Conceived and designed the experiments: RM SLD. Performed the experiments: RM. Analyzed the data: RM MC. Wrote the paper: RM TW SLD.
The authors have declared that no competing interests exist.
Stimulus-specific adaptation (SSA) occurs when the spike rate of a neuron decreases with repetitions of the same stimulus, but recovers when a different stimulus is presented. It has been suggested that SSA in single auditory neurons may provide information to change detection mechanisms evident at other scales (e.g., mismatch negativity in the event related potential), and participate in the control of attention and the formation of auditory streams. This article presents a spiking-neuron model that accounts for SSA in terms of the convergence of depressing synapses that convey feature-specific inputs. The model is anatomically plausible, comprising just a few homogeneously connected populations, and does not require organised feature maps. The model is calibrated to match the SSA measured in the cortex of the awake rat, as reported in one study. The effect of frequency separation, deviant probability, repetition rate and duration upon SSA are investigated. With the same parameter set, the model generates responses consistent with a wide range of published data obtained in other auditory regions using other stimulus configurations, such as block, sequential and random stimuli. A new stimulus paradigm is introduced, which generalises the oddball concept to Markov chains, allowing the experimenter to vary the tone probabilities and the rate of switching independently. The model predicts greater SSA for higher rates of switching. Finally, the issue of whether rarity or novelty elicits SSA is addressed by comparing the responses of the model to deviants in the context of a sequence of a single standard or many standards. The results support the view that synaptic adaptation alone can explain almost all aspects of SSA reported to date, including its purported novelty component, and that non-trivial networks of depressing synapses can intensify this novelty response.
For processing real-life auditory scenes, it is not enough that auditory neurons code only for basic stimulus properties, such as frequency and intensity; at some point, these isolated properties must be woven into a pattern. Stimulus-specific adaptation (SSA), whereby neurons adapt to common stimuli but otherwise remain sensitive to other, rare stimuli, has been proposed as a low-level substrate for such abstract pattern processing. SSA has been previously investigated using ‘oddball sequences’ of tones, in which one frequency is common, the other rare. In this article, we present the first neurocomputational model of SSA and show that it can reproduce a wide range of published data. We also propose a natural generalisation of the oddball paradigm, based on Markov chains, which allows the experimenter to manipulate other characteristics of the sequence such the rate of switching. Finally, we show that a small network of neurons can distinguish novelty from mere rarity; e.g., a B stands out in the sequence ABAAA in a way that it does not in CBADE, even though it is equally probable in both. We demonstrate that cascades of depressing synapses can adequately encode this difference, whereas the simple adaptation-based models proposed to date cannot.
Natural acoustic environments play host to a wide variety of sounds that are either repetitive or follow a regular pattern. If an organism that inhabits one of these environments hears a repeating sound and does not react to the first few salient presentations, then it is unlikely that further repetitions will be behaviourally relevant. On the other hand, if the organism is to respond to changes in its environment, then it cannot adapt to stimuli indiscriminately; rather, it must remain sensitive to even small deviations from an established pattern. It is within such an evolutionary context that the brain has acquired stimulus-specific adaptation (SSA) mechanisms that operate across several time scales and sensory resolutions
SSA in response to tone sequences has been measured in the spiking of single neurons at various stages of the auditory pathway, including the inferior colliculus (IC) in the rat
In this article we describe a neurocomputational model of SSA based on a small network of spiking neurons connected by dynamic synapses. The model components are all drawn from the literature
It is sometimes remarked that the time scale of recovery from adaptation to tones measured in cortex is consistent with the time it takes cortical synapses to recover from synaptic depression
Having configured the model to respond to oddball sequences in a manner consistent with the published physiological data, we then probe it with patterns of standards and deviants generated by first-order Markov chains
Finally, we examine serial arrangements of depressing synapses as a possible basis for certain types of novelty detection. This architecture is motivated by the fact that some neurons respond more vigorously to deviant tones if they are embedded in a background of a single standard frequency than if they appear as one of many, equiprobable random tones
In the current study, we found that cross-channel adaptation within a single layer of depressing synapses was sufficient to account for the excess response to deviants embedded in a single standard provided that
In this section, we first describe the individual components that constitute the model, and then explain how these components are assembled to form networks containing units that exhibit SSA. We then discuss the time-varying patterns supplied as input to these networks, which are taken to represent the kinds of tone stimuli used in physiological SSA experiments. The neurocomputational models presented in this article are constructed from spiking units partitioned into populations, labelled A to D. We consider three types of network, and designate each according to the populations it contains: the AB model, the ABC model and the ABD model. These networks are illustrated schematically in
The blue boxes depict populations, and the figures printed inside state the number of units (or Poisson groups). The number of sub-populations in population A depends on whether the task is two-tone (96) or multi-tone (144). A) AB model consisting of a single layer of depressing synapses. B) ABC model introduces an inhibitory population. C) ABD population consisting of two layers of depressing synapses. The synaptic pathways drawn between populations stand for all-to-all connectivity. An exception is
The units in population A are independent Poisson processes, whose firing rates are modulated by the input stimulus. The units in populations B to D implement the adaptive exponential integrate-and-fire (AdEx) model proposed in
The synapses in the model fall into three classes: fast excitatory, fast inhibitory, and fast excitatory with rapid depression and slow recovery. Fast excitatory and inhibitory synapses are based, respectively, on the simplified kinetic models of the AMPA/kainate and
The depressing synapse model combines features of the AMPA synapse model from
Altogether, three sources of noise may be identified in the model. First, upon initialisation, the parameters of every synapse in the model (time constants,
Secondly, every AdEx neuron is subject to an
The level of spontaneous activity varies amongst SSA studies
Population A comprises sub-populations of Poisson neurons, each of which fires at a rate that depends on the frequency of the input tone. The best frequencies of the sub-populations are spaced uniformly on an octave scale. The number of sub-populations and the range of octaves spanned is task-dependent: two-tone tasks utilise 96 inputs spanning a range of 2 octaves; multi-tone tasks utilise 144 inputs spanning a range of 3 octaves. The firing rate (Hz) of sub-population
As a measure of bandwidth, we take the separation, in octaves, between the frequencies that evoke firing rates half-way between the maximum and spontaneous rates, and denote this quantity
A) Tuning profiles of two Poisson neurons spaced 0.5 octaves apart. B) Graphical explanation of SSA in the AB model. The
The AB model is the simplest instance of an adaptation-based model that exhibits SSA. It consists of two populations labelled A and B (see
Population B consists of 48 AdEx neurons, each of which receives a connection from a distinct Poisson neuron in every sub-population of A via a depressing, excitatory synapse. Thus population A contains
The ABC model extends the AB model by adding an inhibitory population, C, consisting of 48 AdEx neurons, and two additional synaptic pathways,
In this model, the indirect pathway
State transition diagrams (A) and example sequences (B) for three two-state Markov chains with different scaled switching metrics. The transition probabilities are represented using line thickness (see Key). Standards and deviants are indicated in blue and red, respectively. Each block shows ninety-nine tones wrapped onto three lines.
In summary, the SSA responses in the ABC model are essentially generated in the same way as those in the AB model, namely, through the depression and recovery of the
The ABD model extends the AB model by adding population D, which consists of 48 AdEx neurons, and an excitatory synaptic pathway,
Whilst several authors have suggested adaptation on the inputs to a neuron as the mechanism whereby SSA is generated
The original motivation for the ABD model was the suggestion that the responses obtained for deviants embedded in a single standard exceeded those obtained for the same deviants embedded in a “many standards” control condition
Now we consider the many standards configuration.
Oddball stimuli are sequences of tones consisting of two frequencies,
As in
Oddball sequences have been widely used to investigate SSA; but little consideration has been given to the possibility of employing
Two-state Markov chains offer a way to decouple the probability of switching from the probability of a deviant. This generalised Markov chain has two degrees of freedom, and its transition matrix has the form
Multiple tone frequencies are routinely used to evaluate the frequency-response areas of neurons and have also been used to assess stimulus-specific adaptation
Oddball experiments cannot, by themselves, adjudicate the question of whether the enhanced response to a deviant, if present, is due to its
This section reports the response of the AB model to oddball sequences only. The responses of the AB model to other types of sequence are discussed in the ABD Model section.
In the first set of experiments we tested the AB model using eight-hundred tone oddball sequences. The SI was measured for four conditions, setting
A) SI values measured in each condition (column) as a function of
We first consider the effect of the
We next examine the influence of the input bandwidth (
We centre our discussion of the effect of
The SI values measured in population B, though significant, are much lower than those typically observed in physiology
The next task was to calibrate the parameters of the ABC model so that the neurons in population B exhibited similar adaptation characteristics in response to oddball sequences to units in the auditory cortex of the awake rat, according to the results reported by von der Behrens et al.
Von der Behrens et al.
Some useful numerical data for our purposes consisted in the median SI values added to the histograms in
A) Histograms of the neuron-specific SIs collected over the 48 neurons in population B for five stimulus conditions, which are listed above. The median SI is printed in black on each set of axes and marked using a vertical dotted line (*
Finally, we analysed the robustness of the model with respect to the parameters in order to ensure that the SIs obtained did not rely on a fine-balanced set of synaptic weights. We perturbed each of the three main parameters of the model by
In order to investigate the effect of tone rate upon SSA, we presented oddball sequences with
The influence of the tone rate upon SSA has already been explored experimentally in several auditory areas (IC
We next examined the effect of tone duration on SSA. We expected that most synapses would depress within a few milliseconds of the tone onset (see switching oddball discussion above), and that any effect of tone rate on SSA would thus be indirect; that is, shortening the tone would decrease the SI only by virtue of lengthening the silent interval between the offset of one tone and onset of the next. The SIs obtained for various ISIs and tone durations, shown in
Another concern was the response of the model on shorter time scales, such as that revealed by PSTHs averaged over the course of individual tones. Some qualitative features of the responses in
A) Average, tonic firing rate of a neuron in population B during silence and tone input (
The suppression of noise in population B due to inhibition leads to larger SI values in the ABC model than in the AB model, even though the period available for integrating signal-driven spikes is much shorter in the former, as a comparison of
The SI provides a measure of stimulus-specific adaptation over an entire oddball sequence, but it does not convey any information concerning how the response to a deviant tone is affected by the immediate history of tones (unless one initially assumes a model for how SSA comes about). To address this issue, following von der Behrens et al.,
A) Each marker plots the normalised mean response to a deviant as a function of the number of standards since the previous deviant. The normalisation is with respect to the mean response to all tones in that condition (
A good match to the physiological data has been achieved in at least three regards. First, in both figures, the deviant response is shown to increase with the number of preceding standards, and this trend is arguably an increasing form of exponential decay (see fitted curves). Secondly, the data are on the same order of magnitude, and assuming an exponential trend, the asymptotic responses (
The model and the experimental evidence
We next used the ABC model to predict how the neurons in the von der Behrens et al. study would respond to patterns of standards and deviants generated by a two-state Markov chain. The tone duration and tone rate were held fixed at
We measured the mean response of units in population B to tones presented in the block, sequential and random configurations (see
Each row of this figure corresponds to a different presentation mode: block, sequential and random. A) Pattern of tone frequencies. B) Histograms of the mean spike count per tone for population B units. C) Histograms of the mean spike count per tone with depression on
In block mode, of one hundred tones, ninety are preceded by an identical tone, and nine are preceded by an adjacent frequency. Most signals are directed via depressed synapses, and the average output is small. In sequential mode, ninety tones are preceded by an adjacent frequency, and nine are preceded by a tone remote in frequency (i.e., the first tone of each ascending series); consequently, the average output is higher than in the block mode case. Finally, in random mode, it is quite improbable that a tone will be preceded by another of the same frequency (
Pérez-González et al. (
Block, sequential and random stimuli were submitted to the ABD model and the responses in populations B and D were recorded. The patterns in the data were similar to those obtained for the ABC model and can be understood in the same terms. A figure is included in
The firing rates in populations B and D in the ABD model were measured in response to two-state Markov chain stimuli. The sequences were presented at a rate of
A) Mean spike counts per tone (top, middle panels) and SI values (bottom) measured in population B in response to Markov chains with various
A) Mean spike counts per tone in response to deviants (red), standards (blue) and deviants embedded in many control standards (black/red striped) in population B (top panel) and D (middle panel). Each column in the bottom panel indicates the frequency of the deviant (red circle) and the standard (blue circle) used in the single standard condition. In the many standards condition, tones appear in all the positions with uniform probability, but the nominal deviant frequency is still marked by a red circle. The tone positions are spaced at intervals of
In the first experiment, tones could appear in ten positions, spaced uniformly at
The output of population B relies on a single layer of depressing synapses (
The output of population D relies on a two layers of depressing synapses (
These results demonstrate that a two-layer network is able to discriminate true deviants from tones that are simply rare, even given a frequency separation smaller than the tuning curve bandwidths of the input neurons, provided that
In order to address this issue, a second experiment was performed, in which six tone positions were spaced at
The pattern in the results is now unambiguous. The activity in population B evoked by the deviant is very similar, regardless of whether it is novel or not. In population D, the response to the true deviants is larger for all
We have proposed a model of stimulus-specific adaptation in single neurons based on the convergence of depressing synapses. The inputs to the model are Poisson processes, whose mean firing rates depend on stimulus features. In this work, the stimulus feature considered is frequency, represented on an octave scale. The firing-rate profiles are Gaussian-shaped, with bandwidths similar to auditory filters. Although we have concentrated exclusively on frequency as a stimulus feature, SSA in response to other features, such as intensity, duration and modulation, can in principle be modelled, provided that a population encoding of these features is available as input to the model.
The objective was to model the spike counts of individual neurons in response to tones embedded in various types of sequence. The model was initially calibrated to match the SSA recorded for oddball sequences in one study
A second contribution of the work concerns the proposed Markov stimulus paradigm. A two-state Markov chain provides a particularly useful generalisation of the oddball sequence, in that it allows the experimenter to decouple the effects of
The current formulation of the model allows that SSA be generated
Stimulus-specific adaptation in single neurons is likely to remain the subject of intense investigation in the foreseeable future, as it demonstrates a primitive form of auditory memory, upon which other novelty-related neural responses, such as auditory mismatch negativity, could build
This document describes the response of the ABC model to switching oddball sequences, and block, sequential and random tone configurations. It also describes the response of the ABCD model to sequences generated by 3-state Markov chains.
(PDF)
The authors wish to thank István Winkler (Institute for Psychology, Hungarian Academy of Sciences) for helpful comments on draft versions of the manuscript. We also thank Georg Klump and Simon Jones (Carl von Ossietzky Universität, Oldenburg) for useful remarks on the model at various stages of its development. We would also like to express our gratitude to three anonymous reviewers for their insightful suggestions during the review process.