A Model for the Spatiotemporal Design of Gene Regulatory Circuits

Mathematical modeling
assists the design of synthetic regulatory
networks by providing a detailed mechanistic understanding of biological
systems. Models that can predict the performance of a design are fundamental
for synthetic biology since they minimize iterations along the design-build-test
lifecycle. Such predictability depends crucially on what assumptions
(i.e., biological simplifications) the model considers.
Here, we challenge a common assumption when it comes to the modeling
of bacterial-based gene regulation: considering negligible the effects
of intracellular physical space. It is commonly assumed that molecules,
such as transcription factors (TF), are homogeneously distributed
inside a cell, so there is no need to model their diffusion. We describe
a mathematical model that accounts for molecular diffusion and show
how simulations of network performance are decisively affected by
the distance between its components. Specifically, the model focuses
on the search by a TF for its target promoter. The combination of
local searches, via one-dimensional sliding along
the chromosome, and global searches, via three-dimensional
diffusion through the cytoplasm, determine TF-promoter interplay.
Previous experimental results with engineered bacteria in which the
distance between TF source and target was minimized or enlarged were
successfully reproduced by the spatially resolved model we introduce
here. This suggests that the spatial specification of the circuit
alone can be exploited as a design parameter in synthetic biology
to select programmable output levels.