The Contribution of Spike Threshold to Acoustic Feature Selectivity, Spike Information Content, and Information Throughput

Introduction

Two models have been proposed to describe how information from neuronal spike patterns serves as a neural code for unique features of sound. “Feature selective” models assume that sequences of spikes from a single neuron are precisely timed to contingent constellations of stimulus parameters (features) from which the identity of a sound could be precisely determined (Barlow, 1953, 1961; Martin, 1994). Unitary action potentials from an ideal feature detector neuron would signal the occurrence of a highly stereotyped stimulus feature that is usually assumed to be of special behavioral relevance (Simmons et al., 1975; Brenowitz et al., 1997). Feature selectivity has been demonstrated for species-specific vocalizations in auditory cortex of echolocating bats (Suga and Jen, 1976; Suga et al., 1978), area X/Hv of song birds (Brenowitz et al., 1997; Doupe, 1997) and for face representation in high-level primate visual cortices (Fujita et al., 1992; Gross and Sergent, 1992). An orthogonal view of sensory feature encoding is offered by “linear rate coding” models. Linear rate models assume that sensory features are represented by the time-varying firing rate of single neurons or neuronal populations. In principle, the response of a linear neuron is modulated by the overlap between the stimulus and its neuronal receptive field (RF). Thus, in contrast to a classical feature detector, a linear neuron could respond to range of stimulus parameters that are not precisely contingent on each other. Linear selectivities for elementary acoustic features such as spectral modulation frequency and direction have been demonstrated in peripheral auditory stations (Nelken et al., 1997; Yu and Young, 2000), the midbrain inferior colliculus (ICC) and auditory cortex (Kowalski et al., 1996; Calhoun and Schreiner, 1998; Versnel and Shamma, 1998; Schnupp et al., 2001; Escabí and Schreiner, 2002). This simpler class of acoustic selectivity is analogous to grating and directional selectivity in visual neurons (Reid et al., 1991; DeAngelis et al., 1993).

Feature-selective and linear rate-encoded responses represent two extreme response regimens that can be distinguished and quantified if appropriate stimuli are used. Distinguishing these encoding regimens requires that we differentiate the “stimulus specificity” of a neuron from its “stimulus preference.” The stimulus specificity is related to the fidelity in the association between sensory signal and evoked spikes. High specificity is achieved when a neuron responds reliably to a given stimulus or feature but is unresponsive to other stimuli. By comparison, the stimulus preference is an averaged property of the stimulus-response function. The average sound preferences of an auditory neuron, or its spectrotemporal receptive field (STRF), can be estimated by spike-triggered averaging all of the sound waveforms preceding a spike output (Hermes et al., 1981; deCharms et al., 1998; Keller and Takahashi, 2000; Klein et al., 2000; Theunissen et al., 2000; Escabí and Schreiner, 2002).

Calculating the information content in the sensory-related spike train is yet another way to quantify how spiking patterns contribute to the neuronal representation. Measures of spike train information content often make no assumptions about the features being encoded (de Ruyter van Steveninck et al., 1997; Borst and Theunissen, 1999) and do not assume a feature-selective or rate code model.

In the current study, we demonstrate a novel view of auditory sensory encoding by combining information theoretic approaches with measures of feature selectivity and stimulus preference. Single-cell recordings from the cat inferior colliculus demonstrate specific trade-offs between feature selectivity, spike rates, and spike information content. These trade-offs provide a continuum between the fidelity and throughput of the sensory coding and offer complementary modes of information transfer for purely linear and feature-selective strategies. A neuronal model based on sound-evoked synaptically driven input and a spike threshold accurately accounts for these trade-offs and suggests that the spike threshold is the key mechanisms controlling the specificity of the encoding regimen.

Materials and Methods

Electrophysiology. Details of the physiological recording and stimulus presentation methods for this dataset have been presented previously (Escabí and Schreiner, 2002; Escabí et al., 2003). Briefly, single-unit recordings of n = 103 envelope “phase-locking” neurons (Escabí and Schreiner, 2002) were obtained from the central nucleus of the inferior colliculus of five anesthetized cats. Animals were maintained in an areflexive state via continuous infusion of ketamine (2-4 mg · kg^-1 · h^-1) and diazepam (0.4-1 mg · kg^-1 · h^-1) in lactated Ringer's solution (1-4 mg · kg^-1 · h^-1). Body temperature was maintained at ∼37.5°C, and heart rate, breathing rate, temperature, and peripheral reflexes were monitored throughout the experiments. Surgical methods and experimental procedures follow National Institutes of Health and United States Department of Agriculture guidelines.

Dynamic moving ripple (DMR) and/or rippled noise (RN) stimulus sequences (Escabí and Schreiner, 2002) were presented to the animal in a sound-shielded chamber (IAC, Bronx, NY). Both sounds were designed to uniformly cover spectral resolutions from 0 to 4 cycles/octaves and temporal modulation rates from 0 to 350 Hz. Independent sound sequences were presented simultaneously to each ear via a closed, binaural speaker system [electrostatic diaphragms from Stax (Saitama, Japan)]. All stimuli were presented at 30-70 dB per one-third octave for a duration of 8-20 min.

Measuring acoustic feature selectivity. We devised a second-order stimulus-response analysis to characterize the spectrotemporal selectivity of auditory neurons by analyzing the variance of the pre-event stimulus ensemble. First, we computed the STRF, which is the average stimulus pattern that evoked action potentials. The STRF of a neuron is obtained by spike-triggered averaging the stimulus waveforms: (1)

where N is the number of action potentials, S is the stimulus spectrotemporal waveform normalized for unit variance, and the average is conditioned on the ensemble of action potentials times, {t_n}. τ and X_k correspond to the stimulus delay (relative to the spike time, t_n) and the sound frequency in octaves (for the kth frequency channel), respectively.

Next, we measured the variance of the statistically significant spike evoking stimulus patterns. To do this, the STRF was examined for a significance level of p < 0.002. The subset of STRF samples that exceeded the significance criterion (outlined as white contours) (see Fig. 2), along with the overlapping pre-event sound patterns, were treated as vectors. The response-conditioned stimulus variance is given by

where ∥ · ∥ designates the vector norm, STRF is a vector containing L statistically significant STRF samples, and S_n is shorthand for the vector containing the pre-event waveform samples of S(t_n - τ,X_k) that overlap the significant STRF region (Fig. 2, white contours). The magnitude difference between the significant STRF and the nth pre-event spectrotemporal pattern can be expressed as follows: (2)

where (3)

is the response-conditioned stimulus-STRF similarity index (SI) for the nth action potential, and corresponds to the vector dot product. The SI is equivalent to a correlation coefficient between the pre-event stimulus pattern and the STRF and assumes values between -1 and 1; a value of 1 indicates that the STRF and the nth pre-event spectrotemporal pattern have identical shapes; a value of 0 indicates that they bear no resemblance; a value of -1 is unlikely to occur, because it implies that the sound pattern is 180° out of phase with the STRF.

From Equation 2, two independent factors contribute to the response-conditioned stimulus variance. First, the SI determines the similarity in shape between the pre-event stimulus and the STRF. The variance is thus minimized if the SI for all stimulus patterns is near 1. Second, the magnitude of the variance is proportional to the difference in magnitudes between the STRF and pre-event stimulus. Thus, ideally, the variance is precisely 0 if and only if the pre-event pattern of all action potentials are identical in shape to the STRF (SI is unity for all n) and their norms are identical: ∥S_n∥ = ∥ STRF∥ for all n. Here, we take advantage of the fact that our moving ripple stimulus has a fixed peak-to-peak amplitude (Escabí and Schreiner, 2002) and thus a constant norm. This allows us to consider how the stimulus shape (SI) contributes to the neural selectivity without the influence of stimulus norm or contrast, which we previously showed to contribute significantly to neuronal responses in the ICC (Escabí et al., 2003).

We quantified the average specificity (or selectivity) by characterizing the ensemble of SIs. Collectively, we represent these by the SI probability distribution function, p(SI). Our feature selectivity metric consists of measuring the bias in p(SI) in relationship to a hypothetical feature detector, p_fd(SI), or a randomly firing neuron, p_r(SI). First, we removed the bias resulting from idiosyncrasies in irregular firing by computing the SI distribution for a random neuron. This was done by generating a spike train with 12,000 Poisson distributed action potentials over the DMR stimulus duration and then using the original STRF to measure the SI distribution for the random spikes, p_r(SI). This distribution was typically tightly centered about an SI of 0, although some slight skewing was observed that was dependent on STRF shape. Next, we considered the expected distribution of a hypothetical feature detector neuron, p_fd(SI). Because a hypothetical feature detector responds if and only if the shape of the pre-event stimulus precisely matches the STRF, its SI distribution consists of a single peak centered about an SI of 1.

We next measured the bias of our real neuron relative to our random and feature detector control conditions. To do this, we first integrated the probability distribution function of our real, random, and feature detector neurons as follows: (4) and we therefore represented the behavior of each by a cumulative distribution function (CDF) (see Fig. 3, right column). The cumulative distribution of random neurons, P_r(SI), contains a sharp transition at SI = 0. The feature detector CDF, P_fd(SI), has a sharp transition at SI = 1. The CDF of real neurons [P(SI)] typically had a smooth transition somewhere in between. The bias is measured as a feature selectivity index (FSI) as follows: (5)

where the measurements (6)

correspond to the area underneath each cumulative distribution function for the real (A), feature detector (A_fd), and random (A_r) neurons. The FSI takes continuous values from 0 to 1. FSIs of 1 indicate that the neuron behaves like a hypothetical feature detector, whereas values near 0 indicate that the response specificity was low (i.e., random firing neuron).

In the case in which neurons responded binaurally, and therefore produced significant STRFs for the contralateral and ipsilateral inputs (Qiu et al., 2003), the FSI procedure was modified without loss of generality to account for the binaural activation of a neuron. To do this, SIs were measured for each ear, resulting in a contralateral SI_c,n and an ipsiliateral SI_i,n measurement for each action potential, t_n. Because the neuronal responses are now represented by a vector of two simultaneous-SI measurements, the ensemble SI statistics can be represented as joint-binaural SI distribution, p(SI_c,SI_i). The FSI could then be represented as FSI = (V_r - V)/(V_r - V_fd), where

represents the volume measurement underneath the joint-binaural cumulative SI distribution function, P(SI_c,SI_i). The validity of this binaural-FSI procedure was tested for monaural neurons, all of which produced identical measurements as the direct approach using monaural SI distribution (mean correlation coefficient, > 0.99; p < 0.001).

Information calculation. Mutual information was estimated using the methods of Strong et al. (1998) as applied to 5 s ripple noise response rastergrams (125 trials) in Escabí et al. (2003). Briefly, estimates of the mutual information were obtained for n = 42 neurons and for simulations from our model neuron (see below, Spectrotemporal integrate- and-fire neuron model). One neuron was discarded from our sample, because it deviated substantially from the general trends and it was characterized as a significant outlier (p < 0.006, bootstrap estimate). The mutual information was estimated as follows: (7a)

where (7b)

is the total entropy of the spike train, and (7c)

is the entropy associated with the response variability. The distribution of response words, p(w) and p(w|t), were estimated from the response spike rasters (see Fig. 4 A-E). The procedure was bootstrapped across multiple stimulus segments for various word lengths (T = 5, 6, 8, 10, 15, 20, 40, 80, 160, and 200 ms) and data fractions (100, 80, 50, 33, and 25%) and at various temporal resolutions (1, 2, 4, 8, 16 ms). The biases associated with word length and data fraction were removed according to the procedure of Strong et al. (1998).

Spectrotemporal integrate-and-fire neuron model. We devised a simplified model neuron to examine the relationship between feature selectivity, information content, and the spiking properties of a neuron. This coupled two-compartment model consists of a linear synaptic STRF that accounts for the spectrotemporal integration of a neuron and a subsequent integrate-and-fire neuron that accounts for the cell membrane integration, thresholding, and action potential generation.

The integrate-and-fire compartment consists of a conventional leaky integrate-and-fire neuron. The membrane potential is determined from the following linear cell membrane differential equation: (8)

where V(t) = V_m(t) - E_r is the driven intracellular potential of the neuron [i.e., the difference between the membrane potential, V_m(t), and its resting potential, E_r (-60 mV)], i_m(t) is the synaptic current input, n(t) is a white noise current term that is low-pass filtered by the cell membrane, and τ is the membrane time constant. Spikes are generated in the model whenever the membrane potential, V_m, exceeds a specified threshold activation potential, V_T. After activation, a 1 ms refractory period was imposed and the membrane was reset to its resting potential, at which point the integration continued.

The synaptic current activity of the neuron was computed from the synaptic STRF of the neuron, STRF_synaptic. The synaptic STRF models the synaptically driven spectrotemporal activity of the neuron without the influence of the cell membrane integration. The intracellular membrane current provided by each synaptic frequency channel is derived as a spectrotemporal convolution between the sound envelope (at a given frequency) and the synaptic STRF of the neuron as follows: (9a)

Here, i_m,k is the membrane current for the kth frequency channel, and S(t,X_k) is the sound spectrotemporal envelope. The total current that is injected into the neuron is obtained as the sum of the current contributions from each frequency channel as follows: (9b)

where i_m is the total injected current, and G is a gain constant which adjusts the current amplitude to produce an intracellular voltage of desired variance.

To apply the spectrotemporal integrate-and-fire (STIF) model to STRFs from our neuronal data, we devised a procedure for removing the influence of the cell membrane integration from our ICC STRFs. This procedures allows us to closely approximate the synaptic STRF from our spike-derived STRFs, STRF_spike. First, although in all of our real data we did not have access to the membrane STRF directly (because we derived STRFs using extracellular spiking activity), extensive testing on our model revealed that in general STRF_spike ≈ ϵ × STRF_membrane, where ϵ is an amplitude scaling constant that was strongly dependent on the normalized threshold and the internal signal-to-noise ratio (SNR). This empirical finding is consistent with Price's theorem as applied to spike-triggered averaging analysis (de Boer and Kuyper, 1968). We therefore approximated the membrane STRF by its spike-derived counterpart (STRF_membrane ≈ STRF_spike) and then adjusted the arbitrary gain factor G in Equation 9b to produce a desired spike rate or intracellular variance.

Next, the synaptic STRF is related to the membrane STRF of the neuron, STRF_membrane, via a linear deconvolution as follows: (10a)

which removes the membrane impulse response from the STRF of the neuron. Here, STRF_synaptic is obtained by inverse filtering the membrane STRF with the membrane impulse response of the cell, h_membrane(τ) = C^-1e^-t/τu(t), where τ is the membrane integration time constant and C is the membrane capacitance. We implemented this deconvolution in the Laplace transform domain as follows: (10b)

where s is the Laplace variable, and the membrane transfer function is H_membrane(s) = C^-1 (s + 1/τ)^-1.

To examine how the threshold and noise level of the neuron affects its spiking activity, we reduced the intracellular parameters of the neuron to only those that affected the spiking properties. Examination of the model revealed that the analysis could be simplified substantially by noticing that the model output only depends on the “relative” intrinsic drive in relation to the resting and threshold potentials. We therefore defined a dimensionless “normalized threshold” as follows: (11)

which corresponds to the number of intracellular voltage SDs required for spike activation. The intracellular signal-to-noise ratio was defined as follows: (12)

where correspond to the signal and noise intracellular voltage variance, respectively (assuming no spiking).

Population model. To see whether the spiking STRF model could explain our population trends, we simulated a population of neurons by randomly choosing integrate-and-fire (IF) neuron parameters. We then optimized the model results by fitting the model to Figure 4F and tested whether it could account for our remaining population trends (see Fig. 6B-D).

To do this, we first selected a subset of six real neuron STRFs for the STIF model that closely approximated the receptive field preferences in the inferior colliculus and that are representative of our population distribution in a previous study (Qiu et al., 2003). Each receptive field was fitted with a Gabor model as described in Qiu et al. (2003). We performed this procedure to assure that receptive field size or shape in all of our simulations did not bias our results.

We next simulated a population of randomly sampled neurons by sampling STIF neuron parameters and STRFs at 240 independent conditions. At each IF neuron condition, one of the six STRF models was selected randomly, and the predicted intracellular current was then injected into the IF compartment. All IF parameters were then selected randomly from a uniform distribution (initial range: SNR = -20-10 dB; N_T = 0.5-6; τ = 5-15 ms). Optimization of the model was performed by pruning iteratively the upper and lower limit of the SNR and N_T distributions so that the linear regression slope, intercept, and SD of the model spike information versus spike rate trend (see Fig. 6 A) matched the ICC population data (see Fig. 4 F) as closely as possible. Pruning of the SNR and N_T upper and lower limits was performed in 5 dB and 0.5 steps, respectively. This model fitting procedure selected n = 98 (of 240) neurons with uniformly distributed IF parameters (optimized range: SNR =-15-0 dB; threshold, N_T = 1-4) that best matched the spike information versus spike rate data of Figure 4 F. The resulting model parameters were then used to cross-validate the remaining trends (see Fig. 6 B-D).

Results

Discussion

In the ICC, as in the model, neuronal fidelity (spike information, feature selectivity) and throughput (spike rate, information rate) were systematically traded off. Neurons with high spike rates can convey large amounts of stimulus-related information despite unreliable spiking. In contrast, neurons exhibiting sparse responses can signal the occurrence of stereotyped parameter constellations or features with action potentials that convey high information value. The precise nature of this trade-off was accurately reproduced in a population of model neurons by simply considering a distribution of spike threshold levels. Threshold has the effect of enhancing the spiking fidelity at the expense of limiting the communicated information in a manner that closely matches the physiological data. It is plausible that variations in effective spiking threshold in ICC could arise from variation of ascending inhibition, voltage-gated conductance, cell surface areas, input resistance differences, or anesthesia level (see details below). Because these are common mechanisms of altering threshold level in all spiking neurons, the results outline a general encoding principle.

Higher feature selectivity limits the subset of stimulus features that a neuron can potentially respond to as evident in our analysis. By design, the features in the DMR are highly variable, and consequently, average firing rates of neurons with high selectivity are low. Presumably, if the DMR were biased to include many more epochs of the preferred feature, neurons with high FSIs could generate higher mean spike rates. Neurons with low FSIs and highly significant STRFs generally had exceptionally high spike rates. An ideal linear integrating neuron would respond to a large collection of stimulus patterns, provided that stimulus energy is presented within its spectrotemporal filter. Such an idealized neuron should phase-lock to a variety of structured and unstructured inputs with equal efficacy (Escabí and Schreiner, 2002), assuming that sufficient stimulus energy is provided. Neurons with high selectivity may also require highly correlated inputs (so that the stimulus pattern closely resembles the average STRF) to initiate temporally phase-locked action potentials (Escabí and Schreiner, 2002; Hsu et al., 2004). Such an additional requirement would force the neuron to respond exclusively to stimulus patterns that resemble the average.

The relationship between neuronal fidelity and response throughput across the sampled population likely represents a continuum in the neuronal code for the ICC. A distributed code could have a significant impact on sensory information transfer from ICC to auditory thalamus. Single action potentials from high spike rate ICC neurons are not per se very meaningful, but can convey large amounts of information if spikes are pooled together, as required for a “linear” rate code. In contrast, neurons with low spike rates and high feature selectivity would generate sparse responses and low information rates. However, single action potentials from high-FSI neurons are very informative, highly reliable, and are much more likely to convey meaningful information in the precise timing of single neuronal events (Figs. 4 and 5). Whereas the information per spike and feature selectivity of ICC neurons (Figs. 3G,4F) and our model (Fig. 6A,C) were inversely related to driven spike rates, overall information rates were dominated by the average firing rate (Figs. 4G,6B).

An intriguing result predicted by the neuronal analysis and model is that neurons with very similar receptive field preferences could employ vastly different neuronal encoding strategies. Conceptually, two neurons with identical average spectrotemporal preferences could exhibit different levels of selectivity. A neuron with a highly precise stimulus-response relationship would respond reproducibly to a specific stimulus pattern or a specific stimulus combination as for an ideal feature detector neuron (Fig. 1A) or a representative ICC cell (Fig. 2A). The low variance (high FSI) for this example ICC cell indicates that it acts as a frequency modulation up-sweep detector and distinguishes this cell from a neuron with similar-looking STRF that responds to any component within this sweep at different latencies (low FSI) (as for Figs. 1B, 2B). Thus, the concept of selectivity is closely related to the variance of the spike-evoking stimulus ensemble and not to the mean stimulus as previously suggested (deCharms et al., 1998). As a consequence, a meaningful interpretation of STRFs requires knowledge of the response variance expressed in terms of quantitative measures such as FSI or spike information. Neurons with identical STRFs may reflect either the averaged response to a large stimulus ensemble or an exclusive response pattern to a highly stereotyped stimulus feature. This could occur, for instance, if two neurons share similar intracellular activity, but have different spike thresholds or resting potentials as observed for populations of ICC neurons (Kuwada et al., 1997; Sivaramakrishnan and Oliver, 2001).

Numerous nonlinearities have been implicated as serving an essential role for neuronal coding of sensory information. Because linear receptive field models are often not very predictive on their own, their usefulness for modeling single neuron activities has been recently brought into question (Bar-Yosef et al., 2002; Sahani and Linden, 2003; Machens et al., 2004). Nonlinear ionic conductances in the spiking mechanisms are perhaps the most pronounced nonlinearities in single neurons, because they are responsible for converting the continuous intracellular activity to a binary spiking pattern. Higher thresholds would effectively increase the order of the system nonlinearity, thus increasing the response selectivity. Recent extensions of a linear temporal receptive field model that incorporates a simple spike generating threshold has been shown to accurately predict the spiking activity of visual neurons (Keat et al., 2001). Our data further reveal that a linear RF model with an appropriate spike generating nonlinearity accurately reflects trade-offs in the fidelity and throughput as observed in the ICC population.

The threshold nonlinearity in the spike generation mechanism is a key attribute of all spiking neurons and the resulting trade-offs in spiking fidelity and response throughput could represent a general property of the neuronal code. The spike threshold “level” on its own is insufficient for generating the observed population trade-offs, because the resting potential and strength of the synaptic drive also contribute significantly to the observed finding. Conceptually, a higher spike threshold voltage has an equivalent functional outcome for the model as a lower resting potential or a smaller synaptic current drive. Our concept of “normalized” threshold was thus introduced to account for these three factors that together influence the firing rate and spiking fidelity of the model. Although the spike threshold nonlinearity shapes some aspects of neuronal responses in the visual and auditory system (Casseday et al., 1994; Kempter et al., 1998; Bringuier et al., 1999; Priebe et al., 2004), its role in shaping response selectivity and information transmission has not been reported previously. These findings therefore address issues of neuronal information and stimulus coding beyond modality-specific details that likely apply to spiking neurons in general.

Although in the neuronal model, spiking fidelity and throughput are collectively controlled by the combined influence of the spike threshold, resting potential, and the relative size of the synaptic drive, an equivalent functional outcome could be implemented in real neurons with a variety of mechanisms. A reduction in the resting potential via shunting conductance could extend the intracellular voltage range required to generate action potentials leading to an “effective” higher spike threshold level and selectivity. Similarly, a sustained inhibitory input could substantially hyperpolarize the neuron, thus extending the requirements for spike initiation (Casseday et al., 1994; Kuwada et al., 1997). Alternately, the input resistance of a cell could also play a role, because neurons with lower input resistance would require a strong and highly concerted synaptic current drive to reach spike activation (Sivaramakrishnan and Oliver, 2001). Additional enhancement can be provided by nonlinear synaptic conductances (Reyes, 2001; Sivaramakrishnan and Oliver, 2001; Svirskis et al., 2002), which together with the spike threshold could enhance the preference for a particular stimulus component. Collectively, such subthreshold mechanisms combined with the highly nonlinear spike generation threshold would have a common effect of shaping the suprathreshold response rate and refining the stimulus requirements necessary for spike initiation, thereby enhancing (or reducing) the stimulus-response selectivity. Although the level of anesthesia has been shown to alter neuronal responses in the ICC (Kuwada et al., 1989; Ramachandran et al., 1999), it is unlikely that it alone accounts for the observed trade-offs, because a reduced level of excitability (as expected for ketamine; NMDA antagonist) would primarily increase the effective threshold across our population of neurons. This could potentially bias our results toward higher selectivity; however, it would not account for the negative correlation between firing rate and spiking fidelity. A nonlinear mechanism such as the spike threshold is required to produce such an effect.

The possible coding schemes that can be achieved with a simple change in effective threshold level extend from a temporally imprecise “rate code” at low thresholds and high spike rates to a precise “timing code” at higher thresholds with lower spike rates and highly informative action potentials. Lower thresholds are more likely to generate a greater number of unreliable action potentials, because the synaptic activity from a larger number of inputs would surpass the threshold level required for spike activation. Such unreliable spiking activity could, however, be integrated and averaged at the postsynaptic cell to convey a meaningful message. In contrast, higher thresholds could potentially enhance the spiking efficacy in the transmission of information at a postsynaptic neuron, because higher thresholds would presumably favor the intracellular activity of the strongest synaptic link (Swadlow and Gusev, 2002). All or none binary spiking selectivity observed in cortical auditory neurons may in fact be related to a similar threshold mechanism (DeWeese et al., 2003).

One hypothesis regarding the functional segregation of high and low feature selectivity neurons in the population data are that these may correspond to anatomically distinct cell classes, such as disk and stellate cells in the ICC (Oliver and Morest, 1984), or distinct populations of ascending input (Ramachandran et al., 1999). Collicular neurons can differ in many aspects, including intrinsic membrane properties and synaptic receptor characteristics resulting in distinct physiological response types (Sivaramakrishnan and Oliver, 2001). Although it is tempting to speculate that the differences in feature selectivity reflect biophysical properties or morphological differences between cells that affect the intracellular requirements for spike activation, more detailed studies are necessary to establish such relationships. Our model, however, does not require a bimodal distribution of biophysical properties, because the selectivity distribution was accounted for with a continuously defined spike threshold.

Our data and model suggest that thresholding not only affects the average driven activity of a neuron, but it also constrains the rate and specificity of the communicated information in a manner that allows for complementary neuronal codes. Neurons with low spike rates, high thresholds, and high selectivity convey the most information with single spikes that can be used for detecting specific instances of the sensory signal. In contrast, neurons with low thresholds and high spike rates convey the most information if spikes are pooled together and are therefore well suited for encoding sensory information as a rate code. Given that thresholding is a common mechanism of all spiking neurons, such trade-offs in the fidelity and information throughput of the encoded message may represent a general feature of the neuronal code.