Signal-to-noise ratios for simulated and actually observed head optomotor pitch movements.

<p>Signal-to-noise ratios (SNRs) are means across flies (predictions: N = 7, behavior: N = 6) and plotted as functions of time after stimulus motion onset. In order to predict head pitch in the elevated (reduced) motor activity state a first-order (second-order) low-pass filter was used. The SNR of actually observed head movements at the end of the trials in both motor activity states is considerably smaller than predicted for the respective state. At the end of the open-loop interval (grey shaded box and inset), the SNR of the predicted high activity state responses already outreaches the SNR of the head movements recorded in that state (see text for details). Note that the seeming state difference in SNRs of actually observed responses is at least in part the consequence of spontaneous head pitch superimposing on the visually induced response (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0026886#pone.0026886-Rosner1" target="_blank">[16]</a>).</p

Comparison of predicted and actually observed head pitch responses to downward motion.

<p>The same neuronal responses were used for the predictions in (A) and (B). The gain factor was adjusted to fit the mean response amplitude of the behavioral responses. (A) Behavioral responses (red) were recorded while the fly was in a state of elevated motor activity. A first-order low-pass filter (τ = 100 ms) was used to predict head pitch from neuronal responses. Predictions (dark gray) are much less variable than the actually observed responses. All pitch responses recorded in the elevated activity state of one fly are shown. (B) Neuronal and behavioral (blue) responses were recorded while the fly was in a state of reduced motor activity. A second-order low-pass filter (τ₁ = 100 ms, τ₂ = 100 ms) better approximates head pitch in the reduced motor activity state than a first-order filter. Again, predictions (dark gray) are less variable than the actually observed responses. Only a subset of the recorded traces is shown for illustration of response shape and variability. Note the different scales in (A) and (B).</p

Head pitch movements predicted from neuronal responses to downward motion.

<p>A first-order low-pass filter (τ = 150 ms) was applied to neuronal responses of a VS2/3-cell recorded in close temporal succession during the presence (red) or absence (blue) of haltere oscillations.</p

Information theoretical analysis.

<p>A S(f), the power spectral density of the signal (mean response, solid lines), and N(f), the power spectral density of noise (dashed lines), normalized to the signal or noise mean square amplitude. The inset assigns different colors to the different stimulus contrasts. B Signal-to-noise ratios at the six different contrasts used (same color code as in A). Dashed line indicates SNR of 1. C Shannon information as function of frequency at different contrasts (same color code as in A). Information estimated from signal-to-noise ratio as: log₂[1+S(f)/N(f)]. All spectra were smoothed using a 4 point running average. D Shannon information capacity as a function of contrast; average ±95% confidence interval (N = 12). At the 0.31 contrast 14 additional cells were analyzed. Abscissa is interrupted to display zero contrast on the logarithmic scale. Arrow marks the contrast induced by photon shot noise at the mean light intensity. Inset shows the dependence of the information capacity on the amount of data analyzed. The information capacities shown were calculated at zero contrast by using different numbers of trials to estimate the SNR.</p

Kullback-Leibler divergence as a function of the contrast.

<p>Average Kullback-Leibler divergence ±95% confidence interval at the different contrast (N = 12). For each recorded cell the Kullback-Leibler divergence was estimated at each instance of time and was subsequently averaged across time giving a single divergence value for each cell at each contrast level (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0001328#s4" target="_blank">methods</a>). The plotted values are averages of these divergences across the 12 cells.</p

Signal-detection approach.

<p>A Experimental design for the discrimination task at one contrast level. Left hand column: the reference stimulus is repeated 25 times; right hand column: different test stimuli, all statistically equivalent to the reference stimulus. Reference and test stimuli of all five contrasts were presented in a pseudorandom order. B At each contrast level the two distances 〈<i>D_r</i>〉 and 〈<i>D_t</i>〉 were estimated according to equation 5 for each reference response (e.g. the highlighted one in the left box). C Response discriminability as a function of contrast. Dots mark the average discrimination performance (N = 12) ±SEM. Discrimination performances were calculated using data segments of different lengths (see legend). Data were fitted with a sigmoid function ranging from 50 to 100% (equation 6). The arrow marks the contrast which results from photon shot noise at the background light intensity. D Uncertainty of discriminability estimation for different segment lengths. For each cell, the discrimination performance was estimated for all possible data segments. The standard deviation of these discrimination performances was estimated. The box plots describe the distribution of these standard deviations in the cell population. Boxes indicate median (black line) and the upper, respectively lower quartile the whiskers represent the rest of the data. The plus-sign denotes an outlier. The two largest segment lengths used in C subdivided response traces only into one or two segments, thus no S.D. could be calculated.</p