Team:Michigan/Modeling
Modeling
Synthetic biology has a long way to being completely accepted by the public, mainly due to lack of education about the subject. The Michigan Synthetic Biology Team held a few workshops in order to excite and incite younger generations to pursue synthetic biology!
Introduction
Mathematical models greatly aid in the prediction of the outcome of a biological design. Our mathematical model will be employed to test the efficacy of an aptamer based proximity-dependent ligation assay (PLA) in the detection of biomarkers. The proximity dependent ligation assay is an extension to the traditional immunoassay and can be used for protein detection with high specificity and sensitivity. The selectivity of the proximity dependent ligation assay is dramatically enhanced through the double recognition by two oligonucleotide-conjugated aptamers. We sought to optimize the aptamer-protein equilibria to promote the efficient and precise binding of the aptamer with the target molecule.
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).
Assumptions
The ligation of aptamer 1 to the biomarker is independent to the ligation of aptamer 2 to the biomarker; in other words, the binding of an aptamer to the protein would not make the binding of the second aptamer less or more likely. Only one aptamer molecule may bind at a time to a target molecule. We are assume that gibbs free energy of the reaction at equilibrium of the reaction will never exactly be zero. The dozens of aptamer-protein dynamics will although approach zero, will not be exactly zero.
