Phase space characterization for gene circuit design

Genetic circuit design requires characterization of the dynamics of synthetic gene expression. This is a difficult problem since gene expression varies in complex ways over time and across different contexts. Here we present a novel method for characterizing the dynamics of gene expression with a few parameters that account for changes in cellular context (host cell physiology) and compositional context (adjacent genes). The dynamics of gene circuits were characterized by a trajectory through a multi-dimensional phase space parameterized by the expression levels of each of their constituent transcriptional units (TU). These trajectories followed piecewise linear dynamics, with each dynamical regime corresponding to different growth regimes, or cellular contexts. Thus relative expression rates were changed by transitions between growth regimes, but were constant in each regime. We present a plausible two-factor mathematical model for this behavior based on resource consumption. By analyzing different combinations of TUs, we then showed that relative expression rates were significantly affected by the neighboring TU (compositional context), but maintained piecewise linear dynamics across cellular and compositional contexts. Taken together these results show that TU expression dynamics could be predicted by a reference TU up to a context dependent scaling factor. This model provides a framework for design of genetic circuits composed of TUs. A common sharable reference TU may be chosen and measured in the cellular contexts of interest. The output of each TU in the circuit may then be predicted from a simple function of the output of the reference TU in the given cellular context. This will aid in genetic circuit design by providing simple models for the dynamics of gene circuits and their constituent TUs.