Methodology
Using Wolfram Mathematica 10.4, a symbolic mathematical computation program, we will evaluate the minimum Gibbs Free Energy (G) of the aptamer-protein complex for different concentrations of the initial reactants: aptamer 1 ([A1]), aptamer 2 ([A2]), the connector oligonucleotide ([C]), and the target protein ([P]). By finding the minimum Gibbs Free Energy of the system, we will be able to find the concentrations of the final aptamer-protein complexes at chemical equilibrium. The possible aptamer protein complexes at chemical equilibrium include: unbound aptamer 1 [A1], unbound aptamer 2 [A2], unbound connector [C], unbound protein target [P], aptamer 1 and protein complex [A1P], aptamer 2 and protein complex [A2P], aptamer 1, aptamer 2, and protein complex [A1A2P], aptamer 1 and connector complex [A1C], aptamer 2 and connector complex [A2C], aptamer 1, aptamer 2, and connector complex [A1A2C], aptamer 1, protein, and connector complex [A1PC], aptamer 2, protein, and connector complex [A2PC], and the aptamer 1, aptamer 2, protein and connector complex [A1A2PC]. By calculating the concentrations of the above aptamer-proteins complexes at chemical equilibrium at different initial concentrations of the reactants, we can optimize the aptamer-protein equilibria to promote the sensitivity of the aptamer in the presence of the target protein, while lowering the formation of an aptamer-protein complex when there is a lack of the target protein (non-specific reaction formation).