Arthur Vermeulen

The Intrinsic Electrophysiological Characteristics of Fly Lobula Plate Tangential Cells: III. Visual Response Properties

In this last paper in a series (Borst and Haag, 1996; Haag et al., 1997) about the lobula plate tangential cells of the fly visual system (CH, HS, and VS cells), the visual response properties were examined using intracellular recordings and computer simulations. In response to visual motion stimuli, all cells responded mainly by a graded shift of their axonal membrane potential. While ipsilateral motion resulted in a graded membrane potential shift, contralateral motion led to distinct EPSPs. For HS cells, simultaneous extracellular recorded action potentials of a spiking interneuron, presumably the H2 cell, corresponded to the EPSPs in the HS cell in a one-to-one fashion. When HS cells were hyperpolarized during ipsilateral motion, they mainly produced action potentials, but when they were hyperpolarized during contralateral motion only a slight increase of EPSP amplitude, could be observed. Intracellular application of the sodium channel blocker QX 314 abolished action potentials of HS cells while having little effect on the graded membrane response to ipsilateral motion. HS and CH cells were also studied with respect to their spatial integration properties. For both cell types, their graded membrane response was found to increase less than linearly with the size of the ipsilateral motion pattern. However, while for HS cells various amounts of hyperpolarizing current injected during motion stimulation led to different saturation levels, this was not the case for CH cells. In response to a sinusoidal velocity modulation, CH cells followed pattern motion only up to 10 Hz modulation frequency, but HS cells still revealed significant membrane depolarizations up to about 40 Hz.In the computer simulations, the compartmental models of tangential cells, as derived in the previous papers, were linked to an array of local motion detectors. The model cells revealed the same basic response features as their natural counterparts. They showed a response saturation as a function of stimulus size. In CH-models, however, the saturation was less pronounced than in real CH-cells, indicating spatially nonuniform membrane resistances with higher values in the dendrite. As in the experiments, HS models responded to high-frequency velocity modulation with a higher amplitude than did CH models.

Coding of Odor Intensity in a Steady-State Deterministic Model of an Olfactory Receptor Neuron

The coding of odor intensity by an olfactory receptor neuron model was studied under steady-state stimulation. Our model neuron is an elongated cylinder consisting of the following three components: a sensory dendritic region bearing odorant receptors, a passive region consisting of proximal dendrite and cell body, and an axon. First, analytical solutions are given for the three main physiological responses: (1) odorant-dependent conductance change at the sensory dendrite based on the Michaelis-Menten model, (2) generation and spreading of the receptor potential based on a new solution of the cable equation, and (3) firing frequency based on a Lapicque model. Second, the magnitudes of these responses are analyzed as a function of odorant concentration. Their dependence on chemical, electrical, and geometrical parameters is examined. The only evident gain in magnitude results from the activation-to-conductance conversion. An optimal encoder neuron is presented that suggests that increasing the length of the sensory dendrite beyond about 0.3 space constant does not increase the magnitude of the receptor potential. Third, the sensivities of the responses are examined as functions of (1) the concentration at half-maximum response, (2) the lower and upper concentrations actually discriminated, and (3) the width of the dynamic range. The overall gain in sensitivity results entirely from the conductance-to-voltage conversion. The maximum conductance at the sensory dendrite appears to be the main tuning constant of the neuron because it determines the shift toward low concentrations and the increase in dynamic range. The dynamic range of the model cannot exceed 5.7 log units, for a sensitivity increase at low odor concentration is compensated by a sensitivity decrease at high odor concentration.

Why are insect olfactory receptor neurons grouped into sensilla? The teachings of a model investigating the effects of the electrical interaction between neurons on the transepithelial potential and the neuronal transmembrane potential.

Insect olfactory receptor neurons are compartmentalized in sensilla. In a sensillum, typically two receptor neurons are in close contact and can influence each other through electrical interaction during stimulation. This interaction is passive, non-synaptic and a consequence of the electrical structure of the sensillum. It is analysed in a sensillum model and its effects on the neuron receptor potentials are investigated. The neurons in a sensillum can be both sensitive to a given odorant compound with the same sensory threshold or with different thresholds, or only one neuron be sensitive to the odorant. These three types of sensilla are compared with respect to maximum amplitude, threshold and dynamic range of the potentials. It is found that gathering neurons in the same sensillum is disadvantageous if they are identical, but can be advantageous if their thresholds differ. Application of these results to actual recordings from pheromone and food-odour olfactory sensilla is discussed.

Dendritic Integration in Olfactory Sensory Neurons: A Steady-State Analysis of How the Neuron Structure and Neuron Environment Influence the Coding of Odor Intensity

Response properties of the receptor potential at steady state were analyzed in a biophysical model of an olfactory sensory neuron embedded in a multicell environment. The neuron structure was described as a set of several identical dendrites (or cilia) bearing the transduction mechanisms, joined to a nonsensory part—dendritic knob, soma, and axon. The different ionic compositions of the media surrounding the neuron sensory and nonsensory parts and the extraneuronal voltage sources, which both result from the presence of auxiliary cells, were also taken into account. Analytical solutions were found to describe how the receptor potential at the nonsensory part responds to a uniform change in the odorant-dependent conductance resulting from odorant stimulation of the sensory dendrites. We investigated the influence of various geometrical and electrical parameters on the receptor-potential response in the classical model neuron within a homogeneous environment and in the model neuron surrounded with auxiliary cells. First, it was found that the maximum amplitude of the receptor potential is independent of the neuron structure in the absence of auxiliary cells but not in their presence. In the latter case, the amplitude decreases with the length and number of sensory dendrites and with the input resistance of the nonsensory part. Second, the sensitivity (as measured by the increase in membrane conductance at half-maximum response) of the neuron model in the absence of auxiliary cells is higher, but its dynamic range is narrower than in their presence. The dynamic range is wide and the sensitivity low when the input resistance of the nonsensory part is small and the sensory dendrite is unbranched. Both sensitivity and dynamic range are higher for a longer dendrite. These results help understand the morphology of insect olfactory sensilla and can be generalized to other neuron types.

Coding of stimulus intensity in an olfactory receptor neuron: Role of neuron spatial extent and passive dendritic backpropagation of action potentials

The olfactory receptor neuron provides a good opportunity to analyze a biophysical model of a single neuron because its dendritic structure is simple and even close to a cylinder in the case of the moth sex-pheromone receptor cell. We have considered this cylindrical case and studied two main problems. First, we were concerned with the effect of the neurons length on the receptor potential for a constant stimulus-induced conductance change. An analytical solution for the receptor potential was determined by using input resistances. It was shown that the longer the neuron, the greater its ability to code over a wide range of values of the intensity of the stimulus. Second, we studied numerically the passive backpropagation of action potentials into the dendrite and its influence on firing frequency. While propagating along the dendrite, the action potential decreases in amplitude and its shape becomes rounded. The firing frequency in the model with backpropagation was found to be greater than that obtained analytically in the absence of backpropagation. However, for any given conductance change, when normalized with respect to their maxima, both firing frequencies were found to be very similar over a wide range of parameter values. Therefore, the actual firing rate (with backpropagation) may be approximated by the analytical solution without backpropagation if the actual firing rate for a large conductance change is known.

Coding of odour intensity in a sensory neuron

A deterministic biophysical model of an olfactory sensory neuron under constant stimulation is presented with the aim of describing the successive conversion steps, including receptor activation, conductance change, receptor potential and firing frequency, that are involved in the coding of odorant concentration. This model is divided in two parts. The odorant-sensitive part (OSP), consisting of one cylindrical dendrite, is connected to the odorant-insensitive part (OIP), corresponding to passive dendrite, soma and axon. Each part exerts a specific effect on the coding properties of the conversion steps, i.e. their magnitude, sensitivity and dynamic range. The maximum conductance of the OSP affects positively all coding properties whereas the input resistance of the OIP, which depends on its size and shape, affects positively the sensitivity and negatively the dynamic range. These findings are helpful for understanding the input-output properties of many types of neurons.

Membrane potential and its electrode-recorded counterpart in an electrical model of an olfactory sensillum.

Abstract. Insect receptor neurons are surrounded with auxiliary cells and encased in a hair. Their electrical activity is usually recorded with an electrode located at the tip of the hair. Analytical expressions giving the membrane potential along the sensory dendrite and the tip-recorded potential are derived for a neuron in steady-state conditions. They formally close the gap between theoretical models and experimental measurements, when transduction mechanisms and active membrane properties are not taken into account. It is shown that the tip-recorded potential reflects correctly the relative variations of the dendritic membrane potential as a function of stimulus intensity over a large range of parameters. The geometric and electrical characteristics of the sensillum that need be known to compute the dendritic membrane potential from the tip-recorded potential are given.

Basic mechanisms of coding stimulus intensity in the olfactory sensory neuron

A basic deterministic and stochastic model of the olfactory sensory neuron under steady-state conditions is proposed. It is composed of three modules that describe the main steps of the neuron response to a stimulation, i.e. interaction of odorant molecules with membrane receptor sites and opening of dendritic ion channels, generation and passive propagation of receptor potential along dendrite, and conversion of receptor potential into a train of action potentials at the axon initial segment. Explicit mathematical descriptions of these mechanisms are given and their usefulness in interpreting experimental observations is discussed.

A simple analytical method for determining the steady-state potential in models of geometrically complex neurons.

A method is presented for solving the cable equation for a spiking neuron below firing threshold or a nonspiking neuron of arbitrary geometry under constant stimulation. The neuron structure is considered as a tree composed of a set of cylinder cables of three types (terminal, intermediate and branching) characterized by their lengths, diameters and linear membrane properties. The stimulation can result from either a uniform conductance-change over a whole cable segment or a point injection of a current. Other special segments are considered (synapses, voltage clamp, lumped soma). Equations are given for replacing any segment with its Thévenin equivalent, i.e. resistance and electromotive force. The step by step use of these elementary equations allows one to find the Thévenin equivalent of the whole neuron and to determine the steady-state membrane potential at any point.

Electrical circuitry of an insect olfactory sensillum

Abstract A biophysical model of an insect olfactory sensillum in steady-state conditions is presented. The model has two distinguishing features. Firstly, it describes analytically the extracellularly recorded potential, thus closing formally the gap between theoretical models and experimental results. Secondly, it integrates in a single description two extreme models previously investigated: that of the classical neuron located in a homogeneous environment and that of the neuron surrounded with auxiliary cells. The generalized model presented gives the opportunity of studying the response properties of the neuron to odors at various concentrations in a broader context.