Quantization in Molecular Signal Sensing via Biological Agents

Abstract

One of the long-term goals of synthetic biology is to reliably engineer biological systems that perform human-defined functions such as sensing, monitoring, and processing. Molecular sensing via biological cells is often performed through receptors which interact with the signal molecules. The ligand receptors in bacteria are one of the most studied examples of such phenomenon. In this paper, we study the distortion in sensing and estimation of the concentration of molecular signals by synthetic biological agents equipped with ligand receptors. The sensing distortion is caused by random measurement of the molecular signal by the ligand receptors and the quantization of the cell output via finite number of levels. First, we consider the case where the prior distribution of the molecules in the environment is known and study the performance of the optimum as well as uniform quantizers. Next, we consider robust (minimax) quantizers, where the distribution of the molecules is unknown a priori. We study the behavior of the quantizer as a function of the number of ligand receptors and number of quantization levels. By comparing with the theoretical limits, we derive approximate bounds for the number of quantization levels versus the number of ligand receptors for good quantization performance.