Modelling co-translational dimerisation for programmable nonlinearity in synthetic biology

Nonlinearity plays a fundamental role in the performance of both natural and synthetic biological networks. Key functional motifs in living microbial systems, such as the emergence of bistability or oscillations, rely on nonlinear molecular dynamics. Despite its core importance, the rational design of nonlinearity remains an unmet challenge. This is largely due to a lack of mathematical modelling that accounts for the mechanistic basics of nonlinearity. We introduce a model for gene regulatory circuits that explicitly simulates protein dimerization--a well-known source of nonlinear dynamics. Specifically, our approach focusses on modelling co-translational dimerization: the formation of protein dimers during--and not after--translation. This is in contrast to the prevailing assumption that dimer generation is only viable between freely diffusing monomers (i.e., post-translational dimerization). We provide a method for fine-tuning nonlinearity on demand by balancing the impact of co- versus post-translational dimerization. Furthermore, we suggest design rules, such as protein length or physical separation between genes, that may be used to adjust dimerization dynamics in-vivo. The design, build and test of genetic circuits with on-demand nonlinear dynamics will greatly improve the programmability of synthetic biological systems.