Biosensor Arrays for Estimating Molecular Concentration in Fluid Flows

This paper constructs dynamical models and signal processing-based estimation algorithms for computing the concentration of target molecules in a fluid flow using an array of biosensors. Each biosensor is constructed out of protein molecules embedded in a synthetic cell membrane. The concentration evolves according to an advection-diffusion partial differential equation, which is coupled with chemical reaction equations on the biosensor surface. By using asymptotic analysis and the divergence theorem, an approximate model is constructed that describes the asymptotic behavior of the concentration as a system of ordinary differential equations. The estimate of target molecule concentration is then obtained by solving a nonlinear least squares problem. Then, explicit expressions are obtained for the variance and bias of the estimate using the derived approximate model. These expressions can evaluate the achievable improvement in the estimate based on the number of biosensors. As an example, the results are illustrated for a novel biosensor built out of protein molecules.