EFFECT OF CELLULAR MEMBRANE RESISTIVITY INHOMOGENEITY ON THE THERMAL NOISE-LIMIT

Our objective is to generalize the Weaver-Astumian (WA) and Kaune (KA) models of thermal noise limit to the case ofcellular membrane resistivity asymmetry. The asymmetry of resistivity causes different effects in the two models. In the KAmodel, asymmetry decreases the characteristic field strength of the thermal limit over and increases it below the breakingfrequency (10  m), while asymmetry decreases the spectral field strength of the thermal noise limit at all frequencies.We show that asymmetry does not change the character of the models, showing the absence of thermal noise limit at highand low frequencies in WA and KA models, respectively.

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.

Simulations to Derive Membrane Resistivity in Three Phenotypes of Guinea Pig Sympathetic Postganglionic Neuron

The electrotonic behavior of three phenotypes of sympathetic postganglionic neuron has been analyzed to assess whether their distinct cell input capacitances simply reflect differences in morphology. Because the distribution of membrane properties over the soma and dendrites is unknown, compartmental models incorporating cell morphology were used to simulate hyperpolarizing responses to small current steps. Neurons were classified as phasic (Ph), tonic (T), or long-afterhyperpolarizing (LAH) by their discharge pattern to threshold depolarizing current steps and filled with biocytin to determine their morphology. Responses were simulated in models with the average morphology of each cell class using the program NEURON. Specific membrane resistivity, R m, was derived in each model. Fits were acceptable when specific membrane capacitance, C m, and specific resistivity of the axoplasm, R i, were varied within realistic limits and when underestimation of membrane area due to surface irregularities was accounted for. In all models with uniform R m, solutions for R m that were the same for all classes could not be found unless C m or R i were different for each class, which seems unrealistic. Incorporation of a small somatic shunt conductance yielded values for R m for each class close to those derived assuming isopotentiality ( R m approximately 40, 27, and 15 kΩcm2 for T, Ph, and LAH neurons, respectively). It is concluded that R mis distinct between neuron classes. Because Ph and LAH neurons relay selected preganglionic inputs directly, R m generally affects function only in T neurons that integrate multiple subthreshold inputs and are modulated by peptidergic transmitters.

Contribution of Voltage-Dependent Potassium Channels to the Somatic Shunt in Neck Motoneurons of the Cat

Campbell, D. M. and P. K. Rose. Contribution of voltage-dependent potassium channels to the somatic shunt in neck motoneurons of the cat. J. Neurophysiol. 77: 1470–1486, 1997. The specific membrane resistivity of motoneurons at or near the soma ( R ms) is much lower than the specific membrane resistivity of the dendritic tree ( R md). 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 R ms. These channels were blocked with the use of intracellular injections of cesium. Input resistance ( R N), R ms/ R md, a conductance representing voltage-dependent potassium channels on the soma, G K, and a conductance attributed to damage caused by electrode impalement, G Da, 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. R N of control and cesium-loaded motoneurons was similar. Over the course of the recordings, R N of control cells usually increased and this increase was associated with a hyperpolarization. In contrast, increases in R N after successive injections of cesium were closely linked to a depolarization. At corresponding membrane potentials, R ms/ R md of cesium-loaded motoneurons was greater than R ms/ R md of control motoneurons. Over the course of cesium injections, R ms/ R md increased and the membrane potential depolarized. In contrast, increases in R ms/ R md observed during the course of recordings from control cells were associated with a hyperpolarization. Compared with control cells at corresponding membrane potentials, G K was less in cesium-loaded cells. Increases in G K that occurred over the course of recordings in control cells were closely coupled to a depolarization. In cesium-loaded cells, G K usually decreased as the cell depolarized during the injections. In control cells, increases in G Da that occurred during the recording period were closely coupled to a depolarization. In contrast, changes in G Da that occurred during cesium injections were not related to the change in membrane potential and did not explain the corresponding changes in R ms/ R md and membrane potential. The results of this study indicate that voltage-dependent potassium channels contribute to the somatic shunt (low R ms) in neck motoneurons and provide a voltage-dependent mechanism for the dynamic regulation of motoneuron electrotonic properties.

Passive electrical cable properties and synaptic excitation of tiger salamander retinal ganglion cells

The passive electrical properties of 17 ON-OFF retinal ganglion cells were derived from electrophysiological recordings. The parameters for each cells' equivalent model were obtained from the transient current responses to small step changes in clamp potential. Thirteen of the cells could be adequately approximated by a spherical soma connected to an equivalent dendritic cable. Estimates for the cell input conductance (GN), membrane time constant (τm), the dendritic-to-soma conductance ratio (ρ), and the normalized electrotonic length (L) were obtained (mean ± standard deviation, n = 13): GN = 580 ± 530 pS, τm = 97 ±72 ms, ρ = 2.8 ± 2.8, and L = 0.34 ± 0.13. Series resistance averaged 32 ± 11 MΩ The mean of the derived soma diameters was 18 ± 6 μm and the mean diameter and length of the equivalent cables were 1.4 ± 0.6 and 470 ± 90 μm, respectively. The average of the specific membrane conductances, 1.67 ± 1.08 S/cm2, corresponded to a membrane resistivity of 60 kΩ-cm2. Computer simulations of synaptic inputs were performed on a representative model, with an electrode at the soma and using the worst-case configuration, in which all synaptic inputs were confined to the tips of the dendrites. We draw three conclusions from the modeling: (1) Under voltage clamp, fast, spontaneous EPSCs would be significantly attenuated and slowed while the time course of the slower, light-evoked non-NMDA and NMDA EPSCs would be minimally distorted by dendritic filtering. (2) Excitatory synaptic reversal potentials can be accurately determined under voltage clamp. (3) In the absence of GABAergic and glycinergic inhibition, the efficacy at the soma of excitatory conductance changes is essentially independent of their dendritic location. The specific membrane resistivity appears to represent a good compromise between having a small membrane time constant and minimal EPSP attenuation.

Compartmental modeling of rat macular primary afferents from three-dimensional reconstructions of transmission electron micrographs of serial sections

1. We cut serial sections through the medial part of the rat vestibular macula for transmission electron microscopic (TEM) examination, computer-assisted three-dimensional (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 (SIZ)] and the expanded terminal(s) (calyx, calyces). These segments, termed the neuron branches, and the calyces frequently have spinelike processes of various dimensions that morphologically are afferent, efferent, or reciprocal to other macular neural elements. The purpose of this research was to determine whether morphometric data obtained ultrastructurally were essential to compartmental models [i.e., they influenced action potential (AP) generation, latency, or amplitude] or whether afferent parts could be collapsed into more simple units without markedly affecting results. We used the compartmental modeling program NEURON for this research. 2. In the first set of simulations we studied the relative importance of small variations in process morphology on distant depolarization. A process was placed midway along an isolated piece of a passive neuron branch. The dimensions of the four processes corresponded to actual processes in the serial sections. A synapse, placed on the head of each process, was activated and depolarization was recorded at the end of the neuron branch. When we used 5 nS synaptic conductance, depolarization varied by 3 mV. In a systematic study over a representative range of stem dimensions, depolarization varied by 15.7 mV. Smaller conductances produced smaller effects. Increasing membrane resistivity from 5,000 to 50,000 omega cm2 had no significant effect. 3. In a second series of simulations, using whole primary afferents, we examined the combined effects of process location and afferent morphology on depolarization magnitude and latency, and the effect of activating synapses individually or simultaneously. Process location affects peak latency and voltage recorded at the heminode. A synapse on a calyceal process produced < or = 8% more depolarization and a 23% increase in peak latency compared with a synapse on a process of a neuron branch. For whole primary afferents, depolarization decreased 40% between simulations of the smallest and largest afferents. Simulations in which membrane resistivity and synaptic conductance were varied while afferent geometry was kept constant indicated that use of 5,000 omega cm2 and 1.0 nS produced results that best fit electrophysiological findings. Synaptic inputs activated simultaneously did not sum linearly at the heminode. Total depolarization was approximately 14% less than a simple summation of responses of synapses activated one at a time.(ABSTRACT TRUNCATED AT 400 WORDS)