Responses of a bursting pacemaker to excitation reveal spatial segregation between bursting and spiking mechanisms

Central pattern generators (CPGs) frequently include bursting neurons that serve as pacemakers for rhythm generation. Phase resetting curves (PRCs) can provide insight into mechanisms underlying phase locking in such circuits. PRCs were constructed for a pacemaker bursting complex in the pyloric circuit in the stomatogastric ganglion of the lobster and crab. This complex is comprised of the Anterior Burster (AB) neuron and two Pyloric Dilator (PD) neurons that are all electrically coupled. Artificial excitatory synaptic conductance pulses of different strengths and durations were injected into one of the AB or PD somata using the Dynamic Clamp. Previously, we characterized the inhibitory PRCs by assuming a single slow process that enabled synaptic inputs to trigger switches between an up state in which spiking occurs and a down state in which it does not. Excitation produced five different PRC shapes, which could not be explained with such a simple model. A separate dendritic compartment was required to separate the mechanism that generates the up and down phases of the bursting envelope (1) from synaptic inputs applied at the soma, (2) from axonal spike generation and (3) from a slow process with a slower time scale than burst generation. This study reveals that due to the nonlinear properties and compartmentalization of ionic channels, the response to excitation is more complex than inhibition.     

Voltage transients in neuronal dendritic trees.

An analytical method is outlined for calculating the passive voltage transient at each point in an extensively branched neuron model for arbitrary current injection at a single branch. The method is based on a convolution formula that employs the transient response function, the voltage response to an instantaneous pulse of current. For branching that satisfies Rall's equivalent cylinder constraint, the response function is determined explicitly. Voltage transients, for a brief current injected at a branch terminal, are evaluated at several locations to illustrate the attenuation and delay characteristics of passive spread. A comparison with the same transient input terminal input, the fraction of input charge dissipated by various branches in the neuron model is illustrated. These fractions are independent of the input time course. For transient synaptic conductance change at a single branch terminal, a numerical example demonstrates the nonlinear effect of reduced synaptic driving potential. The branch terminal synaptic input is compared with the same synaptic conductance input applied to the soma on the basis of excitatory postsynaptic potential amplitude at the soma and charge delivered to the soma.     

Transient Response in a Dendritic Neuron Model for Current Injected at One Branch

Mathematical expressions are obtained for the response function corresponding to an instantaneous pulse of current injected to a single dendritic branch in a branched dendritic neuron model. The theoretical model assumes passive membrane properties and the equivalent cylinder constraint on branch diameters. The response function when used in a convolution formula enables one to compute the voltage transient at any specified point in the dendritic tree for an arbitrary current injection at a given input location. A particular numerical example, for a brief current injection at a branch terminal, illustrates the attenuation and delay characteristics of the depolarization peak as it spreads throughout the neuron model. In contrast to the severe attenuation of voltage transients from branch input sites to the soma, the fraction of total input charge actually delivered to the soma and other trees is calculated to be about one-half. This fraction is independent of the input time course. Other numerical examples, which compare a branch terminal input site with a soma input site, demonstrate that, for a given transient current injection, the peak depolarization is not proportional to the input resistance at the injection site and, for a given synaptic conductance transient, the effective synaptic driving potential can be significantly reduced, resulting in less synaptic current flow and charge, for a branch input site. Also, for the synaptic case, the two inputs are compared on the basis of the excitatory post-synaptic potential (EPSP) seen at the soma and the total charge delivered to the soma.     

Parallel Computational Subunits in Dentate Granule Cells Generate Multiple Place Fields

A fundamental question in understanding neuronal computations is how dendritic events influence the output of the neuron. Different forms of integration of neighbouring and distributed synaptic inputs, isolated dendritic spikes and local regulation of synaptic efficacy suggest that individual dendritic branches may function as independent computational subunits. In the present paper, we study how these local computations influence the output of the neuron. Using a simple cascade model, we demonstrate that triggering somatic firing by a relatively small dendritic branch requires the amplification of local events by dendritic spiking and synaptic plasticity. The moderately branching dendritic tree of granule cells seems optimal for this computation since larger dendritic trees favor local plasticity by isolating dendritic compartments, while reliable detection of individual dendritic spikes in the soma requires a low branch number. Finally, we demonstrate that these parallel dendritic computations could contribute to the generation of multiple independent place fields of hippocampal granule cells.     

The influences of somatic and dendritic inhibition on bursting patterns in a neuronal circuit model

The balance between inhibition and excitation plays a crucial role in the generation of synchronous bursting activity in neuronal circuits. In human and animal models of epilepsy, changes in both excitatory and inhibitory synaptic inputs are known to occur. Locations and distribution of these excitatory and inhibitory synaptic inputs on pyramidal cells play a role in the integrative properties of neuronal activity, e.g., epileptiform activity. Thus the location and distribution of the inputs onto pyramidal cells are important parameters that influence neuronal activity in epilepsy. However, the location and distribution of inhibitory synapses converging onto pyramidal cells have not been fully studied. The objectives of this study are to investigate the roles of the relative location of inhibitory synapses on the dendritic tree and soma in the generation of bursting activity. We investigate influences of somatic and dendritic inhibition on bursting activity patterns in several paradigms of potential connections using a simplified multicompartmental model. We also investigate the effects of distribution of fast and slow components of GABAergic inhibition in pyramidal cells. Interspike interval (ISI) analysis is used for examination of bursting patterns. Simulations show that the inhibitory interneuron regulates neuronal bursting activity. Bursting behavior patterns depend on the synaptic weight and delay of the inhibitory connection as well as the location of the synapse. When the inhibitory interneuron synapses on the pyramidal neuron, inhibitory action is stronger if the inhibitory synapse is close to the soma. Alterations of synaptic weight of the interneuron can be compensatory for changes in the location of synaptic input. The relative changes in these parameters exert a considerable influence on whether synchronous bursting activity is facilitated or reduced. Additional simulations show that the slow GABAergic inhibitory component is more effective than the fast component in distal dendrites. Taken together, these findings illustrate the potential for GABAergic inhibition in the soma and dendritic tree to play an important modulatory role in bursting activity patterns.     

Synaptic potentials and transfer functions of lamprey spinal neurons

1. Electrotonic and chemical synaptic potentials were measured as a function of frequency of presynaptic action potentials. Over the frequency range from 0.02 to 10 Hz, the electrotonic synaptic potential was constant, while the chemical synaptic potential decreased in magnitude. Above 10 Hz, both synaptic events decreased in magnitude consistent with filtering by the dendritic structures. 2. Electrotonic synaptic transfer functions from 0.5 to 100 Hz were measured for the I1 reticulospinal Müller axon to spinal neuron electrotonic synaptic junction of the lamprey spinal cord using paired recordings from the pre-synaptic terminals and the post-synaptic neurons. In addition to this two-point synaptic transfer function, individual single point impedance functions of both the post-synaptic soma and the pre-synaptic axon terminal were measured. 3. The measured functions were interpreted with a computational model based on a three dimensional reconstruction of a Lucifer yellow filled motoneuron. Simulations of the model for a synaptic location of the I1 synapse were consistent with the measured synaptic transfer functions. 4. Synaptic potentials were simulated for inputs on dendrites near the I1 axon as well as distal dendritic regions. The high frequency filtering increased as the synaptic location was moved from the soma to the periphery, but the potential response on distal dendrites was larger than would have been predicted from the end of the equivalent cylinder of a Rall model that was used to fit soma impedance functions. 5. Electrotonic post-synaptic potentials were enhanced by the activation of a TTX-sensitive negative conductance.(ABSTRACT TRUNCATED AT 250 WORDS)     

Virtual NEURON: a strategy for merged biochemical and electrophysiological modeling

Because of its highly branched dendrite, the Purkinje neuron requires significant computational resources if coupled electrical and biochemical activity are to be simulated. To address this challenge, we developed a scheme for reducing the geometric complexity; while preserving the essential features of activity in both the soma and a remote dendritic spine. We merged our previously published biochemical model of calcium dynamics and lipid signaling in the Purkinje neuron, developed in the Virtual Cell modeling and simulation environment, with an electrophysiological model based on a Purkinje neuron model available in NEURON. A novel reduction method was applied to the Purkinje neuron geometry to obtain a model with fewer compartments that is tractable in Virtual Cell. Most of the dendritic tree was subject to reduction, but we retained the neuron’s explicit electrical and geometric features along a specified path from spine to soma. Further, unlike previous simplification methods, the dendrites that branch off along the preserved explicit path are retained as reduced branches. We conserved axial resistivity and adjusted passive properties and active channel conductances for the reduction in surface area, and cytosolic calcium for the reduction in volume. Rallpacks are used to validate the reduction algorithm and show that it can be generalized to other complex neuronal geometries. For the Purkinje cell, we found that current injections at the soma were able to produce similar trains of action potentials and membrane potential propagation in the full and reduced models in NEURON; the reduced model produces identical spiking patterns in NEURON and Virtual Cell. Importantly, our reduced model can simulate communication between the soma and a distal spine; an alpha function applied at the spine to represent synaptic stimulation gave similar results in the full and reduced models for potential changes associated with both the spine and the soma. Finally, we combined phosphoinositol signaling and electrophysiology in the reduced model in Virtual Cell. Thus, a strategy has been developed to combine electrophysiology and biochemistry as a step toward merging neuronal and systems biology modeling.     

Reliable, responsive pacemaking and pattern generation with minimal cell numbers: the crustacean cardiac ganglion

Investigations of the electrophysiology of crustacean cardiac ganglia over the last half-century are reviewed for their contributions to elucidating the cellular mechanisms and interactions by which a small (as few as nine cells) neuronal network accomplishes extremely reliable, rhythmical, patterned activation of muscular activity-in this case, beating of the neurogenic heart. This ganglion is thus a model for pacemaking and central pattern generation. Favorable anatomy has permitted voltage- and space-clamp analyses of voltage-dependent ionic currents that endow each neuron with the intrinsic ability to respond with rhythmical, patterned impulse activity to nonpatterned stimulation. The crustacean soma and initial axon segment do not support impulse generation but integrate input from stretch-sensitive dendrites and electrotonic and chemically mediated synapses on axonal processes in neuropils. The soma and initial axon produce a depolarization-activated, calcium-mediated, sustained potential, the "driver potential," so-called because it drives a train of impulses at the "trigger zone" of the axon. Extreme reliability results from redundancy and the electrotonic coupling and synaptic interaction among all the neurons. Complex modulation by central nervous system inputs and by neurohormones to adjust heart pumping to physiological demands has long been demonstrated, but much remains to be learned about the cellular and molecular mechanisms of action. The continuing relevance of the crustacean cardiac ganglion as a relatively simple model for pacemaking and central pattern generation is confirmed by the rapidly widening documentation of intrinsic potentials such as plateau potentials in neurons of all major animal groups. The suite of ionic currents (a slowly inactivating calcium current and various potassium currents, with variations) observed for the crustacean cardiac ganglion have been implicated in or proven to underlie a majority of the intrinsic potentials of neurons involved in pattern generation.     

Analysis of membrane heterogeneity and non-linearity of summation of postsynaptic potentials in a simulation model of the Purkinje cell

Propagation and summation of EPSP was studied by means of a numerical model of rat Purkinje neuron. It was shown that the difference between the membrane resistivity of the soma and dendrites can be determined experimentally by the character of EPSP attenuation, while comparing intra- and extracellular recordings. It was also shown that at an increase of synaptic input the nonlinear increase of the potential is more pronounced in the soma that in the synaptic region. The role of this fact for the interpretation of the experimental data is discussed.     

Branch Input Resistance and Steady Attenuation for Input to One Branch of a Dendritic Neuron Model

Mathematical solutions and numerical illustrations are presented for the steady-state distribution of membrane potential in an extensively branched neuron model, when steady electric current is injected into only one dendritic branch. Explicit expressions are obtained for input resistance at the branch input site and for voltage attenuation from the input site to the soma; expressions for AC steady-state input impedance and attenuation are also presented. The theoretical model assumes passive membrane properties and the equivalent cylinder constraint on branch diameters. Numerical examples illustrate how branch input resistance and steady attenuation depend upon the following: the number of dendritic trees, the orders of dendritic branching, the electrotonic length of the dendritic trees, the location of the dendritic input site, and the input resistance at the soma. The application to cat spinal motoneurons, and to other neuron types, is discussed. The effect of a large dendritic input resistance upon the amount of local membrane depolarization at the synaptic site, and upon the amount of depolarization reaching the soma, is illustrated and discussed; simple proportionality with input resistance does not hold, in general. Also, branch input resistance is shown to exceed the input resistance at the soma by an amount that is always less than the sum of core resistances along the path from the input site to the soma.     

Analytical solution of the cable equation with synaptic reversal potentials for passive neurons with tip-to-tip dendrodendritic coupling

A passive cable model is presented for a pair of electrotonically coupled neurons in order to investigate the effects of tip-to-tip dendrodendritic gap junctions on the interaction between excitation and either pre or postsynaptic inhibition. The model represents each dendritic tree by a tapered equivalent cylinder attached to an isopotential soma. Analytical solution of the cable equation with synaptic reversal potentials is considered for each neuron to yield a system of Volterra integral equations for the voltage. The solution to the system of linear integral equations (expressed as a Neumann series) is used to determine the current spread within the two coupled neurons, and to re-examine the sensitivity of the soma potentials (in particular) to the coupling resistance for various loci of synaptic inputs. The model is actually posed generally, so that active as well as passive properties could be considered. In the active case, a system of non-linear integral equations is derived for the voltage.     

Transient response in a somatic shunt cable model for synaptic input activated at the terminal

Rall's neuron model is extended by including a non-uniform time constant together with synaptic input modeled as a square step of conductance. An analytic solution (in series form) for the electrotonic potential is obtained. The major conclusion reached is that a lower somatic time constant attenuates the amplitude of the potential at the soma, brought about by the activation of a synapse located at the distal end of the dendritic cable in an initially polarized neuron.     

A computer based model for realistic simulations of neural networks

The use of computer simulations as a neurophysiological tool creates new possibilities to understand complex systems and to test whether a given model can explain experimental findings. Simulations, however, require a detailed specification of the model, including the nerve cell action potential and synaptic transmission. We describe a neuron model of intermediate complexity, with a small number of compartments representing the soma and the dendritic tree, and equipped with Na⁺, K⁺, Ca²⁺, and Ca²⁺ dependent K⁺ channels. Conductance changes in the different compartments are used to model conventional excitatory and inhibitory synaptic interactions. Voltage dependent NMDA-receptor channels are also included, and influence both the electrical conductance and the inflow of Ca²⁺ ions. This neuron model has been designed for the analysis of neural networks and specifically for the simulation of the network generating locomotion in a simple vertebrate, the lamprey. By assigning experimentally established properties to the simulated cells and their synapses, it has been possible to verify the sufficiency of these properties to account for a number of experimental findings of the network in operation. The model is, however, sufficiently general to be useful for realistic simulation also of other neural systems.     

The axosomatic contacts on the bursting neuron of the snailHelix pomatia. I. ultrastructural features of the axosomatic contacts

The analysis of serial ultrathin sections of the RPAI bursting neuron of the snail Helix pomatia reveals the presence of axosomatic contacts on its surface membrane. These contacts have a number of specific features: the presynaptic axon contains synaptic vesicles and electron-dense granules, typical of peptidergic terminals; the terminal part of the axon forms many finger-like processes which invaginate the neuronal soma; the width of the cleft (80 nm) in the area of the contact is larger than that in usual synaptic contacts; and there is a system of lacoons in the region of the axosomatic contact; this system is formed by protrusions of the soma and it accompanies the contact along its extent. It is suggested that the system of lacoons which communicates with the space between the terminal and the soma may serve as a ramified synaptic cleft into which the secretion from the terminal is released. This system may contribute to a considerable prolongation of the time of action of the secretory product on the membrane of the RPAI neuron.     

Multiplicity of pacemaker zones in Helix pomatia neurons

Intracellular microelectrode recordings from neurons ofHelix pomatia revealed several local zones of action potential generation both on the soma and on some of the branches of the neurons. Under certain conditions the activity of individual loci of the neuron membrane was synchronized to produce a normal action potential. It is suggested that the somatic membrane of neurons is heterogeneous in structure and consists of separate loci of an electrically excitable membrane, incorporating active and latent pacemaker zones. Neurons ofH. pomatia are characterized by two types of action potential with different triggering mechanisms: one (synaptic) type is generated under the influence of the EPSP, the other (pacemaker) arises through activation of endogenous factors for the neuron (pacemaker potentials). The interaction between synaptic and pacemaker potentials during integrative activity of the neuron is discussed.M. V. Lomonosov Moscow State University. Translated from Neirofiziologiya, Vol. 5, No. 1, pp. 88–94, January–February, 1973.     

A cable model for coupled neurons with somatic gap junctions

A cable model is presented for a pair of electrotonically coupled neurons to investigate the spatial effects of soma-somatic gap junctions. The model extends that of Poznanski et al.(1995) in which each neuron is represented by a tapered equivalent cable attached to an isopotential soma with the two somas being electrically coupled. The model is posed generally, so that both active and passive properties can be considered. In the active case a system of nonlinear integral equations is derived for the voltage, whilst in the passive case these have an exact solution that also holds for inputs modelled as synaptic reversal potentials. Analytical and numerical methods are used to examine the sensitivity of the soma potentials (in particular) to the coupling resistance.     

The synaptic vesicle membrane: origin, axonal distribution, protein components, exocytosis and recycling

The paper discusses functional and molecular aspects of the synaptic vesicle membrane during its life cycle. The distribution of the synaptic vesicle membrane compartment in an entire cholinergic neuron is monitored using colloidal gold labelling and a monoclonal antibody against the synaptic vesicle membrane protein SV2. This provides new insights concerning vesicle origin and fate in the various compartments of the neuron. A new synaptic vesicle membrane protein (svp25) of Mr 25,000 with properties similar to synaptophysin as well as a synaptic vesicle binding phosphoprotein of the presynaptic membrane (Mr 92,000) likely to be involved in vesicle exocytosis are described. The membrane compartment recycled on induced transmitter release contains synaptic vesicle but not plasma membrane markers and encloses both newly synthesized transmitter and a sample of extracellular medium.     

Generalized Stein's model for anatomically complex neurons

A neuron with a large dendritic structure is considered. The number of synapses located on the dendrites is substantially higher than on the soma. The synaptic input effect on the neuronal excitability decreases with distance between a synapse ending and the trigger zone. Two areas are distinguished in accordance with the effect of synaptic input--dendritic and somatic. The dendritic area, when compared to the soma, is characterized by much higher intensity of its activation but the amplitudes of synaptically evoked changes of the membrane potential at the trigger zone are in general small. This situation is suitable for a diffusion approximation. However, on the soma, especially in the proximity of the trigger zone, the membrane potential changes are a large fraction of the threshold depolarization. The membrane potential at the trigger zone is modelled by a one-dimensional stochastic process. The diffusion Ornstein-Uhlenbeck process serves as a basis of the model; however, at the moments of somatic synapses activation its voltage changes in jumps. Their sizes represent the amplitudes of the evoked postsynaptic potentials. The unimodal histograms of interspike intervals can be explained by the model. The values of the coefficient of variation greater than one are connected with substantial inhibition.     

Synaptic depression increases the selectivity of a neuron to its preferred pattern and binarizes the neural code

The preferred pattern of a neuron is defined here by the set of features detected by its excitatory inputs. It is shown that the Leaky integrate-and-fire (LIF) model of a neuron has a poor selectivity to its preferred pattern. Its response is determined by the total current injected by input spike trains. Thus, a few inputs with a high activity (an incomplete pattern) can elicit the same response as many inputs (a complete pattern) with a weak activity. A theoretical model of depressing synapse with linear recovery is proposed which eliminates this problem. Using this model, the time-averaged current injected in the soma by a spike train becomes independent on its frequency. The neural code thus becomes binary, and the response strength of the target neuron depends only on the number of active inputs. Simulations show that a biological model of strong synaptic depression has effects similar to those of the ideal linear model. The best selectivity is obtained with long somatic decay time constants (>50 ms) and with depression recovery time constants larger or equal to the somatic decay time constant. Thus, by eliminating information carried in the input firing rate, a neuron can improve its pattern recognition performance.