Static and Dynamic Adaptation of Insect Photoreceptor Responses to Naturalistic Stimuli

We describe a new nonlinear dynamic model of insect phototransduction using a NLN (nonlinear, linear, nonlinear) block structure. The first nonlinear stage provides a single exponential decline in gain and mean following the start of light stimulation. The linear stage uses a two-parameter log-normal convolution model previously applied alone to insect photoreceptors. The final stage is a static quadratic function. The model fitted current and voltage responses of isolated single photoreceptors from three different insect species with reasonable fidelity when they were stimulated by naturalistic time series having wide bandwidth and contrast, over a light intensity range of >1:10⁴. Mean squared error values for receptor current and receptor potential varied over ~2-60%, with many values below 10%. Linear log-normal filter parameters did not vary strongly with species or light intensity. Initial gain reduction was only large for the highest light levels, while the time constant of gain and mean reduction decreased with light intensity. The final nonlinearity changed from positively to negatively quadratic with increasing light intensity, indicating a change from threshold, or expansion to saturating compression with greater signal strength. Photoreceptor information transmission was estimated by linear information capacity and signal entropy measurements of both experimental data and predicted outputs of the model for identical stimuli at each light level. Comparison of actual and predicted data indicated significant added noise during phototransduction, with information being progressively lost by nonlinear behavior with increasing light intensity.