Functional role of receptor neurons in encoding olfactory information

In the present review we have considered the properties of the olfactory receptor neurons and discuss the strategy these cells use to perform their signaling task. Special emphasis is laid on the mechanisms for setting the membrane potential at rest and the mechanisms that the cell can use to respond with action potentials to significant stimuli only. We demonstrate that the firing properties of the receptor neurons depend upon the initial level of the membrane potential. We present the idea that the olfactory glomerulus can function as a unit in olfactory processing. In this perspective the olfactory receptor neuron is a subunit of the olfactory glomerulus. © 1996 John Wiley & Sons, Inc.     

Amplification of trial-to-trial response variability by neurons in visual cortex

The visual cortex responds to repeated presentations of the same stimulus with high variability. Because the firing mechanism is remarkably noiseless, the source of this variability is thought to lie in the membrane potential fluctuations that result from summated synaptic input. Here this hypothesis is tested through measurements of membrane potential during visual stimulation. Surprisingly, trial-to-trial variability of membrane potential is found to be low. The ratio of variance to mean is much lower for membrane potential than for firing rate. The high variability of firing rate is explained by the threshold present in the function that converts inputs into firing rates. Given an input with small, constant noise, this function produces a firing rate with a large variance that grows with the mean. This model is validated on responses recorded both intracellularly and extracellularly. In neurons of visual cortex, thus, a simple deterministic mechanism amplifies the low variability of summated synaptic inputs into the large variability of firing rate. The computational advantages provided by this amplification are not known.     

The sound of silence: ionic mechanisms encoding sound termination

Offset responses upon termination of a stimulus are crucial for perceptual grouping and gap detection. These gaps are key features of vocal communication, but an ionic mechanism capable of generating fast offsets from auditory stimuli has proven elusive. Offset firing arises in the brainstem superior paraolivary nucleus (SPN), which receives powerful inhibition during sound and converts this into precise action potential (AP) firing upon sound termination. Whole-cell patch recording in?vitro showed that offset firing was triggered by IPSPs rather than EPSPs. We show that AP firing can emerge from inhibition through integration of large IPSPs, driven by an extremely negative chloride reversal potential (E(Cl)), combined with a large hyperpolarization-activated nonspecific cationic current (I(H)), with a secondary contribution from a T-type calcium conductance (I(TCa)). On activation by the IPSP, I(H) potently accelerates the membrane time constant, so when the sound ceases, a rapid repolarization triggers multiple offset APs that match onset timing accuracy.     

A Stochastic Model of the Repetitive Activity of Neurons

A recurrent model of the repetitive firing of neurons responding to stimuli of long duration is given. The model assumes a deterministic threshold potential and a membrane potential which is composed of both deterministic and random components. The model accurately reproduces interval statistics obtained from different neurons discharging repetitively over a wide range of discharge rates. It is shown that the model has three important parameters; the time course of threshold recovery following a discharge, the variance of the random component, and the level of excitatory drive. The model is extended, by the use of hyperpolarizing afterpotentials, to include negative correlation between successive interspike intervals.     

Adaptation in the Visual Cortex: Influence of Membrane Trajectory and Neuronal Firing Pattern on Slow Afterpotentials

The input/output relationship in primary visual cortex neurons is influenced by the history of the preceding activity. To understand the impact that membrane potential trajectory and firing pattern has on the activation of slow conductances in cortical neurons we compared the afterpotentials that followed responses to different stimuli evoking similar numbers of action potentials. In particular, we compared afterpotentials following the intracellular injection of either square or sinusoidal currents lasting 20 seconds. Both stimuli were intracellular surrogates of different neuronal responses to prolonged visual stimulation. Recordings from 99 neurons in slices of visual cortex revealed that for stimuli evoking an equivalent number of spikes, sinusoidal current injection activated a slow afterhyperpolarization of significantly larger amplitude (8.5±3.3 mV) and duration (33±17 s) than that evoked by a square pulse (6.4±3.7 mV, 28±17 s; p<0.05). Spike frequency adaptation had a faster time course and was larger during plateau (square pulse) than during intermittent (sinusoidal) depolarizations. Similar results were obtained in 17 neurons intracellularly recorded from the visual cortex in vivo. The differences in the afterpotentials evoked with both protocols were abolished by removing calcium from the extracellular medium or by application of the L-type calcium channel blocker nifedipine, suggesting that the activation of a calcium-dependent current is at the base of this afterpotential difference. These findings suggest that not only the spikes, but the membrane potential values and firing patterns evoked by a particular stimulation protocol determine the responses to any subsequent incoming input in a time window that spans for tens of seconds to even minutes.     

BDNF boosts spike fidelity in chaotic neural oscillations

Oscillatory activity and its nonlinear dynamics are of fundamental importance for information processing in the central nervous system. Here we show that in aperiodic oscillations, brain-derived neurotrophic factor (BDNF), a member of the neurotrophin family, enhances the accuracy of action potentials in terms of spike reliability and temporal precision. Cultured hippocampal neurons displayed irregular oscillations of membrane potential in response to sinusoidal 20-Hz somatic current injection, yielding wobbly orbits in the phase space, i.e., a strange attractor. Brief application of BDNF suppressed this unpredictable dynamics and stabilized membrane potential fluctuations, leading to rhythmical firing. Even in complex oscillations induced by external stimuli of 40 Hz (gamma) on a 5-Hz (theta) carrier, BDNF-treated neurons generated more precisely timed spikes, i.e., phase-locked firing, coupled with theta-phase precession. These phenomena were sensitive to K252a, an inhibitor of tyrosine receptor kinases and appeared attributable to BDNF-evoked Na(+) current. The data are the first indication of pharmacological control of endogenous chaos. BDNF diminishes the ambiguity of spike time jitter and thereby might assure neural encoding, such as spike timing-dependent synaptic plasticity.     

Effects of Polarization of the Receptor Membrane and of the First Ranvier Node in a Sense Organ

It has previously been shown that the site of production of the generator potential in Pacinian corpuscles is the receptor membrane of the non-myelinated ending, and the site of initiation of the nerve impulse, the adjacent (first) Ranvier node. Effects of membrane polarization of these sites were studied in the present work. Nerve ending and first Ranvier node were isolated by dissection, electric activity was recorded from, and polarizing currents were passed through them. All observations were done at steady levels of polarization, seconds after onset of current flow. The following results were obtained: The amount of charge transferred through the excited receptor membrane is a function of the electrical gradients across the membrane. The generator potential in response to equal mechanical stimuli increases with resting potential of the receptor membrane. The refractory state of the generator potential is not affected by polarization. The electrical threshold for impulse firing at the first Ranvier node (measured by the minimal amplitude of generator potential which elicits a nodal impulse) is nearly minimal at normal resting potential of the node. Both, hyperpolarization and depolarization lead to a rise in nodal threshold. For any level of polarization of nodal and receptor membrane, the threshold for production of impulses by adequate (mechanical) stimulation appears determined by the generator potential-stimulus strength relation and by the electrical threshold of the node.     

Mechanism of graded persistent cellular activity of entorhinal cortex layer v neurons

Working memory is an emergent property of neuronal networks, but its cellular basis remains elusive. Recent data show that principal neurons of the entorhinal cortex display persistent firing at graded firing rates that can be shifted up or down in response to brief excitatory or inhibitory stimuli. Here, we present a model of a potential mechanism for graded firing. Our multicompartmental model provides stable plateau firing generated by a nonspecific calcium-sensitive cationic (CAN) current. Sustained firing is insensitive to small variations in Ca2+ concentration in a neutral zone. However, both high and low Ca2+ levels alter firing rates. Specifically, increases in persistent firing rate are triggered only during high levels of calcium, while decreases in rate occur in the presence of low levels of calcium. The model is consistent with detailed experimental observations and provides a mechanism for maintenance of memory-related activity in individual neurons.     

II. Post-Tetanic Potentiation and Depression of Generator Potential in a Single Non-Myelinated Nerve Ending

Repetitive activity at the non-myelinated ending of Pacinian corpuscles leaves the following after-effects: (1) With certain parameters of repetitive mechanical stimulation of the ending a depression in generator potential is produced. The effect is fully reversible and has low energy requirements. The effect is a transient decrease in responsiveness of the receptor membrane which is unrelated to changes in resting membrane potential. It appears to reflect an inactivation process of the receptor membrane. Within certain limits, the depression increases as a function of strength, frequency, and train duration of repetitive stimuli. (2) With other, more critical parameters of repetitive stimulation a hyperpolarization of the ending and of the first intracorpuscular Ranvier node may be produced. This leads to respectively post-tetanic potentiation of generator potential and increase in nodal firing threshold. The balance of these after-effects determines the threshold for the production of nerve impulses by adequate (mechanical) stimulation of the sense organ. The after-effects of activity at the node can be elicited by dromic (mechanical) stimulation of the ending, as well as by antidromic (electric) stimulation of the axon; the after-effects at the ending can only be produced by dromic and not by antidromic stimulation.     

Evidence for transmitter operated electrical synapses (TOES) in ampullary electroreceptor organs

Afferent fibres of ampullary electroreceptor organs in electrosensitive fish fire spontaneously, that is, they fire without external stimulus. In the past it has been postulated that the spontaneous activity originates from a sustained level of neurotransmitter release delivered by the electroreceptor cells. The spontaneous activity can be modulated by electrical stimuli. Blocking of the chemical synapse, however, reduces the susceptibility to electrical stimuli to 2% or less, but the spontaneous activity to 60% only. By evaluating existing experimental evidence it is concluded that spontaneous firing of afferents is based on two processes. (1) A membrane bound oscillator, which does not depend on transmitter release, is almost free of frequency fluctuations, and is described by Hodgkin/Huxley-equations (HH-equations). (2) Release of neurotransmitter, which increases the firing level, adds frequency noise, and raises the susceptibility of the afferent to electrical stimuli. There is evidence that neurotransmitter release acts as a gating process, which makes the generator area of the afferents directly accessible to electrical stimuli from the outside. Apparently, the activated synapse behaves as a transmitter operated electrical synapse (TOES).     

Neural Coding with Graded Membrane Potential Changes and Spikes

The neural encoding of sensory stimuli is usually investigated for spike responses, although many neurons are known to convey information by graded membrane potential changes. We compare by model simulations how well different dynamical stimuli can be discriminated on the basis of spiking or graded responses. Although a continuously varying membrane potential contains more information than binary spike trains, we find situations where different stimuli can be better discriminated on the basis of spike responses than on the basis of graded responses. Spikes can be superior to graded membrane potential fluctuations if spikes sharpen the temporal structure of neuronal responses by amplifying fast transients of the membrane potential. Such fast membrane potential changes can be induced deterministically by the stimulus or can be due to membrane potential noise that is influenced in its statistical properties by the stimulus. The graded response mode is superior for discrimination between stimuli on a fine time scale.     

Activity-mediated accumulation of potassium induces a switch in firing pattern and neuronal excitability type

During normal neuronal activity, ionic concentration gradients across a neuron’s membrane are often assumed to be stable. Prolonged spiking activity, however, can reduce transmembrane gradients and affect voltage dynamics. Based on mathematical modeling, we investigated the impact of neuronal activity on ionic concentrations and, consequently, the dynamics of action potential generation. We find that intense spiking activity on the order of a second suffices to induce changes in ionic reversal potentials and to consistently induce a switch from a regular to an intermittent firing mode. This transition is caused by a qualitative alteration in the system’s voltage dynamics, mathematically corresponding to a co-dimension-two bifurcation from a saddle-node on invariant cycle (SNIC) to a homoclinic orbit bifurcation (HOM). Our electrophysiological recordings in mouse cortical pyramidal neurons confirm the changes in action potential dynamics predicted by the models: (i) activity-dependent increases in intracellular sodium concentration directly reduce action potential amplitudes, an effect typically attributed solely to sodium channel inactivation; (ii) extracellular potassium accumulation switches action potential generation from tonic firing to intermittently interrupted output. Thus, individual neurons may respond very differently to the same input stimuli, depending on their recent patterns of activity and/or the current brain-state.     

Direction selectivity of excitation and inhibition in simple cells of the cat primary visual cortex

Direction selectivity in simple cells of primary visual cortex, defined from their spike responses, cannot be predicted using linear models. It has been suggested that the shunting inhibition evoked by visual stimulation is responsible for the nonlinear component of direction selectivity. Cortical inhibition would suppress a neuron's firing when stimuli move in the nonpreferred direction, but would allow responses to stimuli in the preferred direction. Models of direction selectivity based solely on input from the lateral geniculate nucleus, however, propose that the nonlinear response is caused by spike threshold. By extracting excitatory and inhibitory components of synaptic inputs from intracellular records obtained in vivo, we demonstrate that excitation and inhibition are tuned for the same direction, but differ in relative timing. Further, membrane potential responses combine in a linear fashion. Spike threshold, however, quantitatively accounts for the nonlinear component of direction selectivity, amplifying the direction selectivity of spike output relative to that of synaptic inputs.     

Analysis of the activity of single neurons in stochastic settings

This paper presents a new way of modeling the activity of single neurons in stochastic settings. It incorporates in a natural way many physiological mechanisms not usually found in stochastic models, such as spatial integration, non-linear membrane characteristics and non-linear interactions between excitation and inhibition. The model is based on the fact that most of the neuronal inputs have a finite lifetime. Thus, the stochastic input can be modeled as a simple finite markov chain, and the membrane potential becomes a function of the state of this chain. Firing occurs at states whose membrane potential is above threshold. The main mathematical results of the model are: (i) the input-output firing rate curve is convex at low firing rates and is saturated at high firing rates, and (ii) at low firing rates, firing usually occurs when there is synchronous convergence of many excitatory events.     

Associative learning in a network model of Hermissenda crassicornis

A time-varying Resistance-Capacitance (RC) circuit computer model was constructed based on known membrane and synaptic properties of the visualvestibular network of the marine snail Hermissenda crassicornis. Specific biophysical properties and synaptic connections of identified neurons are represented as lumped parameters (circuit elements) in the model; in the computer simulation, differential equations are approximated by difference equations. The model's output, membrane potential, an indirect measure of firing frequency, closely parallels the behavioral and electrophysiologic outputs of Hermissenda in response to the same input stimuli presented during and after associative learning. The parallelism of the computer modeled and the biologic outputs suggests that the model captures the features necessary and sufficient for associative learning.     

A model for the firing pattern of a paced nerve cell

When a nerve cell is paced by another cell or by external stimuli, its firing pattern is generally not regular. In a given stimulus and frequency interval the cell responds only on a fraction of the stimuli, and this fraction is not necessarily a nice simple fraction as 2, ;, etc. but may be any fraction less than one, why the firing pattern becomes accordingly irregular.The paper demonstrates the rules for these irregularities and supplies a mathematical tool to analyse the firing pattern. In the analysis only a cell with the so-called impulse dependent type of adaptation is considered, but similar analyses may be done with other cell types.The analysis is restricted to a case where a resting cell is stimulated by repetitively applied stimuli of constant strength and repetition frequency. Cases with more than one input, spontaneously firing cells, and transient phenomena are not included in the analysis.     

Modelling natural burst firing in nigral dopamine neurons

The natural burst firing observed in vivo in mesolimbic dopamine neurons is of great significance regarding these neurons' involvement in response to sensory stimuli associated with primary reward. The cellular mechanisms underlying a natural burst have been experimentally characterized previously and hypothesized to be caused by a calcium-sensitive inactivation of a potassium channel. We present a mathematical model of a mesolimbic neuron that demonstrates how such a mechanism can produce realistic bursting patterns, but only when combined with an appropriately timed membrane depolarization from an external source.     

On the stationary state of a network of inhibitory spiking neurons

The background activity of a cortical neural network is modeled by a homogeneous integrate-and-fire network with unreliable inhibitory synapses. For the case of fast synapses, numerical and analytical calculations show that the network relaxes into a stationary state of high attention. The majority of the neurons has a membrane potential just below the threshold; as a consequence the network can react immediately – on the time scale of synaptic transmission- on external pulses. The neurons fire with a low rate and with a broad distribution of interspike intervals. Firing events of the total network are correlated over short time periods. The firing rate increases linearly with external stimuli. In the limit of infinitely large networks, the synaptic noise decreases to zero. Nevertheless, the distribution of interspike intervals remains broad. Action Editor: Misha Tsodyks