# Transport Effects on Multiple-Component Reactions in Optical Biosensors

## Abstract

Optical biosensors are often used to measure kinetic rate constants associated with chemical reactions. Such instruments operate in the *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 biosensors 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.

## Keywords

Biochemistry Optical biosensors Rate constants Integrodifferential equations Numerical methods## References

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