Location of membrane conductance changes by analysis of the input impedance of neurons. II. Implementation

Determination of the Location and Magnitude of Synaptic Conductance Changes in Spinal Motoneurons by Impedance Measurements

The relation between impedance change and the location and magnitude of a tonic synaptic conductance was examined in compartmental motoneuron models based on previously published data. The dependency of motoneuron impedance on system time constant (τ), electrotonic length (L), and dendritic-to-somatic conductance ratio (ρ) was examined, showing that the relation between impedance phase and ρ differed markedly between models with uniform and nonuniform membrane resistivity. Dendritic synaptic conductances decreased impedance magnitude at low frequencies; at higher frequencies, impedance magnitude increased. The frequency at which the change in impedance magnitude reversed from a decrease to an increase—the reversal frequency, Fr—was a good estimator of electrotonic synaptic location. A measure of the average normalized impedance change at frequencies less than Fr, cuΔZ, estimated relative synaptic conductance. Fr and cuΔZ provided useful estimates of synaptic location and conductance in models with nonuniform (step, sigmoidal) and uniform membrane resistivity. Fr also provided good estimates of spatial synaptic location on the equivalent cable in both step and sigmoidal models. Variability in relations between Fr, cuΔZ, and conductance location and magnitude between neurons was reduced by normalization with ρ and τ. The effects on Fr and cuΔZ of noise in experimental recordings, different synaptic distributions, and voltage-dependent conductances were also assessed. This study indicates that location and conductance of tonic dendritic conductances can be estimated from Fr, cuΔZ, and basic electrotonic motoneuron parameters with the exercise of suitable precautions.

Location and Magnitude of Conductance Changes Produced by Renshaw Recurrent Inhibition in Spinal Motoneurons

The mean location of Renshaw synapses on spinal motoneurons and their synaptic conductance were estimated from changes in impedance magnitude produced by sustained recurrent inhibition. Motoneuron impedance was determined by injecting quasi-white noise current into lumbosacral motoneurons of pentobarbital-anesthetized cats. Synaptic location and conductance were estimated by comparing observed impedance changes to simulation results obtained using standard motoneuron models and compartmental models fit to each impedance function. Estimated synaptic locations ranged from 0.10 to 0.41λ, with a mean of 0.19 or 0.24λ, depending on the estimation method. Average dendritic path length was 262 μm. Average synaptic conductance was 23 to 27 nS (range: 6.7 to 57.9 nS), corresponding to conductance changes of 78 to 88% of resting membrane conductance. Estimated accuracy was supported by consistency using different estimation methods, agreement with Fyffe's 1991 morphological data, and comparisons of observed and simulated recurrent IPSP amplitudes. Synaptic location, but not synaptic conductance, was correlated with rheobase, a measure of motoneuron excitability. Synaptic conductance did not depend on synaptic location. A regression analysis demonstrated that synaptic conductance and cell impedance were the principal factors determining recurrent IPSP amplitude. Simulations using the observed values and locations of Renshaw conductance demonstrate that recurrent inhibition can require as much as an additional 14 to 18% sustained excitatory synaptic conductance to depolarize motoneurons sufficiently to activate somatic or dendritic inward currents and recruit motoneurons or amplify excitatory synaptic currents.

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.

Membrane potential and impedance changes in hippocampal pyramidal cells during theta rhythm

Intracellular recordings were made from hippocampal pyramidal cells identified by their depths and their responses to commissural stimulation. Recordings were made during spontaneous bouts of hippocampal theta rhythm in urethane anesthetized rats. Membrane potentials (Vm) of pyramidal cells varied with the phase of the theta rhythm, that is, there was an "intracellular theta rhythm". The changes in Vm averaged about 2 mV peak to peak. Averaged intracellular theta waves showed that CA1 pyramids were most depolarized at the time of the positive peak of the extracellular theta rhythm recorded in (and superficial to) the CA1 pyramidal cell layer (CA1 theta). Peak depolarizations for CA3/4 pyramids were more broadly distributed, but occurred mainly in the interval just before the positive peak to just before the negative peak of the CA1 theta. Input impedance minima that were measurable at frequencies as high as 100 Hz occurred at about the same phases of the extracellular theta rhythm as the peak depolarizations (positive-going zero crossing to negative-going zero crossing of the CA1 theta). Such impedance changes imply conductance changes on the soma. The magnitude and localization of the conductance changes suggests that somatic IPSPs make major contributions to the intracellular theta rhythm. The phase relation between the intracellular and extracellular theta rhythms could be reversed by long duration current pulses that depolarized the cells slightly. This implies that either the intracellular theta-related IPSPs are depolarizing potential changes, or that they occur simultaneously with EPSPs. The phase of the intracellular theta rhythm was generally unaffected by long duration hyperpolarizing current pulses. Chloride leakage that reversed the evoked IPSPs usually had no effect on the phase of the intracellular theta rhythm, although in one case it appeared to cause its amplitude to increase.

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.