  This paper constructs dynamical models and estimation algorithms for the
concentration of target molecules in a fluid flow using an array of novel
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 averaging theory
methods and the divergence theorem, an approximate model is constructed that
describes the asymptotic behaviour of the concentration as a system of ordinary
differential equations. The estimate of target molecules is then obtained by
solving a nonlinear least squares problem. It is shown that the estimator is
strongly consistent and asymptotically normal. An explicit expression is
obtained for the asymptotic variance of the estimation error. As an example,
the results are illustrated for a novel biosensor built out of protein
molecules.
