conical somata and generally had fewer basal dendrites than corticotectal neurons. Many cells with the physiological and morphological characteristics of interhemispheric cells were not back-labeled from the opposite visual cortex, implying that pyramidal cells of this type can have other projection targets (e.g., other cortical sites in the ipsilateral hemisphere).(ABSTRACT TRUNCATED AT 400 WORDS)

Physiology, morphology and detailed passive models of guinea-pig cerebellar Purkinje cells

1. Purkinje cells (PCs) from guinea-pig cerebellar slices were physiologically characterized using intracellular techniques. Extracellular caesium ions were used to linearize the membrane properties of PCs near the resting potential. Under these conditions the average input resistance, RN, was 29 M omega, the average system time constant, tau 0, was 82 ms and the average cable length, LN, was 0.59. 2. Three PCs were fully reconstructed following physiological measurements and staining with horseradish peroxidase. Assuming that each spine has an area of 1 micron 2 and that the spine density over the spiny dendrites is ten spines per micrometre length, the total membrane area of each PC is approximately 150,000 microns 2, of which approximately 100,000 microns 2 is in the spines. 3. Detailed passive cable and compartmental models were built for each of the three reconstructed PCs. Computational methods were devised to incorporate globally the huge number of spines into these models. In all three cells the models predict that the specific membrane resistivity, Rm, of the soma is much lower than the dendritic Rm (approximately 500 and approximately 100,000 omega cm2 respectively). The specific membrane capacitance, Cm, is estimated to be 1.5-2 muF cm-2 and the specific cytoplasm resistivity, Ri, is 250 omega cm. 4. The average cable length of the dendrites according to the model is 0.13 lambda, suggesting that under caesium conditions PCs are electrically very compact. Brief somatic spikes, however, are expected to attenuate 30-fold when spreading passively into the dendritic terminals. A simulated 200 Hz train of fast, 90 mV somatic spikes produced a smooth 12 mV steady depolarization at the dendritic terminals. 5. A transient synaptic conductance increase, with a 1 nS peak at 0.5 ms and a driving force of 60 mV, is expected to produce approximately 20 mV peak depolarization at the spine head membrane. This EPSP then attenuates between 200- and 900-fold into the soma. Approximately 800 randomly distributed and synchronously activated spiny inputs are required to fire the soma. 6. The passive model of the PC predicts a poor resolution of the spatio-temporal pattern of the parallel fibre input. An equally sized, randomly distributed group of approximately 1% of the parallel fibres, activated within a time window of a few milliseconds, would result in approximately the same composite EPSP at the soma.

4-Aminopyridine-induced synaptic GABAB currents in granule cells of the guinea-pig hippocampus

Sharp-electrode and tight-seal perforated-patch and whole-cell recording techniques were used to evaluate K(+)-dependent inhibitory postsynaptic potentials (K-IPSPs) and currents (K-IPSCs) induced by the convulsant 4-aminopyridine (50 mumol l-1) in granule cells of guinea-pig hippocampal slices. The responses were recorded in the presence of blockers for glutamatergic and GABAA-receptor-mediated synaptic transmission, 6-cyano-7-nitroquinoxaline-2,3-dione, picrotoxin and bicuculline. The input resistance was much larger (approximately 300 M omega) in tight-seal recording than in sharp-electrode recording (approximately 100 M omega), but the amplitudes of K-IPSPs recorded at -65 mV holding potential were similar in all three recording configurations. The 4-aminopyridine-induced currents reversed near the K+ equilibrium potential, and the reversal potentials shifted with changes in [K+]out or [K+]in as expected for a K+ current. Slope conductance measurements indicated a conductance increase during the peak of the K-IPSP up to 5 nS (mean 2.4 nS). The peak conductance was underestimated in whole-cell recordings unless the pipette contained Cs+. Considering the high membrane resistance of granule cells, K-IPSCs induced by 4-aminopyridine hyperpolarize the cells considerably and thereby are likely to contribute to the failure of 4-aminopyridine to induce burst discharges in granule cells.

Ethanol uncouples dentate granule neurons by increasing junctional resistance: a multineuronal system model approach

The effects of an acute intoxicating concentration of ethanol (50 mM) on the electrotonic membrane properties of hippocampal dentate granule neurons were studied using a system model incorporating electrotonic coupling between neurons. Uncoupling of cells by other alcohols has been shown in several tissues. The system model allows a quantitative estimation of the changes in coupling and other neuronal electrotonic properties. The input impedance of a neuron was measured from the voltage decay of a short hyperpolarizing current pulse. An analytic expression of the input impedance has been written incorporating somatic, dendritic, and electrical coupling parameters. Using this particular current stimulation, the modelling results showed that ethanol selectively increased the junctional resistance by more than 2.5 times, hence uncoupling the neurons. A 30% increase in the final time-constant, tau 0, was also obtained from the voltage transient. Other parameters were not significantly affected. A neuronal model without electrotonic coupling to other neurons gave rise to physiologically impossible values for the membrane resistance and capacitance. With resistive and capacitive coupling in the model, uncoupling did not occur with ethanol. It is concluded that ethanol uncouples neurons by increasing the effective gap junctional resistance in dentate granule neurons.

The Extent of the Dendritic Tree and the Number of Synapses in the Frog Motoneuron

Frog motoneurons were intracellularly labelled with cobaltic lysine in the brachial and the lumbar segments of the spinal cord, and the material was processed for light microscopy in serial sections. With the aid of the neuron reconstruction system NEUTRACE, the dendritic tree of neurons was reconstructed and the length and surface area of dendrites measured. The surface of somata was determined with the prolate - oblate average ellipsoid calculation. Corrections were made for shrinkage and for optical distortion. The mean surface area of somata was 6710 microm2; lumbar motoneurons were slightly larger than brachial motoneurons. The mean length of the combined dendritic tree of brachial neurons was 29 408 microm and that of lumbar neurons 46 806 microm. The mean surface area was 127 335 microm2 in brachial neurons, and 168 063 microm2 in lumbar neurons. The soma - dendrite surface area ratio was 3 - 5% in most cases. Dendrites with a diameter of </= 1.0 microm constituted approximately 75% of the combined dendritic length in most of the neurons. Unlike in the cat, there was no correlation between the size of stem dendrites and the extent of daughter branches. From the synaptic density estimated in earlier electron microscope investigations of frog motoneuron dendrites (Antal et al., J. Neurocytol., 15, 303 - 310, 1986; 21, 34 - 49, 1992), and from the present data, the number of synapses on the dendritic tree was calculated. The calculations indicated 26 949 synapses on the smallest and 61 519 synapses on the largest neuron if the synaptic density was multiplied by the length of the dendritic tree. If the synaptic density was multiplied by the surface area of the dendritic tree the calculation yielded 23 337 synapses for the smallest and 60 682 synapses for the largest neuron. More than 60% of the combined surface area of dendrites was >600 microm from the soma. This suggests that about two-thirds of the synapses impinged upon distant dendrites >600 microm from the soma. The efficacy of synapses at these large distances is investigated on model neurons in the accompanying paper (Wolf et al., Eur. J. Neurosci., 4 1013 - 1021, 1992).

Dendritic morphology of pyramidal neurones of the visual cortex of the rat. IV: Electrical geometry

Features of the dendritic morphology of pyramidal neurones of the visual cortex of the rat that are relevant to the development of models of their passive electrical geometry were investigated. The sample of 39 neurones that was used came from layers 2/3 and 5. They had been recorded from and injected intracellularly with horseradish peroxidase (HRP) in vitro as part of a previous study (Larkman and Mason, J. Neurosci 10:1407, 1990). These cells had been reconstructed and measured previously by light microscopy. The relationship between the diameters of parent and daughter dendrites during branching was examined. It was found that most dendrites did not closely obey the "3/2 branch power relationship" required for representation of the dendrites as single equivalent cylinders. Estimates of total neuronal membrane area ranged from 27,100 +/- 7,900 microns2 for layer 2/3 cells to 52,200 +/- 11,800 microns2 for thick layer 5 cells. Dendritic spines contributed approximately half the total membrane area. Both neuronal input resistance and the ratio of membrane time constant to input resistance were correlated with neuronal membrane area as measured anatomically. The relative electrical lengths of the different dendrites of individual neurones were investigated, by using simple transformations to take account of the differences in diameter and spine density between dendritic segments. A novel "morphotonic" transformation is described that represents the purely morphological component of electrotonic length. Morphotonic lengths can be converted into electrotonic lengths by division by a "morphoelectric factor" ([Rm/Ri]1/2). This procedure has the advantage of separating the steps involving anatomical and electrical parameters. These transformations indicated that the dendrites of the apical terminal arbor were much longer electrically than the basal or apical oblique dendrites. In relative electrical terms, most apical oblique trees arose extremely close to the soma, and terminated at similar distances to the basals. These results indicate that the dendrites of these pyramidal cells cannot be represented as single equivalent cylinders. The electrotonic lengths of the dendrites were calculated by using the electrical parameters specific membrane capacitance (Cm), intracellular resistivity (Ri), and specific membrane resistivity (Rm). Conventional values were assumed for Cm (1.0 muFcm-2) and Ri (100 omega cm), but three different Rm values were used for each cell. Two of these were within the conventionally accepted range (10,000-20,000 omega cm2), while the third value was an order of magnitude higher, in line with some recent evidence from modeling and whole-cell recording studies.(ABSTRACT TRUNCATED AT 400 WORDS)

Estimation of electrotonic parameters of neurons using an inverse Fourier transform technique

The objective of this paper is to estimate the passive electrotonic parameters of hippocampal granule cells. Accurate estimation of these parameters is important in understanding the information processing of neurons. A shunt cable model, where the somatic and dendritic time constants can be different, is used to describe the potential changes in the soma and along the dendritic tree. For this model, parameter values are estimated by nonlinear least-squares fitting of the model output to the voltage response of the stimulated cell to current pulses. The solutions are obtained in a two-step process: First, the sensitivity functions are derived from the Laplace transform solution of the theoretical model. Second, the time domain solutions are obtained numerically by an inverse FFT. A sensitivity analysis indicates that accurate estimates require the use of a short current pulse injected at the soma and the sampling of the voltage response close to the end of that pulse. This parameter estimation procedure has been tested on hippocampal granule cells. It yields accurate estimation of neural parameters and will be a useful tool for measuring passive properties of neurons.

Impulses and resting membrane properties of small cultured rat hippocampal neurons

1. The impulses and resting membrane parameters of small (soma diameter less than 10 microM) cultured hippocampal neurons from rat embryos were studied with the tight-seal whole-cell recording technique. 2. Mean resting potential was -47 mV, mean input resistance 3.3 G omega, mean capacitance 11 pF, and mean time constant 33 ms. 3. Rectangular suprathreshold current steps elicited regenerative potential responses. The amplitude and time course of the responses were clearly stimulus dependent: stronger current steps caused impulses of larger amplitude. 4. The current threshold was very low: rheobase current was less than 15 pA. 5. The potential response depended on the preceding holding potential, responses from more negative potentials showing sharper peaks than those from more positive potentials. 6. Spontaneous impulses with pre-potentials similar to synaptically induced events were recorded from several cells. The amplitude of the spontaneous impulses varied similarly to that of the stimulus-induced responses.

Effects of ethanol on the excitability of hippocampal granule neurons

The effects of low dose ethanol treatment on neuronal firing threshold were studied in dentate granule neurons using intracellular recording. A higher threshold for orthodromic activation and lower threshold for somatic activation were observed in 50 mM of ethanol, based on an examination of the excitatory postsynaptic potentials, strength duration and repetitive firing properties. Experiments involving blockade of glutamate-receptor subtypes suggest that an N-methyl-D-aspartate (NMDA) receptor mediated mechanism is implicated in this action of ethanol.

Functional elongation of CA1 hippocampal neurons with aging in Fischer 344 rats

Dendritic function of CA1 pyramidal cells was measured during intracellular recording in vitro and correlated with in vivo behavior in Fischer 344 rats. The aged rats (greater than 26 months) were significantly impaired on a water maze test of hippocampal behavioral function. CA1 neurons from these aged rats demonstrated an elevated action potential threshold compared to the young rats. Electrotonic length (L, in lambda), calculated independently from physiological transients and electrotonic cell reconstructions, was significantly longer in neurons from aged rats (L = 0.73 +/- 0.02 lambda; mean +/- SEM) than in neurons from young rats (L = 0.66 +/- 0.02 lambda). Analysis of proximal and distal synaptic potentials pointed to a more distal electrotonic siting of all dendritic synapses in the aged neurons. Thus, electrical lengthening of dendrites, alterations in synaptic location and decreased excitability in neurons from aged rats with behavioral impairment may represent an endpoint of neuronal reactive mechanisms in response to the aging process.

Reconstruction of hippocampal granule cell electrophysiology by computer simulation

A model of the hippocampal granule cells was created that closely approximated most of the measured intracellular responses from a neuron under a variety of stimulus conditions. This model suggests that: (1) A simple, four-conductance model can account for most of the intracellular behavior of these neurons. (2) The repolarization mechanism in granule cells may be different from that in squid axons. A weak potassium conductance may be present in hippocampal granule neurons, which simultaneously give rise to a small, passive depolarizing afterpotential. (3) The strength duration properties may assist in identifying the electronic and sodium channel properties with short stimulus pulse widths. (4) Repetitive firing responses are highly dependent on the cell's recent history of activation and the regulation of the slow potassium conductance and calcium dynamics. (5) The anodic break response is probably not a property of typical granule cells. Through thorough and precise comparison of experimental and model responses, computer simulations can help assembling channel information into verifiable models that accurately reproduce intracellular data.

Quantitative, three-dimensional analysis of granule cell dendrites in the rat dentate gyrus

The three-dimensional organization of dentate granule cell dendritic trees has been quantitatively analyzed with the aid of a computerized microscope system. The dendrites were visualized by iontophoretic injection of horseradish peroxidase into individual granule cells in the in vitro hippocampal slice preparation. Selection criteria insured that the analyzed cells were completely stained and that only neurons with two or fewer cut dendrites in the distal portion of the molecular layer were analyzed. Twenty-nine of the 48 sampled granule cells had no cut dendrites. The granule cells had between one and four primary dendrites. Granule cell dendritic branches were covered with spines and most extended to the hippocampal fissure or pial surface. The mean total dendritic length was 3,221 microns with a range from 2,324 microns to 4,582 microns. The dendrites formed an elliptical plexus with the transverse spread averaging 325 microns and the spread in the septotemporal axis averaging 176 microns. On individual neurons, the maximum branch order ranged from four to eight and the number of dendritic segments ranged from 22 to 40. Approximately 63% of the dendritic branch points occurred in a zone that included the granule cell layer and the inner one-third of the molecular layer. The dendritic tree was organized so that, on average, 30% of the length was in the granule cell layer and proximal third of the molecular layer, 30% was in the middle third, and 40% was in the distal third. Comparisons were made between the dendrites of granule cells in the suprapyramidal and infrapyramidal blades of the dentate gyrus. Suprapyramidal cells had a significantly greater total dendritic length than infrapyramidal cells, their transverse spread was higher, and they had a greater number of dendritic segments. When neurons in the suprapyramidal blade were further subdivided on the basis of somal position within the depth of the cell body layer, superficial neurons were found to have a greater number of primary dendrites, more elliptical trees, and larger transverse spreads of their dendrites. There were no significant differences in dendritic segment number or total dendritic length between superficial and deep cells.

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.

Effects of uniform and non-uniform synaptic 'activation-distributions' on the cable properties of modeled cortical pyramidal neurons

Knowledge of the resting potential and input resistance reveal little about the electrotonic structure of nerve cells since that structure is governed by the background distribution of activated conductances. The background distribution of activated conductances (or 'activation-distribution') is commonly assumed to be uniform, but there is much evidence to suggest that the 'activation-distribution' of cortical pyramidal cells in non-uniform. We investigated effects of uniform and non-uniform activation-distributions with simulations employing passive cable models of an HRP-injected cortical pyramidal neuron. The consequences of 5 different activation-distributions on the effectiveness of synaptic inputs and the electrophysiological properties of the neuron were compared. With non-uniform activation-distributions, (i) the resting membrane potential was non-uniform (with difference of 10-15 mV or more found between soma and distal dendrites), (ii) the electrotonic distances to distal synapses were smaller than with a uniform distribution, and (iii) a two-fold range of variation was seen in the effectiveness of distal synaptic inputs. Differences in time constants, tau 0 and tau 1, obtained from an analysis of transients and in electrotonic length, L, were also found with different activation-distributions. These differences were difficult to assess due to the inherent difficulty in estimating tau 1 (as demonstrated here) and the inappropriateness of the usual formula for L for these cells. Reducing afferent activity (as might happen in tissue slice) increased the effectiveness of distal inputs and reduced the differences in resting potential seen in the neuron. It is concluded that the effectiveness of synaptic inputs and the electrophysiological properties of a neuron can be quite different when the activation-distribution is non-uniform rather than uniform.

Anoxic changes in dentate granule cells

In most of the granule cells recorded, by current clamp and single-electrode voltage-clamp (SEVC), only small depolarizations (or inward currents) and minor conductance increases were observed during brief periods of anoxia (2-3 min). Thus, unlike pyramidal cells, granule cell bodies show little sign of K channel activation by anoxia. Post-anoxic hyperpolarizations were also minimal. Moreover, diazoxide (an activator of ATP-sensitive K conductance (GK(ATP]) had no consistent hyperpolarizing action. The depressant effect of diazoxide on anoxic glutamate release from mossy fibres is therefore likely to be mediated by GK(ATP) channels situated on granule cell axons or terminals rather than on the cell bodies.

A system model for investigating passive electrical properties of neurons

Passive membrane properties of neurons, characterized by a linear voltage response to constant current stimulation, were investigated by busing a system model approach. This approach utilizes the derived expression for the input impedance of a network, which simulates the passive properties of neurons, to correlate measured intracellular recordings with the response of network models. In this study, the input impedances of different network configurations and of dentate granule neurons, were derived as a function of the network elements and were validated with computer simulations. The parameters of the system model, which are the values of the network elements, were estimated using an optimization strategy. The system model provides for better estimation of the network elements than the previously described signal model, due to its explicit nature. In contrast, the signal model is an implicit function of the network elements which requires intermediate steps to estimate some of the passive properties.

Theoretical response of a bifurcating axon with a locally altered axial resistivity

A short region of high axial resistivity at one daughter branch of an axonal bifurcation can produce frequency dependent differential conduction of action potentials. The increase in resistivity need be only a few times that in the rest of the axon and length of the affected region need be only a fraction of a resting length constant (based on the local value of axial resistivity). The typical pattern observed will be that the unaffected daughter branch will conduct action potentials from the parent axon normally at all frequencies of stimulation, but the branch with the high resistance region will only follow action potentials within a restricted frequency range. In that band-pass region, the branch may conduct nearly all or only a small percentage of the action potentials from the parent axon.

Cable properties of cat spinal motoneurones measured by combining voltage clamp, current clamp and intracellular staining

1. Spinal alpha-motoneurones were injected with horseradish peroxidase after measuring their voltage response to a brief current pulse and their current response to a small voltage step. 2. The morphology of each motoneurone was reconstructed from serial sections. The diameters and lengths of dendritic segments were used to build a compartmental model of each neurone's electrotonic structure. The specific resistivity of the membrane (Rm) was assumed to be constant throughout the dendrites, but it was lowered for the somatic membrane by the introduction of a somatic shunt resistance. 3. The specific resistances of the somatic and dendritic membrane were adjusted in the compartmental model until the responses of the model to the same current and voltage steps as those used in the experiment gave the best fits to the recorded transients. Satisfactory fits were obtained for six out of seven motoneurones. Dendritic Rm varied from 7 to 35 k omega cm2 and somatic Rm varied from 100 to 420 omega cm2. The dendritic Rm was 100-300 times the somatic Rm for different neurones. 4. The calculated dendritic Rm was used to determine the geometric profile of the equivalent dendritic cable. This was found to be an approximately uniform cylinder for about 0.5 lambda and thereafter to taper rapidly to a final termination at 2-3 lambda from the soma. 5. The results indicate that motoneurone dendrites are more electrically compact than was hitherto believed. The different Rm values for somatic and dendritic membrane, and the tapering of the dendritic cable, means that the cable model developed by Rall (1959, 1964) must be revised to take account of these spatial and electrical non-uniformities.

Computation of the passive electrical parameters of neurons using a system model

Time-domain analysis of voltage responses to current pulse stimulation has been used to estimate the electrotonic parameters of neurons using the signal model. Errors are likely to accumulate from various steps of the analysis due to noise and electrode artifacts. A system model, which has inherent noise immunity and filtering properties, is presented here. This model employs frequency-domain analysis of the input impedance of a neuronal model (an RC cable). The resistances and capacitances of the system model are estimated from the cell-input impedance using an optimization strategy. Using the expression for the input impedance, any specified number of equalizing time constants can be computed exactly. The accessibility to these equalizing time constants 1) provides greater insight into the charge equalization along the length and circumference of the cable, and 2) improves the estimation of all other passive parameters including the electrotonic length. Thus, the system model approach allows information to be extracted more directly and accurately than the signal model approach.

Electrotonic properties of neostriatal neurons are modulated by extracellular potassium

In order to assess the effects of [K+]o on the passive membrane properties of neostriatal neurons, the cable properties of these cells were determined at two extracellular potassium concentrations (6.25 and 3.0 mM). The effect of tetraethylammonium (TEA) on cable properties was also studied at 6.25 [K+]o. At 6.25 mM [K+]o, the mean input resistance at the resting membrane potential (RMP), and the mean membrane time constant (tau o) were 27 +/- 1.5 M omega and 6.9 +/- 0.5 ms respectively (n = 17), while at 3 mM [K+]o they were 62.9 +/- 4.8 M omega and 14.3 +/- 0.6 ms (n = 15) (mean +/- SEM). With one of the methods used to calculate the electronic parameters, the total electrotonic length of the dendrites (L) and the dendritic to somatic conductance ratio (rho) were 1.3 +/- 0.05 and 5 +/- 0.8 at the higher [K+]o respectively, while they were 0.95 +/- 0.04 and 3 +/- 0.7 at the lower [K+]o. Cells were depolarized in 6.25 as compared to 3 mM [K+]o (RMP = -66 +/- 1.3 mV vs RMP = -80.5 +/- 1.4 mV). After one hour exposure to TEA (10 mM), the input resistance and time constant tripled at 6.25 mM [K+]o. TEA slightly depolarized the cells bathed in 6.25 mM [K+]o. The results suggest that changes in [K+]o, within the physiological range, markedly affect the cable properties of neostriatal neurons, possibly modifying subthreshold, voltage-dependent K+-conductances. TEA seems to block some of these channels.

Overestimation of the electrical length of neuron dendrites and synaptic electrotonic attenuation

The electrical (also termed electrotonic) length of dendrites is a key factor in determining the magnitude of the decay of a postsynaptic potential as it propagates from the dendrites to the soma. The average electrotonic length of dendrites in spinal, hippocampal, and red nucleus neurons have been estimated at 1.2 (range of 0.9-1.5), based on single (equivalent) cylinder models. Synaptic potentials evoked at the terminals of dendrites that are 1.2 space constants in length have been estimated to decay 50% during propagation to the soma, the lost energy being dissipated as heat. The present analysis was conducted because a 50% propagation loss seemed unlikely for such a widespread neuron function as passive dendritic propagation. The explicit and implicit assumptions of the cylinder model were reconsidered. It was found that the simplifying assumption of uniform dendritic electrotonic length has led to a three-fold overestimate of dendritic electrotonic length by previous investigators. The conclusion is that dendrites have a typical electrotonic length of 0.4 rather than 1.2, therefore resulting in a propagation loss of only 7% rather than 50% for distal dendritic synapses.

Measurements of dendritic conductance changes to GABA in granule cells of the rat dentate gyrus

The magnitude of dendritic conductance changes occurring distantly from the somatic site of recording can be difficult to measure. We have used measurements of the neuronal time constant, tau 0, instead of the neuronal input resistance, RN, to estimate the resistance decrease that accompanies the depolarizing response of the dendrites of granule cells when GABA is applied. From the changes in tau 0, we estimated the reversal potential of the response and found that the conductance change accompanying a given GABA-mediated voltage response as measured at the cell body was the same regardless of where in the dendritic tree the drug was applied. On the other hand, RN changes underestimated the increase in conductance of the GABA responses in the distal dendrites and were not accurate for determining the reversal potential.

Electrically coupled but chemically isolated synapses: dendritic spines and calcium in a rule for synaptic modification

An influential model of learning assumes synaptic enhancement occurs when there is pre- and post-synaptic conjunction of neuronal activity, as proposed by Hebb (1949) and studied in the form of long-term potentiation (LTP). There is evidence that LTP has a post-synaptic locus of control and is triggered by an elevation of intracellular calcium ion concentration, [Ca2+]i. Since synapses which undergo LTP are usually situated on dendritic spines, three effects of spine morphology on this system should be considered: (i) synapses on spines are chemically isolated by the barrier to Ca2+ diffusion due to the spine neck dimensions; (ii) the resistance of the spine neck permits a given synaptic current to bring about greater depolarization (of the spine head membrane) than the same current into a dendrite; while (iii) the spine neck resistance does not significantly attenuate current flow (in the dendrite to spine direction) because of the relatively high impedance of the spine head, and this permits electrical coupling via the dendritic tree. The specificity of LTP to activated synapses on depolarized cells has recently been attributed to special properties of the receptor-linked channel specifically activated by N-methyl-D-aspartate (NMDA). This admits calcium and other ions only when there is both depolarization and receptor activation. However, consideration of point (ii) suggests that, for spines with high resistance necks, the current through a synapse on the spine head will cause sufficient depolarization to unblock the NMDA channel. Thus, the properties of the NMDA channel do not account for the requirement for conjunction of pre- and post-synaptic activity, if these channels are located on the spine head. This suggests that additional mechanisms are required to explain why it is necessary to depolarize the post-synaptic cell in order to induce LTP. As an alternative, it is postulated that there exist voltage-sensitive calcium channels (VSCCs) on the spine head membrane, of a type which require greater membrane depolarization for activation. To generate the greater depolarization required, both pre- and post-synaptic activation would be necessary. If so, the role of dendritic or somatically located NMDA channels may be to "prime" neurons for LTP by enchancing voltage-dependent responses. A corollary is that spine resistance may regulate the threshold number of synapses required to produce LTP. It is predicted that, on spines with very high neck resistance (say, greater than 600 M omega), synaptic current alone may produce sufficient depolarization to activate VSCCs.(ABSTRACT TRUNCATED AT 400 WORDS)

Electrotonic parameters of cat spinal alpha-motoneurons evaluated with an equivalent cylinder model that incorporates non-uniform membrane resistivity

The membrane voltage transients in response to constant intracellular current steps were analyzed in cat spinal alpha-motoneurons, using an equivalent cylinder model extended to include spatial non-uniformity in membrane resistivity. The main hypothesis was that the soma membrane resistivity did not differ significantly from the dendritic membrane resistivity. Evidence was found that the uniform-resistance cylinder model cannot be applied to motoneurons on the basis of inconsistencies in calculations of electrotonic length. Assuming a constant membrane capacitance, the membrane resistivity of the dendrites was found to be 500 times that of the soma. We conclude that there is a considerable difference in the membrane resistivity between the soma and dendrites of motoneurons, and that uniform-resistance models should not be applied to spinal alpha-motoneurons.