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. Neirofiziologiya/Neurophysiology, Vol. 32, No. 2, pp. 98–101, March–April, 2000.     

How voltage-gated ion channels alter the functional properties of ganglion and amacrine cell dendrites

The present study compares the structure and function of retinal ganglion and amacrine cell dendrites. Although a superficial similarity exists between amacrine and ganglion cell dendrites, a comparison between the branching pattern of the two cell types reveals differences which can only be appreciated at the microscopic level. Whereas decremental branching is found in ganglion cells, a form of non-decremental or "trunk branching" is observed in amacrine cell dendrites. Physiological differences are also observed in amacrine vs ganglion cells in which many amacrine cells generate dendritic impulses which can be readily distinguished from those of the soma, while separate dendritic impulses in ganglion cell dendrites have not been reported. Despite these differences, both amacrine and ganglion cell dendrites appear to contain voltage-gated ion channels, including TTX-sensitive sodium channels. One way to account for separate dendritic impulses in amacrine cells is to have a higher density of sodium channels and we generally find in modeling studies that a dendritic sodium channel density that is more than about 50% of that in the soma is required for excitatory, synaptic currents to give rise to local dendritic spike activity. Under these conditions, impulses can be generated in the dendrites and propagate for some distance along the dendritic tree. When the soma generates impulse activity in amacrine cells, it can activate, antidromically, the entire dendritic tree. Although ganglion cell dendrites do not appear to generate independent impulses, the presence of voltage-gated ion channels in these structures appears to be important for their function. Modeling studies demonstrate that when dendrites lack voltage-gated ion channels, impulse activity evoked by current applied to the cell body is generated at rates that are much higher than those observed physiologically. However, by placing ion channels in the dendrites at a reduced density compared to those of amacrine cells, the firing rate of ganglion cells becomes more physiological and the relationship between frequency and current (F/I relationship) can be precisely matched with physiological data. Recent studies have demonstrated the presence of T-type calcium channels in ganglion cells and our analysis suggests that they are found in higher density in the dendrites compared to the soma. This is the first voltage-gated ion channel which appears more localized to the dendrites than other cell copartments and this difference alone cries for an interpretation. The presence of a significant T-type calcium channel density in the dendrites can influence their integrative properties in several important ways. First, excitatory synaptic currents can be augmented by the activation of T-type calcium channels, although this is more likely to occur for transient rather than sustained synaptic currents because T-type currents show strong inactivation properties. In addition, T-type calcium channels may serve to limit the electrical load which dendrites impose on the spike initiation process and thus enhance the speed with which impulses can be triggered by the impulse generation site. This role whill enhance the safety factor for impulses traveling in the orthograde direction.     

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.     

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.     

Remote Modulation of Current Transfer from Dendritic Glutamatergic Synapses by GABA-ergic Synapses of the Somatic Zone of Motoneurons: a Simulation Study

Until now, information concerning spatial interaction of postsynaptic excitation and inhibition in neuronal dendrites remains rather limited. In model experiments, we studied spatial effects of tonic co-activation of GABA-ergic synapses situated on the soma and axon hillock of a motoneuron and dendritic glutamatergic synapses with receptors sensitive or insensitive to N-methyl-D-aspartate. We analyzed distribution maps of the transmembrane potentials and excitatory currents transferred toward the soma over the reconstructed dendritic arborization of a rat abducens motoneuron (three-dimensional reconstruction). In the motoneuron, isolated tonic excitation of glutamatergic synapses induced two stable states of low (downstate) or high (upstate) spatially heterogeneous dendritic depolarization, which decayed with unequal rates along different dendritic paths. In this case, the local steady-state current-voltage relation of the dendritic membrane became N-shaped due to a limb of the negative slope within a certain voltage range. The upstate corresponding to plateau potentials associated with stereotyped motor activity patterns was analyzed in detail. In this state, most proximal dendritic sites were the main sources of the excitatory current reaching the soma, while the contribution from distal sites was negligible. Co-activation of GABA-synapses located at the soma and axon hillock reduced this depolarization and shifted the main excitatory current source from a perisomatic location to the middle, structurally more complex, region of the dendritic arborization. The more remote dendritic region having a greater membrane area and receiving a greater number of synaptic contacts became directly involved in the supply of the trigger zone by the excitatory current. We suggest that a special, not described earlier, operational mechanism of postsynaptic inhibition is manifested in the above spatial effects of activation of strategically located inhibitory synapses, and that the list of known crucial inhibitory mechanisms (namely hyperpolarization and shunting of the postsynaptic membrane) must be expanded.     

Structure Dependence of the Calcium Dynamics in Purkinje Neuron Dendrites during Generation of Bursting Discharges: a Simulation Study

In the model of a cerebellar Purkinje neuron with reconstructed active dendrites, we investigated the impact of the ratio between volumes of the endoplasmic reticulum (organellar calcium store) and cytosol on the Ca²⁺ dynamics in asymmetrical parts of the dendritic arborization during generation of different structure-dependent patterns of bursting activity. Tonic synaptic excitation homogeneously distributed over the dendrites (a spatially homogeneous stationary input signal) caused spatially heterogeneous variations of the dendritic membrane potential (MP) accompanied by periodical or nonperiodical bursts of action potentials at the cell output. The MP waveforms recorded from the segments of asymmetrical dendrites were then applied to the membrane of selected dendrite segments as command voltages in a dynamic clamp mode. In these segments, the relative size of the stores was varied. This provided equal to each other local calcium currents and influxes into the cytosol of the segment differently filled with the organellar store. Regardless of the impulse pattern, microgeometry of the segment and the store modulated calcium transients exactly in the same way as in previous studies of electrical and concentration responses to local phasic synaptic excitation of the modeled neuron. Peak values of depolarization-induced elevations of the cytosolic Ca²⁺ concentration increased with the portion of the intracellular volume occupied by the store. The most important factor defining this dependence was the ratio of the membrane area vs the organelle-free cytosol volume of the dendritic segment. Concentrations of Са²⁺ deposited in equal-sized segments of asymmetrical parts of the dendritic arborization where asynchronous unequal variations of the MP were observed during generation of nonperiodical bursting at the output demonstrated considerable specificity. A greater amount of calcium was deposited in the segments staying, on average, in a high-depolarization state for a longer time (this intensified activation of calcium channels and amplified the corresponding Ca²⁺ influx into the cytosol). Hence, local dynamics of the Ca²⁺ concentration depend directly on local microgeometry and indirectly on global macrogeometry of the dendrite arborization, as the latter determines spatial asymmetry-related unequal transients in different parts of the dendritic arborization having active membrane properties.     

Role of Calcium Electrogenesis in Apical Dendrites: Generation of Intrinsic Oscillations by an Axial Current

Dendrites are covered with conductances whose function is still mysterious. Using intracellular recording and calcium imaging, we describe an electrogenic band of calcium channels in distal apical dendrites of layer 5 pyramidal neurons (Yuste et al., 1994). We now explore the functional consequences of this distal electrogenic area with multicompartmental numerical simulations. A calcium imaging and electrophysiological database from a single neuron, recorded under blocked sodium and potassium conductances, is replicated by simulations having increased dendritic calcium current. In these models a significant axial current flows from the apical dendrite into the somatic region, activating low-threshold calcium channels and generating oscillations similar to those seen in the electrophysiological data. We propose that the distal electrogenic area in apical dendrites serves to inject current into the soma and produce intrinsic oscillatory dynamics.     

Somato-dendritic mechanisms underlying the electrophysiological properties of hypothalamic magnocellular neuroendocrine cells: A multicompartmental model study

Magnocellular neuroendocrine cells (MNCs) of the hypothalamus synthesize the neurohormones vasopressin and oxytocin, which are released into the blood and exert a wide spectrum of actions, including the regulation of cardiovascular and reproductive functions. Vasopressin- and oxytocin-secreting neurons have similar morphological structure and electrophysiological characteristics. A realistic multicompartmental model of a MNC with a bipolar branching structure was developed and calibrated based on morphological and in vitro electrophysiological data in order to explore the roles of ion currents and intracellular calcium dynamics in the intrinsic electrical MNC properties. The model was used to determine the likely distributions of ion conductances in morphologically distinct parts of the MNCs: soma, primary dendrites and secondary dendrites. While reproducing the general electrophysiological features of MNCs, the model demonstrates that the differential spatial distributions of ion channels influence the functional expression of MNC properties, and reveals the potential importance of dendritic conductances in these properties. Action Editor: Eric De Schutter     

Suppressing the excitability of spinal motoneurons by extracellularly applied electrical fields: insights from computer simulations.

The effect of extracellularly applied electrical fields on neuronal excitability and firing behavior is attributed to the interaction between neuronal morphology and the spatial distribution and level of differential polarization induced by the applied field in different elements of the neuron. The presence of voltage-gated ion channels that mediate persistent inward currents (PICs) on the dendrites of spinal motoneurons enhances the influence of electrical fields on the motoneuronal firing behavior. The goal of the present study was to investigate, with a realistic motoneuron computer model, the effects of extracellularly applied electrical fields on the excitability of spinal motoneurons with the aim of reducing the increased motoneuronal excitability after spinal cord injury (SCI). Our results suggest that electrical fields could suppress the excitability of motoneurons and reduce their firing rate significantly by modulating the magnitude of their dendritic PIC. This effect was achieved at different field directions, intensities, and polarities. The reduction in motoneuronal firing rate resulted from the reduction in the magnitude of the dendritic PIC reaching the soma by the effect of the applied electrical field. This reduction in PIC was attributed to the dendritic field-induced differential polarization and the nonlinear current-voltage relationship of the dendritic PIC-mediating channels. Because of the location of the motoneuronal somata and initial segment with respect to the dendrites, these structures were minimally polarized by the applied field compared with the extended dendrites. In conclusion, electrical fields could be used for suppressing the hyperexcitability of spinal motoneurons after SCI and reducing the level of spasticity.     

Derivation of cable parameters for a reduced model that retains asymmetric voltage attenuation of reconstructed spinal motor neuron dendrites

Spinal motor neurons have voltage gated ion channels localized in their dendrites that generate plateau potentials. The physical separation of ion channels for spiking from plateau generating channels can result in nonlinear bistable firing patterns. The physical separation and geometry of the dendrites results in asymmetric coupling between dendrites and soma that has not been addressed in reduced models of nonlinear phenomena in motor neurons. We measured voltage attenuation properties of six anatomically reconstructed and type-identified cat spinal motor neurons to characterize asymmetric coupling between the dendrites and soma. We showed that the voltage attenuation at any distance from the soma was direction-dependent and could be described as a function of the input resistance at the soma. An analytical solution for the lumped cable parameters in a two-compartment model was derived based on this finding. This is the first two-compartment modeling approach that directly derived lumped cable parameters from the geometrical and passive electrical properties of anatomically reconstructed neurons.     

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

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. Received: 18 December 1997 / Accepted in revised form: 12 June 1998     

Asymmetry in Signal Propagation between the Soma and Dendrites Plays a Key Role in Determining Dendritic Excitability in Motoneurons

It is widely recognized that propagation of electrophysiological signals between the soma and dendrites of neurons differs depending on direction, i.e. it is asymmetric. How this asymmetry influences the activation of voltage-gated dendritic channels, and consequent neuronal behavior, remains unclear. Based on the analysis of asymmetry in several types of motoneurons, we extended our previous methodology for reducing a fully reconstructed motoneuron model to a two-compartment representation that preserved asymmetric signal propagation. The reduced models accurately replicated the dendritic excitability and the dynamics of the anatomical model involving a persistent inward current (PIC) dispersed over the dendrites. The relationship between asymmetric signal propagation and dendritic excitability was investigated using the reduced models while varying the asymmetry in signal propagation between the soma and the dendrite with PIC density constant. We found that increases in signal attenuation from soma to dendrites increased the activation threshold of a PIC (hypo-excitability), whereas increases in signal attenuation from dendrites to soma decreased the activation threshold of a PIC (hyper-excitability). These effects were so strong that reversing the asymmetry in the soma-to-dendrite vs. dendrite-to-soma attenuation, reversed the correlation between PIC threshold and distance of this current source from the soma. We propose the tight relation of the asymmetric signal propagation to the input resistance in the dendrites as a mechanism underlying the influence of the asymmetric signal propagation on the dendritic excitability. All these results emphasize the importance of maintaining the physiological asymmetry in dendritic signaling not only for normal function of the cells but also for biophysically realistic simulations of dendritic excitability.     

Spatial electrical patterns in simulated neuronal dendrites

Steady state longitudinal distributions of (a) the density of channels conducting an inward transmembrane current of cations, (b) the submembrane concentrations of these cations, and (c) the resting membrane potential, were investigated in a phenomenological model of a cylinder-shaped dendritic process of the neuron. It was found that spatially non-uniform patterns of these distributions occur only if one of the following conditions held (i) an increase in the intracellular concentration of cations conducting an inward passive transmembrane current amplified the active efflux of those cations by the pump and attenuated their passive influx through the voltage dependent channels, with amplification of the efflux lower than attenuation of the influx; (ii) molecules of mobile channels bore a negative electrophoretic charge exposed to the intracellular space and were subject to lateral electrodiffusion in the membrane; (iii) the cations induced a further release of cations from intracellular stores. Numerical simulation studies of the membrane with Na and K channels and Na/K pumps with conditions (i) and (ii) have demonstrat-ed the possibility of the creation of inhomogeneous patterns in the neurites. These inhomogeneous patterns are dissipative structures (DSs), and they can be spatially periodic. Received: 23 October 1996 / Accepted: 21 May 1997     

The electro-dynamics of the dendritic space in Purkinje cells of the cerebellum

The functional geometry of the reconstructed dendritic arborization of Purkinje neurons is the object of this work. The combined effects of the local geometry of the dendritic branches and of the membrane mechanisms are computed in passive configuration to obtain the electrotonic structure of the arborization. Steady-currents applied to the soma and expressed as a function of the path distance from the soma form different clusters of profiles in which dendritic branches are similar in voltages and current transfer effectiveness. The locations of the different clusters are mapped on the dendrograms and 3D representations of the arborization. It reveals the presence of different spatial dendritic sectors clearly separated in 3D space that shape the arborization in ordered electrical domains, each with similar passive charge transfer efficiencies. Further simulations are performed in active configuration with a realistic cocktail of conductances to find out whether similar spatial domains found in the passive model also characterize the active dendritic arborization. During tonic activation of excitatory synaptic inputs homogeneously distributed over the whole arborization, the Purkinje cell generates regular oscillatory potentials. The temporal patterns of the electrical oscillations induce similar spatial sectors in the arborization as those observed in the passive electrotonic structure. By taking a video of the dendritic maps of the membrane potentials during a single oscillation, we demonstrate that the functional dendritic field of a Purkinje neuron displays dynamic changes which occur in the spatial distribution of membrane potentials in the course of the oscillation. We conclude that the branching pattern of the arborization explains such continuous reconfiguration and discuss its functional implications.     

Transmembrane ion currents in pulmonary artery smooth muscle

Transmembrane ionic currents were investigated in the rabbit pulmonary artery smooth muscle under voltage clamp conditions with the use of the double sucrose gap method. With depolarizing pulses, there developed a fast inactivated outward current that was followed by a steady-state outward current. Tetraethylammonium (TEA) partly suppressed the outward current, and the fast inward current that preceded the fast outward one could be seen in these conditions. Appearance of the fast inward current in TEA-containing solution suggests the overlapping of the fast inward and outward currents. It appears that the resultant transmembrane current has an outward direction since in normal conditions the permeability of the fast potassium channels exceeds that of calcium channels. Conditioning hyperpolarization increased and depolarization decreased the fast outward current indicating that at the resting membrane potential a part of the potassium channels is inactivated and this inactivation is removed by hyperpolarization.     

Effects of active versus passive dendritic membranes on the transfer properties of a simulated neuron

In a simulated neuron with a dendritic tree, the relative effects of active and passive dendritic membranes on transfer properties were studied. The simulations were performed by means of a digital computer. The computations calculated the changes in transmembrane voltages of many compartments over time as a function of other biophysical variables. These variables were synaptic input intensity, critical firing threshold, rate of leakage of current across the membrane, and rate of longitudinal current spread between compartments. For both passive and active dendrites, the transfer properties of the soma studied for different rates of longitudinal current spread. With low rates of current spread, graded changes in firing threshold produced correspondingly graded changes in output discharge. With high rates of current spread, the neuron became a bistable operator where spiking was enhanced if the threshold was below a certain level and suppressed if the threshold was above that level. Since alterations in firing threshold were shown to have the same effect on firing rate as alterations in synaptic input intensity, the neuron can be said to change from graded to contrast-enhancing in its response to stimuli of different intensities. The presence or absence of dendritic spiking was found to have a significant effect on the integrative properties of the simulated neuron. In particular, contrast enhancement was considerably more pronounced in neurons with passive than with active dendrites in that somatic spike rates reached a higher maximum when dendrites were passive. With active dendrites, a less intense input was needed to initiate somatic spiking than with passive dendrites because a distal dendritic spike could easily propagate by means of longitudinal current spread to the soma. Once somatic spiking was initiated, though, spike rates tended to be lower with active than with passive dendrites because the soma recovered more slowly from its post-spike refractory period if it was also influenced by refractory periods in the dendrites. The experiment of comparing neurons with active and passive dendrites was repeated at a different, higher value of synaptic input. The same differences in transfer properties between the active and passive cases emerged as before. Spiking patterns in neurons with active dendrites were also affected by the time distribution of synaptic inputs. In a previous study, inputs had been random over both space and time, varying about a predetermined mean, whereas in the present study, inputs were random over space but uniform over time. When inputs were made uniform over time, spiking became more difficult to initiate and the transition from graded to bistable response became less sharp.     

Dependence of Transformation of Intrinsic Rhythmic Impulse Activity of Neurons on Spatio-Temporal Organization of Synaptic Actions on Dendrites: A Simulation Study

The aim of the study to elucidate the biophysical mechanisms able to determine specific transformations of the patterns of output signals of neurons (neuronal impulse codes) depending on the spatio-temporal organization of synaptic actions coming to the dendrites. We studied mathematical models of the neocortical layer 5 pyramidal neurons built according to the results of computer reconstruction of their dendritic arborizations and experimental data on the voltage-dependent conductivities of their dendritic membrane. This work is a continuation of our previous studies that showed the existence of certain relations between the complexity of neural impulse codes, on the one hand, and the complexity, size, metrical asymmetry of branching, and nonlinear membrane properties of the dendrites, on the other hand. This relation determines synchronous (with some phase shifts) or asynchronous transitions of asymmetrical dendritic subtrees between high and low depolarization states during the generation of output impulse patterns in response to distributed tonic activation of dendritic inputs. In this work we demonstrate the first time that the appearance and pattern of transformations of complex periodical impulse trains at the neuron’s output associated with receiving a short series of presynaptic action potentials are determined not only by the time of arrival of such a series, but also by their spatial addressing to asymmetric dendritic subtrees; the latter, in this case, may be in the same (synchronous transitions) or different (asynchronous transitions) electrical states. Biophysically, this phenomenon is based on a significant excess of the driving potential for a synaptic excitatory current in low-depolarization regions, as compared with that in high-depolarization dendritic regions receiving phasic synaptic stimuli. These findings open a novel aspect of the functioning of neurons and neuronal networks.     

An equivalent cable model for neuronal trees with active membrane

A non-uniform equivalent cable model of membrane voltage changes in branching neuronal trees with active ion channels has been developed. A general branching condition is formulated, extending Rall's 3/2 power rule for passive dendritic trees so that non-uniform cable segments can be treated. The theoretical results support the use of the dendritic profile model of Clements and Redman. The theory is then applied to dendrites of different morphological type yielding qualitative different response behaviour. Received: 25 September 1997 / Accepted: 13 November 1997     

Neural activity and branching of embryonic retinal ganglion cell dendrites

The shape of a neuron's dendritic arbor is critical for its function as it determines the number of inputs the neuron can receive and how those inputs are processed. During development, a neuron initiates primary dendrites that branch to form a simple arbor. Subsequently, growth occurs by a process that combines the extension and retraction of existing dendrites, and the addition of new branches. The loss and addition of the fine terminal branches of retinal ganglion cells (RGCs) is dependent on afferent inputs from its synaptic partners, the amacrine and bipolar cells. It is unknown, however, whether neural activity regulates the initiation of primary dendrites and their initial branching. To investigate this, Xenopus laevis RGCs developing in vivo were made to express either a delayed rectifier type voltage-gated potassium (KV) channel, Xenopus Kv1.1, or a human inward rectifying channel, Kir2.1, shown previously to modulate the electrical activity of Xenopus spinal cord neurons. Misexpression of either potassium channel increased the number of branch points and the total length of all the branches. As a result, the total dendritic arbor was bigger than for control green fluorescent protein-expressing RGCs and those ectopically expressing a highly related mutant non-functional Kv1.1 channel. Our data indicate that membrane excitability regulates the earliest differentiation of RGC dendritic arbors.