# Transport Effects on Multiple-Component Reactions in Optical Biosensors

## TL;DR

This paper develops a simplified ODE model for analyzing multi-component reactions in optical biosensors, validated through numerical simulations, to improve the measurement of kinetic rate constants in DNA repair processes.

## Contribution

It introduces a reduced ODE model for complex IDE systems in biosensor experiments, enabling easier parameter estimation and analysis.

## Key findings

- ODE model agrees with IDE simulations
- Simplifies analysis of multi-component biosensor reactions
- Validates the model for DNA translesion synthesis studies

## Abstract

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.