Biosensors, especially those based on transcription and translation, offer plenty of variables which can be manipulated in order to optimize crucial characteristics such as sensitivity and response time. Examples of these variables are promoter strength, gene dosage and amount of repressor proteins. Testing all those conditions is a very laborious task, but it can be greatly facilitated by means of mathematical modeling. By simulating the behavior of the system, it is possible to identify promising leverage points and guide the experiments in the lab. A model can also be very useful in developing a better understanding of biological systems, because a key aspect of modeling is the reduction of a complex system to its principal constituents and reactions. For these reasons, it was clear to us that a model of our novel biosensors would be very helpful to us.

Molecular processes are often influenced by stochastic effects. However, we believe that our biosensors can be described by deterministic equations with sufficient accuracy because all molecules are present in large quantities, which offsets stochastic effects. We performed our simulations with the software package SimBiology^® (MathWorks) and used the solver ode15s for our system of ordinary differential equations (ODE), as we observed that the model behaves as a stiff system.

Modeling CFPS

At first we built a simple model to describe the expression of sfGFP in our cell-free protein synthesis. This model consists of transcription, translation and the maturation of sfGFP. The crucial point was to include the termination of protein synthesis that we observed after a couple of hours. Our experimental data and several publications suggested that the reason is the degradation of translation resources. Thus, we included a species named "TL resources" which catalyzes the translation reaction and degrades over time. The initial concentration of the TL resources and three associated parameters were fitted to our data and validated using an independent data set. The resulting model accurately describes the sfGFP production for various plasmid concentrations. In addition, the model helped us in developing a better understanding of cell-free protein synthesis. »

Repression and induction

In order to model a biosensor, we expanded the CFPS model by the expression and action of a repressor. The important steps are the transcription, translation and dimerization of the repressor, its binding to the operator sequence and the derepression in the presence of an analyte. As it is difficult to obtain specific parameters for the proteins we worked with from the literature, we chose to use the lac operon as a model system. The final model takes into account the competition of reporter mRNA and repressor mRNA for translation resources. This is modeled as a competitive inhibition. »

Applying the model

Our model showed us that the ratio of repressor and reporter plasmid is very important in order to get a strong output signal and little background noise. Consequently, we determined a suitable ratio from the simulations and tested this prediction in the lab. Our simulations also demonstrated that it is possible to precisely adjust the detection limit of a cell-free biosensor and thus build a test strip that can tell the user whether a safety limit is exceeded or not. In the future, the model could be used to quickly determine the optimal repressor concentrations for our biosensors. »

For more information, let´s start with the CFPS model.