Ensemble Bayesian Analysis of Bistability in a Synthetic Transcriptional Switch

Abstract

An overarching goal of synthetic and systems biology is to engineer and understand complex biochemical systems by rationally designing and analyzing their basic component interactions. Practically, the extent to which such reductionist approaches can be applied is unclear especially as the complexity of the system increases. Toward gradually increasing the complexity of systematically engineered systems, programmable synthetic circuits operating in cell-free in vitro environments offer a valuable testing ground for principles for the design, characterization, and analysis of complex biochemical systems. Here we illustrate this approach using in vitro transcriptional circuits (“genelets”) while developing an activatable transcriptional switch motif and configuring it as a bistable autoregulatory circuit, using just four synthetic DNA strands and three essential enzymes, bacteriophage T7 RNA polymerase, Escherichia coli ribonuclease H, and ribonuclease R. Fulfilling the promise of predictable system design, the thermodynamic and kinetic constraints prescribed at the sequence level were enough to experimentally demonstrate intended bistable dynamics for the synthetic autoregulatory switch. A simple mathematical model was constructed based on the mechanistic understanding of elementary reactions, and a Monte Carlo Bayesian inference approach was employed to find parameter sets compatible with a training set of experimental results; this ensemble of parameter sets was then used to predict a test set of additional experiments with reasonable agreement and to provide a rigorous basis for confidence in the mechanistic model. Our work demonstrates that programmable in vitro biochemical circuits can serve as a testing ground for evaluating methods for the design and analysis of more complex biochemical systems such as living cells.

A bistable biomolecular network based on monomeric inhibition reactions

“…This implies the existence of a positive root, thusx is unstable. Lemma (4) only provides a sufficient condition for instability of an equilibrium point of system (4)- (9). Necessity may be shown if a 0 (x) < a 1 (x) < a 2 (x); the expressions for these coefficients suggest that this inequality may hold for most parameter choices, however we are not able to demonstrate this analytically.…”

“…Recovery of enzyme activity is achieved via strand displacement. Potentially, this circuit may function in vivo, in contrast with other recently proposed in vitro designs [4], [5], [9].…”

“…We derive polynomial equilibrium conditions by setting to zero equations (4)- (9). We subtract equations (7) and (8) from equation (4) and we get:…”

“…Lemma 5 If a simple transition to instability occurs at an equilibrim pointx of system (4)- (9), then at least two additional equilibria appear. If exactly two equilibria appear, then they are asymptotically stable.…”

“…A simplified version of this network was analyzed in our previous work [8]. The dynamics are based in vitro transcription reactions [4], [9] and nucleic acid strand displacement [10]. Like other well known networks [4], [11], the circuit is characterized by an overall positive feedback loop created by two branches of transcriptional repression.…”