Signal transmission in lobster olfactory receptor cells: functional significance of electrotonic structure analysed by a compartmental model.

The electrotonic structure of lobster olfactory receptor cells was evaluated using general purpose simulation software in a compartmental model derived from electron-microscopic reconstruction. The model with non-uniform membrane resistance (Rm) was used to (i) simulate current spread and (ii) determine if the electronic structure of the cell improves signal recognition in the soma. The odor-evoked conductance change in dendrites was calculated according to the Michaelis-Menten equation with the assumption that the outer dendritic segments function as independent stimulus detectors. The inflection point of the concentration-response function measured in the soma was shifted to lower concentrations relative to that measured in the ciliary (outer dendritic) arbor. The shift, which was greater for inputs with lower efficacy (represented in the model by smaller Hill coefficients) and for the dynamic phase of the response than for the steady-state phase, effectively increased the selectivity of the somatic response. Randomized input distributed uniformly to progressively more restricted areas of the ciliary arbor showed that stimulation of larger areas (presumably the entire ciliary arbor) decreased the statistical variability of the somatic response.

A model of NMDA receptor-mediated activity in dendrites of hippocampal CA1 pyramidal neurons.

1. The role of synaptic activation of NMDA (N-methyl-D-aspartate) receptor-mediated conductances on CA1 hippocampal pyramidal cells in short-term excitability changes was studied with the use of a computational model. Model parameters were based on experimental recordings from dendrites and somata and previous hippocampal simulations. Representation of CA1 neurons included NMDA and non-NMDA excitatory dendritic synapses, dendritic and somatic inhibition, five intrinsic membrane conductances, and provision for activity-dependent intracellular and extracellular ion concentration changes. 2. The model simulated somatic and dendritic potentials recorded experimentally. The characteristic CA1 spike afterdepolarization was a consequence of the longitudinal spread of dendritic charge, reactivation of slow Ca(2+)-dependent K+ conductances, slow synaptic processes (NMDA-dependent depolarizing and gamma-aminobutyric acid-mediated hyperpolarizing currents) and was sensitive to extracellular potassium accumulation. Calcium currents were found to be less important in generating the spike afterdepolarization. 3. Repetitive activity was influenced by the cumulative activation of the NMDA-mediated synaptic conductances, the frequency-dependent depression of inhibitory synaptic responses, and a shift in the potassium reversal potential. NMDA receptor activation produced a transient potentiation of the excitatory postsynaptic potential (EPSP). The frequency dependence of EPSP potentiation was similar to the experimental data, reaching a maximal value near 10 Hz. 4. Although the present model did not have compartments for dendritic spines, Ca2+ accumulation was simulated in a restricted space near the intracellular surface of the dendritic membrane. The simulations demonstrated that the Ca2+ component of the NMDA-operated synaptic current can be a significant factor in increasing the Ca2+ concentration at submembrane regions, even in the absence of Ca2+ spikes. 5. Elevation of the extracellular K+ concentration enhanced the dendritic synaptic response during repetitive activity and led to an increase in intracellular Ca2+ levels. This increase in dendritic excitability was partly mediated by NMDA receptor-mediated conductances. 6. Blockade of Ca(2+)-sensitive K+ conductances in the dendrites increased the size of EPSPs leading to a facilitation of dendritic and somatic spike activity and increased [Ca2+]i. NMDA receptor-mediated conductances appeared as an amplifying component in this mechanism, activated by the relatively depolarized membrane potential. 7. The results suggest that dendritic NMDA receptors, by virtue of their voltage-dependency, can interact with a number of voltage-sensitive conductances to increase the dendritic excitatory response during periods of repetitive synaptic activation. These findings support experimental results that implicate NMDA receptor-mediated conductances in the short-term response plasticity of the CA1 hippocampal pyramidal neuron.

Electrotonic structure of olfactory sensory neurons analyzed by intracellular and whole cell patch techniques.

1. Experimental studies employing whole cell patch recordings from freshly isolated olfactory sensory neurons of the salamander (Ambystoma tigrinum) yield much higher estimates of specific membrane resistance (Rm) than studies using conventional intracellular recordings from in situ neurons. Because Rm is critical for understanding information transfer in these cells, we have used computational methods to analyze the possible reasons for this difference. 2. Compartmental models were constructed for both the in situ and isolated neurons, using SABER, a general-purpose simulation program. For Rm in the in situ cell, we used a high value of 100,000 omega.cm2, as estimated in the whole cell recordings from isolated cells. A shunt across the cell membrane caused by the penetrating microelectrode was simulated by several types of shunt mechanisms, and its effects on lowering the apparent value of resting membrane potential (MP), input resistance (RN), and membrane time constant (tau m) and increasing the electrotonic length (L) were analyzed. 3. A good approximation of the electrotonic properties recorded intracellularly was obtained in the in situ model with high Rm combined with an electrode shunt consisting of Na and K conductances. A raised K conductance (1-5 nS) helps to maintain the resting MP while contributing to the increased conductance, which lowers RN and shortens the apparent tau m toward the experimental values. 4. Combined shunt resistances of 0.1-0.2 G omega (5-10 nS) gave the best fits with the experimental data. These shunts were two to three orders of magnitude smaller than the values reported from intracellular penetrations in muscle cells and motoneurons. This may be correlated with the smaller electrode tips used in the recordings from these small neurons. We thus confirm the prediction that even small values of electrode shunt have relatively large effects on the recorded electrotonic properties of small neurons, because of their high RN (2-5 G omega). 5. We have further explored the effects on electrotonic structure of a nonuniform Rm by giving higher Rm values to the distally located cilia compared with the proximal soma-dendritic region, as indicated by recent experiments. For the same RN, large increases in ciliary Rm above 100,000 omega.cm2 can be balanced by relatively small decreases below that value in soma-dendritic Rm. A high ciliary Rm appears to be a specialization for transduction of the sensory input, as reported also in photoreceptors and hair cells.

Bidirectional compartmental approximation of realistic nerve cell structures.

Passive electrotonic activity of anatomically complex nerve cells has been computed through a simplified anisotropic "smoothing" of the original structures. The algorithm for this "smoothing" involves a recursive matching of the amplitude, zero and pole of the input impedances for each segment. This algorithm can be used for both spatially and/or electrically inhomogeneous cables. The directional sensitivity of the voltage transfer in non-smooth dendrites has been characterized by a decomposition which reveals the bidirectional segmentation of the core geometry according to the opposite wave fronts of electronic potentials in dendrites. The impedance diagrams can be used to estimate the goodness of the whole procedure in the frequency domain. The bidirectional segmentation of the core geometry may serve as a basis of the compartment simulations of those excitable nerve cells where the voltage spread is modulated by irregular dendritic structures, such as spines.

Nerve cells with irregular processes: demonstration of anisotropic core geometry of a pyramidal cell.

An analytical, recursive method has been developed to demonstrate the anisotropic electrotonic geometry of nerve cells containing varicose or spiny dendrites. The procedure has been based on the distribution of the core geometry of dendrites into modules which consist of module elements where the physical length is much shorter than the actual space constant. The unambiguous representation of the anisotropic core geometry has been possible by plotting the decomposed geometries separated under the condition of the unidirectional spread of the wave front of dendritic potentials. This decomposition has revealed the bidirectional, "smoothed" core geometries as a function of irregular distribution of varicosities or spines. The shape of decomposed core geometries may change according to the position of the input site. The shaping of core geometry reflects the electrotonic effectiveness of a synaptic site to any arbitrary locations which may lead to considerable savings in computations on synaptic effects. The detailed, computer-reconstructed geometry of the apical dendritic field of the pyramidal cell has been analysed by the proposed method. The frequency-dependence of input impedances has been compared between the original and the transformed core geometries assuming that the current is injected into the soma. The significance of dendritic irregularities in the impedance matching has been studied when the shaping of the core geometry has been induced by laminar inputs. The proposed approach may be useful in comparing the input dependence of the receptive fields of different non-smooth cells. The mismatch of the core geometries induced by the opposite travelling waves from the same anatomical location has also been studied and the possible control of the preferred, direction-sensitive activities will be discussed. The important differences between the compartmental modelings based on the known isotropic treatment of dendrites and the more realistic anisotropic approach will be illustrated.

A modified cable model analysis of microscopic axonal and dendritic processes.

The computational background for analysing the passive, subthreshold properties of fine-scale ramifications such as "en-passant" and "terminal ladder" type chains of boutons and spiny dendrites is presented. The segment-by-segment approximation of a cable composed of serial or parallel chains of identical units (modules) is based on the cable representations of boutons, axon, spines and dendrit. Pulse response in the time domain is evaluated from the narrow-bandwidth, recursive estimation of the input and transfer impedances by means of inverse Laplace transformation. The shape of the voltage transients in semi-infinite chain of cable units is found by the input impedance computed under the equilibrium condition. The model predicts differences of subthreshold responses in relation to a change in modular geometry or membrane electrical parameters. The results may help in finding the relationship between the physical and electrotonical geometries of nerve cells with non-smooth processes. The smoothing procedure gives a possibility for the functional unification and simplification of those fine-scale processes of nerve cells where the characteristic space constants are much greater than the intersynaptic distances.

The function of dendritic spines: a theoretical study.

A modeling procedure is proposed which introduces the cable equivalent of dendritic spines into the Rall model of spiny interneurons in the spinal cord. At this point combined morphological and physiological works have given some insight into the possible role of a single spine and the function of a single spine has been studied by theoretical computations [Jack, Noble and Tsien (1975) Electric Current Flow in Excitable Cells, pp. 218-223. Oxford University Press, Oxford; Koch and Poggio (1983) Trends Neurosci. 6, 80-83; Perkel (1983) J. Physiol., Paris 78, 695-699]. The goal of the present paper is two-fold: (a) to stress the gross function of the spine system in the excitability of dendrites; and (b) to emphasize the role of spines in the dynamic input/output function of neurons. The simulation procedure is based on the well-known compartmental method. (1) The kinetics of active somatic and dendritic compartments are taken from a currently available spinal interneuron model to match the physiological data of large dorsal horn neurons carrying spines. (2) Beside the prolongation of the somatic excitatory postsynaptic potential, the model suggests that the spiny neuron increases the differences in the latency and height of excitatory postsynaptic potential as a function of the electrotonic position of input. The characteristics of the excitatory postsynaptic potential can be modified by the changes in spine geometry and the ratio of cytoplasmic resistances of spine stalk to that of main dendritic shaft. (3) Dendritic electroresponsiveness, which was already postulated for dorsal horn neurons, is analysed by the model including calcium and slow potassium systems. It is concluded that the participation of the spine stalk in active processes can highly modify the input dependence of response pattern. Depolarization-dependent Ca2+ accumulation in spines may reflect the interaction of spine stalks. (4) Passive antidromic spread of action potential can be suppressed in spiny cells. Analysis of active antidromic spread shows the probable importance of spines located near the soma. Centripetal vs centrifugal conduction of dendritic action potential may depend on the spine distribution along the tree and change in electrical parameters of spines.

Computer simulation for studying calcium dependent abnormalities in firing mechanism of molluscan neurones.

Computer modelling technique is proposed to assist in physiological research on invertebrate neuronal membranes. The firing mechanism of a single patch of invertebrate neuronal membrane has been studied in dependence on maximum Ca++ conductance. The calculations are based on modification of Hodgkin-Huxley's data completed by a straight line approximation between experimental points of the kinetic parameters of Ca++ current and early transient potassium current. The time course of conductance changes is assumed to be proportional to m2h for Ca++ current. Three distinct potassium currents are involved into the model, viz. transient potassium current, delayed potassium current and Ca++-dependent potassium current. The modified Euler method run on a digital computer has been used for numerical integration of kinetic equations. Significant effects of Ca++ conductance on spike broadening, plateau development and spike afterhyperpolarization are represented. In the range of small Ca++ conductance an infinite spontaneous activity can be triggered by a short (suprathreshold) current pulse which may be considered a model of pacemaker activity. Plateau development resulting from potassium blocking or decreasing potassium equilibrium is facilitated by Ca++ conductance in the range of greater Ca++ conductance. The effects of voltage sensitivity of the coupling coefficient describing the current of Ca++-dependent K+ channels were studied and compared to the voltage independent case. The coupling coefficient seems to be a crucial factor in broadening the range of Ca++ conductance responsible for pacemaker activity. For greater values of Ca++ conductance, a decrease of the coupling coefficient leads to a transition from prolonged bursting to interruption of burst activity by burst-afterhyperpolarization. The blocking effect of 4-aminopyridine on fast outward current has been studied by the model which has a practical significance considering that aminopyridine is known as a convulsive agent. We suppose that it is reasonable to study the convulsive effects of aminopyridine by the model based on the kinetics of the isolated neuronal membrane. The model may help in understanding the ionic background underlying abnormal network activity during epileptic discharges of mammalian neurones.

Comparative study of aminopyridine-induced seizure activities in primary and mirror foci of cat's cortex.

Epileptogenic activity was induced by topical application of 3-Ap on the somatosensory cortex of anaesthetized cats. Surface epileptiform events were recorded and single cell activity was studied with intracellular electrodes both in the primary and in the mirror focus. Surface records showed that soon after the onset of paroxysmal activity in the primary focus, an epileptic mirror focus developed with variable delay. After MnCl2 treatment of the primary focus, the mirror focus generated independent epileptic events. In the primary and in the mirror focus 122 neurones were recorded intracellularly during seizure activity. Different firing patterns were observed. In the primary focus 31% and in the mirror focus 28% of the recorded neurones generated PDSs. The firing of the neurones in both foci was often phase-locked with surface waves. PDSs usually occurred asynchronously with the surface activity. Ionic mechanisms which may underlie the effect of 3-Ap are discussed.

On modelling the variability of interspike intervals during epileptic unit activity.

In spite of the fact that the participation of well defined ionic particles in generating convulsive unit discharges is established, there is a gap between the data on ionic movements and on first-order statistics of firing patterns. Our aim was to tight this gap by studying the effectiveness of functionally separated electrical conductances of membrane during the generation of consecutive interspike interval histograms (IIHs) of unitary discharges. On account of the non-stationarity of the process curve fitting analysis which based on the simple modifications of the integrate-and-fire model has been implemented in the sequential interspike interval histogram procedure (SIIH). The experimental data were recorded from cat cortex treated with 3-Aminopyridine (3-Ap) by glass microelectrodes during nembutal anesthesia. Assuming the normal distribution of input parameters it is concluded, that the efficiency of the fluctuations of the active spike-generating conductance gg and the passive diffusional conductance gl may increase during the generation of the unimodal IIHs and the first mode of the bimodal IIHs. The simple conductance coupling gl=gg + b may participate in gg activation, moreover, the reciprocally coupled mechanism gg=c/gl may be driven by gl activation (a, b, c are the coupling constants). A temporal separation of processes governed by gg or gl respectively was observed. The time-independent occurrences of the reciprocally coupled conductance processes may be involved in the unit activities represented by the prolonged IIHs and second modes of the bimodal IIHs.

Microcomputer method for the analysis of spontaneous bursting activity of units in epileptic cat cortex.

Exact probability analysis of the spontaneous bursting activity of epileptic units is a common problem. A microcomputer method, suitable for the calculation of the scalar function of two variables of the spike occurrence of this type of discharge, has been developed. The time measured from the first spike of a burst and the duration of the preceding interburst interval were chosen as the variables of the evaluated functions. A typical unit activity was analysed by the program. The method may be useful for the classification of different bursting patterns.

Aminopyridine-induced seizure activity.

Typical seizure activity can be induced by applying 3-aminopyridine to the surface of the cat cortex. The well known characteristics of epileptiform discharges were readily observed by simultaneous recording from both the surface and deeper layers.

Simulation of the ionic mechanisms of molluscan neurons under pentylenetetrazol-induced effects.

Some effects of the convulsant drug pentylenetetrazol (PTZ) on molluscan neurons were simulated. The calculations were based on the voltage clamp results of Connor and Stevens as well as Williamson and Crill. The normal repetitive state and the PTZ-controlled state were compared and threshold phenomena shown by prolonged depolarizations were studied by injection of hyperpolarizing currents into the first segment of the cable model, which is a widely used description of electrical spread in neuronal membranes. The potassium leakage (concentration per unit area) occurring simultaneously with the fluctuations of the ionic components was also evaluated. It is concluded that the PTZ-controlled state may alter the profile of the potassium leakage both quantitatively and dynamically. The hyperpolarizing and depolarizing current sequences may be functionally related to the intracellular epileptiform discharges.