Multiple-Component Reactions in Optical Biosensors

Many biological reactions of interest involve a stream of chemical reactants flowing through a fluid-filled volume, over a surface to which receptors are confined. Examples of such surface-volume include blood clotting and DNA damage repair. Optical biosensors are a popular way to measure these reactions in real time without disturbing the underlying system, and correctly interpreting biosensor data requires having an accurate mathematical model for the process. Since biosensors typically only measure mass changes, it is difficult to analyze data that arises from multiple simultaneous reactions.

We will discuss a mathematical model for this system. Our model takes the form of an advection-diffusion-reaction system. In certain asymptotic limits this model reduces to a set of coupled nonlinear integrodifferential equations. The reduced model can be solved numerically and analytically using perturbation methods. We will discuss the challenge of fitting the associated reaction rate constants to biosensor data.

This is joint work with David A. Edwards.

Speaker Bio: Ryan Evans is originally from Harrisburg, Pennsylvania. He earned a Ph.D. in Applied Mathematics from the University of Delaware in 2015. In addition, he has earned an M.S. and B.S. in Mathematics from the University of Delaware and Bloomsburg University of Pennsylvania, respectively. He has presented his research at the Mathematical Problems in Industry Workshop.

Presentation Slides: PDF

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