Estimating Parameters of Sampled Diffusion Processes in Affinity Biosensors

Affinity biosensors rely on chemical attraction between targets of interest (mRNA and DNA sequences, proteins) and their molecular complements, probes, which serve as biological sensing elements. The attraction between complementary sequences leads to binding, in which probes capture target molecules. Molecular binding is a stochastic process and hence the number of captured analytes at any time is a random variable. Real-time affinity biosensors acquire multiple temporal samples of the binding process. In this paper, estimation of the amounts of target molecules in real-time affinity-based biosensors is studied. The problem is mapped to the inference of the parameters of a temporally sampled diffusion process. To solve it, we employ a sequential Monte Carlo algorithm which relies on transition density of the sampled diffusion process to approximate posteriori distributions of the unknown variables given the acquired measurements. The transition density is not available in a closed form and is therefore approximated using Hermite polynomial expansion. We show that when the number of target molecules is much smaller than the number of probe molecules, the binding reaction can be described by the so-called Cox-Ingersoll-Ross process. Limits of performance of the parameter estimation are characterized by means of the Cramer-Rao lower bound (CRLB). Simulations and experimental results demonstrate that the proposed scheme outperforms existing techniques for estimation in affinity biosensors.