Sensory-Driven Enhancement of Calcium Signals in Individual Purkinje Cell Dendrites of Awake Mice

1. Download : Download full-size image

     

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.     

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.     

Network Bursting Dynamics in Excitatory Cortical Neuron Cultures Results from the Combination of Different Adaptive Mechanism

In the brain, synchronization among cells of an assembly is a common phenomenon, and thought to be functionally relevant. Here we used an in vitro experimental model of cell assemblies, cortical cultures, combined with numerical simulations of a spiking neural network (SNN) to investigate how and why spontaneous synchronization occurs. In order to deal with excitation only, we pharmacologically blocked GABA_Aergic transmission using bicuculline. Synchronous events in cortical cultures tend to involve almost every cell and to display relatively constant durations. We have thus named these “network spikes” (NS). The inter-NS-intervals (INSIs) proved to be a more interesting phenomenon. In most cortical cultures NSs typically come in series or bursts (“bursts of NSs”, BNS), with short (∼1 s) INSIs and separated by long silent intervals (tens of s), which leads to bimodal INSI distributions. This suggests that a facilitating mechanism is at work, presumably short-term synaptic facilitation, as well as two fatigue mechanisms: one with a short timescale, presumably short-term synaptic depression, and another one with a longer timescale, presumably cellular adaptation. We thus incorporated these three mechanisms into the SNN, which, indeed, produced realistic BNSs. Next, we systematically varied the recurrent excitation for various adaptation timescales. Strong excitability led to frequent, quasi-periodic BNSs (CV∼0), and weak excitability led to rare BNSs, approaching a Poisson process (CV∼1). Experimental cultures appear to operate within an intermediate weakly-synchronized regime (CV∼0.5), with an adaptation timescale in the 2–8 s range, and well described by a Poisson-with-refractory-period model. Taken together, our results demonstrate that the INSI statistics are indeed informative: they allowed us to infer the mechanisms at work, and many parameters that we cannot access experimentally.     

Resonantlike Synchronization and Bursting in a Model of Pulse-Coupled Neurons with Active Dendrites

We analyze the dynamical effects of active, linearized dendritic membranes on the synchronization properties of neuronal interactions. We show that a pair of pulse-coupled integrate-and-fire neurons interacting via active dendritic cables can exhibit resonantlike synchronization when the frequency of the oscillators is approximately matched to the resonant frequency of the membrane impedance. For weak coupling the neurons are phase-locked with constant interspike intervals whereas for strong coupling periodic bursting patterns are observed. This bursting behavior is reflected by the occurrence of a Hopf bifurcation in the firingrates of a corresponding rate-coded model.     

Regulation of Electrical Bursting in a Spatiotemporal Model of a GnRH Neuron

Gonadotropin-releasing hormone (GnRH) neurons are hypothalamic neurons that control the pulsatile release of GnRH that governs fertility and reproduction in mammals. The mechanisms underlying the pulsatile release of GnRH are not well understood. Some mathematical models have been developed previously to explain different aspects of these activities, such as the properties of burst action potential firing and their associated Ca²⁺ transients. These previous studies were based on experimental recordings taken from the soma of GnRH neurons. However, some research groups have shown that the dendrites of GnRH neurons play very important roles. In particular, it is now known that the site of action potential initiation in these neurons is often in the dendrite, over 100 μm from the soma. This raises an important question. Since some of the mechanisms for controlling the burst length and interburst interval are located in the soma, how can electrical bursting be controlled when initiated at a site located some distance from these controlling mechanisms? In order to answer this question, we construct a spatio-temporal mathematical model that includes both the soma and the dendrite. Our model shows that the diffusion coefficient for the spread of electrical potentials in the dendrite is large enough to coordinate burst firing of action potentials when the initiation site is located at some distance from the soma.     

Simulation Study of Non-Organellar Binding of Calcium by Fast and Slow Buffers in Dendrites Containing an Organellar Store

Dependences of intracellular calcium signals on the concentrations of endogenous buffers (slow, parvalbumin, and fast, calmodulin) and a calcium-sensitive fluorophore (Fura-4F) were investigated on mathematical models of compartments of the reconstructed dendrite of a cerebellum Purkinje neuron. A Ca²⁺-storing cistern of the endoplasmic reticulum (ER) was present in the dendrite. Calcium signals developed when the neuron generated responses to single synaptic excitation or intrinsic non-periodical impulse activity. The dynamics of the buffer binding capacity were also studied; this capacity was characterized by the ratio of concentrations of bound and free calcium or concentration increments of the latter. The plasma membrane of the dendrite possessed ion channels (including those of synaptic currents) and the calcium pump characteristic of the mentioned neuron. Model equations took into account Ca²⁺ exchange between the cytosol, buffers, ER, and extracellular medium, as well as diffusion processes. The ER membrane contained the calcium pump, leakage channels, and channels of calcium-induced release and inositol-3-phosphate-dependent releases of Ca²⁺. The ER cistern occupied 1 to 36% of the intracellular volume. Upon different occupancies of the dendrite by the organelle store, an increase in the concentration of the slow buffer insignificantly decreased the cytosolic Ca²⁺ transients with no effect on their shape. The fast buffer and the dye with similar kinetic properties caused slowing down of the rising phase of Ca²⁺ transients, decrease in the early component, and increase in the late component of the latter. In the case of nonperiodical and asynchronous intrinsic oscillations of the membrane potential typical of asymmetrical active dendrites, the slow buffer, like the ER store, bound more Ca²⁺ in compartments of compatible sizes and fillings by the organelles belonging to those metrically asymmetrical branches, which, on average, stayed longer in the state of high depolarization; this provided a greater Ca²⁺ entry from outside. Hence, the pattern of structural/functional organization of calcium signalization in the dendrites can be complemented in the part of both the direct influences of local microgeometry of the dendrite and the indirect ones related to global macrogeometry of the dendritic arborization.     

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.     

Topography in the Bursting Dynamics of Entorhinal Neurons

1. Download : Download high-res image (131KB)
2. Download : Download full-size image

     

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.     

Impact of Geometrical Characteristics of the Organellar Store and Organelle-Free Cytosol on Intracellular Calcium Dynamics in the Dendrite: a Simulation Study

The dependence of intracellular calcium dynamics on geometrical size relations between calcium-exchanging parts of the intracellular space was studied in mathematical models corresponding to a thin fragment of the Purkinje neuron spiny dendrite. The plasma membrane contained ion channels typical of this cell type, including channels that conduct an excitatory synaptic current, and ion pumps. The model equations took into account calcium exchange between the cytosol, extracellular medium, intracellular store (a cistern of the endoplasmic reticulum, ER), endogenous calcium buffers, and an exogenous buffer (fluorescent dye used in the experiments). The ER membrane contained the calcium pump and channels of calcium-dependent and inositol-3-phosphate-dependent calcium release, as well as leakage channels. With the compartment size fixed, the ER cistern diameter was varied so that the proportion of the organelle in the total volume changed from 1 to 36%. Under these conditions, identical synaptic excitation caused similar electrical reactions (calcium spikes) but different concentration responses. Equal increments in the ER diameter led to unequal, more pronounced at thicker diameters, increments of the peak cytosolic concentrations of Са²⁺ ([Ca²⁺] _i ) and of a Са²⁺-fluorescent dye complex [CaD], as well as those of the Са²⁺ concentration in the dendrite ER (characterized by a shift from the basal level, Δ[Ca²⁺]_ER). The changes in [Ca²⁺] _i and [CaD] followed more adequately those in the volume of the organelle-free cytosol, while Δ[Ca²⁺]_ER changes were more similar to those in the ER membrane area. Therefore, the relative occupancy of the intracellular volume by organellar calcium stores and their sizes in a dendritic compartment are important structural factors that essentially modulate the calcium dynamics, and this structural dependence can be adequately reflected in the experiments using fluorophores. Neirofiziologiya/Neurophysiology, Vol. 41, No. 1, pp. 19–31, January–February, 2009.     

Molecular Dynamics Simulation Studies of the Density and Temperature Dependence of Self-diffusion in a Cylindrical Micropore

We report Molecular Dynamics calculations of radial density profiles and self-diffusion coefficients of Lennard-Jones fluids in a cylindrical pore of radius 2σ, for a wide range of temperatures and densities. At n _p σ³ = 0.825 the self-diffusion coefficient parallel to the pore walls D _∥*. follows a monotonic (nearly linear) increase with kT/ε and is very similar to that of the bulk self-diffusion coefficient D _b *. At n _p σ³ = 0.4 and kT/ε ≤ 1.0 the curve of D _∥* vs. kT/ε shows a distinct inflection in the region 0.7 ≤ kT/ε ≤ 0.9 and values of D _∥* are much less than D _b * decreasing to near solid state values at very low temperatures. At the highest temperature studied, kT/ε = 2.98, D _∥* is almost inversely proportional to density and in a fairly close agreement with that of D _b *. At KT/ε = 0.49, D _∥* is much smaller than D _b *. The motion of adsorbate particles normal to the walls is also discussed.     

High Prevalence of Multistability of Rest States and Bursting in a Database of a Model Neuron

Flexibility in neuronal circuits has its roots in the dynamical richness of their neurons. Depending on their membrane properties single neurons can produce a plethora of activity regimes including silence, spiking and bursting. What is less appreciated is that these regimes can coexist with each other so that a transient stimulus can cause persistent change in the activity of a given neuron. Such multistability of the neuronal dynamics has been shown in a variety of neurons under different modulatory conditions. It can play either a functional role or present a substrate for dynamical diseases. We considered a database of an isolated leech heart interneuron model that can display silent, tonic spiking and bursting regimes. We analyzed only the cases of endogenous bursters producing functional half-center oscillators (HCOs). Using a one parameter (the leak conductance ()) bifurcation analysis, we extended the database to include silent regimes (stationary states) and systematically classified cases for the coexistence of silent and bursting regimes. We showed that different cases could exhibit two stable depolarized stationary states and two hyperpolarized stationary states in addition to various spiking and bursting regimes. We analyzed all cases of endogenous bursters and found that 18% of the cases were multistable, exhibiting coexistences of stationary states and bursting. Moreover, 91% of the cases exhibited multistability in some range of . We also explored HCOs built of multistable neuron cases with coexisting stationary states and a bursting regime. In 96% of cases analyzed, the HCOs resumed normal alternating bursting after one of the neurons was reset to a stationary state, proving themselves robust against this perturbation.     

Plasma Approach to Describing the Electric Dynamics of a Neuron

The electric excitation of a neuron is interpreted as the formation of a nonlinear solitary ion acoustic wave of the charge density of sodium and hydrogen ions in an electrolytic intracellular fluid, which is treated as a dense plasma. It is shown that such a wave can be described by the coupled sine-Gordon and Korteweg-de Vries equations, having a solution in the form of a soliton whose internal vibrational structure is described by the Fermi-Pasta-Ulam spectrum. It is concluded that a nerve impulse can be interpreted as a low-frequency solitary wave of the charge density of sodium ions with a trapped high-frequency charge density wave of protons.     

Calcium Involvement in Regulation of Neuronal Bursting in Disinhibited Neuronal Networks: Insights from Calcium Studies in a Spherical Cell Model

Cytosolic calcium is involved in the regulation of many intracellular processes. Intracellular calcium may therefore potentially affect the behavior of both single neurons and synaptically connected neuronal assemblies. In computer model studies, we investigated calcium dynamics in spherical neurons during periods of recurrent neuronal bursting that were simulated in a disinhibited neuronal network. The model takes into account calcium influx via voltage-gated calcium channels, extrusion through the cell membrane, and binding to two different buffers representing fixed and mobile endogenous calcium buffers. Throughout the duration of the simulated recurrent neuronal bursting, the concentration of free fixed buffers shows a hyperbolic decrease in time at a rate that is not uniform inside a neuron. Recurrent calcium influxes associated with bursting lead to the formation of gradients in the concentration of the fixed buffer in the radial direction, and are accompanied by the redistribution of mobile buffers acting to compensate for these gradients. Simulated intracellular calcium transients have a slow component characterized by a gradual increase in the calcium baseline level that reaches a plateau 120-200 s after the onset of recurrent bursting. Using this model, we demonstrate what we believe is a novel mechanism of regulation of network excitability that occurs in conditions of prolonged and recurrent neuronal bursting in disinhibited networks. This mechanism is expressed via interaction of calcium clearance systems inside neurons with calcium-dependent potassium regulation of neuronal excitability in membranes. This is a network phenomenon because it arises largely by synaptic interactions. Therefore, it can serve as a network safety mechanism to prevent excessive and uncontrolled neuronal firing resulting from the lack of inhibition or after acute suppression of the inhibitory drive.     

Estimation of the Capacity of Heterogeneously Distributed Endogenous Calcium Buffers in a Neuron

The value of the ratio of half-decay times of calcium transients recorded using calcium sensitive fluorescent dyes with low and high ffinities can be used for estimating the cytosolic endogenous Ca²⁺ buffer capacity (k _buf); for this purpose, the parameters obtained in the model and in real experiments are compared. However, if the distribution of endogenous buffers is characterized by a high heterogeneity, the ratio of half-decay times of fluorescence transients depends not only on the k _buf but also on the pattern of distribution of Ca²⁺ channels. Our simulations showed that in spite of a considerable slowing down of fluorescence responses, when Oregon Green BAPTA-1 Ca²⁺ indicator is used, the k _buf value in the dendritic endings of cerebellar granule cells (GrCs) can reach 300 to 500. This can happen in the cases where, according to our suggestion [1], a high-capacity calcium buffer is localized in the apical parts of dendritic endings of the above cells.