  Optical biosensors are often used to measure kinetic rate constants
associated with chemical reactions. Such instruments operate in the
\textit{surface-volume} configuration, in which ligand molecules are convected
through a fluid-filled volume over a surface to which receptors are confined.
Currently, scientists are using optical biosenors to measure the kinetic rate
constants associated with DNA translesion synthesis--a process critical to DNA
damage repair. Biosensor experiments to study this process involve multiple
interacting components on the sensor surface. This multiple-component biosensor
experiment is modeled with a set of nonlinear integrodifferential equations
(IDEs). It is shown that in physically relevant asymptotic limits these
equations 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.
