S. M. Korogod

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.

Geometry-induced features of current transfer in neuronal dendrites with tonically activated conductances

Abstract. The impact of dendritic geometry on somatopetal transfer of the current generated by steady uniform activation of excitatory synaptic conductance distributed over passive, or active (Hodgkin-Huxley type), dendrites was studied in simulated neurons. Such tonic activation was delivered to the uniform dendrite and to the dendrites with symmetric or asymmetric branching with various ratios of branch diameters. Transfer effectiveness of the dendrites with distributed sources was estimated by the core current increment directly related to the total membrane current per unit path length. The effectiveness decreased with increasing path distance from the soma along uniform branches. The primary reason for this was the asymmetry of somatopetal vs somatofugal input core conductance met by synaptic current due to a greater leak conductance at the proximal end of the dendrite. Under these conditions, an increasing somatopetal core current and a corresponding drop of the depolarization membrane potential occurred. The voltage-dependent extrasynaptic conductances, if present, followed this depolarization. Consequently, the driving potential and membrane current densities decreased with increasing path distance from the soma. All path profiles were perturbed at bifurcations, being identical in symmetrical branches and diverging in asymmetrical ones. These perturbations were caused by voltage gradient breaks (abrupt change in the profile slope) occurring at the branching node due to coincident inhomogeneity of the dendritic core cross-section area and its conductance. The gradient was greater on the side of the smaller effective cross-section. Correspondingly, the path profiles of the somatopetal current transfer effectiveness were broken and/or diverged. The dendrites, their paths, and sites which were more effective in the current transfer from distributed sources were also more effective in the transfer from single-site inputs. The effectiveness of the active dendrite depended on the activation-inactivation kinetics of its voltage-gated conductances. In particular, dendrites with the same geometry were less effective with the Hodgkin-Huxley membrane than with the passive membrane, because of the effect of the noninactivating K+-conductance associated with the hyperpolarization equilibrium potential. Such electrogeometrical coupling may form a basis for path-dependent input-output conversion in the dendritic neurons, as the output discharge rate is defined by the net current delivered to the soma.

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.

Structure-Dependent Electrical and Concentration Processes in the Dendrites of Pyramidal Neurons of Superficial Neocortical Layers: Model Study

On mathematical models of pyramidal neurons localized in the neocortical layers 2/3, whose reconstructed dendritic arborization possessed passive linear or active nonlinear membrane properties, we studied the effect of morphology of the dendrites on their passive electrical transfer characteristics and also on the formation of patterns of spike discharges at the output of the cell under conditions of tonic activation via uniformly distributed excitatory synapses along the dendrites. For this purpose, we calculated morphometric characteristics of the size, complexity, metric asymmetry, and function of effectiveness of somatopetal transmission of the current (with estimation of the sensitivity of this efficacy to changes in the uniform membrane conductance) for the reconstructed dendritic arborization in general and also for its apical and basal subtrees. Spatial maps of the membrane potential and intracellular calcium concentration, which corresponded to certain temporal patterns of spike discharges generated by the neuron upon different intensities of synaptic activation, were superimposed on the 3D image and dendrograms of the neuron. These maps were considered “spatial autographs” of the above patterns. The main discharge pattern included periodic two-spike bursts (dublets) generated with relatively stable intraburst interspike intervals and interburst intervals decreasing with a rise in the intensity of activation. Under conditions of intense activation, the interburst intervals became close to the intraburst intervals, so the cell began to generate continuous trains of action potentials. Such a repertoire (consisting of two patterns of the activity, periodical dublets and continuous discharges) is considerably scantier than that described earlier in pyramidal neurons of the neocortical layer 5. Under analogous conditions of activation, we observed in the latter cells a variety of patterns of output discharges of different complexities, including stochastic ones. A relatively short length of the apical dendrite subtree of layer 2/3 neurons and, correspondingly, a smaller metric asymmetry (differences between the lengths of the apical and basal dendritic branches and paths), as compared with those in layer 5 pyramidal neurons, are morphological factors responsible for the predominance of periodic spike dublets. As a result, there were two combinations of different electrical states of the sites of dendritic arborization (“spatial autographs”). In the case of dublets, these were high depolarization of the apical dendrites vs. low depolarization of the basal dendrites and a reverse combination; only the latter (reverse) combination corresponded to the case of continuous discharges. The relative simplicity and uniformity of spike patterns in the cells, apparently, promotes the predominance of network interaction in the processes of formation of the activity of pyramidal neurons of layers 2/3 and, thereby, a higher efficiency of the processes of intracortical association.

Electrodiffusion of synaptic receptors: a mechanism to modify synaptic efficacy?

We analysed physical forces that act on synaptic receptor‐channels following the release of neurotransmitter. These forces are: 1) electrostatic interaction between receptors, 2) stochastic Brownian diffusion in the membrane, 3) transient electric field force generated by currents through open channels, 4) viscous drag force elicited by the flowing molecules and 5) strong in‐membrane friction. By considering α‐amino‐3‐hydroxy‐5‐methyl‐4‐isoxazolepropionic acid (AMPA) type receptors, we show that, depending on the size and electrophoretic charge of the extracellular receptor domain, release of an excitatory neurotransmitter (glutamate) can induce receptor clustering towards the release site on a fast time scale (8–100 ms). This clustering progresses whenever repetitive synaptic activation exceeds a critical frequency (20–100 s‐1, depending on the currents through individual channels). As a result, a higher proportion of the receptors is exposed to higher glutamate levels. This should increase by 50–100% the peak synaptic current induced by the same amount of released neurotransmitter. In order for this mechanism to contribute to long‐term changes of synaptic efficacy, we consider the possibility that the in‐membrane motility of the AMPA receptors is transiently increased during synaptic activity, e.g., through the breakage of receptor anchors in the postsynaptic membrane due to activation of N‐methyl‐d‐aspartic acid receptors. Synapse 35:26–38, 2000.

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.

Biophysical Mechanism of Parasympathetic Excitation of Urinary Bladder Smooth Muscle Cells: a Simulation Study

Using the Hodgkin-Huxley formalism, we developed a computer model of a smooth muscle cell (SMC) of the urinary bladder detrusor; the model included the main types of ion channels and pumps, as well as intracellular calcium regulatory mechanisms inherent in the prototype cell. The biophysical mechanisms of generation of action potentials (APs) necessary for initiation of muscle contraction and those of calcium transients in response to parasympathetic activation of metabotropic М2/М3-cholinoreceptors and co-activation of Р2Х-purinoreceptors were investigated. The simulated SMC in response to a depolarizing current pulse generated an AP that was, by a number of indices, similar to real APs and was also accompanied by a transient elevation of the intracellular calcium concentration. We demonstrated a possibility of generation of such APs in response to a transient increase in the conductivity of channels of calcium-dependent chloride current accompanied by increase in the conductivity of channels associated with Р2Х-receptors (the conductivity ratio was 95 to 5 % and similar to that in the prototype). For the AP generation, temporal relations of the processes of increases in the mentioned conductances simulating the final effect of activation of М2/М3- and Р2Х-receptors were significant. These results obtained on the rather simplified model allow researchers to use the latter as an appropriate starting point for the development of more detailed models (in particular, those representing cascades of metabolic reactions triggered by a parasympathetic action).