Definition and In Vivo Evaluation of Mathematical Models to Predict the Effects of Copy Number Variations and Cell Burden in Interconnected Synthetic Circuits

The predictability of bottom-up designed synthetic circuits is a major issue in biological engineering. Several aspects currently prevent the quantitative prediction of circuits output, e.g., retroactivity, crosstalk among parts, limited cell resources, noise and context-dependent variability of components. For these reasons, the potential of synthetic biology cannot be fully exploited in high-impact application fields, thus requiring trial-and-error approaches, and time-consuming re-characterization or debugging of the constructed biological systems.

Mathematical models are usually adopted to support the design of synthetic circuits. Empirical and mechanistic models of gene regulatory networks have been used in different works to capture the quantitative behaviour of circuits, predict the output of new interconnected systems, and support early design or debugging steps.

The objective of this work is to define and test predictive models of interconnected synthetic circuits, considering copy number variation of components and cell burden. Such models can be exploited for the quantitative prediction of circuits output when individual pre-characterized components providing a burden to the chassis are connected, and the copy number of some of their subparts is changed.

Copy number of biological components is known to dramatically affect the quantitative behaviour of synthetic circuits with different network motifs. Empirical models of gene networks, usually based on Hill functions to describe gene regulations, are not able to capture copy number variation effects of promoters or regulatory genes. Mechanistic models can be adopted to describe the molecular interactions in circuits. Although they are able to capture the copy number change of every model species, they often have a higher number of parameters than empirical models. Here, we define different models and provide a steady-state algebraic solution for the output of commonly adopted systems, e.g., tetR-, lacI- and luxR-based regulations, considering different assumptions. For each model, identifiability analysis is also performed and the results are used to drive the design of suitable in vivo experiments on model systems in which regulatory proteins and/or promoter copy number are varied.

Cell burden derives from limited resource availability (e.g., polymerases and ribosomes) in living organisms. For this reason, when synthetic circuits are incorporated they can alter cellular resources and, on the other hand, the functioning of the circuit could be significantly affected. Models to describe the effects of resource limitation have been recently proposed, together with a reporter gene-based experimental method to quantify cell burden. In this context, a major challenge is to quantitatively predict the burden and the effects on circuit output from the knowledge of individual genetic modules connected in the circuit. To carry out this task, existing models were selected and applied to study model systems. Transcriptional regulators cascades were used to test in vivo a rigorous bottom-up approach in which individual components are characterized, model parameters are estimated, simulation are carried out on a model of interconnected circuit and predictions are compared with experimental output.

This work provides a modelling framework and in vivo testing to support the quantitative prediction of synthetic circuits output considering two factors currently limiting the bottom-up design in biological engineering.