Conclusion
In order to confirm that our mathematical model was, indeed, functional, we confirmed the patterns that were to be predicted in the model. For example, a higher Kd value would lead to less aptamer-protein complex formation. As expected, this pattern was seen in our model, as a 2-fold decrease in the Kd value, generally led to a greater than 10-fold decrease in the protein-aptamer complex that was expected to form.
Our mathematical model was also able to show that lower concentrations of the protein with constant concentrations of aptamer 1, aptamer 2, and the connector would lead to lower overall complex formations. In other words, when the protein is missing in the system, it is very unlikely for unspecific reactions to take place, and thereby give a false positive signal. As the protein concentration was gradually increased, the number of aptamer-protein complexes increased at an exponential rate, indicating the sensitivity of the aptamer-protein complex. In other words, only a small amount of the target protein is needed for the complex to form.
To further characterize our system, we would need to modify the concentrations of aptamer 1, aptamer 2, and the connector at a constant protein concentration to find the concentrations of reactants that would optimize the highly sensitive formation of the aptamer-protein complex in the presence of a protein. Unfortunately, with our oversimplified model, no clear pattern was seen when the concentrations of aptamer 1, aptamer 2, and the connector was modified. We are only able to provide conclusions on the general patterns that were seen when the protein concentration was modified. This pattern was also limited to a specific range of protein concentrations (insensible reactant concentrations and gibbs free energy values were seen at several protein concentrations that were tested). A more realistic mathematical model would be needed to quantitatively, rather than qualitatively, discern the complex behavior of the proximity dependent ligation assay.