Capacity and energy cost of information in biological and silicon photoreceptors

We outline a theoretical framework to analyze information processing in biological sensory organs and in engineered microsystems. We employ the mathematical tools of communication theory and model natural or synthetic physical structures as microscale communication networks, studying them under physical constraints at two different levels of abstraction. At the functional level, we examine the operational and task specification, while at the physical level, we examine the material specification and realization. Both levels of abstraction are characterized by Shannon's channel capacity, as determined by the channel bandwidth, the signal power, and the noise power. The link between the functional level and the physical level of abstraction is established through models for transformations on the signal, physical constraints on the system, and noise that degrades the signal. As a specific example, we present a comparative study of information capacity (in bits per second) versus energy cost of information (in joules per bit) in a biological and in a silicon adaptive photoreceptor. The communication channel model for each of the two systems is a cascade of linear bandlimiting sections followed by additive noise. We model the filters and the noise from first principles whenever possible and phenomenologically otherwise. The parameters for the blowfly model are determined from biophysical data available in the literature, and the parameters of the silicon model are determined from our experimental data. This comparative study is a first step toward a fundamental and quantitative understanding of the tradeoffs between system performance and associated costs such as size, reliability, and energy requirements for natural and engineered sensory microsystems.