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

The dendrites of single brain-stem motoneurons intracellularly labelled with horseradish peroxidase in the cat. Morphological and electrical differences

The geometrical differences between individual dendrites of a given motoneuron were investigated in the cat. We chose two brain-stem motoneurons involved in different motor activities. One abducens and one laryngeal motoneuron were selected from two series of experiments which had combined intracellular recording and horseradish peroxidase staining. Three-dimensional reconstructions were made using a computer-aided microscope to obtain high-resolution measurements from serial histological sections. Each dendrite was characterized by computer dissection. Comparisons between dendrites were made on the basis of the following parameters: spatial projections, length, diameters, tapering, branching pattern, daughter--branch ratio and branching power. The present findings show that each dendrite projects to specific terminal fields for both motoneurons and are different in the complexity of their geometry and branching structure. The consequences of this complexity for the cable properties of the motoneurons were analysed. The dendrites of the two motoneurons were partitioned into a series of contiguous regions deemed short enough to be considered an isopotential cylinder and the steady-state properties were calculated for each segment. The properties of each segment were then combined for each dendrite for the following parameters: electronic distance, somatopetal and somatofugal voltage attenuation, input resistance and charge transfer effectiveness ratio. The present results show significant differences in the electrical behaviour of individual dendrites. Branch-to-branch computation reveals low attenuation pathways between branches suggesting the possibility of local influences within the distal branches of the dendritic arborization. It is proposed that the individual dendrites of the motoneuron function as distinct channels and/or integrators for afferent inputs.

Transient response in a somatic shunt cable model for synaptic input activated at the terminal

Rall's neuron model is extended by including a non-uniform time constant together with synaptic input modeled as a square step of conductance. An analytic solution (in series form) for the electrotonic potential is obtained. The major conclusion reached is that a lower somatic time constant attenuates the amplitude of the potential at the soma, brought about by the activation of a synapse located at the distal end of the dendritic cable in an initially polarized neuron.

Passive cable properties and morphological correlates of neurones in the lateral geniculate nucleus of the cat

1. We used an in vivo preparation of the cat to study the passive cable properties of sixteen X and twelve Y cells in the lateral geniculate nucleus. Cells were modelled as equivalent cylinders according to Rall's formulations (Rall, 1959a, 1969, 1977). We injected intracellular current pulses into these geniculate neurones, and we analysed the resulting voltage transients to obtain the cable parameters of these cells. In addition, fifty-four physiologically characterized neurones were labelled with horseradish peroxidase (HRP) and analysed morphologically. 2. Analysis of HRP-labelled geniculate neurones showed that the dendritic branching pattern of these cells adheres closely to the 3/2 power rule. That is, at each branch point, the diameter of the parent branch raised to the 3/2 power equals the sum of the diameters of the daughter dendrites after each is raised to the 3/2 power. Furthermore, preliminary data indicate that the dendritic terminations emanating from each primary dendrite occur at the same electrotonic distance from the soma. These observations suggest that both X and Y cells meet the geometric constraints necessary for reduction of their dendritic arbors into equivalent cylinders. 3. We found a strong linear relationship between the diameter of each primary dendrite and the membrane surface area of the arbor emanating from it. We used this relationship to derive an algorithm for determining the total somatic and dendritic membrane surface area of an X and Y cell simply from knowledge of the diameters of its soma and primary dendrites. 4. Both geniculate X and Y cells display current-voltage relationships that were linear within +/- 20 mV of the resting membrane potential. This meant that we could easily remain within the linear voltage range during the voltage transient analyses. 5. X and Y cells clearly differ in terms of many of their electrical properties, including input resistance, membrane time constant and electrotonic length. The difference in input resistance between X and Y cells cannot be attributed solely to the smaller average size of X cells, but it also reflects a higher specific membrane resistance (Rm) of the X cells. Furthermore, X cells exhibit electrotonic lengths slightly larger than those of Y cells, but both neuronal types display electrotonic lengths of roughly 1. This indicates that even the most distally located innervation to these cells should have considerable influence on their somatic and axonal responses.(ABSTRACT TRUNCATED AT 400 WORDS)

A quantitative analysis of the geometry of cat motoneurons innervating neck and shoulder muscles

The geometry of the somata and dendritic trees of motoneurons innervating neck and shoulder muscles was investigated by using intracellular injections of HRP. In general, these motoneurons did not belong to a homogeneous population of motoneurons. Differences in average primary dendritic diameter, number of primary dendrites, and other measures of dendritic tree size were found between different neck and shoulder motoneuron groups. Several indices of proximal dendritic tree size (number of primary dendrites, sum of dendritic diameters, Rall's dendritic trunk parameter, and the sum of dendritic holes) were weakly correlated with the diameter or surface area of the soma. Some of these correlations depended on the muscle supplied by the motoneuron. The total combined dendritic length ranged from 66,660 to 95,390 microns. There was a weak, but positive, correlation between the diameter of primary dendrites and combined dendritic length. This relationship varied from motoneuron to motoneuron. The diameters of all dendrites of three trapezius motoneurons were examined in detail. The total dendritic surface area examined ranged from 415,000 to 488,100 microns 2 and represented approximately 99% of the total neuronal surface area. Last-order dendrites showed a high degree (39.9%) of taper. Dendritic tapering, by itself, was a major factor in the decrease of the (sum of dendritic diameters)3/2 measured at progressively distal sites from the soma. Although few parent and daughter dendrites obeyed the "three-halves law," the average exponent was 1.57. The diameters of primary dendrites and dendritic surface area were weakly correlated. The correlation between dendritic diameter and combined dendritic length or surface area improved if the weighted average of the diameter of second-order dendrites was used as a measure of dendrite size. Second-order dendrites, whose branches terminated in different regions of the spinal cord, showed different relationships between dendritic diameter and combined dendritic length or surface area. Comparisons between the motoneurons examined in the present study and motoneurons innervating other muscles indicate that, although all spinal motoneurons share several common features (e.g., long dendrites, dendritic tapering), each motoneuron group has a set of unique features (e.g., soma shape, relationship between primary dendrite diameter and dendritic surface area). Thus, the rules governing motoneuron dendritic geometry are not fixed but depend on the species of the motoneuron.

Cable properties of a neuron model with non-uniform membrane resistivity

We propose an exact, self-closed and simple method for simultaneous estimation of the electrotonic length of the equivalent dendritic cylinder, and the ratio of dendritic to somatic input conductance in the Rall's motoneuron model (1969), from a voltage transient at the soma in response to a current step applied to the soma. We prove the theoretical constraint in the Rall's motoneuron model that one half of the ratio of amplitudes of the first two peeled exponentials in a membrane voltage transient caused by a current step, must be smaller than the ratio of the corresponding first two time constants. This theoretical prediction is not satisfied for several types of neurons, and our method to estimate cable parameters is not applicable to these neurons. By extending the Rall's neuron model, we develop a neuron model, which contains two membrane resistance per unit area; one for somatic membrane and one for dendritic membrane. In this model we obtain the transient solution of membrane potential at the soma in response to a current step applied to the soma. It is shown that the amplitude ratio can be larger than double of the time constant ratio when the somatic resistance is lower than the dendritic resistance. Moreover, we give a purely electrophysiological method to estimate cable parameters of the extended model from soma transient in response to a current step.

The somatic shunt cable model for neurons

The derivation of the equations for an electrical model of nerve cells is presented. The model consists of an equivalent cylinder, a lumped somatic impedance, and a variable shunt at the soma. This shunt was introduced to take into account the fast voltage decays observed following the injections of current pulses in some motoneurons and hippocampal granule cells that could not be explained by existing models. The shunt can be interpreted either by penetration damage with the electrode or by a lower membrane specific resistance at the soma than in the dendrites. A solution of the model equations is presented that allows the estimation of the electrotonic length L, the membrane time constant tau m, the dendritic dominance ratio rho, and the shunt parameter epsilon, based only on the measurement of the first two coefficients and time constants in the multiexponential voltage response to injected current pulses.

Segmental cable evaluation of somatic transients in hippocampal neurons (CA1, CA3, and dentate)

This study describes a detailed cable model of neuronal structure, which can predict the effects of discrete transient inputs. Neurons in in vitro hippocampal slices (CA1 and CA3 pyramidal cells and dentate granule neurons; n = 4 each) were physiologically characterized and stained with horseradish peroxidase (HRP). The HRP morphology was approximated with numerous small segments. The cable model included both these segments and spatially dispersed dendritic spines. The transient response function at the soma of the segmental model was numerically derived, and charging responses to simulated current inputs were computed. These simulations were compared with the physiological charging responses from the somatic penetrations, using an analysis of the charging time constants (tau i) and intercepts. The time constant ratio (tau 0/tau 1) did not significantly differ between the observed and simulated responses. A second index of comparison was the equivalent cylinder electrotonic length (L), which was derived using only the tau i values and their intercepts. The L values also did not differ significantly between the observed and simulated transients and averaged 0.91 length constant. Thus, using criteria based only on analysis of charging responses, the segmental cable model recreated accurately the observed transients at the soma. The equivalent cylinder model (with a lumped soma) could also adequately simulate the observed somatic transients, using the same criteria. However, the hippocampal neurons (particularly the pyramidal cells) did not appear to satisfy the equivalent cylinder assumption anatomically. Thus, the analysis of somatic charging transients alone may not be sufficient to discriminate between the two models of hippocampal neurons. Anatomical evidence indicates that, particularly for discrete dendritic inputs, the detailed segmental model may be more appropriate than the equivalent cylinder model.

Decreased neuronal inhibition in vitro after long-term administration of ethanol

The pathophysiology of brain dysfunction was studied with an animal model of chronic alcoholism. Rats were fed a liquid diet with or without ethanol for 20 weeks and then the diet without ethanol for three more weeks. Hippocampal slices were prepared and intracellular recordings were obtained from dentate granule and CA1 cells. Significant depression of orthodromically elicited inhibitory postsynaptic potentials and postspike afterhyperpolarizations was observed in neurons from ethanol-exposed animals. No differences were observed in other active or passive membrane characteristics. These results suggest that a loss of neuronal inhibition could contribute to brain dysfunction in chronic alcoholism.