Mathematical Modeling of Single Nucleotide Polymorphisms via Micro-Array Analysis
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In this project, our goal is to create a mathematical model that can accurately simulate a sample of specific DNA when run through a micro-array slide. A micro-array slide has probes calibrated to bind onto specific target DNA strands. As these strands bind to the micro-array, levels of fluorescence are emitted and eventually an equilibrium intensity of fluorescence is reached. From this, we can create an intensity vs time curve. If a competing single nucleotide polymorphism (SNP) of the target DNA is introduced in this DNA sample, both DNA will compete for the micro-array probes. Consequently, as the ratio of mutated or SNP DNA to target DNA increases, the equilibrium intensity decreases. Using the law of mass action, we were able to create a pair of ordinary differential equations which can simulate the concentration of SNP and target DNA strands over time. Next, by scaling both intensity vs time curves and our model curves, we can relate intensity to concentration. Furthermore, by solving our ODE exactly in the case of no SNP DNA, we have developed a method to find the equilibrium constant. This allows us to model a situation where there are no mutations in the DNA sample. The end goal is to be able to deduce the concentration of the SNP DNA from our model given an intensity curve. This would then enable people to detect SNP DNA through a micro-array.