Spatial heterogeneity of passive electrical transfer properties of neuronal dendrites due to their metrical asymmetry.

The complex and diverse geometry of neuronal dendrites determines the different morphological types of neurons and influences the generation of complex and diverse discharge patterns at the cell output. The recent finding that each temporal pattern has its spatial signature in the form of a combination of high- and low-depolarization states of asymmetrical dendritic branches with active membrane properties raises the question of the nature of such characteristic spatial heterogeneity of electrical states. To answer this, we consider passive dendrites as a conventional reference case using the known current transfer functions, which we complete by corresponding parametric sensitivity functions. These functions for metrically asymmetrical bifurcations of different sizes, as the simplest elements constituting arborizations of arbitrary geometry, are analyzed under different membrane conductivity conditions related to the intensity of activation of ion channels. Characteristic relationships are obtained on the one hand among the size (branch lengths), metrical asymmetry (difference between sister branches in length and/or diameter), and membrane conductivity, and on the other hand, for the difference between the branches in their current transfer effectiveness as an indicator of their electrical asymmetry (heterogeneity). These relationships (i) allow the introduction of a biophysically based criterion for the electrical distinction between metrically asymmetrical branches, (ii) show how the difference first increases and then decreases with increasing membrane conductivity, and (iii) show that the greatest electrical heterogeneity occurs in a lower or higher range of conductivity, corresponding to larger or smaller bifurcation size. As a consequence, the characteristic low-, medium-, and high-conductance states are derived such that metrically asymmetrical parts of simple and complex trees are electrically distinct when the membrane conductivity lies in the size-related medium range, and indistinct otherwise.

Parameter sensitivity of distributed transfer properties of neuronal dendrites: a passive cable approximation.

Geometry and membrane properties of the dendrites crucially determine input-output relations in neurons. Unlike geometry often available in detail from computer reconstruction, the membrane resistivity is fragmentarily known if at all. Moreover, it varies during ongoing activity. In this study we address the question: what is the impact of the variation in membrane resistivity on the transfer properties of dendrites? Following a standard approach of the control system theory, we derive and explore the sensitivity functions complementary to the transfer functions of the passive dendrites with arbitrary geometrical parameters (length and diameter) and boundary conditions. We use the location-dependent somatopetal current transfer ratio (the reciprocal of the somatofugal voltage) as the transfer function, and its membrane resistivity derivatives, as the sensitivity functions. In the dendrites, at every path distance from the origin, the sensitivity function in a common form relates the transfer function, membrane resistivity, characteristic input conductance of semi-infinite cable and directional somatofugal input conductances at the given internal site and origin, and the length. Plotted in membrane resistivity versus path distance coordinates, the sensitivity functions display common features: along any coordinate there are low and high ranges, in which the sensitivity, respectively, increases and decreases. The ranges and corresponding rates depend on morphology and boundary conditions in a characteristic manner. These features predict existence of the geometry-dependent range of membrane resistivity (the earlier unattended mid-conductance state), such that the dendrites with a given metrical asymmetry are most distinguished in their transfer properties and electrical states if membrane resistivity is within the range and are not otherwise.

Electric fields of synaptic currents could influence diffusion of charged neurotransmitter molecules.

Rapid activation of synaptic receptor-channels evokes an ion current that flows through the narrow synaptic cleft; this exerts a significant voltage drop and therefore strong electric field (10(4) V/m range) directed towards the current sinks in the cleft. To what extent this field affects fast diffusion of charged neurotransmitter molecules is not known. We draw a theoretical framework for this complex electrodiffusion phenomenon and establish the basic relationships between the synaptic current and the time course of neurotransmitter in the cleft. The analyses predict that excitatory currents could significantly accelerate the dispersion of negatively charged molecules from the cleft while attracting the positively charged molecules towards the current sinks. This previously unrecognized mechanism should affect the kinetics of synaptic receptor currents, thus contributing to fast synaptic signaling in the brain.

Heterogeneous synaptic covering and differential charge transfer sensitivity among the dendrites of a reconstructed abducens motor neurone: correlations between electron microscopic and computer simulation data.

Ultrastructural studies on the synaptology of dendritic arborizations of motoneurones have been problematic because dendrites are very thin in relation to their great length, and most of the studies on this topic have therefore dealt with only small parts of the dendritic tree. Here we compared the ultrastructural characteristics of the axon terminals distributed along the various dendrites of a single motoneurone. For this purpose, the light microscopic 3D reconstruction of the dendritic arborization of an intracellularly labelled abducens motoneurone was combined with an electron microscopic analysis of its synaptic contacts. Dendritic profiles were randomly sampled along the various dendrites and the axon terminals they received were classified on the basis of their ultrastructural features and their GABA-immunoreactivity. It emerged that the various dendrites differed according to the type and local arrangement of their synaptic inputs. Our second aim was to incorporate the morphological data obtained into a model giving the charge transfer effectiveness T(x) of the dendritic sites. The sensitivity S(x) of T(x) to changes in the membrane resistivity (Rm) simulating various levels of tonic synaptic activity was calculated. It turned out that both the proximal and distal regions of the dendritic arborization have a dense synaptic covering and a weak sensitivity to changes in the Rm, whereas the intermediate dendrites have a sparse synaptic covering and a high sensitivity to changes in tonic synaptic activity. This pattern of organisation might mediate the "gating" of a population of synapses covering some dendritic regions in a state-dependent fashion.

Theoretical estimation of the capacity of intracellular calcium stores in the Bergmann glial cell.

We propose a mathematical model for calcium dynamics ([Ca2+]i) during metabotropic activation of a specialized astrocyte, the cerebellar Bergmann glial cell. The model adequately describes the experimentally observed behaviour of the prototype in response to single and repetitive metabotropic stimuli and to the inhibition of Ca2+ uptake into the store. By means of the model, the capacity of the intracellular calcium store for two types of calcium buffer was estimated. The estimated buffer capacity of the store lies within the following intervals: (0.8-15.5).10-19 mol calmodulin, and (0.6-12.3).10-19 mol calbindin. This result reveals, that, in the store of a small Ca2+-containing compartment optically detected in the Bergmann glial cell process after electrical stimulation of parallel fibres, the amount of releasable Ca2+ does not exceed 25,000 ions. The quantitative estimates were obtained from experimentally based theoretical relationships between the capacity and volume of the store and parameters of the cytoplasmic calcium buffer. In these relationships, the estimated store capacity was proportional to the total buffer concentration, inversely proportional to the constant of buffer affinity for calcium and was smaller for a greater relative store volume.