Phase sensitivity of complex cells in primary visual cortex

Neurons in the primary visual cortex are often classified as either simple or complex based on the linearity (or otherwise) of their response to spatial luminance contrast. In practice, classification is typically based on Fourier analysis of a cell's response to an optimal drifting sine-wave grating. Simple cells are generally considered to be linear and produce responses modulated at the fundamental frequency of the stimulus grating. In contrast, complex cells exhibit significant nonlinearities that reduce the response at the fundamental frequency. Cells can therefore be easily and objectively classified based on the relative modulation of their responses - the ratio of the phase-sensitive response at the fundamental frequency of the stimulus (F₁) to the phase-invariant sustained response (F₀). Cells are classified as simple if F₁/F₀>1 and complex if F₁/F₀<1. This classification is broadly consistent with criteria based on the spatial organisation of cells' receptive fields and is accordingly presumed to reflect disparate functional roles of simple and complex cells in coding visual information. However, Fourier analysis of spiking responses is sensitive to the number of spikes available - F₁/F₀ increases as the number of spikes is reduced, even for phase-invariant complex cells. Moreover, many complex cells encountered in the laboratory exhibit some phase sensitivity, evident as modulation of their responses at the fundamental frequency. There currently exists no objective quantitative means of assessing the significance or otherwise of these modulations. Here we derive a statistical basis for objectively assessing whether the modulation of neuronal responses is reliable, thereby adding a level of statistical certainty to measures of phase sensitivity. We apply our statistical analysis to neuronal responses to moving sine-wave gratings recorded from 367 cells in cat primary visual cortex. We find that approximately 60% of complex cells exhibit statistically significant (α<0.01) modulation of their responses to optimal moving gratings. These complex cells are phase sensitive and reliably encode spatial phase.