Team:Vilnius-Lithuania/Model
Consider a permeable strip with length X greater than width Y. On one end of the strip we have a sample pad onto which we drop analytes A that are the oligos we want to test. Beneath the sample pad is the conjugate pad that holds gold nanoparticles P. Analytes and nanoparticles diffuse and react to form a complex C. We also assume that this end of the strip is dipped into a volume (or "bath") of water that starts permeating into the strip with flow velocity $V(t)$. Somewhere along the strip at points $L \leq x \leq U$ is a test line with fixed probes R that are specific to the oligo sequence we want to test. Probes R react with the complex C to form the signal S.
The goal is to provide a mathematical basis for a fast and open-source app that helps in the design of a lateral flow assay test. \begin{align} \begin{split} \ce{A + P <=>[\ce{k_1}][\ce{k_{-1}}] C}, \\ \\ \ce{C + R <=>[\ce{k_2}][\ce{k_{-2}}] S}. \end{split} \end{align}
Corresponding to the description we form the model:
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