Mathematical Modeling: Bridging the Gap between Concept and Realization in Synthetic Biology

Figure 1

The role of mathematical modeling in synthetic biology. Computer-aided mathematical modeling bridges a design concept to realization in synthetic biology. Solid lines depict typical steps that have to be performed while developing a model; dashed lines depict unusual scenarios or conditions under which the steps shown by the corresponding solid lines are trivial or can be bypassed. A concept or ideas for designing a circuit for a particular function may be inspired by data from experiments or the literature. A mathematical model is then formulated on the basis of certain assumptions. The framework of a model could be deterministic or stochastic. The development of a model generally begins with the estimation of parameters that govern the model; this is a process that involves sensitivity analysis, bifurcation analysis, and, under certain circumstances, metabolic and transcription (regulatory) network analysis. The dashed line from design concepts to deterministic model indicates that, in some cases, parameter estimation is trivial or can be bypassed for this type of model. A stochastic model is developed by employing statistical functions to mimic system dynamics and considering fluctuations in the data. The dashed line from parameter estimation to stochastic model indicates that in some cases, parameter estimation may offer information in choosing statistical functions when constructing a stochastic model. Optimization is required for both models and is complete when the model exhibits an agreement (goodness of fit) with experimental data. A good agreement enables reliable prediction of system behavior and further biological realization, whereas unsatisfactory agreement requires the revision of the initial assumptions and the beginning of the next modeling cycle. See text and Figure 2 for explanations of terms.