Graham I. Cummins

Dejittered Spike-Conditioned Stimulus Waveforms Yield Improved Estimates of Neuronal Feature Selectivity and Spike-Timing Precision of Sensory Interneurons

What is the meaning associated with a single action potential in a neural spike train? The answer depends on the way the question is formulated. One general approach toward formulating this question involves estimating the average stimulus waveform preceding spikes in a spike train. Many different algorithms have been used to obtain such estimates, ranging from spike-triggered averaging of stimuli to correlation-based extraction of “stimulus-reconstruction” kernels or spatiotemporal receptive fields. We demonstrate that all of these approaches miscalculate the stimulus feature selectivity of a neuron. Their errors arise from the manner in which the stimulus waveforms are aligned to one another during the calculations. Specifically, the waveform segments are locked to the precise time of spike occurrence, ignoring the intrinsic “jitter” in the stimulus-to-spike latency. We present an algorithm that takes this jitter into account. “Dejittered” estimates of the feature selectivity of a neuron are more accurate (i.e., provide a better estimate of the mean waveform eliciting a spike) and more precise (i.e., have smaller variance around that waveform) than estimates obtained using standard techniques. Moreover, this approach yields an explicit measure of spike-timing precision. We applied this technique to study feature selectivity and spike-timing precision in two types of sensory interneurons in the cricket cercal system. The dejittered estimates of the mean stimulus waveforms preceding spikes were up to three times larger than estimates based on the standard techniques used in previous studies and had power that extended into higher-frequency ranges. Spike timing precision was ∼5 ms.

Dendritic Design Implements Algorithm for Synaptic Extraction of Sensory Information

While sensory information is encoded by firing patterns of individual sensory neurons, it is also represented by spatiotemporal patterns of activity in populations of the neurons. Postsynaptic interneurons decode the population response and extract specific sensory information. This extraction of information represented by presynaptic activities is a process critical to defining the input–output function of postsynaptic neuron. To understand the “algorithm” for the extraction, we examined directional sensitivities of presynaptic and postsynaptic Ca2+ responses in dendrites of two types of wind-sensitive interneurons (INs) with different dendritic geometries in the cricket cercal sensory system. In IN 10-3, whose dendrites arborize with various electrotonic distances to the spike-initiating zone (SIZ), the directional sensitivity of dendritic Ca2+ responses corresponded to those indicated by Ca2+ signals in presynaptic afferents arborizing on that dendrite. The directional tuning properties of individual dendrites varied from each other, and the directional sensitivity of the nearest dendrite to the SIZ dominates the tuning properties of the spiking response. In IN 10-2 with dendrites isometric to the SIZ, directional tuning properties of different dendrites were similar to each other, and each response property could be explained by the directional profile of the spatial overlap between that dendrite and Ca2+-elevated presynaptic terminals. For IN 10-2, the directional sensitivities extracted by the different dendritic-branches would contribute equally to the overall tuning. It is possible that the differences in the distribution of synaptic weights because of the dendritic geometry are related to the algorithm for extraction of sensory information in the postsynaptic interneurons.

Temporal encoding in a nervous system.

We examined the extent to which temporal encoding may be implemented by single neurons in the cercal sensory system of the house cricket Acheta domesticus. We found that these neurons exhibit a greater-than-expected coding capacity, due in part to an increased precision in brief patterns of action potentials. We developed linear and non-linear models for decoding the activity of these neurons. We found that the stimuli associated with short-interval patterns of spikes (ISIs of 8 ms or less) could be predicted better by second-order models as compared to linear models. Finally, we characterized the difference between these linear and second-order models in a low-dimensional subspace, and showed that modification of the linear models along only a few dimensions improved their predictive power to parity with the second order models. Together these results show that single neurons are capable of using temporal patterns of spikes as fundamental symbols in their neural code, and that they communicate specific stimulus distributions to subsequent neural structures.

Responses of cricket cercal interneurons to realistic naturalistic stimuli in the field

SUMMARY The ability of the insect cercal system to detect approaching predators has been studied extensively in the laboratory and in the field. Some previous studies have assessed the extent to which sensory noise affects the operational characteristics of the cercal system, but these studies have only been carried out in laboratory settings using white noise stimuli of unrealistic nature. Using a piston mimicking the natural airflow of an approaching predator, we recorded the neural activity through the abdominal connectives from the terminal abdominal ganglion of freely moving wood crickets (Nemobius sylvestris) in a semi-field situation. A cluster analysis of spike amplitudes revealed six clusters, or ‘units’, corresponding to six different subsets of cercal interneurons. No spontaneous activity was recorded for the units of larger amplitude, reinforcing the idea they correspond to the largest giant interneurons. Many of the cercal units are already activated by background noise, sometimes only weakly, and the approach of a predator is signaled by an increase in their activity, in particular for the larger-amplitude units. A scaling law predicts that the cumulative number of spikes is a function of the velocity of the flow perceived at the rear of the cricket, including a multiplicative factor that increases linearly with piston velocity. We discuss the implications of this finding in terms of how the cricket might infer the imminence and nature of a predatory attack.

Structural and biophysical mechanisms underlying dynamic sensitivity of primary sensory interneurons in the cricket cercal sensory system

Abstract We constructed probabilistic models of afferent inputs and compartmental models of interneurons in the cricket cercal system to examine the effects of dendritic morphology, distribution of synaptic inputs, and membrane properties on interneuron directional tuning properties. The mean directional tuning of afferent inputs to an interneuron was an excellent predictor of its directional tuning. Location of the synapses on the interneurons’ dendrites was not essential to determining tuning characteristics, but had a substantial effect on sensitivity. Thus, we conclude that both sampling of the afferent population, and anatomical distribution of synaptic inputs are important determinants of an interneurons directional response.

Characterizing the fine structure of a neural sensory code through information distortion

We present an application of the information distortion approach to neural coding. The approach allows the discovery of neural symbols and the corresponding stimulus space of a neuron or neural ensemble simultaneously and quantitatively, making few assumptions about the nature of either code or relevant features. The neural codebook is derived by quantizing sensory stimuli and neural responses into small reproduction sets, and optimizing the quantization to minimize the information distortion function. The application of this approach to the analysis of coding in sensory interneurons involved a further restriction of the space of allowed quantizers to a smaller family of parametric distributions. We show that, for some cells in this system, a significant amount of information is encoded in patterns of spikes that would not be discovered through analyses based on linear stimulus-response measures.

Inhibition does not affect the timing code for vocalizations in the mouse auditory midbrain.

Many animals use a diverse repertoire of complex acoustic signals to convey different types of information to other animals. The information in each vocalization therefore must be coded by neurons in the auditory system. One way in which the auditory system may discriminate among different vocalizations is by having highly selective neurons, where only one or two different vocalizations evoke a strong response from a single neuron. Another strategy is to have specific spike timing patterns for particular vocalizations such that each neural response can be matched to a specific vocalization. Both of these strategies seem to occur in the auditory midbrain of mice. The neural mechanisms underlying rate and time coding are unclear, however, it is likely that inhibition plays a role. Here, we examined whether inhibition is involved in shaping neural selectivity to vocalizations via rate and/or time coding in the mouse inferior colliculus (IC). We examined extracellular single unit responses to vocalizations before and after iontophoretically blocking GABAA and glycine receptors in the IC of awake mice. We then applied a number of neurometrics to examine the rate and timing information of individual neurons. We initially evaluated the neuronal responses using inspection of the raster plots, spike-counting measures of response rate and stimulus preference, and a measure of maximum available stimulus-response mutual information. Subsequently, we used two different event sequence distance measures, one based on vector space embedding, and one derived from the Victor/Purpura Dq metric, to direct hierarchical clustering of responses. In general, we found that the most salient feature of pharmacologically blocking inhibitory receptors in the IC was the lack of major effects on the functional properties of IC neurons. Blocking inhibition did increase response rate to vocalizations, as expected. However, it did not significantly affect spike timing, or stimulus selectivity of the studied neurons. We observed two main effects when inhibition was locally blocked: (1) Highly selective neurons maintained their selectivity and the information about the stimuli did not change, but response rate increased slightly. (2) Neurons that responded to multiple vocalizations in the control condition, also responded to the same stimuli in the test condition, with similar timing and pattern, but with a greater number of spikes. For some neurons the information rate generally increased, but the information per spike decreased. In many of these neurons, vocalizations that generated no responses in the control condition generated some response in the test condition. Overall, we found that inhibition in the IC does not play a substantial role in creating the distinguishable and reliable neuronal temporal spike patterns in response to different vocalizations.

Influence of inhibition on encoding vocalizations in the mouse auditory midbrain

Inhibition is well known to shape responses to sensory stimuli. In the auditory system, it can affect frequency response curves and responses to complex stimuli. Here, we examined how inhibition affects response to vocalizations inferior colliculus (IC) of female CBA/CaJ mice. We studied two cases in awake mice: normal auditory processing (control) and auditory processing after pharmacological blocks of inhibition (test, application of bicuculline and strychnine to block GABA A and glycine receptors). We observed several types of response across 23 tested cells. Four cells were not stimulus responsive, but their spontaneous firing rate did increase in the test condition. Three cells generated distinct stimulus-dependent responses that did not change significantly in the test condition. One cell changed its response pattern significantly in the test condition. Six cells responded only to one or two stimuli. These cells maintained the same selectivity, but on average increased their firing rates in the test condition. The remaining cells followed a pattern where responses present in the control condition also occurred in the test condition, with similar temporal pattern, but with more, or more reliable, spikes. In many of these cells additional responses occurred in the test condition in response to stimuli that generated no response in the control condition. This is consistent with the hypothesis of a single response structure in both conditions, more of which exceeds threshold in the absence of inhibition, but in the case of changing from no visible response to some response, we cannot rule out a change in the underlying code. We do establish that the degree of temporal precision required to discriminate different response patterns is typically the same in both conditions, and that the responses to groups of stimuli show similar structural relationships in both conditions, within the subset of stimulus conditions that generate some response in both conditions. Our observations are thus mostly consistent with inhibition changing the overall excitability of cells, but not changing the underlying stimulus-dependent response patterns. We evaluated cells using inspection of the response rasters, spike-counting measures, stimulus/response mutual information, and hierarchical clustering based on several event sequence distance measures. We measured the rate of mutual information loss with increasing amounts of noise in the timing of response rates. We take this rate of loss to indicate the degree to which the stimulus encoding depends on the precise timing of response events. We used clustering of the stimuli, based on their sets of evoked responses, to evaluate the similarities between the structures of response to various vocalizations. We measured the rate of loss of mutual information with increasing amounts of noise in the timing of response rates. This rate of loss indicates the degree to which the stimulus encoding depends on the precise timing of response events.

Dejittering of neural responses by use of their metric properties

We have adapted the dejittering technique [1,2] to analyze neural response patterns. In the original manuscript [2], we developed the idea of transformation-invariant stimulus processing in order to characterize local stimulus transformations that leave the neural response invariant. Currently, the method assumes that the neural responses are identical to within a fixed temporal precision, and the stimuli that induce them are variable. In this submission, we invert the dejittering method to operate on sets of variable neural responses associated with a fixed stimulus. We now ask the question “What are the natural transformations of neural responses that leave the neural message invariant?” The novelty and difficulty in this adaptation is the nature of the response set, which cannot be embedded naturally in a linear vector space. For example, a naive embedding of spike/no-spike to 0/1 in a time bin does not technically comprise a vector space, since linear combinations of such objects do not yield spike trains. Convolving spike trains with Gaussians suffers from the same constraints, while introducing additional assumptions about the metric and geometric structure of spike trains. Thus, the cost function used in stimulus dejittering (the Mahalanobis distance between a given stimulus and a Gaussian model of the set of stimuli), cannot be evaluated naturally on sets of spike trains. However, Victor and Purpura’s metric space distance (Dq) [3], does provide an intrinsic measure of the natural cost of transformation and can replace the Mahalanobis distance in the adapted algorithm. The metric space approach is based on providing a set of transformations that can convert one response into another. The distance between responses is the total cost of the “cheapest” set of transformations that can interconvert the signals. There have been several extension of the metric space approach, but, in the original, which we use, these transformations are the insertion or deletion of a spike (cost 1), or the translation of a spike in time (cost q per sample point of translation). The set of Dq s provides a measure of the variance of a response class without the need to embed the spike trains in a space where subtraction is defined. A response class is characterized by the set of within condition distances, ⟨Dq (i,j)⟩j, the average distance of spike train i to the rest of the responses to the same stimulus. With this measure of variance, we investigate the effects of temporal shifts of individual spike trains on the overall variance of the response class. As in [2], we then minimize the joint variance ⟨Dq(i,j)⟩t + σt2, where σt2 is the variance of temporal shifts and ⟨Dq(i,j)⟩t is the average distance between spike trains from the same response class after temporal shifts have been applied to them. Furthermore, a measurement of Dq corresponds to a set of modifications to a spike train, each of which occurs at a specific time. Thus, we can pinpoint specific regions of neural responses that are responsible for any observed large-scale temporal changes.

Modeling ion channels from the cricket cercal sensory system

Abstract We are interested in understanding how information about air-current dynamics is represented and processed in the primary sensory interneurons of the cricket cercal system. In this work, we develop channel models based on voltage–clamp data from Kloppenburg and Horner (J. Exp. Biol. 201 (1998) 2529), use channel ensembles to construct model neurons, and analyze the underlying mathematical structure of these excitable systems. We also examine the behavior of the model neurons in response to constant frequency stimuli and its dependence on channel kinetics. This study provides a crucial step toward developing models for studying the contributions of channel dynamics to mechanisms underlying information processing in this system.