Nonlinear modeling predicts spike timing direction selectivity and modulation index for simple and complex cells.

<p><b>A.</b> Schematic of the nonlinear model structure. The stimulus is filtered by a set of receptive fields k<i>_i</i> and further processed by associated nonlinearities <i>f_i</i>(.) and temporal combination term h<i>_i</i>_. Outputs of multiple expanding and suppressive modules are summed together and converted into a firing rate prediction <i>r</i>(<i>t</i>) via the spiking nonlinearity <i>F</i>. <b>B.</b> Cross-validated log-likelihood (<i>LL</i>) improvement compared to a model based on the average firing rate. The different levels of STC-based models demonstrate that models with two filters (STC2 and EM) offer large improvements in <i>LL</i> over a model based on the STA alone. However, including the full set of detected filters (STC and <i>loc</i>) more than doubles model performance. STC2 refers to the model containing only the first two STC filters shown in <b>1B,</b> (last row), EM to the two STC filters found for small amounts of data (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058666#pone-0058666-g001" target="_blank">Fig. <b>1B</b></a>, first row), STC to all filters shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058666#pone-0058666-g001" target="_blank">Fig. <b>1B</b></a> (last row), and <i>loc</i> to the localized features (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058666#pone-0058666-g002" target="_blank">Fig <b>2B</b></a><b>,</b> last row). <b>C.</b> Simulated responses of a simple and a complex cell (model as shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058666#pone-0058666-g003" target="_blank">Figure <b>3A</b></a>) to optimally oriented drifting gratings demonstrate the ability of models fit to random bar stimuli to predict response properties to gratings consistent with their cell classification. The responses of the simple cell (<i>gray</i>) and complex cell (<i>black</i>) are shown relative to the temporal stimulus modulation at a given spatial location (<i>top</i>). <b>D</b>. Modulation index (MI) and direction selectivity measurements for 51 V1 cells stimulated with optimally oriented drifting gratings (Rust et. al. 2005). The models of all neurons in the study were used to generate predicted Direction Selectivity Index (DSI) and MI (<i>vertical axis</i>), which are in agreement with those values measured experimentally (<i>horizontal axis</i>), for simple (<i>red,</i> correlation coefficient CC = 0.93) and complex (<i>black,</i> CC = 0.84) cells, with CC = 0.85 overall. MI is predicted with similar fidelity (<i>right</i>, CC = 0.9).