In vitro implementation of robust gene regulation in a synthetic biomolecular integral controller

Abstract

Feedback mechanisms play a critical role in the maintenance of cell homeostasis in the presence of disturbances and uncertainties. Motivated by the need to tune the dynamics and improve the robustness of synthetic gene circuits, biological engineers have proposed various designs that 2 mimic natural molecular feedback control mechanisms. However, practical and predictable implementations have proved challenging because of the complexity of synthesis and analysis of complex biomolecular networks. Here, we analyze and experimentally validate a first synthetic biomolecular controller executed in vitro. The controller is based on the interaction between a sigma and an anti-sigma factor, which ensures that gene expression tracks an externally imposed reference level, and achieves this goal even in the presence of disturbances. Our design relies upon an analog of the well-known principle of integral feedback in control theory. We implement the controller in an Escherichia coli cell-free transcription-translation (TXTL) system, a platform that allows rapid prototyping and implementation. Modeling and theory guide experimental implementation of the controller with well-defined operational predictability.

In vivoFeedback Control of an Antithetic Molecular-Titration Motif inEscherichia coliusing Microfluidics

“…The module is based on an orthogonal /anti-pair that was firstly presented in our previous work and is similar to those recently used for the implementation of antithetic feedback controllers in vivo and in vitro (Aoki et al, 2019, Agrawal et al, 2019. The experimental validation we provide here integrates the quasi-static experimental investigation of the /anti-motif of interest which was started in complementing it with microfluidics data that gives useful information on typical response times and the overall behaviour of the module when stimulated in real-time.…”

“…More specifically, these modules can be used to compare some desired reference input of interest with a signal related to the phenotype one wishes to control, so as to provide an error signal that the molecular control device can use to regulate its behaviour. Molecular titration motifs are crucial for the implementation of embedded antithetic feedback controllers both in vivo (Aoki et al, 2019) and in vitro (Agrawal et al, 2019), and also for the realization of multicellular control strategies as first suggested in .…”

Compact attractors of an antithetic integral feedback system have a simple structure

“…In one of them, an in vivo construct was reported in [4] that is based on Bacillus subtilis sigW and its anti-factor rsiW as the two antithetic species. In another, in [2] we constructed and analyzed an in vitro synthetic biomolecular integral controller that precisely controls the protein production rate of an output gene, based on a sequestration reaction between E. coli σ 28 and anti-σ 28 factors.…”

“…We study this system in the nonnegative orthant R 4 + , which is a (positively) invariant set of the dynamics and is the natural biological space to consider since these variables represent chemical species concentrations. This system is (with minor variations) also studied in [2], [1], where local stability and some partial global stability results are obtained.…”

“…The analysis of k-cooperative dynamical systems is based on the work of Sanchez [23] on dynamical systems with invariant cones of rank k (see also the more recent work [10]). A set C ⊂ R n is called a cone of rank k if: (1) C is closed, (2) x ∈ C implies that ax ∈ C for all a ∈ R, and (3) C contains a subspace of dimension k and no subspace of a higher dimension. For example, it is straightforward to verify that R 2 + ∪ (−R 2 + ) is an invariant cone of rank 1.…”