Tuning curves, neuronal variability, and sensory coding

Abstract

Tuning curves are widely used to characterize the responses of sensory neurons to external stimuli, but there is an ongoing debate as to their role in sensory processing. Commonly, it is assumed that a neuron's role is to encode the stimulus at the tuning curve peak, because high firing rates are the neuron's most distinct responses. In contrast, many theoretical and empirical studies have noted that nearby stimuli are most easily discriminated in high-slope regions of the tuning curve. Here, we demonstrate that both intuitions are correct, but that their relative importance depends on the experimental context and the level of variability in the neuronal response. Using three different information-based measures of encoding applied to experimentally measured sensory neurons, we show how the best-encoded stimulus can transition from high-slope to high-firing-rate regions of the tuning curve with increasing noise level. We further show that our results are consistent with recent experimental findings that correlate neuronal sensitivities with perception and behavior. This study illustrates the importance of the noise level in determining the encoding properties of sensory neurons and provides a unified framework for interpreting how the tuning curve and neuronal variability relate to the overall role of the neuron in sensory encoding.

Figure 1. Illustration of Slope-to-Peak Transition in the SSI with Increasing Level of Neuronal Variability

(A) Typical tuning curve of a neuron, with mean firing rate (thick line) and standard deviation (thin lines) shown as a function of the stimulus parameter θ. These are reproduced as thin lines for reference in (B) and (D). In this example, the standard deviation of the firing rate for a given value of θ increases with increasing firing rate from a baseline value, although the particular form of noise chosen does not qualitatively affect our results. (B and D) The SSI(θ) is maximum in regions of high slope in the low-noise case (B), and maximum at the tuning curve peak in the high-noise case (D). (C and E) The specific information (solid line) in the low- and high-noise cases shown as a function of normalized firing rate. p( r|θ) is shown for reference at θ _S (left) and θ ₀ = 0 (right).

Figure 2. The SSI for Experimentally Measured Neurons

(A) The SSI for two orientation-tuned V1 neurons: one with the average firing rate of the studied population (bottom) and one with 3× the average firing rate (top). Since the neuronal variability is given by Poisson statistics [ 8], higher firing rates correspond to lower noise (see text). (B) SSI for a cricket cercal neuron [ 9] for low (1×, top) or high (3×, bottom) noise levels.

Figure 3. Population SSI and Marginal SSI in the Context of a Four-Neuron Population

(A) Tuning curves of the cricket cercal system interneurons studied. (B–D) Population SSI (thin line) and marginal SSI of the center neuron (thick line) for low (1×), medium (3×), and high (5×) noise cases, demonstrating a transition in the maximum marginal SSI from slope (1) to intersection (2) to peak (3).

Figure 4. The Maximum SSI Is Independent of the Noise Level in Two-Alternative Discrimination Tasks

(A) The average SSI of the neuron from Figure 1 for a discrimination task with two stimuli located at ±3° centered around the angle θ, for low-noise (solid) and high-noise (dashed) conditions. The dotted line shows the average SSI for 4× the high-noise condition, demonstrating that there is no transition from slope to peak. For reference, the tuning curve of the neuron is shown as a thin solid line. (B) The same neuron for a discrimination task with stimuli at +0° or +180° from θ in the three noise conditions mentioned.