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Slow Gain Fluctuations Limit Benefits of Temporal Integration in Visual Cortex

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Slow Gain Fluctuations Limit Benefits of Temporal Integration in Visual Cortex

Robbe L T Goris et al. J Vis.

Abstract

Sensory neurons represent stimulus information with sequences of action potentials that differ across repeated measurements. This variability limits the information that can be extracted from momentary observations of a neuron's response. It is often assumed that integrating responses over time mitigates this limitation. However, temporal response correlations can reduce the benefits of temporal integration. We examined responses of individual orientation-selective neurons in the primary visual cortex of two macaque monkeys performing an orientation-discrimination task. The signal-to-noise ratio of temporally integrated responses increased for durations up to a few hundred milliseconds but saturated for longer durations. This was true even when cells exhibited little or no adaptation in their response levels. These observations are well explained by a statistical response model in which spikes arise from a Poisson process whose stimulus-dependent rate is modulated by slow, stimulus-independent fluctuations in gain. The response variability arising from the Poisson process is reduced by temporal integration, but the slow modulatory nature of variability due to gain fluctuations is not. Slow gain fluctuations therefore impose a fundamental limit on the benefits of temporal integration.

Figures

Figure 1
Figure 1
The benefits of temporal integration of V1 activity are limited. (A) Temporal evolution of the reliability (SNR2, orange line) of the momentary response (top, 1 moment = 10 ms) and of the integrated response (bottom) for an example neuron. Tick marks in the top panel indicate spikes; the dashed line in the bottom panels illustrates the prediction for temporally uncorrelated response variability. (B) Same as (A) for a different example neuron. (C) Geometric mean of the reliability of the momentary response (top) and the integrated response (bottom) for a population of V1 neurons. The dashed line in the bottom panel is the mean uncorrelated prediction.
Figure 2
Figure 2
The effects of temporal integration on the neurometric function. (A) Mean neurometric function for a population of V1 neurons recorded from monkey 2, computed for three different integration windows. (B) Temporal evolution of the median orientation-discrimination threshold (estimated from the slope of the neurometric function) for a population of V1 neurons, recorded from two monkeys. The dashed line illustrates the prediction for a model with identical spike-count mean and variance for all time bins but uncorrelated across time. Under this model, thresholds decrease in proportion to the square root of integration time.
Figure 3
Figure 3
The modulated Poisson model accounts for the effects of temporal integration. (A) Predicted temporal evolution of the SNR2 of integrated activity for two levels of gain fluctuations, for a model neuron with constant momentary reliability. (B) Left: Predicted variance-to-mean relationship for two levels of gain fluctuations, for the same simulated neuron. Middle: Variance-to-mean relationship of example neuron 1 (see Figure 1), measured with variable duration windows. Right: Variance-to-mean relationship of example neuron 2 (see Figure 1). (C) Distribution of the reliability after 500 ms of integration, relative to the uncorrelated prediction, for a population of V1 neurons. Filled entries in the distribution indicate neurons for which SNR2 differed significantly from the uncorrelated prediction (1,000-fold bootstrap, p < 0.05). (D) Relative reliability after 500 ms of integration plotted against strength of gain fluctuations, estimated for a population of V1 neurons. Points are shaded according to the mean firing rate (over 500 ms). Orange and blue points correspond to neurons 1 and 2, respectively. (E) Relative amplitude of transient of the momentary response plotted against strength of gain fluctuations.
Figure 4
Figure 4
Comparison of multiplicative and additive noise models. (A) Simulated relative reliability after 500 ms of integration plotted against mean firing rate for three levels of multiplicative noise. (B) Simulated relative reliability after 500 ms of integration plotted against mean firing rate for three levels of additive noise. (C) Relative reliability after 500 ms of integration plotted against mean firing rate, estimated for a population of V1 neurons. Points are shaded according to the strength of gain fluctuations. Orange and blue points correspond to neurons 1 and 2, respectively. (D) Relative reliability after 500 ms of integration plotted against predictions derived from the modulated Poisson model using Equation 4.
Figure 5
Figure 5
The primary determinant of encoded information changes with time. (A) The relationship between reliability of integrated activity and mean firing rate after 100 ms (left) and 500 ms (right) of stimulus exposure for a population of V1 neurons. (B) The relationship between reliability of integrated activity and estimates of formula image after 100 and 500 ms of stimulus exposure for the same population of V1 neurons. (C) Temporal evolution of the Spearman correlation (rs) between the SNR2 of integrated activity and mean firing rate (left, red), and formula image (left, black); and between the SNR2 of integrated activity and the relative amplitude of the transient of the momentary response (right).
Figure 6
Figure 6
Limited benefits of temporal integration are also found in neurons from cortical area MT. (A) Data in the same format as Figure 1C for the population of MT neurons reported by Britten et al. (1992). (B) Analysis as in Figure 3C for the population of MT neurons. (C) Analysis as in Figure 3D for the population of MT neurons. (D) Analysis as in Figure 4D for the population of MT neurons. (E) Analysis as in Figure 5C for the population of MT neurons.

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