Modelling the signal delivered by a population of first-order neurons in a moth olfactory system

Stimulus duration encoding occurs early in the moth olfactory pathway

Pheromones convey rich ethological information and guide insects' search behavior. Insects navigating in turbulent environments are tasked with the challenge of coding the temporal structure of an odor plume, obliging recognition of the onset and offset of whiffs of odor. The coding mechanisms that shape odor offset recognition remain elusive. We designed a device to deliver sharp pheromone pulses and simultaneously measured the response dynamics from pheromone-tuned olfactory receptor neurons (ORNs) in male moths and Drosophila. We show that concentration-invariant stimulus duration encoding is implemented in moth ORNs by spike frequency adaptation at two time scales. A linear-nonlinear model fully captures the underlying neural computations and offers an insight into their biophysical mechanisms. Drosophila use pheromone cis-vaccenyl acetate (cVA) only for very short distance communication and are not faced with the need to encode the statistics of the cVA plume. Their cVA-sensitive ORNs are indeed unable to encode odor-off events. Expression of moth pheromone receptors in Drosophila cVA-sensitive ORNs indicates that stimulus-offset coding is receptor independent. In moth ORNs, stimulus-offset coding breaks down for short ( < 200 ms) whiffs. This physiological constraint matches the behavioral latency of switching from the upwind surge to crosswind cast flight upon losing contact with the pheromone.

Principles of odor coding in vertebrates and artificial chemosensory systems

The biological olfactory system is the sensory system responsible for the detection of the chemical composition of the environment. Several attempts to mimic biological olfactory systems have led to various artificial olfactory systems using different technical approaches. Here we provide a parallel description of biological olfactory systems and their technical counterparts. We start with a presentation of the input to the systems, the stimuli, and treat the interface between the external world and the environment where receptor neurons or artificial chemosensors reside. We then delineate the functions of receptor neurons and chemosensors as well as their overall I-O relationships. Up to this point, our account of the systems goes along similar lines. The next processing steps differ considerably: while in biology the processing step following the receptor neurons is the "integration" and "processing" of receptor neuron outputs in the olfactory bulb, this step has various realizations in electronic noses. For a long period of time, the signal processing stages beyond the olfactory bulb, i.e., the higher olfactory centers were little studied. Only recently there has been a marked growth of studies tackling the information processing in these centers. In electronic noses, a third stage of processing has virtually never been considered. In this review, we provide an up-to-date overview of the current knowledge of both fields and, for the first time, attempt to tie them together. We hope it will be a breeding ground for better information, communication, and data exchange between very related but so far little connected fields.

Adaptive integrate-and-fire model reproduces the dynamics of olfactory receptor neuron responses in a moth

In order to understand how olfactory stimuli are encoded and processed in the brain, it is important to build a computational model for olfactory receptor neurons (ORNs). Here, we present a simple and reliable mathematical model of a moth ORN generating spikes. The model incorporates a simplified description of the chemical kinetics leading to olfactory receptor activation and action potential generation. We show that an adaptive spike threshold regulated by prior spike history is an effective mechanism for reproducing the typical phasic-tonic time course of ORN responses. Our model reproduces the response dynamics of individual neurons to a fluctuating stimulus that approximates odorant fluctuations in nature. The parameters of the spike threshold are essential for reproducing the response heterogeneity in ORNs. The model provides a valuable tool for efficient simulations of olfactory circuits.

Odorant mixtures elicit less variable and faster responses than pure odorants

In natural environments, odors are typically mixtures of several different chemical compounds. However, the implications of mixtures for odor processing have not been fully investigated. We have extended a standard olfactory receptor model to mixtures and found through its mathematical analysis that odorant-evoked activity patterns are more stable across concentrations and first-spike latencies of receptor neurons are shorter for mixtures than for pure odorants. Shorter first-spike latencies arise from the nonlinear dependence of binding rate on odorant concentration, commonly described by the Hill coefficient, while the more stable activity patterns result from the competition between different ligands for receptor sites. These results are consistent with observations from numerical simulations and physiological recordings in the olfactory system of insects. Our results suggest that mixtures allow faster and more reliable olfactory coding, which could be one of the reasons why animals often use mixtures in chemical signaling.

Efficiency of rate and latency coding with respect to metabolic cost and time

Recent studies on the theoretical performance of latency and rate code in single neurons have revealed that the ultimate accuracy is affected in a nontrivial way by aspects such as the level of spontaneous activity of presynaptic neurons, amount of neuronal noise or the duration of the time window used to determine the firing rate. This study explores how the optimal decoding performance and the corresponding conditions change when the energy expenditure of a neuron in order to spike and maintain the resting membrane potential is accounted for. It is shown that a nonzero amount of spontaneous activity remains essential for both the latency and the rate coding. Moreover, the optimal level of spontaneous activity does not change so much with respect to the intensity of the applied stimulus. Furthermore, the efficiency of the temporal and the rate code converge to an identical finite value if the neuronal activity is observed for an unlimited period of time.

Accuracy of rate coding: When shorter time window and higher spontaneous activity help

It is widely accepted that neuronal firing rates contain a significant amount of information about the stimulus intensity. Nevertheless, theoretical studies on the coding accuracy inferred from the exact spike counting distributions are rare. We present an analysis based on the number of observed spikes assuming the stochastic perfect integrate-and-fire model with a change point, representing the stimulus onset, for which we calculate the corresponding Fisher information to investigate the accuracy of rate coding. We analyze the effect of changing the duration of the time window and the influence of several parameters of the model, in particular the level of the presynaptic spontaneous activity and the level of random fluctuation of the membrane potential, which can be interpreted as noise of the system. The results show that the Fisher information is nonmonotonic with respect to the length of the observation period. This counterintuitive result is caused by the discrete nature of the count of spikes. We observe also that the signal can be enhanced by noise, since the Fisher information is nonmonotonic with respect to the level of spontaneous activity and, in some cases, also with respect to the level of fluctuation of the membrane potential.

Presynaptic Spontaneous Activity Enhances the Accuracy of Latency Coding

The time to the first spike after stimulus onset typically varies with the stimulation intensity. Experimental evidence suggests that neural systems use such response latency to encode information about the stimulus. We investigate the decoding accuracy of the latency code in relation to the level of noise in the form of presynaptic spontaneous activity. Paradoxically, the optimal performance is achieved at a nonzero level of noise and suprathreshold stimulus intensities. We argue that this phenomenon results from the influence of the spontaneous activity on the stabilization of the membrane potential in the absence of stimulation. The reported decoding accuracy improvement represents a novel manifestation of the noise-aided signal enhancement.

Efficient information transfer by Poisson neurons

Recently, it has been suggested that certain neurons with Poissonian spiking statistics may communicate by discontinuously switching between two levels of firing intensity. Such a situation resembles in many ways the optimal information transmission protocol for the continuous-time Poisson channel known from information theory. In this contribution we employ the classical information-theoretic results to analyze the efficiency of such a transmission from different perspectives, emphasising the neurobiological viewpoint. We address both the ultimate limits, in terms of the information capacity under metabolic cost constraints, and the achievable bounds on performance at rates below capacity with fixed decoding error probability. In doing so we discuss optimal values of experimentally measurable quantities that can be compared with the actual neuronal recordings in a future effort.

Firing and intrinsic properties of antennal lobe neurons in the Noctuid moth Agrotis ipsilon

The antennal lobe (AL) of the Noctuid moth Agrotis ipsilon has emerged as an excellent model for studying olfactory processing and its plasticity in the central nervous system. Odor-evoked responses of AL neurons and input-to-output transformations involved in pheromone processing are well characterized in this species. However, the intrinsic electrical properties responsible of the firing of AL neurons are poorly known. To this end, patch-clamp recordings in current- and voltage-clamp mode from neurons located in the two main clusters of cell bodies in the ALs were combined with intracellular staining on A. ipsilon males. Staining indicated that the lateral cluster (LC) is composed of 85% of local neurons (LNs) and 15% of projection neurons (PNs). The medial cluster (MC) contains only PNs. Action potentials were readily recorded from the soma in LNs and PNs located in the LC but not from PNs in the MC where recordings showed small or no action potentials. In the LC, the spontaneous activity of about 20% of the LNs presented irregular bursts while being more regular in PNs. We also identified a small population of LNs lacking voltage-gated Na(+) currents and generating spikelets. We focused on the firing properties of LNs since in about 60% of LNs, but not in PNs, action potentials were followed by depolarizing afterpotentials (DAPs). These DAPs could generate a second action potential, so that the activity was composed of action potential doublets. DAPs depended on voltage, Ca(2+)-channels and possibly on Ca(2+)-activated non-specific cationic channels. During steady state current injection, DAPs occurred after each action potential and did not require high-frequency firing. The amplitude of DAPs increased when the interspike interval was small, typically within bursts, likely arising from a Ca(2+) build up. DAPs were more often found in bursting than in non-bursting LNs but do not support bursting activity. DAPs and spike doublets also occurred during odor-evoked activity suggesting that they can mediate olfactory integration in the AL.

Heterogeneity and convergence of olfactory first-order neurons account for the high speed and sensitivity of second-order neurons

In the olfactory system of male moths, a specialized subset of neurons detects and processes the main component of the sex pheromone emitted by females. It is composed of several thousand first-order olfactory receptor neurons (ORNs), all expressing the same pheromone receptor, that contact synaptically a few tens of second-order projection neurons (PNs) within a single restricted brain area. The functional simplicity of this system makes it a favorable model for studying the factors that contribute to its exquisite sensitivity and speed. Sensory information—primarily the identity and intensity of the stimulus—is encoded as the firing rate of the action potentials, and possibly as the latency of the neuron response. We found that over all their dynamic range, PNs respond with a shorter latency and a higher firing rate than most ORNs. Modelling showed that the increased sensitivity of PNs can be explained by the ORN-to-PN convergent architecture alone, whereas their faster response also requires cell-to-cell heterogeneity of the ORN population. So, far from being detrimental to signal detection, the ORN heterogeneity is exploited by PNs, and results in two different schemes of population coding based either on the response of a few extreme neurons (latency) or on the average response of many (firing rate). Moreover, ORN-to-PN transformations are linear for latency and nonlinear for firing rate, suggesting that latency could be involved in concentration-invariant coding of the pheromone blend and that sensitivity at low concentrations is achieved at the expense of precise encoding at high concentrations.

Understanding how sensory signals are optimally encoded by nervous systems is of strong interest to neuroscientists, and also to engineers as it may lead to more efficient artificial detection systems. This is particularly relevant to olfaction, because the current electronic noses are far outperformed by their biological counterparts in terms of speed and sensitivity. We here use the moth sex pheromone processing system as a relatively simple model to understand early olfactory coding. We found that performance increases when olfactory information passes from first- to second-order neurons. Second-order neurons respond on average with shorter latency and higher sensitivity than first-order neurons. We show that two critical factors, convergent architecture and neuronal heterogeneity, are needed to account for increased performance.

A spiking neural network model of self-organized pattern recognition in the early mammalian olfactory system

Olfactory sensory information passes through several processing stages before an odor percept emerges. The question how the olfactory system learns to create odor representations linking those different levels and how it learns to connect and discriminate between them is largely unresolved. We present a large-scale network model with single and multi-compartmental Hodgkin-Huxley type model neurons representing olfactory receptor neurons (ORNs) in the epithelium, periglomerular cells, mitral/tufted cells and granule cells in the olfactory bulb (OB), and three types of cortical cells in the piriform cortex (PC). Odor patterns are calculated based on affinities between ORNs and odor stimuli derived from physico-chemical descriptors of behaviorally relevant real-world odorants. The properties of ORNs were tuned to show saturated response curves with increasing concentration as seen in experiments. On the level of the OB we explored the possibility of using a fuzzy concentration interval code, which was implemented through dendro-dendritic inhibition leading to winner-take-all like dynamics between mitral/tufted cells belonging to the same glomerulus. The connectivity from mitral/tufted cells to PC neurons was self-organized from a mutual information measure and by using a competitive Hebbian-Bayesian learning algorithm based on the response patterns of mitral/tufted cells to different odors yielding a distributed feed-forward projection to the PC. The PC was implemented as a modular attractor network with a recurrent connectivity that was likewise organized through Hebbian-Bayesian learning. We demonstrate the functionality of the model in a one-sniff-learning and recognition task on a set of 50 odorants. Furthermore, we study its robustness against noise on the receptor level and its ability to perform concentration invariant odor recognition. Moreover, we investigate the pattern completion capabilities of the system and rivalry dynamics for odor mixtures.

The effect of interspike interval statistics on the information gain under the rate coding hypothesis

The question, how much information can be theoretically gained from variable neuronal firing rate with respect to constant average firing rate is investigated. We employ the statistical concept of information based on the Kullback-Leibler divergence, and assume rate-modulated renewal processes as a model of spike trains. We show that if the firing rate variation is sufficiently small and slow (with respect to the mean interspike interval), the information gain can be expressed by the Fisher information. Furthermore, under certain assumptions, the smallest possible information gain is provided by gamma-distributed interspike intervals. The methodology is illustrated and discussed on several different statistical models of neuronal activity.

Metabolic cost of neuronal information in an empirical stimulus-response model

The limits on maximum information that can be transferred by single neurons may help us to understand how sensory and other information is being processed in the brain. According to the efficient-coding hypothesis (Barlow, Sensory Comunication, MIT press, Cambridge, 1961), neurons are adapted to the statistical properties of the signals to which they are exposed. In this paper we employ methods of information theory to calculate, both exactly (numerically) and approximately, the ultimate limits on reliable information transmission for an empirical neuronal model. We couple information transfer with the metabolic cost of neuronal activity and determine the optimal information-to-metabolic cost ratios. We find that the optimal input distribution is discrete with only six points of support, both with and without a metabolic constraint. However, we also find that many different input distributions achieve mutual information close to capacity, which implies that the precise structure of the capacity-achieving input is of lesser importance than the value of capacity.

Population coding is essential for rapid information processing in the moth antennal lobe

We investigated how odorant information is transmitted by neurons in the moth antennal lobe (AL). The neurons were repeatedly stimulated by three different odorants and their activity was intracellularly recorded. First, the response properties of single neurons were analyzed. The neurons exhibited highly reliable responses to the odorants and 43% of AL neurons responded to two or three odorants. The population distribution of firing rates in response to odorant stimulation was relatively broad in moth AL neurons, which is consistent across insects. Second, we attempted to decode the odorant identity from the activity of the recorded neurons using the maximum likelihood method. The decoding performance rapidly improves with increasing the number of neurons. Notably, an increase in the size of neural population results in faster transfer of information and increased the duration to retain odorant information. In conclusion, the AL neurons encode odorant information reliably and the population coding can transmit odorant information to olfactory centers. Population coding allows AL to encode and transmit olfactory information faster than the discrimination latency demonstrated in behavioral experiments. This article is part of a Special Issue entitled Neural Coding 2012.

Information capacity and its approximations under metabolic cost in a simple homogeneous population of neurons

We calculate and analyze the information capacity-achieving conditions and their approximations in a simple neuronal system. The input-output properties of individual neurons are described by an empirical stimulus-response relationship and the metabolic cost of neuronal activity is taken into account. The exact (numerical) results are compared with a popular "low-noise" approximation method which employs the concepts of parameter estimation theory. We show, that the approximate method gives reliable results only in the case of significantly low response variability. By employing specialized numerical procedures we demonstrate, that optimal information transfer can be near-achieved by a number of different input distributions. It implies that the precise structure of the capacity-achieving input is of lesser importance than the value of capacity. Finally, we illustrate on an example that an innocuously looking stimulus-response relationship may lead to a problematic interpretation of the obtained Fisher information values.

Identification of noisy response latency

In many physical systems there is a time delay before an applied input (stimulation) has an impact on the output (response), and the quantification of this delay is of paramount interest. If the response can only be observed on top of an indistinguishable background signal, the estimation can be highly unreliable, unless the background signal is accounted for in the analysis. In fact, if the background signal is ignored, however small it is compared to the response and however large the delay is, the estimate of the time delay will go to zero for any reasonable estimator when increasing the number of observations. Here we propose a unified concept of response latency identification in event data corrupted by a background signal. It is done in the context of information transfer within a neural system, more specifically on spike trains from single neurons. The estimators are compared on simulated data and the most suitable for specific situations are recommended.

Glomerular latency coding in artificial olfaction

Sensory perception results from the way sensory information is subsequently transformed in the brain. Olfaction is a typical example in which odor representations undergo considerable changes as they pass from olfactory receptor neurons (ORNs) to second-order neurons. First, many ORNs expressing the same receptor protein yet presenting heterogeneous dose–response properties converge onto individually identifiable glomeruli. Second, onset latency of glomerular activation is believed to play a role in encoding odor quality and quantity in the context of fast information processing. Taking inspiration from the olfactory pathway, we designed a simple yet robust glomerular latency coding scheme for processing gas sensor data. The proposed bio-inspired approach was evaluated using an in-house SnO₂ sensor array. Glomerular convergence was achieved by noting the possible analogy between receptor protein expressed in ORNs and metal catalyst used across the fabricated gas sensor array. Ion implantation was another technique used to account both for sensor heterogeneity and enhanced sensitivity. The response of the gas sensor array was mapped into glomerular latency patterns, whose rank order is concentration-invariant. Gas recognition was achieved by simply looking for a “match” within a library of spatio-temporal spike fingerprints. Because of its simplicity, this approach enables the integration of sensing and processing onto a single-chip.