Commentary: Robust quantification of orientation selectivity and direction selectivity

摘要

Mazurek et al. ( 2014 ) provided an important step forward in changing the old-fashioned manner of reporting orientation and/or direction selectivity of cells that involved the infamous OI–orientation index, DI, and related quantities such as orientation bias and direction bias (OB/DB, see Leventhal et al., 2003 ; OB/DB are the normalized or./dir. vector lengths, defined as L _( ori )and L _( dir )on p. 4 in Mazurek et al., 2014 ). At the beginning of their Results section, they demonstrated the unwanted features of these indexes, and showed that even non tuned cells can exhibit strong values of OI/DI. Therefore, they emphasized that little information was provided by these indexes (which I heartily welcome since it means I no longer have to discuss them with researchers and students) and investigated a statistical method of testing whether a cell is orientation- or direction-tuned. In this commentary, first I would put forward what should be the first basic report in physiological studies: tuning characteristics. Second, I extend Mazurek et al.'s analysis and compare their proposed test to the fitting approach, which they only advocated for extracting tuning parameters. I conclude by mentioning the issue of tuning decision based on p -value and related questions. First, OBs and associates cannot be the first analyses and reports since they are based on the tuning properties (see Figure 1 of Mazurek et al., 2014 ; and in my commentary, Figure 1A ). Even when a cell is clearly tuned, these indexes have the highly unwanted feature of depending on at least two of the tuning characteristics: background rate, tuning width, and amplitude(s) (mentioned by the authors, pp. 9–10). Consequently, one compares data sets using unknowingly biased values, without clear interpretation of what changed in the tuning properties (see Figure 1B ). As such, it is regrettable that the authors continue reporting results and statistical reliability with respect to OI/DI, when they should first have analyzed the tuning characteristics of the cells and how the decision criteria regarding the presence of tuning (e.g., their T ~(2)-test) depend on those parameters. Once the tuned cells are gathered and their parameters analyzed with respect to the hypotheses tested, then one may consider whether a composite index is appropriate for reporting the effects that are observed (e.g., SNR, OI, etc.). Figure 1 Illustration of tuning, index variations, and statistical decision about tuning presence . (A) Examples of two theoretical orientation-tuned cells only differing in background firing rate (r_(0)of 10 and 30 Hz; Gaussian curves with amplitudes of 40 Hz and σ of 25°) and their associated OI/OB (A, amplitude; hwhm, half-width at half-maximum). (B) Illustration of the variation of the orientation bias index (Leventhal et al., 1995 ) for Gaussian orientation-tuned cells when only one of the three parameters varies, with the two other fixed (see legend), demonstrating the difficulty of interpreting OI/OB variables without knowledge of the tuning parameters. (C) Proportion of detected tuned cells of a given amplitude (abscissa) when applying the Hotelling T ~(2)-test (red curves) or F -test (black curves), and for two different background firing rates (5 Hz in solid lines, 30 Hz in dashed lines). The model response was a von Mises direction-tuned cell (parameters: r_(0), a_(1)= 50 Hz, a_(2)= 0 Hz, k = 0.95, giving hwhm~32.6°; see Swindale, 1998 ), experimental sampling was every 15° (e.g., Schmolesky et al., 2000 ) with 10 repetitions per direction, and random noise around the mean was simulated as Poisson type. A total of 200 cells were simulated for each amplitude (each symbol in the plot) with random jitter of the preferred orientation across simulations within a 40° window. Each simulation was fitted with the von Mises two amplitude function (here unconstrained), and the statistical tests applied at α = 0.05/100 for multiple tests adjustment (Matlab code available on demand, or on http://www.researchgate.net/profile/Tzvetomir_Tzvetanov ). Second, the authors describe a method of testing whether a cell is tuned to orientation/motion direction (p.7). They propose creating sub-samples of single trial per orientation/direction from the measures, then computing the orientation/direction vector for each sub-sample and performing a Hotelling's T ~(2)-test to check whether the neuron's responses represent tuning against the hypothesis of uniform circular tuning. Later in their text (p. 11), they use fitting (Swindale, 1998 ), on those cells that were previously found to be tuned with the T ~(2)-test, to extract the tuning characteristics. Nevertheless, any model-based fitting approach allows one to test if a cell is tuned (H0, mean uniform response; and H1, the model describes the cell responses better than the mean) by using any relevant test statistics, for example an F -test between two nested models [ F = (SS1 ? SS2)/(df1 ? df2)/(SS2/df2)]. Fi