Before revision:  In physically relevant parameter regimes, these integrodifferential equations further reduce to a nonlinear set of ordinary differential equations, which may be used to estimate rate constants from biosensor data. We verify our results with a semi-implicit finite difference algorithm .
After revision:  In physically relevant parameter regimes, these integrodifferential equations further reduce to a much simpler set of Ordinary Differential Equations (ODEs). To verify the validity of our ODE approximation, a numerical method for the IDE system is developed and studied. Results from the ODE model agree with simulations of the IDE model, rendering our ODE model useful for parameter estimation .