A comparative study of information capacity for biophysical and silicon photoreceptors

We employ communication theory to analyze information processing in a silicon photoreceptor and in a biophysical model of the blowfly photoreceptor. We take channel capacity to be a quantitative measure of performance which is independent of any particular task. The physical instantiation of any channel determines the noise, the signal constraints and the channel capacity. The channel model for each of the two systems is a cascade of linear bandlimiting sections followed by additive noise. Filters and noise are modelled from first principles when possible. Parameters for the blowfly model are determined from biophysical data available in the literature. Such a comparative study is a first step towards understanding the performance, and the tradeoffs between system performance and associated costs such as size, reliability and energy requirements for natural and engineered sensory systems. 1. SENSORY INFORMATION PROCESSING IN PHYSICAL SYSTEMS We seek to gain better understanding of sensory information processing in physical systems both natural and engineered. To do so we must understand how t o relate function to structure. We must also understand the tradeoffs between system performance and associated costs such as size, reliability and energy requirements. An information theoretic framework for quantifying those tradeoffs in VLSI was presented in [4] for a variety of delay circuits; we utilize the same basic ideas to investigate two photoreceptors. In this work we compare the functional properties and performance of a biological photoreceptor and an engineered photoreceptor. For both systems we construct a communication channel model that incorporates physical transformations between input and output, as well as degradation by noise. This model allows us to investigate tradeoffs between cost and performance and provides a starting point for investigation into the efficiency of information processing. The research reported In this paper IS supported by a DARPA/ONR MURI N00014-95-1-0409. 2. COMMUNICATION CHANNEL MODEL Information processing often involves transformations between different physical degrees of freedom, as information is communicated from one physical structure to another: photons, conformational state of proteins, concentrations of various chemicals, current, voltage. We model these transformations as a cascade of communication channels that have bandwidth limitations. We model each noise source as an independent, additive contribution t o the channel. In each model. the signal power Sn(f) at any stage n is the result of a cascade of linear filters Hi(f), and the noise power Nn( f ) is the summed power of m independent, additive noise sources Nj(f) which are also transformed by the cascade of linear filters. Explicitly, the signal and noise at stage n are given by: n S n U ) n IH* (~ ) I ' s~ (~ ) (1)