The outputs from neuronal systems adapt following a change in a stimulus, through a variety of mechanisms acting on different timescales. Many systems show a rapid form of adaptation through which stimuli are encoded relative to the context within which they were presented. This form of context-modulated coding is ubiquitous through sensory and higher-level systems, and may support the ability of the nervous system to efficiently encode complex natural stimuli. Experiments have shown that this form of gain control occurs both in neural systems and in single neurons in the cortex. On longer timescales, neural systems show a decrease of activity after long exposure to a constant stimulus. It is proposed that this behavior is a reflection of intrinsic neuronal dynamics that may contribute to the efficient coding of the slowly-varying stimulus envelope. This project will further develop the hypothesis that these slow dynamics may reflect the system's ongoing estimate of the changing statistical characteristics of the input. The mechanisms for these adaptive behaviors will be pursued with a combination of theoretical analysis and simulation of realistic neuronal models. The project's goal is to elucidate the mathematical basis of fundamental neural mechanisms for the efficient encoding of time-varying signals and reveal optimal strategies for sampling and representing complex natural environments. This work examines neural coding mechanisms that apply to multiple sensory and higher brain systems and will help to develop a language and methodology that can translate across these areas. The interdisciplinary nature of the work will provide training opportunities for undergraduate and graduate students crossing over from mathematics and physics to biology. The project includes the development of a summer course for advanced high school students.
