Shifting and scaling adaptation to dynamic stimuli in somatosensory cortex

Authors

  • J. A. Garcia-Lazaro,

  • S. S. M. Ho,

  • A. Nair,

  • J. W. H. Schnupp

Errata

This article corrects:


    In the published manuscript of Garcia-Lazaro et al. (2007) there were some mistakes in Figure 6 and the text due to a programming mistake the data analysis routine which attributed data points (firing rates) to the wrong stimulus parameters. In the article, it was stated that neural response gain appeared to be increasing with increased stimulus variance, whereas in reality it decreased. Corrections have been marked in bold in the text below.

    Last paragraph of the introduction

    “Response level functions tended to become systematically steeper if the mean of the stimulus distribution was held approximately constant but stimulus variance was decreased. These changes in the steepness of the neural response functions might be described as ‘adaptation in neural response gain’, in agreement with recent findings by Maravall and colleagues (2007), but they were not observed in our single cell compartmental models.”

    Results section “Adaptation to changes in stimulus variance...”

    The rate-level curves associated with higher stimulus variances tended to have shallower slopes or saturated at lower spike rates…. … If the neurons responded to the increase in variance with a pure scaling of their rate response functions then we would expect the slopes and the firing rates at the 50% points to decrease, and we would not expect the abscissa of the 50% to change…… The firing rates at the 50% points (and therefore the maximum firing rates) were always greatest for the stimuli with the lowest variance (the black diamonds in figure 6D are always below their corresponding green squares and red circles). But the 50% points for higher variance stimuli occurred typically at higher stimulus amplitudes (the black diamonds in figure 6D are usually to the right of their corresponding green squares and red circles). This was due, not to the whole rate level curve shifting as we had seen when the HPRs were shifted, but instead because the rate level curves obtained with the higher variance stimuli often leveled off later than those obtained with lower variance stimuli, as can be seen in the examples shown in Fig. 6B and supplementary figure 2 C and D. Increasing stimulus variance did not appear to produce threshold shifts.

    We mentioned earlier that the slope of rate-level function can be considered as a measure of ‘neuronal response gain’. Maravall and colleagues (2007) concluded from their results that gain scales with stimulus variance. Expressed mathematically, this means that the gain (or slope) g observed at given stimulus variance v should be proportional to v, i.e.

    image(5)

    where a is a proportionality factor specific for the particular unit. Note that α can be less than one, i.e. increasing stimulus variance would lead to a decrease in neural sensitivity. Taking logarithms of Eqn (5) and exploiting the fact that

    image

    we get

    image(6)

    “Consequently, if we assume that gain scales inversely with variance (a < 1 and log(a) is negative), then we expect a scatter plot of the log of unit gain against the log of stimulus variance should fall along a line of slope -1, offset by the log of the unit’s gain factor a...... The distribution peaks at minus one, as one might expect if gain does indeed scale inversely with variance.”

    inline image

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