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

Series resistance errors in whole cell voltage clamp measured directly with dual patch-clamp recordings: not as bad as you think

Whole cell patch clamp has provided much insight into the function of voltage-gated ion channels in central neurons. However, voltage errors caused by the resistance of the recording electrode [series resistance (Rs)] limit its application to relatively small ionic currents. Ohm's law is often applied to estimate and correct the membrane potential for these voltage errors. We tested this assumption in brainstem motoneurons of adult frogs with dual patch-clamp recordings, one performing whole cell voltage clamp of K+ currents and the other directly recording the membrane potential. We hypothesized that Ohm's law-based correction would approximate the measured voltage error. We found that voltage errors averaged <5 mV for currents considered to be large for patch clamp (∼7-13 nA) and <10 mV for massive currents thought to be experimentally intractable (25-30 nA), each error falling within commonly accepted inclusion limits. In most cases Ohm's law-based correction overpredicted these measured voltage errors by roughly 2.5-fold. Consequently, the use of Ohm's law to correct for voltage errors led to erroneous current-voltage (I-V) relationships, showing the greatest distortion for inactivating currents. Finally, recordings with low electrode Rs compensated moderately by the amplifier circuitry appeared to have smaller voltage errors than those with larger Rs and high compensation despite the same "effective Rs" and current magnitude. Therefore, when Rs is low, large currents may be studied with better-than-expected voltage control. These results suggest that patch-clamp may be used to study ionic currents often interpreted to be off limits because of size.NEW & NOTEWORTHY Voltage errors occur in whole cell voltage clamp. We make, to our knowledge, the first direct measurements of these errors and find that voltage errors are far smaller than standard calculations would predict. Since voltage errors were often minimal during the measurement of large ion channel currents, this technique may be applied to large neurons of adults to gain insight into ion channel function across the life span and progression of disease.

Cholinergic Transmission at Muscarinic Synapses in the Striatum Is Driven Equally by Cortical and Thalamic Inputs

The release of acetylcholine from cholinergic interneurons (ChIs) directly modulates striatal output via muscarinic receptors on medium spiny neurons (MSNs). While thalamic inputs provide strong excitatory input to ChIs, cortical inputs primarily regulate MSN firing. Here, we found that, while thalamic inputs do drive ChI firing, a subset of ChIs responds robustly to stimulation of cortical inputs as well. To examine how input-evoked changes in ChI firing patterns drive acetylcholine release at cholinergic synapses onto MSNs, muscarinic M4-receptor-mediated synaptic events were measured in MSNs overexpressing G-protein gated potassium channels (GlRK2). Stimulation of both cortical and thalamic inputs was sufficient to equally drive muscarinic synaptic events in MSNs, resulting from the broad synaptic innervation of the stimulus-activated ChI population across many MSNs. Taken together, this indicates an underappreciated role for the extensive cholinergic network, in which small populations of ChIs can drive substantial changes in post-synaptic receptor activity across the striatum.

Mamaligas et al. find that, while cortical inputs were previously thought to provide weak input to striatal cholinergic interneurons, they can drive firing in a subset of cells. As a result of the broad connectivity of cholinergic cells, cortical and thalamic inputs equally drive synaptic acetylcholine release onto MSNs.

Exact solutions to cable equations in branching neurons with tapering dendrites

Neurons are biological cells with uniquely complex dendritic morphologies that are not present in other cell types. Electrical signals in a neuron with branching dendrites can be studied by cable theory which provides a general mathematical modelling framework of spatio-temporal voltage dynamics. Typically such models need to be solved numerically unless the cell membrane is modelled either by passive or quasi-active dynamics, in which cases analytical solutions can be reduced to calculation of the Green's function describing the fundamental input-output relationship in a given morphology. Such analytically tractable models often assume individual dendritic segments to be cylinders. However, it is known that dendritic segments in many types of neurons taper, i.e. their radii decline from proximal to distal ends. Here we consider a generalised form of cable theory which takes into account both branching and tapering structures of dendritic trees. We demonstrate that analytical solutions can be found in compact algebraic forms in an arbitrary branching neuron with a class of tapering dendrites studied earlier in the context of single neuronal cables by Poznanski (Bull. Math. Biol. 53(3):457-467, 1991). We apply this extended framework to a number of simplified neuronal models and contrast their output dynamics in the presence of tapering versus cylindrical segments.

Genistein Inhibits Aβ25-35-Induced Neuronal Death with Changes in the Electrophysiological Properties of Voltage-Gated Sodium and Potassium Channels

We established a model of Alzheimer's disease in vitro by exposing primary hippocampal neurons of neonatal Wistar rats to the β-Amyloid peptide fragment 25-35, Aβ_25-35. We then observed the effects of genistein, a type of soybean isoflavone, on Aβ_25-35-incubated hippocampal neuron viability, and the electrophysiological properties of voltage-gated sodium channels (Na_V) and potassium channels (K_V) in the hippocampal neurons. Aβ_25-35 exposure reduced the viability of hippocampal neurons, decreased the peak amplitude of voltage-activated sodium channel currents (I_Na), and significantly reduced I_Na at different membrane potentials. Moreover, Aβ_25-35 shifted the activation curve toward depolarization, shifted the inactivation curve toward hyperpolarization, and increased the time constant of recovery from inactivation. Aβ_25-35 exposure significantly shifted the inactivation curve of transient outward K⁺ currents (I_A) toward hyperpolarization and increased its time constant of recovery from inactivation. In addition, Aβ_25-35 significantly decreased the peak density of outward-delayed rectifier potassium channel currents (I_DR) and significantly reduced I_DR value at different membrane potentials. We found that genistein partially reversed the decrease in hippocampal neuron viability, and the alterations in electrophysiological properties of Na_V and K_V induced by Aβ_25-35. Our results suggest that genistein could inhibit Aβ_25-35-induced neuronal damage with changes in the electrophysiological properties of Na_V and K_V.

Whole-Cell Patch Clamp Recordings from Oligodendrocyte Lineage Cells in Brain Slices

The whole-cell configuration of the patch-clamp technique is widely used to study electrically active cells and passive membrane properties, as well as the properties and pharmacology of ion channels, neurotransmitter receptors, and electrogenic transporters, in almost any cell type. In the brain, in addition to neurons, oligodendrocyte precursor cells (OPCs) that give rise to myelinating oligodendrocytes (OLs) are also excitable. Electrophysiological techniques provide the main tool for the thorough investigation of the electrogenic capacity of such cell types. Although there are many published protocols for whole-cell recordings, there are very few that touch upon the electrophysiological characteristics of oligodendrocyte lineage cells. Here we provide a detailed methodology for how to acquire and analyze whole-cell recordings from excitable cells, with a focus on oligodendrocyte lineage cells. We provide a protocol on how to successfully identify OPCs and OLs in brain slices, either with the use of transgenic animal models or through morphological and electrophysiological profiling. The method described can also be easily adopted for whole-cell recordings from oligodendrocyte lineage cells in vitro.

Directional excitatory input to direction-selective ganglion cells in the rabbit retina

Directional responses in retinal ganglion cells are generated in large part by direction-selective release of γ-aminobutyric acid from starburst amacrine cells onto direction-selective ganglion cells (DSGCs). The excitatory inputs to DSGCs are also widely reported to be direction-selective, however, recent evidence suggests that glutamate release from bipolar cells is not directional, and directional excitation seen in patch-clamp analyses may be an artifact resulting from incomplete voltage control. Here, we test this voltage-clamp-artifact hypothesis in recordings from 62 ON-OFF DSGCs in the rabbit retina. The strength of the directional excitatory signal varies considerably across the sample of cells, but is not correlated with the strength of directional inhibition, as required for a voltage-clamp artifact. These results implicate additional mechanisms in generating directional excitatory inputs to DSGCs.

Kv3.3b expression defines the shape of the complex spike in the Purkinje cell

The complex spike (CS) in cerebellar Purkinje Cells (PC) is not an all-or-nothing phenomena as originally proposed, but shows variability depending on the spiking behavior of the Inferior Olive and intrinsic variability in the number and shape of spikelets. The potassium channel Kv3.3b, which has been proposed to undergo developmental changes during the postnatal PC maturation, has been shown to be crucial for the repolarization of the spikelets in the CS. We address here the regulation of the intrinsic CS variability by the expression of inactivating Kv3.3 channels in PCs by combining patch-clamp recordings and single-cell PCR methods on the same neurons, using a technique that we recently optimized to correlate single cell transcription levels with membrane ion channel electrophysiology. We show that while the inactivating TEA sensitive Kv3.3 current peak intensity increases with postnatal age, the channel density does not, arguing against postnatal developmental changes of Kv3.3b expression. Real time PCR of Kv3.3b showed a high variability from cell to cell, correlated with the Kv3.3 current density, and suggesting that there are no mechanisms regulating these currents beyond the mRNA pool. We show a significant correlation between normalized quantity of Kv3.3b mRNA and both the number of CS spikelets and their rate of voltage fluctuation, linking the intrinsic CS shape directly to the Kv3.3b mRNA pool. Comparing the observed cell-to-cell variance with studies on transcriptional noise suggests that fluctuations of the Kv3.3b mRNA pool are possibly not regulated but represent merely transcriptional noise, resulting in intrinsic variability of the CS.

The firing patterns of spinal neurons: in situ patch-clamp recordings reveal a key role for potassium currents

Neuron firing patterns underpin the detection and processing of stimuli, influence synaptic interactions, and contribute to the function of networks. To understand how intrinsic membrane properties determine firing patterns, we investigated the biophysical basis of single and repetitive firing in spinal neurons of hatchling Xenopus laevis tadpoles, a well-understood vertebrate model; experiments were conducted in situ. Primary sensory Rohon-Beard (RB) neurons fire singly in response to depolarising current, and dorsolateral (DL) interneurons fire repetitively. RB neurons exhibited a large tetrodotoxin-sensitive sodium current; in DL neurons, the sodium current density was significantly lower. High-voltage-activated calcium currents were similar in both neuron types. There was no evidence of persistent sodium currents, low-voltage-activated calcium currents, or hyperpolarisation-activated currents. In RB neurons, the potassium current was dominated by a tetraethylammonium-sensitive slow component (I(Ks) ); a fast component (I(Kf) ), sensitive to 4-aminopyridine, predominated in DL neurons. Sequential current-clamp and voltage-clamp recordings in individual neurons suggest that high densities of I(Ks) prevent repetitive firing; where I(Ks) is small, I(Kf) density determines the frequency of repetitive firing. Intermediate densities of I(Ks) and I(Kf) allow neurons to fire a few additional spikes on strong depolarisation; this property typifies a novel subset of RB neurons, and may activate escape responses. We discuss how this ensemble of currents and firing patterns underpins the operation of the Xenopus locomotor network, and suggest how simple mechanisms might underlie the similar firing patterns seen in the neurons of diverse species.

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

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

Quantal analysis reveals a functional correlation between presynaptic and postsynaptic efficacy in excitatory connections from rat neocortex

At many central synapses, the presynaptic bouton and postsynaptic density are structurally correlated. However, it is unknown whether this correlation extends to the functional properties of the synapses. To investigate this, we made recordings from synaptically coupled pairs of pyramidal neurons in rat visual cortex. The mean peak amplitude of EPSPs recorded from pairs of L2/3 neurons ranged between 40 microV and 2.9 mV. EPSP rise times were consistent with the majority of the synapses being located on basal dendrites; this was confirmed by full anatomical reconstructions of a subset of connected pairs. Over a third of the connections could be described using a quantal model that assumed simple binomial statistics. Release probability (P(r)) and quantal size (Q), as measured at the somatic recording site, showed considerable heterogeneity between connections. However, across the population of connections, values of P(r) and Q for individual connections were positively correlated with one another. This correlation also held for inputs to layer 5 pyramidal neurons from both layer 2/3 and neighboring layer 5 pyramidal neurons, suggesting that during development of cortical connections presynaptic and postsynaptic strengths are dependently scaled. For 2/3 to 2/3 connections, mean EPSP amplitude was correlated with both Q and P(r) values but uncorrelated with N, the number of functional release sites mediating the connection. The efficacy of a cortical connection is thus set by coordinated presynaptic and postsynaptic strength.

Differences in excitatory transmission between thalamic and cortical afferents to single spiny efferent neurons of rat dorsal striatum

The striatum is crucially involved in motor and cognitive function, and receives significant glutamate input from the cortex and thalamus. The corticostriatal pathway arises from diverse regions of the cortex and is thought to provide information to the basal ganglia from which motor actions are selected and modified. The thalamostriatal pathway arises from specific thalamic nuclei and is involved in attention and possibly strategy switching. Despite these fundamental functional differences, direct comparisons of the properties of these pathways are lacking. N-methyl-D-aspartate (NMDA) receptors at synapses powerfully affect postsynaptic processing, and incorporation of different NR2 subunits into NMDA receptors has profound effects on the pharmacological and biophysical properties of the receptor. Utilization of different NMDA receptors at thalamostriatal and corticostriatal synapses could allow for afferent-specific differences in information processing. We used a novel rat brain slice preparation preserving corticostriatal and thalamostriatal pathways to medium spiny neurons to examine the properties of NMDA receptor-mediated excitatory postsynaptic currents (EPSCs) recorded using the whole-cell, patch-clamp technique. Within the same neuron, the NMDA/non-NMDA ratio is greater for excitatory responses evoked from the thalamostriatal pathway than for those evoked from the corticostriatal pathway. In addition, reversal potentials and decay kinetics of the NMDA receptor-mediated EPSCs suggest that the thalamostriatal synapse is more distant on the dendritic arbor. Finally, results obtained with antagonists specific for NR2B-containing NMDA receptors imply that NMDA receptors at corticostriatal synapses contain more NR2B subunits. These synapse-specific differences in NMDA receptor content and pharmacology provide potential differential sites of action for NMDA receptor subtype-specific antagonists proposed for the treatment of Parkinson's disease.

Space-clamp problems when voltage clamping neurons expressing voltage-gated conductances

The voltage-clamp technique is applicable only to spherical cells. In nonspherical cells, such as neurons, the membrane potential is not clamped distal to the voltage-clamp electrode. This means that the current recorded by the voltage-clamp electrode is the sum of the local current and of axial currents from locations experiencing different membrane potentials. Furthermore, voltage-gated currents recorded from a nonspherical cell are, by definition, severely distorted due to the lack of space clamp. Justifications for voltage clamping in nonspherical cells are, first, that the lack of space clamp is not severe in neurons with short dendrites. Second, passive cable theory may be invoked to justify application of voltage clamp to branching neurons, suggesting that the potential decay is sufficiently shallow to allow spatial clamping of the neuron. Here, using numerical simulations, we show that the distortions of voltage-gated K(+) and Ca(2+) currents are substantial even in neurons with short dendrites. The simulations also demonstrate that passive cable theory cannot be used to justify voltage clamping of neurons due to significant shunting to the reversal potential of the voltage-gated conductance during channel activation. Some of the predictions made by the simulations were verified using somatic and dendritic voltage-clamp experiments in rat somatosensory cortex. Our results demonstrate that voltage-gated K(+) and Ca(2+) currents recorded from branching neurons are almost always severely distorted.

Withdrawal From Intermittent Ethanol Exposure Increases Probability of Burst Firing in VTA Neurons In Vitro

Changing the activity of ventral tegmental area (VTA) dopamine neurons from pacemaker to burst firing is hypothesized to increase the salience of stimuli, such as an unexpected reward, and likely contributes to withdrawal-associated drug-seeking behavior. Accordingly, pharmacological, behavioral, and electrophysiological data suggest an important role of the VTA in mediating alcohol-dependent behaviors. However, the effects of repeated ethanol exposure on VTA dopamine neuron ion channel function are poorly understood. Here, we repeatedly exposed rats to ethanol (2 g/kg ethanol, ip, twice per day for 5 days), then examined the firing patterns of VTA dopamine neurons in vitro after 7 days withdrawal. Compared with saline-treated animals, the function of the small conductance calcium-dependent potassium channel (SK) was reduced in ethanol-treated animals. Consistent with a role for SK in regulation of burst firing, NMDA applied during firing facilitated the transition to bursting in ethanol-treated but not saline-treated animals; NMDA consistently induced bursting only in saline-treated animals when SK was inhibited. Also, enhanced bursting in ethanol-treated animals was not a result of differences in NMDA-induced depolarization. Further, Ih was also reduced in ethanol-treated animals, which delayed recovery from hyperpolarization, but did not account for the increased NMDA-induced bursting in ethanol-treated animals. Finally, repeated ethanol exposure and withdrawal also enhanced the acute locomotor-activating effect of cocaine (15 mg/kg, ip). Thus withdrawal after repeated ethanol exposure produced several alterations in the physiological properties of VTA dopamine neurons, which could ultimately increase the ability of VTA neurons to produce burst firing and thus might contribute to addiction-related behaviors.

Neuronal integrative analysis of the "Dumbbell" model for passive neurons

We analyze the so called "Dumbbell" model of Jackson (J. Neurophysiol. 69 (1993) pp. 464) for a single neuron consisting of a patch-clamped cell body attached to dendritic cable of finite length terminating in an oblique derivative ("natural termination") boundary condition representing a dendritic swelling or a natural ending sealed by a continuous surface of the cell membrane. The model is solved analytically via the Green's function method. Large and small time asymptotic behavior of the membrane potential is developed when there is a somatic voltage-clamp imposed. We discuss the difference in the voltage distribution if a sealed-end (Neumann) termination is used instead of the natural termination boundary condition. If the access resistance is large the differences between the potentials corresponding to the two boundary conditions are small at the soma, but can vary significantly near the dendritic termination. This discrepancy is amplified at the soma if there is a synaptic stimulus introduced between the soma and dendritic tip.

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.

Simulations of voltage clamping poorly space-clamped voltage-dependent conductances in a uniform cylindrical neurite

Significant error is made by using a point voltage clamp to measure active ionic current properties in poorly space-clamped cells. This can even occur when there are no obvious signs of poor spatial control. We evaluated this error for experiments that employ an isochronal I(V) approach to analyzing clamp currents. Simulated voltage clamp experiments were run on a model neuron having a uniform distribution of a single voltage-gated inactivating ionic current channel along an elongate, but electrotonically compact, process. Isochronal Boltzmann I(V) and kinetic parameter values obtained by fitting the Hodgkin-Huxley equations to the clamp currents were compared with the values originally set in the model. Good fits were obtained for both inward and outward currents for moderate channel densities. Most parameter errors increased with conductance density. The activation rate parameters were more sensitive to poor space clamp than the I(V) parameters. Large errors can occur despite "normal"-looking clamp curves.

Pathway-specific properties of AMPA and NMDA-mediated transmission in CA1 hippocampal pyramidal cells

CA1 pyramidal cells receive glutamatergic input from the entorhinal cortex through the perforant path (PP) and from CA3 through Schaffer collaterals (SC). The PP input terminates in the stratum lacunosum molecular approximately 300 microm from the cell body, whereas SC synapses have a more proximal location in the stratum radiatum. We compared the properties of AMPA- and NMDA-mediated transmission at these two inputs. The AMPA-mediated components have linear voltage dependence in both inputs. The reversal potential in the PP is only slightly more positive than in the SC, indicating that distal membrane voltage could be effectively set. The NMDA-mediated responses in the two pathways, however, are very different. The PP exhibits inward rectification, as evidenced by very low outward currents. The rectification persists in the absence of extracellular Mg2+. It cannot be attributed to clamping problems, because large outward AMPA currents can be observed even when conditions are modified to have the AMPA currents kinetically match the NMDA currents. Thus, it appears that the PP NMDA channels have novel properties. A second difference between the PP and SC pathways is that the PP has a larger NMDA/AMPA charge ratio. This difference could be observed under many conditions, including block of all voltage-dependent conductances and elimination of the negative resistance of NMDA channels by removing extracellular Mg2+. The difference in ratio thus cannot be attributed to regenerative currents. The higher NMDA component of the distal PP synapses could help to make these synapses more powerful under depolarizing conditions.

Pathway-specific properties of AMPA and NMDA-mediated transmission in CA1 hippocampal pyramidal cells

CA1 pyramidal cells receive glutamatergic input from the entorhinal cortex through the perforant path (PP) and from CA3 through Schaffer collaterals (SC). The PP input terminates in the stratum lacunosum molecular approximately 300 microm from the cell body, whereas SC synapses have a more proximal location in the stratum radiatum. We compared the properties of AMPA- and NMDA-mediated transmission at these two inputs. The AMPA-mediated components have linear voltage dependence in both inputs. The reversal potential in the PP is only slightly more positive than in the SC, indicating that distal membrane voltage could be effectively set. The NMDA-mediated responses in the two pathways, however, are very different. The PP exhibits inward rectification, as evidenced by very low outward currents. The rectification persists in the absence of extracellular Mg2+. It cannot be attributed to clamping problems, because large outward AMPA currents can be observed even when conditions are modified to have the AMPA currents kinetically match the NMDA currents. Thus, it appears that the PP NMDA channels have novel properties. A second difference between the PP and SC pathways is that the PP has a larger NMDA/AMPA charge ratio. This difference could be observed under many conditions, including block of all voltage-dependent conductances and elimination of the negative resistance of NMDA channels by removing extracellular Mg2+. The difference in ratio thus cannot be attributed to regenerative currents. The higher NMDA component of the distal PP synapses could help to make these synapses more powerful under depolarizing conditions.

Compartmental models of rat cerebellar Purkinje cells based on simultaneous somatic and dendritic patch-clamp recordings

1. Simultaneous dendritic and somatic patch-clamp recordings were made from Purkinje cells in cerebellar slices from 12- to 21-day-old rats. Voltage responses to current impulses injected via either the dendritic or the somatic pipette were obtained in the presence of the selective I(h) blocker ZD 7288 and blockers of spontaneous synaptic input. Neurons were filled with biocytin for subsequent morphological reconstruction. 2. Four neurons were reconstructed and converted into detailed compartmental models. The specific membrane capacitance (C(m)), specific membrane resistance (R(m)) and intracellular resistivity (R(i)) were optimized by direct fitting of the model responses to the electrophysiological data from the same cell. Mean values were: C(m), 0.77 +/- 0.17 microF cm(-2) (mean +/- S.D.; range, 0.64-1.00 microF cm(-2)), R(m), 122 +/- 18 kOmega cm(2) (98-141 kOmega cm(2)) and R(i), 115 +/- 20 Omega cm (93-142 Omega cm). 3. The steady-state electrotonic architecture of these cells was compact under the experimental conditions used. However, somatic voltage-clamp recordings of parallel fibre and climbing fibre synaptic currents were substantially filtered and attenuated. 4. The detailed models were compared with a two-compartment model of Purkinje cells. The range of synaptic current kinetics that can be faithfully recorded using somatic voltage clamp is predicted fairly well by the two-compartment model, even though some of its underlying assumptions are violated. 5. A model of I(h) was constructed based on voltage-clamp data, and inserted into the passive compartmental models. Somatic EPSP amplitude was substantially attenuated compared to the amplitude of dendritic EPSPs at their site of generation. However, synaptic efficacy of the same quantal synaptic conductance, as measured by the somatic EPSP amplitude, was only weakly dependent on synaptic location on spiny branchlets. 6. The passive electrotonic structure of Purkinje cells is unusual in that the steady-state architecture is very compact, while voltage transients such as synaptic potentials and action potentials are heavily filtered.

Two-compartment model for whole-cell data analysis and transient compensation

Recording and analysis of neuronal patch-clamp data involve many assumptions about membrane properties and cell morphology. Some of these assumptions introduce large errors or oversimplifications into the results. In particular, dendritic branching with high intracellular resistance leads to difficulty with capacitance calculation and transient subtraction, and may significantly distort measured currents. A two-compartment model, presented in detail here, provides a simple method of reducing many of these problems for the relatively simple case of cultured neurons studied with whole-cell patch electrodes. Some passive membrane properties may be accurately calculated, and the results may be used to correct recorded currents for resulting series resistance, intracellular resistance, and capacitive transient errors. The model may be tailored to particular cell types or experimental conditions. Programs to implement the algorithms are available from http://www.its.caltech.edu/ approximately nadeau/Rscomp.html.

Signal transfer in passive dendrites with nonuniform membrane conductance

In recent years it became clear that dendrites possess a host of ion channels that may be distributed nonuniformly over their membrane surface. In cortical pyramids, for example, it was demonstrated that the resting membrane conductance G(m)(x) is higher (the membrane is "leakier") at distal dendritic regions than at more proximal sites. How does this spatial nonuniformity in G(m)(x) affect the input-output function of the neuron? The present study aims at providing basic insights into this question. To this end, we have analytically studied the fundamental effects of membrane non-uniformity in passive cable structures. Keeping the total membrane conductance over a given modeled structure fixed (i.e., a constant number of passive ion channels), the classical case of cables with uniform membrane conductance is contrasted with various nonuniform cases with the following general conclusions. (1) For cylindrical cables with "sealed ends," monotonic increase in G(m)(x) improves voltage transfer from the input location to the soma. The steeper the G(m)(x), the larger the improvement. (2) This effect is further enhanced when the stimulation is distal and consists of a synaptic input rather than a current source. (3) Any nonuniformity in G(m)(x) decreases the electrotonic length, L, of the cylinder. (4) The system time constant tau(0) is larger in the nonuniform case than in the corresponding uniform case. (5) When voltage transients relax with tau(0), the dendritic tree is not isopotential in the nonuniform case, at variance with the uniform case. The effect of membrane nonuniformity on signal transfer in reconstructed dendritic trees and on the I/f relation of the neuron is also considered, and experimental methods for assessing membrane nonuniformity in dendrites are discussed.

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.

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.

Signal transfer in passive dendrites with nonuniform membrane conductance

In recent years it became clear that dendrites possess a host of ion channels that may be distributed nonuniformly over their membrane surface. In cortical pyramids, for example, it was demonstrated that the resting membrane conductance G(m)(x) is higher (the membrane is "leakier") at distal dendritic regions than at more proximal sites. How does this spatial nonuniformity in G(m)(x) affect the input-output function of the neuron? The present study aims at providing basic insights into this question. To this end, we have analytically studied the fundamental effects of membrane non-uniformity in passive cable structures. Keeping the total membrane conductance over a given modeled structure fixed (i.e., a constant number of passive ion channels), the classical case of cables with uniform membrane conductance is contrasted with various nonuniform cases with the following general conclusions. (1) For cylindrical cables with "sealed ends," monotonic increase in G(m)(x) improves voltage transfer from the input location to the soma. The steeper the G(m)(x), the larger the improvement. (2) This effect is further enhanced when the stimulation is distal and consists of a synaptic input rather than a current source. (3) Any nonuniformity in G(m)(x) decreases the electrotonic length, L, of the cylinder. (4) The system time constant tau(0) is larger in the nonuniform case than in the corresponding uniform case. (5) When voltage transients relax with tau(0), the dendritic tree is not isopotential in the nonuniform case, at variance with the uniform case. The effect of membrane nonuniformity on signal transfer in reconstructed dendritic trees and on the I/f relation of the neuron is also considered, and experimental methods for assessing membrane nonuniformity in dendrites are discussed.

A simple hardware model for the direct observation of voltage-clamp performance under realistic conditions

A new hardware cell model for electrophysiological recording has been constructed which allows for the assessment of voltage clamp accuracy in different recording situations. Each compartment consists of a capacitor in parallel with a variable resistor and can be connected to other compartments by a variable axial resistance. The simulated membrane resistance can be changed extrinsically by a command voltage input which is optically coupled to the cell without any direct galvanic contact. Each compartment possesses a buffer amplifier which reads out the potential at the simulated membrane element, (e.g. 'somatic' or 'dendritic' potential). The model allows for the direct observation of typical situations and problems arising in electrophysiological experiments. We used the model to monitor deviations between the 'intracellular' and the command voltage, e.g. due to series resistance errors. We also used the model to simulate synaptic currents which were generated by triangular membrane conductance changes. The results demonstrate the strong influence of synaptic location and series resistance on voltage clamp fidelity. The cell model is a new and easy-to-handle tool for the observation of voltage control under realistic experimental conditions.

Developmental regulation of basket/stellate cell-->Purkinje cell synapses in the cerebellum

We used paired recordings to study the development of synaptic transmission between inhibitory interneurons of the molecular layer and Purkinje cells in the cerebellar cortex of the rat. The electrophysiological data were combined with a morphological study of the recorded cells using biocytin or Lucifer yellow staining. Thirty-one interneuron-Purkinje cell pairs were obtained, and 11 of them were recovered morphologically. The age of the rats ranged from 11 to 31 d after birth. During this period synaptic maturation resulted in an 11-fold decrease in the average current evoked in a Purkinje cell by a spike in a presynaptic interneuron. Unitary IPSCs in younger animals exhibited paired-pulse depression, whereas paired-pulse facilitation was found in more mature animals. These data suggest that reduction in transmitter release probability contributed to the developmental decrease of unitary IPSCs. However, additional mechanisms at both presynaptic and postsynaptic loci should also be considered. The decrease of the average synaptic current evoked in a Purkinje cell by an action potential in a single interneuron suggests that as development proceeds interneuron activities must be coordinated to inhibit efficiently Purkinje cells.

Electrotonic measurements by electric field-induced polarization in neurons: theory and experimental estimation

We present a theory for estimation of the dendritic electrotonic length constant and the membrane time constant from the transmembrane potential (TMP) induced by an applied electric field. The theory is adapted to morphologically defined neurons with homogeneous passive electric properties. Frequency characteristics and transients at the onset and offset of the DC field are considered. Two relations are useful for estimating the electrotonic parameters: 1) steady-state polarization versus the dendritic electrotonic length constant; 2) membrane time constant versus length constant. These relations are monotonic and may provide a unique estimate of the electrotonic parameters for 3D-reconstructed neurons. Equivalent tip-to-tip electrotonic length of the dendritic tree was estimated by measuring the equalization time of the field-induced TMP. For 11 turtle spinal motoneurons, the electrotonic length from tip to tip of the dendrites was in the range of 1-2.5 lambda, whereas classical estimation using injection of current pulses gave an average dendrite length of 0.9-1.1 lambda. For seven ventral horn interneurons, the estimates were 0.7-2.6 lambda and 0.6-0.9 lambda, respectively. The measurements of the field-induced polarization promise to be a useful addition to the conventional methods using microelectrode stimulation.

Developmental regulation of basket/stellate cell-->Purkinje cell synapses in the cerebellum

We used paired recordings to study the development of synaptic transmission between inhibitory interneurons of the molecular layer and Purkinje cells in the cerebellar cortex of the rat. The electrophysiological data were combined with a morphological study of the recorded cells using biocytin or Lucifer yellow staining. Thirty-one interneuron-Purkinje cell pairs were obtained, and 11 of them were recovered morphologically. The age of the rats ranged from 11 to 31 d after birth. During this period synaptic maturation resulted in an 11-fold decrease in the average current evoked in a Purkinje cell by a spike in a presynaptic interneuron. Unitary IPSCs in younger animals exhibited paired-pulse depression, whereas paired-pulse facilitation was found in more mature animals. These data suggest that reduction in transmitter release probability contributed to the developmental decrease of unitary IPSCs. However, additional mechanisms at both presynaptic and postsynaptic loci should also be considered. The decrease of the average synaptic current evoked in a Purkinje cell by an action potential in a single interneuron suggests that as development proceeds interneuron activities must be coordinated to inhibit efficiently Purkinje cells.

GABAA-mediated IPSCs in piriform cortex have fast and slow components with different properties and locations on pyramidal cells

GABAA-mediated IPSCs in piriform cortex have fast and slow components with different properties and locations on pyramidal cells. J. Neurophysiol. 78: 2531-2545, 1997. A recent study in piriform (olfactory) cortex provided evidence that, as in hippocampus and neocortex, gamma-aminobutyric acid-A (GABAA)-mediated inhibition is generated in dendrites of pyramidal cells, not just in the somatic region as previously believed. This study examines selected properties of GABAA inhibitory postsynaptic currents (IPSCs) in dendritic and somatic regions that could provide insight into their functional roles. Pharmacologically isolated GABAA-mediated IPSCs were studied by whole cell patch recording in slices. To compare properties of IPSCs in distal dendritic and somatic regions, local stimulation was carried out with tungsten microelectrodes, and spatially restricted blockade of GABAA-mediated inhibition was achieved by pressure-ejection of bicuculline from micropipettes. The results revealed that largely independent circuits generate GABAA inhibition in distal apical dendritic and somatic regions. With such independence, a selective decrease in dendritic-region inhibition could enhance integrative or plastic processes in dendrites while allowing feedback inhibition in the somatic region to restrain system excitability. This could allow modulatory fiber systems from the basal forebrain or brain stem, for example, to change the functional state of the cortex by altering the excitability of interneurons that mediate dendritic inhibition without increasing the propensity for regenerative bursting in this highly epileptogenic system. As in hippocampus, GABAA-mediated IPSCs were found to have fast and slow components with time constants of decay on the order of 10 and 40 ms, respectively, at 29 degrees C. Modeling analysis supported physiological evidence that the slow time constant represents a true IPSC component rather than an artifactual slowing of the fast component from voltage clamp of a dendritic current. The results indicated that, whereas both dendritic and somatic-region IPSCs have both fast and slow GABAA components, there is a greater proportion of the slow component in dendrites. In a companion paper, the hypothesis is explored that the resulting slower time course of the dendritic IPSC increases its capacity to regulate the N-methyl--aspartate component of EPSPs. Finally, evidence is presented that the slow GABAA-mediated IPSC component is regulated by presynaptic GABAB inhibition whereas the fast is not. Based on the requirement for presynaptic GABAB-mediated block of inhibition for expression of long-term potentiation, this finding is consistent with participation of the slow GABAA component in regulation of synaptic plasticity. The lack of susceptibility of the fast GABAA component to the long-lasting, activity-induced suppression mediated by presynaptic GABAB receptors is consistent with a protective role for this process in preventing seizure activity.

Estimating the time course of the excitatory synaptic conductance in neocortical pyramidal cells using a novel voltage jump method

We introduce a method that permits faithful extraction of the decay time course of the synaptic conductance independent of dendritic geometry and the electrotonic location of the synapse. The method is based on the experimental procedure of Pearce (1993), consisting of a series of identical somatic voltage jumps repeated at various times relative to the onset of the synaptic conductance. The progression of synaptic charge recovered by successive jumps has a characteristic shape, which can be described by an analytical function consisting of sums of exponentials. The voltage jump method was tested with simulations using simple equivalent cylinder cable models as well as detailed compartmental models of pyramidal cells. The decay time course of the synaptic conductance could be estimated with high accuracy, even with high series resistances, low membrane resistances, and electrotonically remote, distributed synapses. The method also provides the time course of the voltage change at the synapse in response to a somatic voltage-clamp step and thus may be useful for constraining compartmental models and estimating the relative electrotonic distance of synapses. In conjunction with an estimate of the attenuation of synaptic charge, the method also permits recovery of the amplitude of the synaptic conductance. We use the method experimentally to determine the decay time course of excitatory synaptic conductances in neocortical pyramidal cells. The relatively rapid decay time constant we have estimated (tau approximately 1.7 msec at 35 degrees C) has important consequences for dendritic integration of synaptic input by these neurons.

Estimating the time course of the excitatory synaptic conductance in neocortical pyramidal cells using a novel voltage jump method

We introduce a method that permits faithful extraction of the decay time course of the synaptic conductance independent of dendritic geometry and the electrotonic location of the synapse. The method is based on the experimental procedure of Pearce (1993), consisting of a series of identical somatic voltage jumps repeated at various times relative to the onset of the synaptic conductance. The progression of synaptic charge recovered by successive jumps has a characteristic shape, which can be described by an analytical function consisting of sums of exponentials. The voltage jump method was tested with simulations using simple equivalent cylinder cable models as well as detailed compartmental models of pyramidal cells. The decay time course of the synaptic conductance could be estimated with high accuracy, even with high series resistances, low membrane resistances, and electrotonically remote, distributed synapses. The method also provides the time course of the voltage change at the synapse in response to a somatic voltage-clamp step and thus may be useful for constraining compartmental models and estimating the relative electrotonic distance of synapses. In conjunction with an estimate of the attenuation of synaptic charge, the method also permits recovery of the amplitude of the synaptic conductance. We use the method experimentally to determine the decay time course of excitatory synaptic conductances in neocortical pyramidal cells. The relatively rapid decay time constant we have estimated (tau approximately 1.7 msec at 35 degrees C) has important consequences for dendritic integration of synaptic input by these neurons.

Rapid kinetics and inward rectification of miniature EPSCs in layer I neurons of rat neocortex

With the use of the whole cell patch-clamp technique combined with visualization of neurons in brain slices, we studied the properties of miniature excitatory postsynaptic currents (mEPSCs) in rat neocortical layer I neurons. At holding potentials (-50 to -70 mV) near the resting membrane potential (RMP), mEPSCs had amplitudes of 5-100 pA and were mediated mostly by alpha-amino-3-hydroxy-5-methyl-4-isoxazoleproprionate (AMPA) receptors. Amplitude histograms were skewed toward large events. An N-methyl-D-aspartate (NMDA) component was revealed by depolarization to -30 mV or by the use of a Mg2+-free bathing solution. At RMP, averaged AMPA mEPSCs had a 10-90% rise time of approximately 0.3 ms (uncorrected for instrument filtering). The decay of averaged mEPSCs was best fit by double-exponential functions in most cases. The fast, dominating component had a decay time constant of approximately 1.2 ms and comprised approximately 80% of the total amplitude. A small slow component had a decay time constant of approximately 4 ms. Positive correlations were found between rise and decay times of both individual and averaged mEPSCs, indicative of dendritic filtering. Some large-amplitude mEPSCs and spontaneous EPSCs (recorded in the absence of tetrodotoxin) had slower kinetics, suggesting a role of asynchronous transmitter release in shaping EPSCs. The amplitudes of mEPSCs were much smaller at +60 mV than at -60 mV, indicating that synaptic AMPA-receptor-mediated currents were inwardly rectifying. These results suggest that neocortical layer I neurons receive both NMDA- and AMPA-receptor-mediated synaptic inputs. The rapid decay of EPSCs appears to be largely determined by AMPA receptor deactivation. The observed rectification of synaptic responses suggests that synaptic AMPA receptors in layer I neurons may lack GluR-2 subunits and may be Ca2+ permeable.

Multimodal distribution of amplitudes of miniature and spontaneous EPSPs recorded in rat trigeminal motoneurones

1. The whole-cell variant of the patch recording method has been used to obtain voltage recordings from trigeminal motoneurones in tissue slices (500 microns thick) taken from rats aged 8 days. Membrane properties (input resistance, membrane time constant and rheobase, i.e. threshold current required to elicit an action potential) of the motoneurones were determined and recordings made of the (untriggered) EPSP activity. 2. Untriggered EPSP activity was recorded in standard artificial cerebrospinal fluid (ACSF), ACSF with added tetrodotoxin (TTX) and in nominally Ca(2+)-free ACSF with added TTX. In each case the amplitude distributions of single EPSPs were peaky and could be fitted by a model consisting of the sum of equidistant Gaussians (n = 7/9 cells). In contrast, the amplitude distribution of the noise was always unimodal. 3. All EPSP activity recorded in the presence of TTX was abolished by addition of 6-cyano-7-nitroquinoxaline-2-3-dione (CNQX; 10 microM), suggesting the activity was all mediated by glutamate acting primarily at AMPA/kainate receptors. 4. In the majority of cases, there was no correlation between the amplitude of EPSPs underlying each Gaussian and the EPSP rise time but there was a positive correlation between the EPSP half-width and EPSP rise time. The rise times of EPSPs underlying the first, and all, fitted Gaussians were similar to that for the total sample of EPSPs in each motoneurone. Taken together, this suggests that the EPSPs underlying each Gaussian arise from inputs to different dendritic compartments, and that the range of compartments is similar for EPSPs underlying successive Gaussians. 5. Two conclusions are drawn. First, EPSPs of different dendritic origin have similar amplitudes at the soma. Second, the multimodal distribution of EPSP amplitudes recorded in the presence of TTX raises the possibility that individual boutons may contain multiple release sites, with each perhaps operating on a separate functional group of postsynaptic receptors.

Spontaneous excitatory postsynaptic currents in hippocampal CA1 pyramidal neurons of the gerbil after transient ischemia

The changes in the spontaneous excitatory postsynaptic currents (sEPSCs) after transient cerebral ischemia were studied using whole-cell recording from CA1 pyramidal neurons in the gerbil. In neurons recorded 1-2 days after ischemia, sEPSCs had a slowed time course with the decay time constant fitted by a single exponential and it progressively increased after ischemia. Frequency and amplitude distribution of sEPSCs in ischemic neurons were not significantly different from those in the control neurons. The results support the view that abnormal non-N-methyl-D-aspartic acid currents originate at the degenerated postsynaptic site, unrelated to the presynaptic releasing mechanisms.

Enhancement of NMDA receptor mediated synaptic potentials of rat hippocampal neurones in vitro by thyrotropin releasing hormone

The effects of thyrotropin releasing hormone (TRH) on excitatory postsynaptic potentials (EPSPs) evoked by electrical stimulation of Schaffer collaterals on CA1 neurones of the adult rat hippocampal slice preparation were investigated using intracellular recording under current clamp conditions. At resting membrane potential and in the presence of extracellular Mg2+, TRH (10-20 microM) largely potentiated NMDA receptor-mediated EPSPs while leaving those mediated by non-NMDA receptors unaffected. This phenomenon had a brief duration (approximately 2 min) and was not accompanied by changes in resting membrane potential or input conductance. It is suggested that TRH provided a transient upregulation of synaptic responses due to NMDA receptor activation.

Voltage-imaging and simulation of effects of voltage- and agonist-activated conductances on soma-dendritic voltage coupling in cerebellar Purkinje cells

We investigated the spread of membrane voltage changes from the soma into the dendrites of cerebellar Purkinje cells by using voltage-imaging techniques in combination with intracellular recordings and by performing computer simulations using a detailed compartmental model of a cerebellar Purkinje cell. Fluorescence signals from single Purkinje cells in cerebellar cultures stained with the styryl dye di-4-ANEPPS were detected with a 10 x 10 photodiode array and a charge coupled device (CCD). Fluorescence intensity decreased and increased with membrane depolarization and hyperpolarization, respectively. The relation between fractional fluorescence change (delta F/F) and membrane potential could be described by a linear function with a slope of up to -3%/100 mV. Hyperpolarizing and depolarizing voltage jumps applied to Purkinje cells voltage-clamped with an intrasomatic recording electrode induced dendritic dye signals, demonstrating that these voltage transients invaded the dendrites. Dye signals induced by depolarizing somatic voltage jumps were weaker in the dendrites, when compared with those induced by hyperpolarizing voltage jumps. Dendritic responses to hyperpolarizing voltage steps applied at the soma were attenuated when membrane conductance was increased by muscimol, an agonist for GABA(A) receptors. Corresponding experimental protocols were applied to a previously developed detailed compartmental model of a Purkinje cell. In the model, as in the electrophysiological recordings, voltage attenuation from soma to dendrites increased under conditions where membrane conductance is increased by depolarization or by activation of GABA(A) receptors, respectively. We discuss how these results affect voltage clamp studies of synaptic currents and synaptic integration in Purkinje cells.

Denervation-induced dendritic alterations in CA1 pyramidal cells following kainic acid hippocampal lesions in rats

Kainic acid (KA) lesions of the CA3 region of the hippocampus lead to denervation of ipsilateral CA1 neurons. To assess denervation-induced post-synaptic changes, intracellular physiological recordings were performed in the CA1 region in vitro, from both control and KA-treated tissue. The neurons were intracellularly stained with neurobiotin, reconstructed using a quantitative three-dimensional system and analyzed for morphometric and electrotonic parameters. Total dendritic length was slightly longer in the denervated CA1 cells and there was a selective and significant increase in both branches and terminals in the mid-stratum radiatum (300-550 microns from the soma using Sholl analysis) in the KA-treated rats compared to untreated controls, particularly for cells at 5 days post-lesion and later, which exhibited graded synaptically-evoked bursts. However, there was no significant difference in the basal dendritic arborization. Electrotonic modelling of the dendritic structure revealed specific membrane resistivity values of 33.4 k omega.cm2 for the normal CA1 cells and 29.8 K omega-cm2 for the KA-treated cells, assuming an internal resistivity of 200 omega.cm2, shrinkage correction of 1.57 and a spatial distribution of dendritic spines. The number of dendritic terminals of these denervated CA1 neurons at electrotonic distances between 0.5 lambda and 0.7 lambda also significantly increased in the cells from KA-treated animals. These findings indicate that there is a selective and specific increase in the number of apical terminals and dendritic branches following the unilateral kainic acid lesion. These apical branch changes may represent dendritic sprouting as a post-synaptic response to the denervation, which was particularly marked in neurons exhibiting graded synaptic bursting behavior.

Mechanisms shaping glutamate-mediated excitatory postsynaptic currents in the CNS

Excitatory postsynaptic currents in neurones of the central nervous system have a dual-component time course that results from the co-activation of AMPA/kainate-type and NMDA-type glutamate receptors. New approaches in electrophysiology and molecular biology have provided a better understanding of the factors that determine the kinetics of excitatory postsynaptic currents. Recent studies suggest that the time course of neurotransmitter concentration in the synaptic cleft, the gating properties of the native channels, and the glutamate receptor subunit composition all appear to be important factors.

Solutions for transients in arbitrarily branching cables: IV. Nonuniform electrical parameters

Solutions for transients in arbitrarily branching passive cable neurone models with a soma are extended to models with nonuniform electrical parameters and multiple dendritic shunts. The response to an injected current can again be represented as an infinite series of exponentially decaying components with system time constants obtained from the roots of a recursive transcendental equation. The reciprocity relations and global parameter dependencies are the same as for uniform models. Infinitely many "raw" electro-morphological models map onto a given "core" electrotonic model; local as well as global raw parameter trade-offs are now possible. The solutions are illustrated by means of biologically relevant examples: (i) the effects of nonuniform electrical parameters in a two-cylinder + soma cortical pyramidal cell model, (ii) the errors that can occur when uniformity is incorrectly assumed in a single cylinder model, (iii) nonsumming interactions between cells and electrodes that can dramatically increase the duration of the effective capacitative electrode artefact, and (iv) shunting inhibition and double impalements in a hippocampal CA1 pyramidal cell "cartoon" representation. These solutions should complement compartmental modelling techniques.

Heterogeneity in presynaptic regulation of GABA release from hippocampal inhibitory neurons

Release of GABA from the terminals of hippocampal inhibitory neurons is inhibited by activation of GABAB autoreceptors and mu opioid receptors. However, it is not known whether these presynaptic processes affect all inhibitory synapses equally. We examined the effects of the GABAB receptor agonist baclofen and the mu opioid receptor agonist DAGO on postsynaptic currents evoked by minimal stimulation of inhibitory fibers (meIPSCs) in area CA3. Baclofen reversibly depressed approximately half of the meIPSCs evoked in the stratum pyramidale. The remaining meIPSCs were unaffected despite a coincident depression of spontaneous IPSCs. In contrast, all meIPSCs were depressed by DAGO. In addition, minimal stimulation in the stratum radiatum evoked meIPSCs that were always depressed by baclofen. These results indicate that regulation of GABA release by GABAB autoreceptors occurs at a subset of inhibitory synapses and that GABAB-resistant inhibitory synapses are located on pyramidal neuron somata. Hippocampal inhibitory neurons may be heterogeneous with respect to presynaptic receptor-mediated regulation of GABA release.

Quantal components of unitary EPSCs at the mossy fibre synapse on CA3 pyramidal cells of rat hippocampus

1. Excitatory postsynaptic currents (EPSCs) were recorded in CA3 pyramidal cells of hippocampal slices of 15- to 24-day-old rats (22 degrees C) using the whole-cell configuration of the patch clamp technique. 2. Composite EPSCs were evoked by extracellular stimulation of the mossy fibre tract. Using the selective blockers 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX) and D-2-amino-5-phosphonopentanoic acid (APV), a major alpha-amino-3-hydroxy-5-methylisoxazole-4-propionate (AMPA)/kainate receptor-mediated component and a minor NMDA receptor-mediated component with slower time course were distinguished. For the AMPA/kainate receptor-mediated component, the peak current-voltage (I-V) relation was linear, with a reversal potential close to 0 mV. The half-maximal blocking concentration of CNQX was 353 nM. 3. Unitary EPSCs of the mossy fibre terminal (MF)-CA3 pyramidal cell synapse were evoked at membrane potentials of -70 to -90 mV by low-intensity extracellular stimulation of granule cell somata using fine-tipped pipettes. The EPSC peak amplitude as a function of stimulus intensity showed all-or-none behaviour. The region of low threshold was restricted to a few micrometres. This suggests that extracellular stimulation was focal, and that the stimulus-evoked EPSCs were unitary. 4. Latency and rise time histograms of EPSCs evoked by granule cell stimulation showed narrow unimodal distributions within each experiment. The mean latency was 4.2 +/- 1.0 ms, and the mean 20-80% rise time was 0.6 +/- 0.1 ms (23 cells). When fitted within the range 0.7 ms to 20 ms after the peak, the decay of the EPSCs with the fastest rise (rise time 0.5 ms or less) could be described by a single exponential function; the mean time constant was in the range 3.0-6.6 ms with a mean of 4.8 ms (8 cells). 5. Peak amplitudes of the EPSCs evoked by suprathreshold granule cell stimulation fluctuated between trials. The apparent EPSC peak conductance in normal extracellular solution (2 mM Ca2+, 1 mM Mg2+), excluding failures, was 1 nS. Reducing the Ca2+ concentration and increasing the Mg2+ concentration reduced the mean peak amplitude in a concentration-dependent manner. 6. Peaks in EPSC peak amplitude distributions were apparent in low Ca2+ and high Mg2+. Using the criteria of equidistance and the presence of peaks and dips in the autocorrelation function, five of nine EPSC peak amplitude distributions were judged to be quantal.(ABSTRACT TRUNCATED AT 400 WORDS)

Solutions for transients in arbitrarily branching cables: II. Voltage clamp theory

Analytical solutions are derived for arbitrarily branching passive neurone models with a soma and somatic shunt, for synaptic inputs and somatic voltage commands, for both perfect and imperfect somatic voltage clamp. The solutions are infinite exponential series. Perfect clamp decouples different dendritic trees at the soma: each exponential component exists only in one tree; its time constant is independent of stimulating and recording position within the tree; its amplitude is the product of a factor constant over that entire tree and factors dependent on stimulating and recording positions. Imperfect clamp to zero is mathematically equivalent to voltage recording with a shunt. As the series resistance increases, different dendritic trees become more strongly coupled. A number of interesting response symmetries are evident. The solutions reveal parameter dependencies, including an insensitivity of the early parts of the responses to specific membrane resistivity and somatic shunt, and an approximately linear dependence of the slower time constants on series resistance, for small series resistances. The solutions are illustrated using a "cartoon" representation of a CA1 pyramidal cell and a two-cylinder + soma model.

Solutions for transients in arbitrarily branching cables: I. Voltage recording with a somatic shunt

An analytical solution is derived for voltage transients in an arbitrarily branching passive cable neurone model with a soma and somatic shunt. The response to injected currents can be represented as an infinite series of exponentially decaying components with different time constants and amplitudes. The time constants of a given model, obtained from the roots of a recursive transcendental equation, are independent of the stimulating and recording positions. Each amplitude is the product of three factors dependent on the corresponding root: one constant over the cell, one varying with the input site, and one with the recording site. The amplitudes are not altered by interchanging these sites. The solution reveals explicitly some of the parameter dependencies of the responses. An efficient recursive root-finding algorithm is described. Certain regular geometries lead to "lost" roots; difficulties associated with these can be avoided by making small changes to the lengths of affected segments. Complicated cells, such as a CA1 pyramid, produce many closely spaced time constants in the range of interest. Models with large somatic shunts and dendrites of unequal electrotonic lengths can produce large amplitude waveform components with surprisingly slow time constants. This analytic solution should complement existing passive neurone modeling techniques.