Designing Conservation Relations in Layered Synthetic Biomolecular Networks

Thomas P Prescott & Antonis Papachristodoulou

In Synthetic Biology, biomolecular networks are designed and constructed to perform specified tasks. Design strategies for these networks tend to centre on tuning the parameters of mathematical models to achieve the specified behaviour, and implementing these parameters experimentally. For example, we typically manipulate the strength and rates of the interactions between transcription factors and genetic promoters to design the dynamics of genetic regulatory networks. This design strategy assumes a fixed stoichiometric structure to the network, which pre-defines its possible behaviours by constraining the space in which the concentrations can take values. These constraints are manifested as a number of fixed, linear conservation relations. Such a pre-definition may be too restrictive for the purposes of designing the specified dynamics. Our recent work has investigated the extent to which the state space of a synthetic network can also be designed and shaped by parametric tuning. We have exploited layered timescale separation to implement new, nonlinear, tuneable conservation relations, which hold for all times beyond a fast transient and remain satisfied for all possible slow-scale dynamics. This strategy can be applied to the design of genetic regulatory networks through the construction of fast protein-protein interactions. Hence we can flexibly constrain the state space of a genetic regulatory network such that new, nonlinear, tuneable constraints can be independently imposed on the allowed trajectories of an arbitrary genetic regulatory network.