Uncertainty in physiology and physics

It was hypothesized in an earlier work that sensory perception can occur only when the perceiving system is uncertain about the nature of the event being perceived. In the absence of any uncertainty, perception will not take place. The response of the sensory afferent neuron (impulse transmission rate) was calculated using Shannon's measure of uncertainty or entropy. It will now be shown that when the event being perceived is the position and momentum of a particle, Shannon's measure of uncertainty leads to the Heisenberg Uncertainty relationship.     

Physical Entropy And The Senses

With reference to two specific modalities of sensation, the taste of saltiness of chloride salts, and the loudness of steady tones, it is shown that the laws of sensation (logarithmic and power laws) are expressions of the entropy per mole of the stimulus. That is, the laws of sensation are linear functions of molar entropy. In partial verification of this hypothesis, we are able to derive an approximate value for the gas constant, a fundamental physical constant, directly from psychophysical measurements. The significance of our observation lies in the linking of the phenomenon of “sensation” directly to a physical measure. It suggests that if the laws of physics are universal, the laws of sensation and perception are similarly universal. It also connects the sensation of a simple, steady physical signal with the molecular structure of the signal: the greater the number of microstates or complexions of the stimulus signal, the greater the magnitude of the sensation (saltiness or loudness). The hypothesis is currently tested on two sensory modalities.     

White-noise analysis of nonlinear behavior in an insect sensory neuron: Kernel and cascade approaches

A functional expansion was used to model the relationship between a Gaussian white noise stimulus current and the resulting action potential output in the single sensory neuron of the cockroach femoral tactile spine. A new precise procedure was used to measure the kernels of the functional expansion. Very similar kernel estimates were obtained from separate sections of the data produced by the same neuron with the same input noise power level, although some small time-varying effects were detectable in moving through the data. Similar kernel estimates were measured using different input noise power levels for a given cell, or when comparing different cells under similar stimulus conditions. The kernels were used to identify a model for sensory encoding in the neuron, comprising a cascade of dynamic linear, static nonlinear, and dynamic linear elements. Only a single slice of the estimated experimental second-order kernel was used in identifying the cascade model. However, the complete second-order kernel of the cascade model closely resembled the estimated experimental kernel. Moreover, the model could closely predict the experimental action potential train obtained with novel white noise inputs.     

A template theory to relate visual processing to digital circuitry

Simple stimulus patterns, in this case visual, are represented by spatiotemporal Boolean functions that can be summarized in a 4 x 4 look-up table of 16 templates behind each sensory neuron. These groups of templates correspond to groups of neurons in columns behind each receptor. They abstract specific combinations of input in simple combinations and include two successive states in time. A template is like a neuron field at threshold, and responds as the field is convolved with the stimulus pattern. The same structure can be repeated in successive layers to make progressive categorization and to reject inappropriate combinations. At any level, the templates act in groups, so providing a very large number of combinations that can represent more complex stimulus patterns at deeper levels.     

Interactions of mechanical stimuli and sex pheromone information in antennal lobe neurons of a male moth,<Emphasis Type="Italic"> Spodoptera littoralis</Emphasis>

Male moths respond to sex pheromone sources with up-wind flight behaviour. Localization of the odour source requires not only detection of the olfactory stimulus, but also other sensory input regarding, e.g. visual and mechanical stimuli. Thus, integration of different types of sensory input is necessary. It is, however, not known where in the central nervous system the integration of information regarding different sensory modalities takes place. Using intracellular recording and staining techniques, we investigated neurons in the antennal lobe of Spodoptera littoralis, during stimulation with a mechanical stimulus and a sex pheromone. Fifteen percent of all the neurons investigated responded to the mechanical stimulus and the majority of these neurons showed altered responses if the olfactory stimulus was added. A receptor neuron responding only to the wind stimulus was found to arborise in the antennal lobe. Most projection neurons responded with an enhanced action potential frequency to the combined stimulus. In local interneurons, enhancement, depression, or no change of the responses to the wind stimulus was found when the olfactory stimulus was added. The results suggest that neurons present in the antennal lobe integrate mechanosensory and olfactory input, possibly assisting the moths to orient during up-wind flight towards an odour source.     

Signaling by sensory receptors

Sensory systems detect small molecules, mechanical perturbations, or radiation via the activation of receptor proteins and downstream signaling cascades in specialized sensory cells. In vertebrates, the two principal categories of sensory receptors are ion channels, which mediate mechanosensation, thermosensation, and acid and salt taste; and G-protein-coupled receptors (GPCRs), which mediate vision, olfaction, and sweet, bitter, and umami tastes. GPCR-based signaling in rods and cones illustrates the fundamental principles of rapid activation and inactivation, signal amplification, and gain control. Channel-based sensory systems illustrate the integration of diverse modulatory signals at the receptor, as seen in the thermosensory/pain system, and the rapid response kinetics that are possible with direct mechanical gating of a channel. Comparisons of sensory receptor gene sequences reveal numerous examples in which gene duplication and sequence divergence have created novel sensory specificities. This is the evolutionary basis for the observed diversity in temperature- and ligand-dependent gating among thermosensory channels, spectral tuning among visual pigments, and odorant binding among olfactory receptors. The coding of complex external stimuli by a limited number of sensory receptor types has led to the evolution of modality-specific and species-specific patterns of retention or loss of sensory information, a filtering operation that selectively emphasizes features in the stimulus that enhance survival in a particular ecological niche. The many specialized anatomic structures, such as the eye and ear, that house primary sensory neurons further enhance the detection of relevant stimuli.     

Capability of intensity discrimination in multiple receptor model of insect taste

A simple model in which one CNS taste neuron integrates inputsfrom multiple peripheral receptors is introduced in order toinvestigate the mechanism of acute intensity taste discriminationin flies. Information theory is applied to evaluate the acuteability of discrimination provided by the model. The presentanalysis is carried out under two statistical conditions concerningthe uncertainty of receptor response. Based on experimentaldata obtained by Smith et al. (1983), we estimate the mutualinformation entropy of the model. The numerical results obtainedhere indicate that the uncertainty observed in a single receptorresponse is dramatically reduced by the central integration.Furthermore, each of the eleven stimulus intensity levels experimentallyapplied by Smith et al., can be discriminated completely byintegrating the responses of the realistic number of receptors(33–212). Such a great improvement of the differentialsensitivity in the model resolves the discrepancy between thelow differential sensitivity of single sugar receptors (Smithet al., 1983) and the high sensitivity obtained in the feedingbehavior (Dethier and Rhoades, 1954; Dethier and Bowdan, 1984)of the blowfly.     

Stimulus-dependent Maximum Entropy Models of Neural Population Codes

Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. For large populations, direct sampling of these distributions is impossible, and so we must rely on constructing appropriate models. We show here that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. We introduce the stimulus-dependent maximum entropy (SDME) model—a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. We find that the SDME model gives a more accurate account of single cell responses and in particular significantly outperforms uncoupled models in reproducing the distributions of population codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like average surprise and information transmission in a neural population.     

Heterogeneous Sensory Innervation and Extensive Intrabulbar Connections of Olfactory Necklace Glomeruli

The mammalian nose employs several olfactory subsystems to recognize and transduce diverse chemosensory stimuli. These subsystems differ in their anatomical position within the nasal cavity, their targets in the olfactory forebrain, and the transduction mechanisms they employ. Here we report that they can also differ in the strategies they use for stimulus coding. Necklace glomeruli are the sole main olfactory bulb (MOB) targets of an olfactory sensory neuron (OSN) subpopulation distinguished by its expression of the receptor guanylyl cyclase GC-D and the phosphodiesterase PDE2, and by its chemosensitivity to the natriuretic peptides uroguanylin and guanylin and the gas CO₂. In stark contrast to the homogeneous sensory innervation of canonical MOB glomeruli from OSNs expressing the same odorant receptor (OR), we find that each necklace glomerulus of the mouse receives heterogeneous innervation from at least two distinct sensory neuron populations: one expressing GC-D and PDE2, the other expressing olfactory marker protein. In the main olfactory system it is thought that odor identity is encoded by a combinatorial strategy and represented in the MOB by a pattern of glomerular activation. This combinatorial coding scheme requires functionally homogeneous sensory inputs to individual glomeruli by OSNs expressing the same OR and displaying uniform stimulus selectivity; thus, activity in each glomerulus reflects the stimulation of a single OSN type. The heterogeneous sensory innervation of individual necklace glomeruli by multiple, functionally distinct, OSN subtypes precludes a similar combinatorial coding strategy in this olfactory subsystem.     

To Burst or Not to Burst?

It is well known that some neurons tend to fire packets of action potentials followed by periods of quiescence (bursts) while others within the same stage of sensory processing fire in a tonic manner. However, the respective computational advantages of bursting and tonic neurons for encoding time varying signals largely remain a mystery. Weakly electric fish use cutaneous electroreceptors to convey information about sensory stimuli and it has been shown that some electroreceptors exhibit bursting dynamics while others do not. In this study, we compare the neural coding capabilities of tonically firing and bursting electroreceptor model neurons using information theoretic measures. We find that both bursting and tonically firing model neurons efficiently transmit information about the stimulus. However, the decoding mechanisms that must be used for each differ greatly: a non-linear decoder would be required to extract all the available information transmitted by the bursting model neuron whereas a linear one might suffice for the tonically firing model neuron. Further investigations using stimulus reconstruction techniques reveal that, unlike the tonically firing model neuron, the bursting model neuron does not encode the detailed time course of the stimulus. A novel measure of feature detection reveals that the bursting neuron signals certain stimulus features. Finally, we show that feature extraction and stimulus estimation are mutually exclusive computations occurring in bursting and tonically firing model neurons, respectively. Our results therefore suggest that stimulus estimation and feature extraction might be parallel computations in certain sensory systems rather than being sequential as has been previously proposed.     

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.     

Simple molecular model for sensing and adaptation based on receptor modification with application to bacterial chemotaxis

A series of simple models to explain adaptation in a sensory system based on reversible covalent modification is developed. The models are applied to the reversible methylation of chemoreceptors in bacteria and by analogy to other sensory transduction systems. The receptor modification system exhibits sensing and adaptation, i.e. raising the stimulus to a new level generates a transient response followed by a return to prestimulus behavior. By means of an analytical solution of the kinetic equation that governs the evolution of the receptor system. an exact expression is obtained for the time required for adaptation. The results account for the most conspicuous properties of the bacterial sensory system; namely, the response times in relation to stimulus changes, the proportionality of receptor modification to receptor occupancy, and the additivity of response times. The analysis indicates how these properties depend upon the parameters of the system, e.g. the rates of covalent modification and demodification, the accuracy of the detector, and the molecular nature of the response regulator. The theory developed for analysis of the bacterial system revealed properties that will be applicable to any system processing sensory information.     

A theory of taste stimulation

The treatment in this paper of available quantitative data on the response of taste receptors to sodium salt stimulation clearly indicates that the ions of the chemical stimulus are loosely bound to some substance of the taste receptor. This can be thought of as an initial reaction which ultimately leads to stimulation of the receptor and an eventual depolarization of the associated sensory neuron. The speed of the total reaction suggests that the receptor substance is located on or near the surface of the receptor. The recently proposed (7) enzymatic reactions for chemoreceptors do not appear plausible for sodium salt stimulation of the taste receptors of the rat.     

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.     

Dorsal longitudinal stretch receptor of Drosophila melanogaster larva - fine structure and maturation

Insects possess two types of sensory neurons: ciliated type I sensory neurons that innervate external sensory organs and chordotonal organs, and type II sensory neurons that form a subepidermal plexus or innervate stretch receptors. Among stretch receptors, a dorsel longitudinal stretch receptor is highly conserved in insects, being found in all insect orders investigated. Here we describe the topology and anatomical structure of this receptor in the fruit fly embryo and larva using transmission electron microscopy and single cell staining for fluorescence microscopy. The receptor is composed of the dorsal bipolar dendrite neuron, which arises from an archetypal cell lineage, its sister glial cell and the peripheral glial cell accompanying the nerve. The neuron is situated among the muscles in the dorsal body wall on the intersegmental nerve. Its two dendrites stretch the length of the segment to the segmental folds. The neuron is wrapped by both glial cells and surrounded by a common basal lamina, which fans out at the dendritic tips to attach them to the epidermal cells at the segmental borders.     

Receptive field properties of neurons in the electrosensory lateral line lobe of the weakly electric fish, <Emphasis Type="Italic">Gnathonemus petersii</Emphasis>

The receptive field of a sensory neuron is known as that region in sensory space where a stimulus will alter the response of the neuron. We determined the spatial dimensions and the shape of receptive fields of electrosensitive neurons in the medial zone of the electrosensory lateral line lobe of the African weakly electric fish, Gnathonemus petersii, by using single cell recordings. The medial zone receives input from sensory cells which encode the stimulus amplitude. We analysed the receptive fields of 71 neurons. The size and shape of the receptive fields were determined as a function of spike rate and first spike latency and showed differences for the two analysis methods used. Spatial diameters ranged from 2 to 36 mm (spike rate) and from 2.45 to 14.12 mm (first spike latency). Some of the receptive fields were simple consisting only of one uniform centre, whereas most receptive fields showed a complex and antagonistic centre-surround organisation. Several units had a very complex structure with multiple centres and surrounding-areas. While receptive field size did not correlate with peripheral receptor location, the complexity of the receptive fields increased from rostral to caudal along the fish's body.     

On intensity characteristics of sensory receptors: A generalized function

An attempt is made at finding general mathematical expressions for intensity characteristics of sensory receptors. Analysis of responses of an auditory nerve unit and of a Pacinian corpuscle lead to the derivation of two simple equations that describe the relationships between the stimulus energy, or a variable proportional to it, and either the average receptor potential or the average firing rate of receptor units. The transformation between the two equations reflects the relationship between the two response stages. The equations imply that the receptors first linearly integrate an energy-proportional variable, then perform a power-function transformation on the result. An exponential function is derived for the response saturation at sufficiently high stimulus levels. The equations generate numerical values in close agreement with empirical intensity characteristics of auditory and other mechanoreceptors, of photoreceptors, and of chemoreceptors. Usually, a power of approximately 0.5 is followed, but gustatory receptors appear to obey a power of 1.0.     

Why do olfactory neurons have unspecific receptive fields?

Biological olfactory neurons are deployed as a population, most responding to a large variety of chemical compounds, that is, they possess unspecific receptive fields. The question of whether this unspecificity results from some physical constraint placed upon chemical transduction, or on the other hand, is beneficial to system performance is unclear. In this paper we employ the notion of Fisher information to address this question by quantifying how both the distribution and the tunings of the receptive fields within olfactory receptor populations affect the optimal estimation performance of the system. Our results show that overlapping sensory neuron tunings that respond to common chemical compounds have better estimation performance than perfectly specific tunings. Our results suggest two phenomena that might represent general principles of organization within biological sensory systems responding to multiple stimuli: maximization of the diversity of tunings and homogeneity in the distribution of these different receptive fields across the stimulus space (independent of the statistics of the input stimuli). Our model predicts that a local randomized mechanism controlling receptor specificities generates optimal multidimensional stimulus estimation, for which there is some experimental evidence from the biology.