Following reconstruction with high spatial resolution of the 3-D geometry of the dendritic arborizations of two abducens motoneurons, we simulated the distribution of electronic voltage over the whole dendritic tree. Here, we demonstrate that the complex stochastic electronic 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 electronic 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 k omega.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.
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.
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