Coding of odor intensity

First-passage-time densities and avoiding probabilities for birth-and-death processes with symmetric sample paths

For truncated birth-and-death processes with two absorbing or two reflecting boundaries, necessary and sufficient conditions on the transition rates are given such that the transition probabilities satisfy a suitable spatial symmetry relation. This allows one to obtain simple expressions for first-passage-time densities and for certain avoiding transition probabilities. An application to an M/M/1 queueing system with two finite sequential queueing rooms of equal sizes is finally provided.

First-passage-time densities and avoiding probabilities for birth-and-death processes with symmetric sample paths

For truncated birth-and-death processes with two absorbing or two reflecting boundaries, necessary and sufficient conditions on the transition rates are given such that the transition probabilities satisfy a suitable spatial symmetry relation. This allows one to obtain simple expressions for first-passage-time densities and for certain avoiding transition probabilities. An application to an M/M/1 queueing system with two finite sequential queueing rooms of equal sizes is finally provided.

Statistical approach in search for optimal signal in simple olfactory neuronal models

Several models (concentration detectors and a flux detector) for coding of odor intensity in olfactory sensory neurons are investigated. Behavior of the system is described by different stochastic processes of binding the odorant molecules to the receptors and their activation. Characteristics how well the odorant concentration can be estimated from the knowledge of response, the number of activated neurons, are studied. The approach is based on the Fisher information and analogous measures. These measures of optimality are computed and applied to locate the odorant concentration which is most suitable for coding. The results are compared with the classical deterministic approach which judges the optimal odorant concentration via steepness of the input-output function.

A mnemonic theory of odor perception

The psychological basis of odor quality is poorly understood. For pragmatic reason, descriptions of odor quality generally rely on profiling odors in terms of what odorants they bring to mind. It is argued here that this reliance on profiling reflects a basic property of odor perception, namely that odor quality depends on the implicit memories that an odorant elicits. This is supported by evidence indicating that odor quality as well as one's ability to discriminate odors is affected by experience. Developmental studies and cross-cultural research also point to this conclusion. In this article, these findings are reviewed and a model that attempts to account for them is proposed. Finally, the model's consistency with both neurophysiological and neuropsychological data is examined.

Spiking frequency versus odorant concentration in olfactory receptor neurons

The spiking response of receptor neurons to various odorants has been analyzed at different concentrations. The interspike intervals were measured extracellularly before, during and after the stimulation from the olfactory epithelium of the frog Rana ridibunda. First, a quantitative method was developed to distinguish the spikes in the response from the spontaneous activity. Then, the response intensity, characterized by its median instantaneous frequency, was determined. Finally, based on statistical analyses, this characteristic was related to the concentration and quality of the odorant stimulus. It was found that the olfactory neuron is characterized by a low modulation in frequency and a short range of discriminated intensities. The significance of the results is discussed from both a biological and a modelling point of view.

Perireceptor and receptor events in olfaction. Comparison of concentration and flux detectors: a modeling study

Transduction in chemosensory cells begins with the association of ligand molecules to receptor proteins borne by the cell membrane. The receptor-ligand complexes formed act as signaling compounds that trigger a G-protein cascade. This receptor-ligand interaction, described here by a single-step or double-step reaction, depends on factors controlling the access of the ligand molecules to the cell membrane. Two basic mechanisms can be distinguished: concentration detectors (CD), in which the ligand can freely diffuse to the membrane, and flux detectors (FD), in which it accumulates irreversibly in a distinct perireceptor space where it is chemically deactivated. These two systems, plus their generalization, are investigated and compared. The transient and steady-state numbers of complexes are studied as a function of the external ligand concentration. The biological significance of the results is shown in a well-studied example of FD, the insect sex-pheromone olfactory receptor neuron. How the number of complexes can code for the intensity of stimulation is analyzed using the size, dynamic range and sensitivity of the steady-state responses, and the time needed to reach a predefined level of the transient responses. It is shown that the FD design affords a large increase in sensitivity (a shift of the threshold response towards low concentration) with respect to the CD design, which is paid for by a lesser ability to follow fast changes in stimulus intensity.

Odorant concentration and receptor potential in olfactory sensory neurons

The first step of olfactory transduction consists of the interaction of odorant molecules with receptor proteins. This interaction can be described either as a single-step reaction (binding only) or as a double-step one (binding and activation). The number of bound or activated receptors is analyzed as a function of the external concentration of odorant molecules in two models of the neuron environment. In one model the odorant molecules can freely access and leave the vicinity of receptors, whereas in the other a real perireceptor space, partly isolated from the external environment is considered. The steady state and time variable responses to the stimulus are investigated.

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.

Dynamic information processing in natural and artificial olfactory systems

A new strategy for building artificial gas sensing systems is suggested based on knowledge of the dynamic response mechanism of the olfactory system. Difficulties with the processing of time-dependent inputs by neural networks are discussed.

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.

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 sensitivities 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.

Modeling insect olfactory neuron signaling by a network utilizing disinhibition

A male moth locates a conspecific female by detecting her sexual-pheromone blend. This detection is carried out in the antennal lobe, the first stage of olfactory information processing, where local inhibitory neurons and projection (relay) neurons interact. Antennal-lobe neurons exhibit low-frequency (< 10 Hz) background activity and bursting (> 100 Hz) activity in response to pheromone stimulation. We describe this behavior by a realistic biophysical neuron model. The bursting behavior of the model is the result of both intrinsic cellular properties and network interaction. A slowly activating and inactivating calcium channel provides a depolarizing current for bursting and disinhibition is shown to be a feasible network mechanism for triggering this calcium channel. Small neural networks utilizing disinhibition are presented with local neurons intercalated between receptor and projection neurons. The firing behaviors of projection neurons in response to stimulation by the pheromone blend or its components are in accordance with experimental results. This network architecture offers an alternative view of olfactory processing from the classical architecture derived from vertebrate studies.

Spontaneous activity of first- and second-order neurons in the frog olfactory system

The spontaneous activity of first-order neurons (neuroreceptors of the mucosa) and second-order neurons (mitral cells of the bulb) was recorded extracellularly in the frog olfactory system. To assess the influence of peripheral inputs upon mitral cells, the bulb was either normally connected or partially deafferented. Our first set of findings concern the firing behavior. We found that most neurons generated interspike intervals (ISIs) that were stationary in mean and variance, and were not serially correlated at first and second order. Individual spikes in mitral cells and bursts of spikes in neuroreceptors were found to be generated by a Poisson process. Stochastic modeling suggests that the Poissonian behavior depends on the mean value of the membrane potential at the axon hillock. In these models, the mean potential in mitral cells would be far below the firing threshold and in neuroreceptors it would fluctuate at random between two states, one close to resting potential (between bursts) and the other close to the firing threshold with occasional crossings (within bursts). Secondly, partially deafferented mitral cells had significantly higher activity and lower variance than mitral cells receiving normal afferent input. This effect gives evidence that peripheral inputs influence mitral cells at rest not only through direct excitation but also through indirect inhibition exerted by local neurons. Thus, the unstimulated state of the olfactory bulb would not be qualitatively different from its stimulated state in the sense that both states involve the same types of synaptic interactions. Consequently, understanding the synaptic relationships that take place in the bulb network can benefit from studies of its spontaneous activity.

Stochastic model neuron without resetting of dendritic potential: application to the olfactory system

A two-dimensional neuronal model, in which the membrane potential of the dendrite evolves independently from that at the trigger zone of the axon, is proposed and studied. In classical one-dimensional neuronal models the dendritic and axonal potentials cannot be distinguished, and thus they are reset to resting level after firing of an action potential, whereas in the present model the dendritic potential is not reset. The trigger zone is modelled by a simplified leaky integrator (RC circuit) and the dendritic compartment can be described by any of the classical one-dimensional neuronal models. The new model simulates observed features of the firing dynamics which are not displayed by classical models, namely positive correlation between interspike intervals and endogenous bursting. It gives a more natural account of features already accounted for in previous models, such as the absence of an upper limit for the coefficient of variation of intervals (i.e. irregular firing). It allows the first- and second-order neurons of the olfactory system to be described with the same basic assumptions, which was not the case in one-point models. Nevertheless it keeps the main qualitative properties found previously, such as the existence of three regimens of firing with increasing stimulus concentration and the sigmoid shape of the firing frequency of first-order neurons as a function of the logarithm of stimulus concentration.