Representation of sensory information in the cricket cercal sensory system. II. Information theoretic calculation of system accuracy and optimal tuning-curve widths of four primary interneurons

A micromachined silicon multielectrode for multiunit recording

A 16-channel multielectrode was used to record propagating action potentials from multiple units in the ventral nerve cord of the cricket Gryllus bimaculatus. The multielectrode was fabricated using photolithographic and bulk silicon etching techniques. The fabrication differs from standard methods in its use of deep reactive ion etching (DRIE) to form the bulk electrode structure. This technique enables the fabrication of relatively thick (>100 microm), rigid structures whose top surface can have any form of thin film electronics. The multielectrode tested in this paper consists of 16 narrow silicon bridges, 150 microm wide and 350 microm tall, spaced evenly over a centimeter, with passive rectangular gold recording sites on the top surface. The nerve cord was placed perpendicularly across the bridges. In this geometry, the nerve spans a 350 microm deep, 450 microm wide trench between each recording site, permitting adequate isolation of recording sites from each other and a platinum ground plane. Spike templates for eight neurons were formed using principle component analysis and clustering of the concatenated multichannel waveforms. Clean templates were generated from a 40 s recording of stimulus evoked activity. Conduction velocities ranged from 2.59+/-0.05 to 4.99+/-0.12 m/s. Two limitations of extracellular electrode arrays are the resolution of overlapping spikes and relation of discriminated units to known anatomy. The high density, precise positioning, and controlled impedance of recording sites achievable in microfabricated devices such as this one will aid in overcoming these limitations. The rigid devices fabricated using this process offer stable positioning of recording sites over relatively large distances (several millimeters) and are suitable for clamping or squeezing of nerve cords.

Firing sequence storage using inhibitory synapses in networks of pulsatil nonhomogeneous integrate-and-fire neural oscillators

We discuss a nonhomogeneous population of pulsatil integrate-and-fire neural oscillators, coupled through purely inhibitory synapses. For instantaneous communication, we provide a strategy to generate synaptic couplings to obtain simple periodic and stable firing patterns. We provide restrictions under which each stored firing pattern is a unique attractor for the population dynamics. In the case of Peskin's leaky integrator we show results obtained from numerical simulations.

A communication channel model for information transmission in the blowfly photoreceptor

Biological photoreceptors transduce and communicate information about visual stimuli to other neurons through a series of signal transformations among physical states such as concentration of a chemical species, current, or the number of open ion channels. We present a communication channel model to quantify the transmission and degradation of visual information in the blowfly photoreceptor cell. The model is a cascade of linear transfer functions and noise sources that are derived from fundamental principles whenever possible, and whose parameters are estimated from physiological data. We employ the model to calculate the information capacity of blowfly phototransduction; our results compare favorably with estimates of the capacity derived from experimental measurements by de Ruyter van Steveninck and Laughlin (Nature 379 (1996) 642-645) and Juusola (J. Gen. Physiol. 104 (1994) 593-621). The model predicts that photon shot noise and ion channel noise are the dominant noise sources that limits information transmission in the blowfly photoreceptor.

Statistical and information properties of head direction cells

The human channel capacity for identifying sensory stimuli is compared with channel capacities based on neurophysiological findings. Studies have shown that cells in the postsubiculum (PoS) and the anterior dorsal thalamus (ADN) of the rat discharge as a function of the animal's head direction in the horizontal plane. We compute the statistical properties of the firing rates of head direction (HD) cells and the potential amount of information transmitted by these cells according to two theoretical models. The ceU response model for single cells indicates that information transmitted is much less than 0.5 bits. The population response model developed for cell ensembles generates values in the range of 1-3.2 bits, suggesting that a cell population can distinguish between two and nine head directions, depending on the value used for the standard deviation of directions over which a cell fires. These values are similar to those found in human psychophysical studies of the channel capacity for unidimensional sensory attributes.

Optimal firing rate estimation

We define a measure for evaluating the quality of a predictive model of the behavior of a spiking neuron. This measure, information gain per spike (Is), indicates how much more information is provided by the model than if the prediction were made by specifying the neuron's average firing rate over the same time period. We apply a maximum Is criterion to optimize the performance of Gaussian smoothing filters for estimating neural firing rates. With data from bullfrog vestibular semicircular canal neurons and data from simulated integrate-and-fire neurons, the optimal bandwidth for firing rate estimation is typically similar to the average firing rate. Precise timing and average rate models are limiting cases that perform poorly. We estimate that bullfrog semicircular canal sensory neurons transmit in the order of 1 bit of stimulus-related information per spike.

Identified nerve cells and insect behavior

Studies of insect identified neurons over the past 25 years have provided some of the very best data on sensorimotor integration; tracing information flow from sensory to motor networks. General principles have emerged that have increased the sophistication with which we now understand both sensory processing and motor control. Two overarching themes have emerged from studies of identified sensory interneurons. First, within a species, there are profound differences in neuronal organization associated with both the sex and the social experience of the individual. Second, single neurons exhibit some surprisingly rich examples of computational sophistication in terms of (a) temporal dynamics (coding superimposed upon circadian and shorter-term rhythms), and also (b) what Kenneth Roeder called "neural parsimony": that optimal information can be encoded, and complex acts of sensorimotor coordination can be mediated, by small ensembles of cells. Insect motor systems have proven to be relatively complex, and so studies of their organization typically have not yielded completely defined circuits as are known from some other invertebrates. However, several important findings have emerged. Analysis of neuronal oscillators for rhythmic behavior have delineated a profound influence of sensory feedback on interneuronal circuits: they are not only modulated by feedback, but may be substantially reconfigured. Additionally, insect motor circuits provide potent examples of neuronal restructuring during an organism's lifetime, as well as insights on how circuits have been modified across evolutionary time. Several areas where future advances seem likely to occur include: molecular genetic analyses, neuroecological syntheses, and neuroinformatics--the use of digital resources to organize databases with information on identified nerve cells and behavior.

Information theoretic analysis of pulmonary stretch receptor spike trains

Primary afferent neurons transduce physical, continuous stimuli into discrete spike trains. Investigators have long been interested in interpreting the meaning of the number or pattern of action potentials in attempts to decode the spike train back into stimulus parameters. Pulmonary stretch receptors (PSRs) are visceral mechanoreceptors that respond to deformation of the lungs and pulmonary tree. They provide the brain stem with feedback that is used by cardiorespiratory control circuits. In anesthetized, paralyzed, artificially ventilated rabbits, we recorded the action potential trains of individual PSRs while continuously manipulating ventilator rate and volume. We describe an information theoretic-based analytical method for evaluating continuous stimulus and spike train data that is of general applicability to any continuous, dynamic system. After adjusting spike times for conduction velocity, we used a sliding window to discretize the stimulus (average tracheal pressure) and response (number of spikes), and constructed co-occurrence matrices. We systematically varied the number of categories into which the stimulus and response were evenly divided at 26 different sliding window widths (5, 10, 20, 30,..., 230, 240, 250 ms). Using the probability distributions defined by the co-occurrence matrices, we estimated associated stimulus, response, joint, and conditional entropies, from which we calculated information transmitted as a fraction of the maximum possible, as well as encoding and decoding efficiencies. We found that, in general, information increases rapidly as the sliding window width increases from 5 to approximately 50 ms and then saturates as observation time increases. In addition, the information measures suggest that individual PSRs transmit more "when" than "what" type of information about the stimulus, based on the finding that the maximum information at a given window width was obtained when the stimulus was divided into just a few (usually <6) categories. Our results indicate that PSRs provide quite reliable information about tracheal pressure, with each PSR conveying about 31% of the maximum possible information about the dynamic stimulus, given our analytical parameters. When the stimulus and response are divided into more categories, slightly less information is transmitted, and this quantity also saturates as a function of observation time. We consider and discuss the importance of information contained in window widths on the time scales of an excitatory postsynaptic potential and Hering-Breuer reflex central delay.

Wind direction coding in the cockroach escape response: winner does not take all

Cockroaches respond to the approach of a predator by turning away and then running. Three bilateral pairs of giant interneurons are involved in determining the direction of the sensory stimulus and setting the turn direction. Each of these six interneurons has a different directional response to wind stimuli. We have tested whether these six cells use a winner-take-all mechanism to perform this directional determination: that is, each of these cells suppressing the motor response that each of the other cells promotes. Such a mechanism is found in similar behaviors of some other animals. By adding spikes to identified giant interneurons through intracellular stimulation during the sensory-induced behavior and analyzing the resulting directional leg movements, we find that a winner-take-all is not used in this system. Rather, directional determination appears to be based on collaborative calculation of direction by the giant interneurons as a group.

Population vector coding by the giant interneurons of the cockroach

We tested two alternative models of integration among the cockroach giant interneurons (GIs) for determining the directions of wind-evoked escape turns. One model, called steering wheel, pits contralateral GIs against one another; the other, called population vector model, involves a vector computation among the GIs. In testing each model theoretically, the population vector was found to account far better for the actual behavior. Both models could account for the results of previous behavioral-physiological experiments in which spikes had been added to the right GI3 together with wind stimuli from the right side. The two models revealed a critical behavioral-physiological experimental test that we then performed; namely, when delivering wind from the right side, adding spikes experimentally to the right GI2 should increase turn size according to the steering wheel model but should decrease turn size according to the population vector model. The latter result was obtained. The population vector, but not the steering wheel, model also could account for previous behavioral-physiological experiments in which spikes were added experimentally to a GI contralateral to the wind stimuli. The results support the population vector model as accounting for direction determination among the cockroach GIs.

Extraction of sensory parameters from a neural map by primary sensory interneurons

We examine the anatomical basis for the representation of stimulus parameters within a neural map and examine the extraction of these parameters by sensory interneurons (INs) in the cricket cercal sensory system. The extraction of air current direction by these sensory interneurons can be understood largely in terms of the anatomy of the system. There are two critical anatomical constraints. (1) The arborizations of afferents with similar directional tuning properties are located near each other within the neural map. Therefore, a continuous variation in stimulus direction causes a continuous variation in the spatial pattern of activation. (2) The restriction of the synaptic connections of an interneuron to a unique set of afferents results from the unique anatomy of that interneuron: its dendritic arbors are located within restricted regions of the afferent map containing afferents with a limited subset of directional sensitivities. The functional organization of the set of four interneurons studied here is equivalent to a Cartesian coordinate system for computing the stimulus direction vector. For any air current stimulus direction, the firing rates of the active interneurons could be decoded as Cartesian coordinates by neurons at successive processing stages. The implications of this Cartesian coordinate system are discussed with respect to optimal coding strategies and developmental constraints on the cellular implementation of this coding scheme.

Detecting and estimating signals in noisy cable structure, I: neuronal noise sources

In recent theoretical approaches addressing the problem of neural coding, tools from statistical estimation and information theory have been applied to quantify the ability of neurons to transmit information through their spike outputs. These techniques, though fairly general, ignore the specific nature of neuronal processing in terms of its known biophysical properties. However, a systematic study of processing at various stages in a biophysically faithful model of a single neuron can identify the role of each stage in information transfer. Toward this end, we carry out a theoretical analysis of the information loss of a synaptic signal propagating along a linear, one-dimensional, weakly active cable due to neuronal noise sources along the way, using both a signal reconstruction and a signal detection paradigm. Here we begin such an analysis by quantitatively characterizing three sources of membrane noise: (1) thermal noise due to the passive membrane resistance, (2) noise due to stochastic openings and closings of voltage-gated membrane channels (NA+ and K+), and (3) noise due to random, background synaptic activity. Using analytical expressions for the power spectral densities of these noise sources, we compare their magnitudes in the case of a patch of membrane from a cortical pyramidal cell and explore their dependence on different biophysical parameters.

Detecting and estimating signals in noisy cable structures, II: information theoretical analysis

This is the second in a series of articles that seek to recast classical single-neuron biophysics in information-theoretical terms. Classical cable theory focuses on analyzing the voltage or current attenuation of a synaptic signal as it propagates from its dendritic input location to the spike initiation zone. On the other hand, we are interested in analyzing the amount of information lost about the signal in this process due to the presence of various noise sources distributed throughout the neuronal membrane. We use a stochastic version of the linear one-dimensional cable equation to derive closed-form expressions for the second-order moments of the fluctuations of the membrane potential associated with different membrane current noise sources: thermal noise, noise due to the random opening and closing of sodium and potassium channels, and noise due to the presence of "spontaneous" synaptic input. We consider two different scenarios. In the signal estimation paradigm, the time course of the membrane potential at a location on the cable is used to reconstruct the detailed time course of a random, band-limited current injected some distance away. Estimation performance is characterized in terms of the coding fraction and the mutual information. In the signal detection paradigm, the membrane potential is used to determine whether a distant synaptic event occurred within a given observation interval. In the light of our analytical results, we speculate that the length of weakly active apical dendrites might be limited by the information loss due to the accumulated noise between distal synaptic input sites and the soma and that the presence of dendritic nonlinearities probably serves to increase dendritic information transfer.

Information theory and neural coding

Information theory quantifies how much information a neural response carries about the stimulus. This can be compared to the information transferred in particular models of the stimulus-response function and to maximum possible information transfer. Such comparisons are crucial because they validate assumptions present in any neurophysiological analysis. Here we review information-theory basics before demonstrating its use in neural coding. We show how to use information theory to validate simple stimulus-response models of neural coding of dynamic stimuli. Because these models require specification of spike timing precision, they can reveal which time scales contain information in neural coding. This approach shows that dynamic stimuli can be encoded efficiently by single neurons and that each spike contributes to information transmission. We argue, however, that the data obtained so far do not suggest a temporal code, in which the placement of spikes relative to each other yields additional information.

Reconstruction of natural scenes from ensemble responses in the lateral geniculate nucleus

A major challenge in studying sensory processing is to understand the meaning of the neural messages encoded in the spiking activity of neurons. From the recorded responses in a sensory circuit, what information can we extract about the outside world? Here we used a linear decoding technique to reconstruct spatiotemporal visual inputs from ensemble responses in the lateral geniculate nucleus (LGN) of the cat. From the activity of 177 cells, we have reconstructed natural scenes with recognizable moving objects. The quality of reconstruction depends on the number of cells. For each point in space, the quality of reconstruction begins to saturate at six to eight pairs of on and off cells, approaching the estimated coverage factor in the LGN of the cat. Thus, complex visual inputs can be reconstructed with a simple decoding algorithm, and these analyses provide a basis for understanding ensemble coding in the early visual pathway.

Multimodal efferent and recurrent neurons in the medial lobes of cockroach mushroom bodies

Previous electrophysiological studies of cockroach mushroom bodies demonstrated the sensitivity of efferent neurons to multimodal stimuli. The present account describes the morphology and physiology of several types of efferent neurons with dendrites in the medial lobes. In general, efferent neurons respond to a variety of modalities in a context-specific manner, responding to specific combinations or specific sequences of multimodal stimuli. Efferent neurons that show endogenous activity have dendritic specializations that extend to laminae of Kenyon cell axons equipped with many synaptic vesicles, termed "dark" laminae. Efferent neurons that are active only during stimulation have dendritic specializations that branch mainly among Kenyon cell axons having few vesicles and forming the "pale" laminae. A new category of "recurrent" efferent neuron has been identified that provides feedback or feedforward connections between different parts of the mushroom body. Some of these neurons are immunopositive to antibodies raised against the inhibitory transmitter gamma-aminobutyric acid. Feedback pathways to the calyces arise from satellite neuropils adjacent to the medial lobes, which receive axon collaterals of efferent neurons. Efferent neurons are uniquely identifiable. Each morphological type occurs at the same location in the mushroom bodies of different individuals. Medial lobe efferent neurons terminate in the lateral protocerebrum among the endings of antennal lobe projection neurons. It is suggested that information about the sensory context of olfactory (or other) stimuli is relayed by efferent neurons to the lateral protocerebrum where it is integrated with information about odors relayed by antennal lobe projection neurons.

Neural mapping of direction and frequency in the cricket cercal sensory system

Primary mechanosensory receptors and interneurons in the cricket cercal sensory system are sensitive to the direction and frequency of air current stimuli. Receptors innervating long mechanoreceptor hairs (>1000 microm) are most sensitive to low-frequency air currents (<150 Hz); receptors innervating medium-length hairs (900-500 microm) are most sensitive to higher frequency ranges (150-400 Hz). Previous studies demonstrated that the projection pattern of the synaptic arborizations of long hair receptor afferents form a continuous map of air current direction within the terminal abdominal ganglion (). We demonstrate here that the projection pattern of the medium-length hair afferents also forms a continuous map of stimulus direction. However, the afferents from the long and medium-length hair afferents show very little spatial segregation with respect to their frequency sensitivity. The possible functional significance of this small degree of spatial segregation was investigated, by calculating the relative overlap between the long and medium-length hair afferents with the dendrites of two interneurons that are known to have different frequency sensitivities. Both interneurons were shown to have nearly equal anatomical overlap with long and medium hair afferents. Thus, the differential overlap of these interneurons with the two different classes of afferents was not adequate to explain the observed frequency selectivity of the interneurons. Other mechanisms such as selective connectivity between subsets of afferents and interneurons and/or differences in interneuron biophysical properties must play a role in establishing the frequency selectivities of these interneurons.

Characterizing complex chemosensors: information-theoretic analysis of olfactory systems

The mechanisms that underlie a wine lover's ability to identify a favorite vintage and a dog's ability to track the scent of a lost child are still deep mysteries. Our understanding of these olfactory phenomena is confounded by the difficulty encountered when attempting to identify the parameters that define odor stimuli, by the broad tuning and variability of neurons in the olfactory pathway,and by the distributed nature of olfactory encoding. These issues pertain to both biological systems and to newly developed 'artificial noses' that seek to mimic these natural processes. Information theory, which quantifies explicitly the extent to which the state of one system (for example, the universe of all odors) relates to the state of another (for example, the responses of an odor-sensing device),can serve as a basis for analysing both natural and engineered odor sensors. This analytical approach can be used to explore the problems of defining stimulus dimensions, assessing strategies of neuronal processing, and examining the properties of biological systems that emerge from interactions among their complex components. It can also serve to optimize the design of artificial olfactory devices for a variety of applications, which include process control, medical diagnostics and the detection of explosives.

Representation of touch location by a population of leech sensory neurons

To form accurate representations of the world, sensory systems must accurately encode stimuli in the spike trains of populations of neurons. The nature of such neuronal population codes is beginning to be understood. We characterize the entire sensory system underlying a simple withdrawal reflex in the leech, a bend directed away from the site of a light touch. Our studies show that two different populations of mechanosensory neurons each encode touch information with an accuracy that can more than account for the behavioral output. However, we found that only one of the populations, the P cells, is important for the behavior. The sensory representation of touch location is based on the spike counts in all of the four P cells. Further, fewer than three action potentials in the P cell population, occurring during the first 100 ms of a touch stimulus, may be required to process touch location information to produce the appropriately directed bend.

Quantitative analysis of a directed behavior in the medicinal leech: implications for organizing motor output

The local bend is a directed behavior produced by the leech, Hirudo medicinalis, in response to a light touch. Contraction of longitudinal muscles near the touched location results in a bend directed away from the stimulus. We quantify the relationship between the location of touch around the body perimeter and the behavioral output by using video analysis, muscle tension measurements, and electromyography. On average, the direction of the behavioral output differed from the touch location by <8% of the total body perimeter. We discuss our results in the context of two contrasting behavioral strategies: a Continuous strategy, in which the local bend is directed exactly opposite to stimulus location, and a Categorical strategy, in which there are four distinct bend directions, each elicited by stimuli given in a single quadrant of the body perimeter. To distinguish between these strategies, we delivered two competing stimuli simultaneously. The resulting behavioral output is best described by an average of the effects of each stimulus given alone and thus provides support for the Continuous strategy. We also use a simple model, based on anatomical and physiological data, to predict the responses of the known motor neurons to different stimulus locations. The model shows that the activation of two of the motor neurons (D and V) is inconsistent with a Categorical strategy. However, these neurons are known to be active during the local bend behavior. This result, along with our experimental observations, suggests that the local bend network uses a Continuous strategy to encode stimulus location and produce directed behavioral output.

Population coding and behavioral choice

Many individual behavioral acts are produced by the combined activity of large populations of broadly tuned neurons, and the neuronal populations for different behaviors can overlap. Recent experiments monitoring and manipulating neuronal activity during behavioral decisions have begun to shed light on the mechanisms that enable overlapping populations of neurons to generate choices between categorically distinct behaviors.

Decoding visual information from a population of retinal ganglion cells

Decoding visual information from a population of retinal ganglion cells. J. Neurophysiol. 78: 2336-2350, 1997. This work investigates how a time-dependent visual stimulus is encoded by the collective activity of many retinal ganglion cells. Multiple ganglion cell spike trains were recorded simultaneously from the isolated retina of the tiger salamander using a multielectrode array. The stimulus consisted of photopic, spatially uniform, temporally broadband flicker. From the recorded spike trains, an estimate was obtained of the stimulus intensity as a function of time. This was compared with the actual stimulus to assess the quality and quantity of visual information conveyed by the ganglion cell population. Two algorithms were used to decode the spike trains: an optimized linear filter in which each action potential made an additive contribution to the stimulus estimate and an artificial neural network trained by back-propagation to match spike trains with stimuli. The two methods performed indistinguishably, suggesting that most of the information about this stimulus can be extracted by linear operations on the spike trains. Individual ganglion cells conveyed information at a rate of 3.2 +/- 1.7 bits/s (mean +/- SD), with an average information content per spike of 1.6 bits. The maximal possible rate of information transmission compatible with the measured spiking statistics was 13.9 +/- 6.3 bits/s. On average, ganglion cells used 22% of this capacity to encode visual information. When a decoder received two spike trains of the same response type, the reconstruction improved only marginally over that obtained from a single cell. However, a decoder using an ON and an OFF cell extracted as much information as the sum of that obtained from each cell alone.Thus cells of opposite response type encode different and nonoverlapping features of the stimulus. As more spike trains were provided to the decoder, the total information rate rapidly saturated, with 79% of the maximal value obtained from a local cluster of just four neurons of different functional types. The decoding filter applied to a given neuron's spikes within such a multiunit decoder differed substantially from the filter applied to that same neuron in a single-unit decoder. This shows that the optimal interpretation of a ganglion cell's action potential depends strongly on the simultaneous activity of other nearby cells. The quality of the stimulus reconstruction varied greatly with frequency: flicker components below 1 Hz and above 10 Hz were reconstructed poorly, and the performance was optimal near 2.5 Hz. Further analysis suggests that temporal encoding by ganglion cell spike trains is limited by slow phototransduction in the cone photoreceptors and a corrupting noise source proximal to the cones.

How reliably does a neuron in the visual motion pathway of the fly encode behaviourally relevant information?

How reliably neurons convey information depends on the extent to which their activity is affected by stochastic processes which are omnipresent in the nervous system. The functional consequences of neuronal noise can only be assessed if the latter is related to the response components that are induced in a normal behavioural situation. In the present study the reliability of neural coding was investigated for an identified neuron in the pathway processing visual motion information of the fly (Lucilia cuprina). The stimuli used to investigate the neuronal performance were not exclusively defined by the experimenter. Instead, they were generated by the fly itself, i.e. by its own actions and reactions in a behavioural closed-loop experiment, and subsequently replayed to the animal while the activity of an identified motion-sensitive neuron was recorded. Although the time course of the neuronal responses is time-locked to the stimulus, individual response traces differ slightly from each other due to stochastic fluctuations in the timing and number of action potentials. Individual responses thus consist of a stimulus-induced and a stochastic response component. The stimulus-induced response component can be recovered most reliably from noisy neuronal signals if these are smoothed by intermediate-sized time windows (40-100 ms). At this time scale the best compromise is achieved between smoothing out the noise and maintaining the temporal resolution of the stimulus-induced response component. Consequently, in the visual motion pathway of the fly, behaviourally relevant motion stimuli can be resolved best at a time scale where the timing of individual spikes does not matter.

Parameter extraction from population codes: a critical assessment

In perceptual systems, a stimulus parameter can be extracted by determining the center-of-gravity of the response profile of a population of neural sensors. Likewise at the motor end of a neural system, center-of-gravity decoding, also known as vector decoding, generates a movement direction from the neural activation profile. We evaluate these schemes from a statistical perspective, by comparing their statistical variance with the minimum variance possible for an unbiased parameter extraction from the noisy neuronal ensemble activation profile. Center-of-gravity decoding can be statistically optimal. This is the case for regular arrays of sensors with gaussian tuning profiles that have an output described by Poisson statistics, and for arrays of sensors with a sinusoidal tuning profile for the (angular) parameter estimated. However, there are also many cases in which center-of-gravity decoding is highly inefficient. This includes the important case where sensor positions are very irregular. Finally, we study the robustness of center-of-gravity decoding against response nonlinearities at different stages of an information processing hierarchy. We conclude that, in neural systems, instead of representing a parameter explicitly, it is safer to leave the parameter coded implicitly in a neuronal ensemble activation profile.

Broadband neural encoding in the cricket cercal sensory system enhanced by stochastic resonance

Sensory systems are often required to detect a small amplitude signal embedded in broadband background noise. Traditionally, ambient noise is regarded as detrimental to encoding accuracy. Recently, however, a phenomenon known as stochastic resonance has been described in which, for systems with a nonlinear threshold, increasing the input noise level can actually improve the output signal-to-noise ratio over a limited range of signal and noise strengths. Previous theoretical and experimental studies of stochastic resonance in physical and biological systems have dealt exclusively with single-frequency sine stimuli embedded in a broadband noise background. In the past year it has been shown in a theoretical and modelling study that stochastic resonance can be observed with broadband signals. Here we demonstrate that broadband stochastic resonance is manifest in the peripheral layers of neural processing in a simple sensory system, and that it plays a role over a wide range of biologically relevant stimulus parameters. Further, we quantify the functional significance of the phenomenon within the context of signal processing, using information theory.

Using reflexive behaviors of the medicinal leech to study information processing

The interneuronal network that produces local bending in the leech is distributed, in the sense that most of the interneurons involved are activated in all forms of local bending, even those in which their outputs would produce inappropriate movements. Such networks have been found to control a number of different behaviors in a variety of animals. This article reviews three issues: the physiological and modeling observations that led to the conclusion that local bending in leeches is controlled by a distributed system; what distributed processing means for this and other behaviors; and why the leech interneuronal network may have evolved to be distributed in the first place.

Temporal encoding in nervous systems: a rigorous definition

We propose a rigorous definition for the term temporal encoding as it is applied to schemes for the representation of information within patterns of neuronal action potentials, and distinguish temporal encoding schemes from those based on window-averaged mean rate encoding. The definition relies on the identification of an encoding time window, defined as the duration of a neuron's spike train assumed to correspond to a single symbol in the neural code. The duration of the encoding time window is dictated by the time scale of the information being encoded. We distinguish between the concepts of the encoding time window and the integration time window, the latter of which is defined as the duration of a stimulus signal that affects the response of the neuron. We note that the duration of the encoding and integration windows might be significantly different. We also present objective, experimentally assessable criteria for identifying neurons and neuronal ensembles that utilize temporal encoding to any significant extent. The definitions and criteria are made rigorous within the contexts of several commonly used analytical approaches, including the stimulus reconstruction analysis technique. Several examples are presented to illustrate the distinctions between and relative capabilities of rate encoding and temporal encoding schemes. We also distinguish our usage of temporal encoding from the term temporal coding, which is commonly used in reference to the representation of information about the timing of events by rate encoding schemes.

Simple codes versus efficient codes

Transmission of information is an important function of cortical neurons, so it is conceivable that they have evolved to transmit information efficiently, with low noise and high temporal precision. Such precision is consistent with the output generated by various working models that mimick neuronal activity, from simple integrate-and-fire models to elaborate numerical simulations of realistic-looking neurons. But our current inability to match this data with neurons' detailed spike-generating mechanisms in vivo allows us a wide latitude in interpreting the significance of the various components of their spike code. One extreme hypothesis, the 'simple' model, is that each neuron is noisy and slow, performing a simple computation and transmitting a small amount of information. A competing hypothesis, the 'efficient' model, postulates that a neuron transmits large amounts of information through precise, complex, single-spike computations. Both hypotheses are broadly consistent with the available data. The conflict may only be resolved with the development of new measurement techniques that will allow one to investigate directly the properties that make a neuron efficient--that is, to be able to measure highly transient, localized events inside the thinnest dendrites, which are currently experimentally inaccessible.

Construction and analysis of a database representing a neural map

We describe the development and analysis of a quantitative database representing the global structural and functional organization of an entire sensory map. The database was derived from measurements of anatomical characteristics of a statistical sample of typical mechanosensory afferents in the cricket cercal sensory system. Anatomical characteristics of the neurons were measured quantitatively in three dimensions using a computer reconstruction system. The reconstructions of all neurons were aligned and scaled to a common standard set of dimensions, according to a highly reproducible set of intrinsic fiducial marks. The database therefore preserves accurate information about spatial relationships between the neurons within the ensemble. Algorithms were implemented to allow the integration of electrophysiological data about the stimulus/response characteristics of the reconstructed neurons into the database. The algorithms essentially map a physiological function onto a "field" representing the continuous distribution of synaptic terminals throughout the neural structure. Subsequent analysis allowed quantitative predictions of several important functional characteristics of the sensory map that emerge from its global organization. First, quantitative and testable predictions were made about ensemble response patterns within the map. The predicted patterns are presented as graphical images, similar to images that might be observed with activity-dependent dyes in the real neural system. Second, the synaptic innervation patterns from the sensory afferent map onto the dendrites of a postsynaptic target interneuron were predicted by calculating the overlap between the interneuron's dendrites with the afferent map. By doing so, several aspects of the stimulus/response properties of the interneuron were accurately predicted.

Information Processing in Dendritic Trees

This review considers the input-output behavior of neurons with dendritic trees, with an emphasis on questions of information processing. The parts of this review are (1) a brief history of ideas about dendritic trees, (2) a review of the complex electrophysiology of dendritic neurons, (3) an overview of conceptual tools used in dendritic modeling studies, including the cable equation and compartmental modeling techniques, and (4) a review of modeling studies that have addressed various issues relevant to dendritic information processing.

Neural coding. Neurons cleverer than we thought?

Neurons may encode information in more subtle ways than their average firing rate; encoding by more complex features of a neuron's firing pattern may allow more efficient information transmission.

Decoding neuronal firing and modelling neural networks

Biological neural networks are large systems of complex elements interacting through a complex array of connexions. Individual neurons express a large number of active conductances (Connors et al. 1982; Adams & Gavin, 1986; Llinás, 1988; McCormick, 1990; Hille, 1992) and exhibit a wide variety of dynamic behaviours on time scales ranging from milliseconds to many minutes (Llinás, 1988; Harris-Warrick & Marder, 1991; Churchland & Sejnowski, 1992; Turrigiano et al. 1994).

Vector reconstruction from firing rates

In a number of systems including wind detection in the cricket, visual motion perception and coding of arm movement direction in the monkey and place cell response to position in the rat hippocampus, firing rates in a population of tuned neurons are correlated with a vector quantity. We examine and compare several methods that allow the coded vector to be reconstructed from measured firing rates. In cases where the neuronal tuning curves resemble cosines, linear reconstruction methods work as well as more complex statistical methods requiring more detailed information about the responses of the coding neurons. We present a new linear method, the optimal linear estimator (OLE), that on average provides the best possible linear reconstruction. This method is compared with the more familiar vector method and shown to produce more accurate reconstructions using far fewer recorded neurons.

Critical parameters of the spike trains in a cell assembly: coding of turn direction by the giant interneurons of the cockroach

Cockroaches (Periplaneta americana) respond to air displacement produced by an approaching predator by turning and running away. A set of 4 bilateral pairs of ventral giant interneurons is important in determining turn direction. Wind from a given side is known to produce more spikes, an earlier onset of the spike trains, and different fine temporal patterning, in the ipsilateral vs the contralateral set of these interneurons. Here we investigate which of these spike train parameters the cockroach actually uses to determine the direction it will turn. We delivered controlled wind puffs from the right front, together with intracellular injection of spike trains in a left ventral giant interneuron, under conditions where the animal could make normally directed turning movements of the legs and body. In trials where our stimuli caused the left side to give both the first spike and more total spikes than the right, but where our injected spike train included none of the normal fine temporal patterning, 92% of the evoked turns were to the right-opposite of normal (Figs. 4-6). In trials where the left side gave the first spike, but the right side gave more spikes, 100% of the turns were to the left--the normal direction (Figs. 8, 9). Comparable results were obtained when each of the left giant interneurons 1, 2 or 3 were electrically stimulated, and when either weak or stronger wind puffs were used. Stimulating a left giant interneuron electrically in the absence of a wind puff evoked an escape-like turn on 9% of the trials, and these were all to the right (Fig. 9). These results indicate that fine temporal patterning in the spike trains is not necessary, and information about which side gives the first spike is not sufficient, to determine turn direction. Rather, the key parameter appears to be relative numbers of action potentials in the left vs the right group of cells. These conclusions were supported by similar experiments in which extracellular stimulation of several left giant interneurons was paired with right wind (Figs. 11, 12).

Neuronal basis of behavior

In addition to describing behavior in terms of neuronal properties and interconnections, some studies are using these well defined neuronal circuits to see how the circuits interact, how they develop, and how they are modified by experience, hormones and neuromodulators. The ready availability of computers and computational techniques has helped in some efforts, as have improvements in physiological and morphological techniques. The major insights, however, still come from experiments that ask clear and direct questions. This review highlights some of the promising approaches and suggests some general features of how neuronal circuits produce behavior.