Rate-distortion in molecular signal sensing with ligand receptors

Molecular communication between biological entities is a new paradigm in which biological nodes sense the environment, communicate and cooperate with each other. Ligand receptors are among the most common mechanisms used by biological entities such as bacteria to sense the molecular signals in their surroundings. In such a mechanism, molecules (i.e., ligands) bind to certain proteins (i.e., receptors) and activate a signaling cascade inside the cell. In this paper, we study the distortion in sensing and estimation of the concentration of molecular signals by ligand receptors in biological agents. The sensing distortion is caused by both the randomness in the ligand reception and the quantization of the final receiver output. The random measurement of the signal by the binding activity differentiates this case from classical quantization problems. We propose an optimal random quantization technique that minimizes the overall distortion described above. The performance of this optimal technique is compared with a uniform quantizer design and the regions where the optimal quantizer can offer a considerable advantage are identified. Furthermore, we analyze the effect of the number of the output levels (i.e., the output rate) on the overall distortion compared with the theoretical limit given by Shannon. Following this, the best practical number of levels beyond which no significant improvement can be made is presented.