Model Reduction Tools For Phenomenological Modeling of Input-Controlled Biological Circuits

We present a Python-based software package to automatically obtain phenomenological models of input-controlled synthetic biological circuits from descriptive models. From the parts and mechanism description of a synthetic biological circuit, it is easy to obtain a chemical reaction model of the circuit under the assumptions of mass-action kinetics using various existing tools. However, using these models to guide design decisions during an experiment is difficult due to a large number of reaction rate parameters and species in the model. Hence, phenomenological models are often developed that describe the effective relationships among the circuit inputs, outputs, and only the key states and parameters. In this paper, we present an algorithm to obtain these phenomenological models in an automated manner using a Python package for circuits with inputs that control the desired outputs. This model reduction approach combines the common assumptions of time-scale separation, conservation laws, and species abundance to obtain the reduced models that can be used for design of synthetic biological circuits. We consider an example of a simple gene expression circuit and another example of a layered genetic feedback control circuit to demonstrate the use of the model reduction procedure.