I. B. Kulagina

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.

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.

Organization of Activity of Hippocampal Pyramidal Neurons under Coactivation of Dendritic Glutamate- and GABA-Sensitive Receptors: a Simulation Study

Using the model of a hippocampal pyramidal neuron with reconstructed dendritic arborization having active electrical properties of the membrane, we investigated the effects of tonic activation of dendritic receptor channels sensitive to glutamate and GABA on the patterns of impulse activity in the axon and on the corresponding electrical processes in the dendrites. Activation of these types of receptors was represented by introducing the uniformly distributed membrane conductivities Gse and Gsi associated with the current reversal potentials of 0 and -60 mV, respectively. It was found that the dendritic membrane with voltage-gated ion channels typical of this-type neurons became, under the influence of suprathreshold activation of glutamate receptors, a source of self-oscillations of the membrane potential or persistent depolarization of the membrane with characteristic differences of the electrical processes in metrically asymmetrical parts of the dendritic arborization. At the neuronal output, regular periodic or stochastic sequences of action potentials (APs) were generated; their average repetition frequency f depended logarithmically on the Gse. Coactivation of GABA receptors (Gsi > 0) led to an increase in the threshold and a decrease in the frequency of auto-oscillations in the dendrites (in this case, the autooscillations were renewed in the branches where persistent depolarization developed previously), as well as to a decrease in the mean frequency of AP firing, whereas the logarithmic dependence of f on the Gse remained. An earlier undescribed effect was revealed; the transformation of firing patterns (irregular, stochastic, and regular, periodic) at certain ratios of the conductivities Gse and Gsi occurred. It is assumed that the above-described features of the firing pattern formation in hippocampal pyramidal neurons are due to dynamical spatial coupling of the local auto-oscillatory processes. This coupling depends on the geometry and membrane conductivities of the dendrites, is modulated by coactivation of receptors of different types, and is determined by the parametric sensitivity of the dendritic transfer functions.

Impulse Coding of Electrical and Synaptic Input Actions by Nucl. Abducens Motoneurons with Active Dendrites: A Simulation Study

The study was carried out on models of nucl. abducens motoneurons with dendritic arborizations reconstructed with a high spatial resolution. The arborizations had membranes with nonlinear electrical properties due to the presence of glutamatergic NMDA-type synaptic conductivity with voltage dependent kinetics of ligand activation. We studied rules governing the transformation of electrical influences on the soma and of tonic excitatory synaptic actions on dendritic arborizations into output discharges of action potentials (APs), i.e., the processes of formation of “intrinsic” neuronal codes. The electrical action was a depolarizing current applied to the soma, and the synaptic action was a tonic synaptic excitation homogeneously distributed over the dendrites; this excitation was simulated by introducing a synaptic conductivity, which was homogeneous over the dendritic membrane surface and constant in time. We recorded impulse patterns generated at different intensities of the applied current or synaptic excitation. The only pattern generated in response to the current application was a continuous rhythmic discharge of APs with equal interspike intervals (ISIs); increases in the mean frequency of AP firing with increasing current intensity obeyed the logarithmic law. An increase in the synaptic activation intensity also led to an increase in the mean firing frequency, but in this case the “intensity-to-frequency” conversion obeyed the polynomial law. A feature of the patterns generated under these conditions was the existence of essential dissimilarities in the type and complexity observed at three ranges of the synaptic intensity, low, medium, and high. The medium range corresponded to complex multiburst output patterns, both periodical and non-periodical. At intensities corresponding to the low and high ranges, continuous AP discharges were generated with constant (or slightly varying) ISIs similar to those observed upon application of the depolarizing current. In the complex patterns, the interburst intervals demonstrated the greatest variability. Their duration was mainly determined by processes in the dendrites, whereas the variability of the intraburst ISIs was mostly due to fast processes in the trigger zone and was an order of magnitude smaller. Electrical states of the dendritic arborization were essentially heterogeneous during generation of AP bursts in the multiburst patterns, less heterogeneous during generation of simple patterns, and practically homogeneous within interburst time intervals.

Features of Active Electrical States of Asymmetrical Dendrites of Brainstem Motoneurons during Generation of Stochastic Implulse Patterns: a Simulation Study

On models of motoneurons of the n. abducens nucleus with reconstructed dendritic arborizations having an active membrane, we investigated features of the relationships between passive transfer properties and dynamics of excitation states of asymmetrical dendrites during generation of complex periodical and stochastic impulse patterns (output neuronal codes). Various patterns were obtained by varying the intensity of tonic synaptic excitation homogeneously distributed over the dendrites. The electrical states of sites belonging to branches of the same dendrite or different dendrites were compared. For this comparison, branches were selected, which, according to the earlier performed cluster analysis, were assigned to the groups (electrotonic clusters) with a high and a low effectiveness of passive transfer of the somatopetal current. The selection took into account features of the dendritic structure of neurons of the exemined type. These were: (i) the presence of groups of the asymmetrical branches differing from each other according to their belonging to different clusters (high or low transfer effectiveness) in different dendrites, and (ii) the presence of branches belonging to different dendrites characterized by significantly different orientations in three-dimensional space of the brainstem within each electrical cluster. Comparative analysis showed that, in a given dendrite during generation of a complex periodical pattern, the asymmetrical branches belonging to high- or low-efficiency clusters were characterized by being in different states (high or low depolarization) in different phases of generation of repeated sequences of action potentials (APs). This relationship was consistent with those previously detected in neurons of other types and in other specimens of neurons of the above-mentioned type. During generation of such periodical spike patterns, the branches of different dendrites belonging to the same electrotonic cluster were in similar states. Similar relationships between the states of the branches of the same dendrite belonging to different clusters were also observed during generation of complex stochastic (non-periodical) impulse patterns. In the latter case, however, the essential feature was that the branches of different dendrites belonging to the same electrotonic cluster were often in opposite states. Thus, the number of combinations of discrete electrical states of asymmetrical parts of the dendritic arborization was much greater. Probably, it is precisely this circumstance that determined the quasi-stochastic nature of the output impulse pattern.

Electrical bistability in a neuron model with monostable dendritic and axosomatic membranes

In a two-compartment mathematical model, we studied the reason for and conditions of manifestation of electrical bistability in a neuron composed of monostable parts. One compartment of the model simulated the dendrites; their membrane was monostable at high depolarization and characterized by an N-shaped steady current-voltage (I–V) characteristic endowed by inward synaptic current through voltage-dependent channels sensitive to N-methyl-D-aspartate (NMDA). Another compartment simulated the axosomatic region with a positively sloped linearizedI–V characteristic of the membrane monostable at the resting membrane potential. For the whole cell, bistability was obvious at a subcritical intensity of NMDA activation; the reason was the current directed from the more depolarized dendritic region into the somatic region, and the necessary condition was that the above somatopetal core current must exceed the net inward transmembrane current (the latter was the sum of the inward synaptic and outward passive extrasynaptic currents) of the dendritic compartment. This relation essentially depended on the size of the dendrites.

Patterns of Impulsation Generated by Abducens Motoneurons with Active Reconstructed Dendrites: a Simulation Study

Mathematical models of abducens motoneurons with reconstructed dendritic arborizations were investigated. The two types of models differed from each other in electrical properties of the dendrites, either passive (model group 1) or active and non-linear (model group 2). The relations between morphology of the dendrites, their electrical transfer characteristics, and formation of impulse patterns at the cell output were studied under conditions of tonic activation of glutamatergic (NMDA-type) excitatory synapses homogeneously distributed over the dendrites. For reconstructed dendritic arborizations, their morphometric characteristics (size, complexity, and metrical asymmetry) and electrical ones (somatopetal current transfer effectiveness function and sensitivity of the latter to variations of the homogeneous membrane conductivity) were computed. Changes in the membrane potential were also studied in different parts of the dendritic arborization during generation of various patterns of discharges of action potentials (APs) at the neuronal output under different intensities of synaptic activation; this allowed us to reveal “spatial signatures” of the above-mentioned temporal patterns. The output patterns and their “spatial signatures” changed in a certain manner with increase in the intensity of synaptic activation. A simple periodical discharge of low-frequency APs with constant interspike intervals was replaced by a complex periodical or nonperiodical (stochastic) bursting pattern, which then was replaced again by a simple rhythmic but high-frequency discharge. Simple periodical patterns were associated with generation of synchronous oscillatory dendritic depolarizations phase-shifted in metrically asymmetrical parts of the arborization. In the case of generation of complex periodical or stochastic patterns, depolarization processes in asymmetrical dendritic parts were asynchronous and differed from each other in their amplitude and duration. Such a structure-dependent repertoire of output discharge patterns was quite compatible with that observed earlier in examined simulated neocortical pyramidal and cerebellar Purkinje neurons. This fact is indicative of a possible similarity of the rules governing the formation of specific output patterns in neurons with active membrane properties of the dendrites based on intrinsic mophological/functional features of the dendritic arborization of a given neuron.

Transfer properties of neuronal dendrites with tonically activated conductances

The somatopetal current transfer was studied in the mathematical models of a reconstructed brainstem motoneuron with tonically activated excitatory synaptic inputs uniformly distributed over dendritic arborization. The soma and axon provided a constant passive leak. The extrasynaptic dendritic membrane was either passive or active (of a Hodgkin-Huxley type). The longitudinal membrane current density (per unit path length) was used as an estimate of the current transfer effectiveness of different dendritic paths. Introduction of a steady uniform voltage-independent conductance per unit membrane area simulated such a synaptic activation. This actions always produced a spatially inhomogeneous membrane depolarization decaying from the distal dendritic tips toward the soma. The reason for such an inhomogeneity was the preponderance of somatopetal over somatofugal input conductance at every site in the dendrites with sealed distal ends and a leaky somatic end. In active dendrites, partial voltage-dependent extrasynaptic conductances followed this depolarization according to their activation-inactivation kinetics. The greater the local depolarization, the greater the contribution of the non-inactivating potassium conductance to the total membrane conductance. The contribution of the inactivated sodium conductance was one order of magnitude smaller. Correspondingly, the effective equilibrium potential of the total transmembrane current became spatially inhomogeneous and shifted to the potassium equilibrium potential. In the passive dendrites, the equilibrium potential remained spatially homogeneous. Inhomogeneities of the dendritic geometry (abrupt change in the diameter and, especially, asymmetrical branching) caused characteristic perturbations in the voltage gradient, so that the path profiles of the voltage, conductances, and currents diverged. This indicated a geometry-induced separation of the dendritic paths in their transfer effectiveness. Active dendrites of the same geometry were less effective than passive ones due to the effect of the potassium conductance associated with the hyperpolarizing equilibrium potential.