Detection of target molecules using surface-based biosensor arrays in fluid flows

In this paper, the concentration of target molecules in a fluid flow is estimated using an array of biosensors. The concentration evolves according to an advection-diffusion partial differential equation which is coupled with chemical reaction equations on the biosensor surface. An approximate characterization of the system is developed as a system of ordinary differential equations by exploiting the multiple-time scale behaviour of the system and using the divergence theorem. The estimate of target molecules is then obtained by solving a nonlinear least squares problem. An explicit expression for the asymptotic variance of the estimation error is obtained. To demonstrate the accuracy of proposed method, we illustrate our results on a novel biosensor built out of protein molecules.