Paul Gogan

Electrotonic Clusters in the Dendritic Arborization of Abducens Motoneurons of the Rat

Following reconstruction with high spatial resolution of the 3‐D geometry of the dendritic arborizations of two abducens motoneurons, we simulated the distribution of electrotonic voltage over the whole dendritic tree. Here, we demonstrate that the complex stochastic electrotonic structure of both motoneurons can be reduced to a statistically significant small set of well discriminated clusters. These clusters are formed by dendritic branches belonging to different dendrites of the neuron but with similar electrotonic properties. A cluster analysis was performed to estimate quantitatively the partition of the branches between the dendritic clusters. The contents of the clusters were analysed in relation to their stability under different values of specific membrane resistivity (Rm), to their remoteness from the soma and their location in 3‐D space. The cluster analysis was executed in a 2‐D parameter space in which each dendritic branch was described by the mean electrotonic voltage and gradient. The number of clusters was found to be four for each motoneuron when computations were made with Rm= 3 kΩ.cm2. An analysis of the cluster composition under different Rm revealed that each cluster contained invariant and variant branches. Mapping the clusters upon the dendritic geometry of the arborizations allowed us to describe the cluster distribution in terms of the 3‐D space domain, the 2‐D path distance domain and the total surface area of the tree. As the cluster behaviour reflects both the geometry and the changes in the neuronal electrotonic structure, we conclude that cluster analysis provides a tool to handle the functional complexity of the arborizations without losing relevant information. In terms of synaptic activities, the stable dendritic branches in each cluster may process the synaptic inputs in a similar manner. The high percentage of stable branches indicates that geometry is a major factor of stability for the electrotonic clusters. Conversely, the variant branches introduce the conditions for mechanisms of functional postsynaptic plasticity.

Stochastic Geometry and Electrotonic Architecture of Dendritic Arborization of Brain Stem Motoneuron

We describe how the stochastic geometry of dendritic arborization of a single identified motoneuron of the rat affects the local details of its electrotonic structure. After describing the 3D dendritic geometry at high spatial resolution, we simulate the distribution of voltage gradients along dendritic branches under steady‐state and transient conditions. We show that local variations in diameters along branches and asymmetric branchings determine the non‐monotonous features of the heterogeneous electrotonic structure. This is defined by the voltage decay expressed as a function of the somatofugal paths in physical distances (voltage gradient). The fan‐shaped electrotonic structure demonstrates differences between branches which are preserved when simulations are computed from different values of specific membrane resistivity although the absolute value of their voltages is changed. At given distances from soma and over long paths, some branches display similar voltages resulting in their grouping which is also preserved when specific membrane resistivity is changed. However, the mutual relation between branches inside the group is respecified when different values of specific membrane resistivity are used in the simulations. We find that there are some invariant features of the electrotonic structure which are related to the geometry and not to the electrical parameters, while other features are changed by altering the electrical parameters. Under transient conditions, the somatofugal invasion of the dendritic tree by a somatic action potential shifts membrane potentials (above 10 mV) of dendritic paths for unequal distances from the soma during several milliseconds. Electrotonic reconfigurations and membrane shifts might be a mechanism for postsynaptic plasticity.

Activity-dependent reconfiguration of the effective dendritic field of motoneurons

A neuron in vivo receives a continuous bombardment of synaptic inputs that modify the integrative properties of dendritic arborizations by changing the specific membrane resistance (Rm). To address the mechanisms by which the synaptic background activity transforms the charge transfer effectiveness (Tx) of a dendritic arborization, the authors simulated a neuron at rest and a highly excited neuron. After in vivo identification of the motoneurons recorded and stained intracellularly, the motoneuron arborizations were reconstructed at high spatial resolution. The neuronal model was constrained by the geometric data describing the numerized arborization. The electrotonic structure and Tx were computed under different Rm values to mimic a highly excited neuron (1 kOhm.cm2) and a neuron at rest (100 kOhm.cm2). The authors found that the shape and the size of the effective dendritic fields varied in the function of Rm. In the highly excited neuron, the effective dendritic field was reduced spatially by switching off most of the distal dendritic branches, which were disconnected functionally from the somata. At rest, the entire dendritic field was highly efficient in transferring current to the somata, but there was a lack of spatial discrimination. Because the large motoneurons are more sensitive to variations in the upper range of Rm, they switch off their distal dendrites before the small motoneurons. Thus, the same anatomic structure that shrinks or expands according to the background synaptic activity can select the types of its synaptic inputs. The results of this study demonstrate that these reconfigurations of the effective dendritic field of the motoneurons are activity‐dependent and geometry‐dependent. J. Comp. Neurol. 422:18–34, 2000.

Fluorescence imaging of local membrane electric fields during the excitation of single neurons in culture

The spatial distribution of depolarized patches of membrane during the excitation of single neurons in culture has been recorded with a high spatial resolution (1 micron2/pixel) imaging system based on a liquid-nitrogen-cooled astronomical camera mounted on an inverted microscope. Images were captured from rat nodose neurons stained with the voltage-sensitive dye RH237. Conventional intracellular microelectrode recordings were made in synchrony with the images. During an action potential the fluorescence changes occurred in localized, unevenly distributed membrane areas, which formed clusters of depolarized sites of different sizes and intensities. When fast conductances were blocked by the addition of tetrodotoxin, a reduction in the number and the intensities of the depolarized sites was observed. The blockade by tetrodotoxin of voltage-clamped neurons also reduced the number of depolarized sites, although the same depolarizing voltage step was applied. Similarly, when a voltage-clamped neuron was depolarized by a constant-amplitude voltage step, the number of depolarized sites varied according to the degree of activation of the voltage-sensitive channels, which was modified by changing the holding potential. These results suggest that the spatial patterns of depolarization observed during excitation are related to the operations of ionic channels in the membrane.

Neuronal morphology data bases: morphological noise and assesment of data quality.

For technical, instrumental and operator-related reasons, three-dimensional reconstructions of neurons obtained from intracellularly stained neuronal pieces scattered in serial sections are blurred by some morphological noise. This noise may strongly invalidate conclusions drawn from models built using the three-dimensional reconstructions and it must be taken into account when retrieving digitized neurons from available databases. We analyse the main generating sources of the noise and its consequences for the ‘quality’ of the data. We provide tools for detecting and evaluating the noise in any database providing sufficient information is given in the database. We propose a unified format for submitting data and a new neuron viewer/editor to analyse the digitized neurons with our tools.

Differential back-invasion of a single complex dendrite of an abducens motoneuron by N-methyl-d-aspartate-induced oscillations: a simulation study

Intracellular recording of abducens motoneurons in vivo has shown that ionophoretic applications of N-methyl-D-aspartate produced long-lasting membrane potential oscillations including a slow depolarization plateau with a burst of fast action potentials. This complex N-methyl-D-aspartate pattern was reproduced in the model of abducens motoneuron in vivo identified, intracellularly stained with horseradish peroxidase and reconstructed at high spatial resolution. The excitable soma of the simulated cell contained voltage-gated Ca, Na and K conductances, N-methyl-D-aspartate-gated voltage-sensitive Ca-Na-K conductance and Ca-dependent K conductance. The dendrite was passive either completely or with the exception of branching nodes containing N-methyl-D-aspartate conductances of the same slow kinetics but of lower values than at the soma. In the completely passive case, the N-methyl-D-aspartate pattern decayed with different rates along different dendritic paths depending on the geometry and topology of the reconstructed dendrite. The branches formed four clusters discriminated in somatofugal attenuations of steady voltages, and were correspondingly discriminated in attenuation of the complex N-methyl-D-aspartate pattern. Fast spikes decayed more than the slow depolarization plateau so that the prevalence of slow over fast components in the transformed pattern increased with somatofugal path distance. As a consequence, the lower the electrotonic effectiveness of a branch in the cluster or in the whole arborization, the lower both the voltage level and the frequency range of its voltage modulation by N-methyl-D-aspartate oscillations. In the case of active branching points, the somatic pattern changed depending on the level of activation of dendritic N-methyl-D-aspartate conductances with slow kinetics of voltage sensitivity. The higher this level, the longer the plateau and burst, and the greater the discharge rate; and the spikes in the burst were smaller. When the pattern spread in the dendrite, the fast spikes decayed and the slow plateau was boosted, with a greater effect along the somatofugal path containing more branching points. These results show how the somatofugal back-invasion along the dendrites by activity patterns generated at the soma can tune voltage-sensitive dendritic conductances. The dendritic back-invasion is geometry- and topology-dependent. It is proposed as a subtle feedback mechanism for the neuron to control its own synaptic inputs.

Imaging stochastic spatial variability of active channel clusters during excitation of single neurons

Topographical maps of membrane voltages were obtained during action potentials by imaging, at 1 microm resolution, live dissociated neurons stained with the voltage sensitive dye RH237. We demonstrate with a theoretical approach that the spatial patterns in the images result from the distribution of net positive charges condensed in the inner sites of the membrane where clusters of open ionic channels are located. We observed that, in our biological images, this spatial distribution of open channels varies randomly from trial to trial while the action potentials recorded by the microelectrode display similar amplitudes and time-courses. The random differences in size and intensity of the spatial patterns in the images are best evidenced when the time of observation coincides with the duration of single action potentials. This spatial variability is explained by the fact that only part of the channel population generates an action potential and that different channels open in turn in different trials due to their stochastic operation. Such spatial flicker modifies the direction of lateral current along the neuronal membrane and may have important consequences on the intrinsic processing capabilities of the neuron.

Spatial reconfiguration of charge transfer effectiveness in active bistable dendritic arborizations.

The aim of this work was to explore the electrical spatial profile of the dendritic arborization during membrane potential oscillations of a bistable motoneuron. Computational simulations provided the spatial counterparts of the temporal dynamics of bistability and allowed simultaneous depiction the electrical states of any sites in the arborization. We assumed that the dendritic membrane had homogeneously distributed specific electrical properties and was equipped with a cocktail of passive extrasynaptic and NMDA synaptic conductances. The electrical conditions for evoking bistability in a single isopotential compartment and in a whole dendritic arborization were computed and showed differences, revealing a crucial effect of dendritic geometry. Snapshots of the whole arborization during bistability revealed the spatial distribution of the density of the transmembrane current generated at the synapses and the effectiveness of the current transfer from any dendritic site to the soma. These functional maps changed dynamically according to the phase of the oscillatory cycle. In the low depolarization state, the current density was low in the proximal dendrites and higher in the distal parts of the arborization while the transfer effectiveness varied in a narrow range with small differences between proximal and distal dendritic segments. When the neuron switched to high depolarization state, the current density was high in the proximal dendrites and low in the distal branches while a large domain of the dendritic field became electrically disconnected beyond 200 µm from the soma with a null transfer efficiency. These spatial reconfigurations affected dynamically the size and shape of the functional dendritic field and were strongly geometry‐dependent.

Dendritic spatial flicker of local membrane potential due to channel noise and probabilistic firing of hippocampal neurons in culture

Whole-cell recordings and imaging of dissociated hippocampal neurons stained with voltage sensitive dye provide a new microscopic picture of neuronal excitation. This is the first attempt to combine imaging of active channel clusters on the geometry of live neurons and a theoretical approach. During single somatic action potentials and the back-invasion into the neurites, local mean potentials are generated at sites of active channel clusters which are unevenly distributed in the neuronal membrane. Similar mean membrane potentials are observed in the neurites and at the soma. Identical action potentials produce different spatial patterns of mean membrane potentials from trial to trial. This spatial variability is explained by the stochastic behavior of the channels in the clusters. When hippocampal neurons are excited by synaptic inputs, their evoked responses are probabilistic and generate variable spatial patterns of mean membrane potential trial after trial. Our stochastic model reproduces this random behavior by assuming that the voltage fluctuations generated by channel noise are added to the synaptic potentials reaching the soma. We demonstrate that the probability of action potential initiation depends on the strength of the synaptic input, the diameter of the dendrites and the relative positions of the channel clusters, of the synapse and of the soma.

The dendritic architecture of motoneurons: A case study

Within a historical perspective, different experimental approaches are reviewed that have used new tools and new concepts to gain an insight into the functional significance of the architecture of dendritic arborizations of nerve cells. A single type of neurons, the motoneurons, were taken as a case study to show how different fields, such as histology, morphology, electrophysiology, and neuronal modeling, have developed in parallel and accumulated a wealth of new data, and how consideration of these new informations led to new working hypotheses. Matching geometrical and electrical parameters of dendrites is critically analyzed as a basis for understanding of the dendritic functions.