Response of electrically coupled spiking neurons: a cellular automaton approach

Experimental data suggest that some classes of spiking neurons in the first layers of sensory systems are electrically coupled via gap junctions or ephaptic interactions. When the electrical coupling is removed, the response function (firing rate {\it vs.} stimulus intensity) of the uncoupled neurons typically shows a decrease in dynamic range and sensitivity. In order to assess the effect of electrical coupling in the sensory periphery, we calculate the response to a Poisson stimulus of a chain of excitable neurons modeled by $n$-state Greenberg-Hastings cellular automata in two approximation levels. The single-site mean field approximation is shown to give poor results, failing to predict the absorbing state of the lattice, while the results for the pair approximation are in good agreement with computer simulations in the whole stimulus range. In particular, the dynamic range is substantially enlarged due to the propagation of excitable waves, which suggests a functional role for lateral electrical coupling. For probabilistic spike propagation the Hill exponent of the response function is $\alpha=1$, while for deterministic spike propagation we obtain $\alpha=1/2$, which is close to the experimental values of the psychophysical Stevens exponents for odor and light intensities. Our calculations are in qualitative agreement with experimental response functions of ganglion cells in the mammalian retina.Comment: 11 pages, 8 figures, to appear in the Phys. Rev.

Efficient Olfactory Coding in the Pheromone Receptor Neuron of a Moth

The concept of coding efficiency holds that sensory neurons are adapted, through both evolutionary and developmental processes, to the statistical characteristics of their natural stimulus. Encouraged by the successful invocation of this principle to predict how neurons encode natural auditory and visual stimuli, we attempted its application to olfactory neurons. The pheromone receptor neuron of the male moth Antheraea polyphemus, for which quantitative properties of both the natural stimulus and the reception processes are available, was selected. We predicted several characteristics that the pheromone plume should possess under the hypothesis that the receptors perform optimally, i.e., transfer as much information on the stimulus per unit time as possible. Our results demonstrate that the statistical characteristics of the predicted stimulus, e.g., the probability distribution function of the stimulus concentration, the spectral density function of the stimulation course, and the intermittency, are in good agreement with those measured experimentally in the field. These results should stimulate further quantitative studies on the evolutionary adaptation of olfactory nervous systems to odorant plumes and on the plume characteristics that are most informative for the ‘sniffer’. Both aspects are relevant to the design of olfactory sensors for odour-tracking robots

A biophysical model of the early olfactory system of honeybees

Experimental measurements often can only provide limited data from an animal’s sensory system. In addition, they exhibit large trial-to-trial and animal-to-animal variability. These limitations pose challenges to building mathematical models intended to make biologically relevant predictions. Here, we present a mathematical model of the early olfactory system of honeybees aiming to overcome these limitations. The model generates olfactory response patterns which conform to the statistics derived from experimental data for a variety of their properties. This allows considering the full dimensionality of the sensory input space as well as avoiding overfitting the underlying data sets. Several known biological mechanisms, including processes of chemical binding and activation of receptors, and spike generation and transmission in the antennal lobe network, are incorporated in the model at a minimal level. It can therefore be used to study how experimentally observed phenomena are shaped by these underlying biophysical processes. We verified that our model can replicate some key experimental findings that were not used when building it. Given appropriate data, our model can be generalized to the early olfactory systems of other insects. It hence provides a possible framework for future numerical and analytical studies of olfactory processing in insects

Computational Model of the Insect Pheromone Transduction Cascade

A biophysical model of receptor potential generation in the male moth olfactory receptor neuron is presented. It takes into account all pre-effector processes—the translocation of pheromone molecules from air to sensillum lymph, their deactivation and interaction with the receptors, and the G-protein and effector enzyme activation—and focuses on the main post-effector processes. These processes involve the production and degradation of second messengers (IP3 and DAG), the opening and closing of a series of ionic channels (IP3-gated Ca2+ channel, DAG-gated cationic channel, Ca2+-gated Cl− channel, and Ca2+- and voltage-gated K+ channel), and Ca2+ extrusion mechanisms. The whole network is regulated by modulators (protein kinase C and Ca2+-calmodulin) that exert feedback inhibition on the effector and channels. The evolution in time of these linked chemical species and currents and the resulting membrane potentials in response to single pulse stimulation of various intensities were simulated. The unknown parameter values were fitted by comparison to the amplitude and temporal characteristics (rising and falling times) of the experimentally measured receptor potential at various pheromone doses. The model obtained captures the main features of the dose–response curves: the wide dynamic range of six decades with the same amplitudes as the experimental data, the short rising time, and the long falling time. It also reproduces the second messenger kinetics. It suggests that the two main types of depolarizing ionic channels play different roles at low and high pheromone concentrations; the DAG-gated cationic channel plays the major role for depolarization at low concentrations, and the Ca2+-gated Cl− channel plays the major role for depolarization at middle and high concentrations. Several testable predictions are proposed, and future developments are discussed

Odour Maps in the Brain of Butterflies with Divergent Host-Plant Preferences

Butterflies are believed to use mainly visual cues when searching for food and oviposition sites despite that their olfactory system is morphologically similar to their nocturnal relatives, the moths. The olfactory ability in butterflies has, however, not been thoroughly investigated. Therefore, we performed the first study of odour representation in the primary olfactory centre, the antennal lobes, of butterflies. Host plant range is highly variable within the butterfly family Nymphalidae, with extreme specialists and wide generalists found even among closely related species. Here we measured odour evoked Ca2+ activity in the antennal lobes of two nymphalid species with diverging host plant preferences, the specialist Aglais urticae and the generalist Polygonia c-album. The butterflies responded with stimulus-specific combinations of activated glomeruli to single plant-related compounds and to extracts of host and non-host plants. In general, responses were similar between the species. However, the specialist A. urticae responded more specifically to its preferred host plant, stinging nettle, than P. c-album. In addition, we found a species-specific difference both in correlation between responses to two common green leaf volatiles and the sensitivity to these compounds. Our results indicate that these butterflies have the ability to detect and to discriminate between different plant-related odorants

Analytical Processing of Binary Mixture Information by Olfactory Bulb Glomeruli

Odors are rarely composed of a single compound, but rather contain a large and complex variety of chemical components. Often, these mixtures are perceived as having unique qualities that can be quite different than the combination of their components. In many cases, a majority of the components of a mixture cannot be individually identified. This synthetic processing of odor information suggests that individual component representations of the mixture must interact somewhere along the olfactory pathway. The anatomical nature of sensory neuron input into segregated glomeruli with the bulb suggests that initial input of odor information into the bulb is analytic. However, a large network of interneurons within the olfactory bulb could allow for mixture interactions via mechanisms such as lateral inhibition. Currently in mammals, it is unclear if postsynaptic mitral/tufted cell glomerular mixture responses reflect the analytical mixture input, or provide the initial basis for synthetic processing with the olfactory system. To address this, olfactory bulb glomerular binary mixture representations were compared to representations of each component using transgenic mice expressing the calcium indicator G-CaMP2 in olfactory bulb mitral/tufted cells. Overall, dorsal surface mixture representations showed little mixture interaction and often appeared as a simple combination of the component representations. Based on this, it is concluded that dorsal surface glomerular mixture representations remain largely analytical with nearly all component information preserved

Spiking Patterns and Their Functional Implications in the Antennal Lobe of the Tobacco Hornworm Manduca sexta

Bursting as well as tonic firing patterns have been described in various sensory systems. In the olfactory system, spontaneous bursts have been observed in neurons distributed across several synaptic levels, from the periphery, to the olfactory bulb (OB) and to the olfactory cortex. Several in vitro studies indicate that spontaneous firing patterns may be viewed as “fingerprints” of different types of neurons that exhibit distinct functions in the OB. It is still not known, however, if and how neuronal burstiness is correlated with the coding of natural olfactory stimuli. We thus conducted an in vivo study to probe this question in the OB equivalent structure of insects, the antennal lobe (AL) of the tobacco hornworm Manduca sexta. We found that in the moth's AL, both projection (output) neurons (PNs) and local interneurons (LNs) are spontaneously active, but PNs tend to produce spike bursts while LNs fire more regularly. In addition, we found that the burstiness of PNs is correlated with the strength of their responses to odor stimulation – the more bursting the stronger their responses to odors. Moreover, the burstiness of PNs was also positively correlated with the spontaneous firing rate of these neurons, and pharmacological reduction of bursting resulted in a decrease of the neurons' responsiveness. These results suggest that neuronal burstiness reflects a physiological state of these neurons that is directly linked to their response characteristics

Differential Interactions of Sex Pheromone and Plant Odour in the Olfactory Pathway of a Male Moth

Most animals rely on olfaction to find sexual partners, food or a habitat. The olfactory system faces the challenge of extracting meaningful information from a noisy odorous environment. In most moth species, males respond to sex pheromone emitted by females in an environment with abundant plant volatiles. Plant odours could either facilitate the localization of females (females calling on host plants), mask the female pheromone or they could be neutral without any effect on the pheromone. Here we studied how mixtures of a behaviourally-attractive floral odour, heptanal, and the sex pheromone are encoded at different levels of the olfactory pathway in males of the noctuid moth Agrotis ipsilon. In addition, we asked how interactions between the two odorants change as a function of the males' mating status. We investigated mixture detection in both the pheromone-specific and in the general odorant pathway. We used a) recordings from individual sensilla to study responses of olfactory receptor neurons, b) in vivo calcium imaging with a bath-applied dye to characterize the global input response in the primary olfactory centre, the antennal lobe and c) intracellular recordings of antennal lobe output neurons, projection neurons, in virgin and newly-mated males. Our results show that heptanal reduces pheromone sensitivity at the peripheral and central olfactory level independently of the mating status. Contrarily, heptanal-responding olfactory receptor neurons are not influenced by pheromone in a mixture, although some post-mating modulation occurs at the input of the sexually isomorphic ordinary glomeruli, where general odours are processed within the antennal lobe. The results are discussed in the context of mate localization