Synthetic in vitro transcriptional oscillators

The construction of synthetic biochemical circuits from simple components illuminates how complex behaviors can arise in chemistry and builds a foundation for future biological technologies. A simplified analog of genetic regulatory networks, in vitro transcriptional circuits, provides a modular platform for the systematic construction of arbitrary circuits and requires only two essential enzymes, bacteriophage T7 RNA polymerase and Escherichia coli ribonuclease H, to produce and degrade RNA signals. In this study, we design and experimentally demonstrate three transcriptional oscillators in vitro. First, a negative feedback oscillator comprising two switches, regulated by excitatory and inhibitory RNA signals, showed up to five complete cycles. To demonstrate modularity and to explore the design space further, a positive-feedback loop was added that modulates and extends the oscillatory regime. Finally, a three-switch ring oscillator was constructed and analyzed. Mathematical modeling guided the design process, identified experimental conditions likely to yield oscillations, and explained the system's robust response to interference by short degradation products. Synthetic transcriptional oscillators could prove valuable for systematic exploration of biochemical circuit design principles and for controlling nanoscale devices and orchestrating processes within artificial cells

Bistability of an In Vitro Synthetic Autoregulatory Switch

The construction of synthetic biochemical circuits is an essential step for developing quantitative understanding of information processing in natural organisms. Here, we report construction and analysis of an in vitro circuit with positive autoregulation that consists of just four synthetic DNA strands and three enzymes, bacteriophage T7 RNA polymerase, Escherichia coli ribonuclease (RNase) H, and RNase R. The modularity of the DNA switch template allowed a rational design of a synthetic DNA switch regulated by its RNA output acting as a transcription activator. We verified that the thermodynamic and kinetic constraints dictated by the sequence design criteria were enough to experimentally achieve the intended dynamics: a transcription activator configured to regulate its own production. Although only RNase H is necessary to achieve bistability of switch states, RNase R is necessary to maintain stable RNA signal levels and to control incomplete degradation products. A simple mathematical model was used to fit ensemble parameters for the training set of experimental results and was then directly applied to predict time-courses of switch dynamics and sensitivity to parameter variations with reasonable agreement. The positive autoregulation switches can be used to provide constant input signals and store outputs of biochemical networks and are potentially useful for chemical control applications

Ensemble Bayesian Analysis of Bistability in a Synthetic Transcriptional Switch

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

Neural network computation by in vitro transcriptional circuits

The structural similarity of neural networks and genetic regulatory networks to digital circuits, and hence to each other, was noted from the very beginning of their study [1, 2]. In this work, we propose a simple biochemical system whose architecture mimics that of genetic regulation and whose components allow for in vitro implementation of arbitrary circuits. We use only two enzymes in addition to DNA and RNA molecules: RNA polymerase (RNAP) and ribonuclease (RNase). We develop a rate equation for in vitro transcriptional networks, and derive a correspondence with general neural network rate equations [3]. As proof-of-principle demonstrations, an associative memory task and a feedforward network computation are shown by simulation. A difference between the neural network and biochemical models is also highlighted: global coupling of rate equations through enzyme saturation can lead to global feedback regulation, thus allowing a simple network without explicit mutual inhibition to perform the winner-take-all computation. Thus, the full complexity of the cell is not necessary for biochemical computation: a wide range of functional behaviors can be achieved with a small set of biochemical components

Robustness analysis of a nucleic acid controller for a dynamic biomolecular process using the structured singular value

In the field of synthetic biology, theoretical frameworks and software tools are now available that allow control systems represented as chemical reaction networks to be translated directly into nucleic acid-based chemistry, and hence implement embedded control circuitry for biomolecular processes. However, the development of tools for analysing the robustness of such controllers is still in its infancy. An interesting feature of such control circuits is that, although the transfer function of a linear system can be easily implemented via a chemical network of catalysis, degradation and annihilation reactions, this introduces additional nonlinear dynamics, due to the annihilation kinetics. We exemplify this problem for a dynamical biomolecular feedback system, and demonstrate how the structured singular value (μ) analysis framework can be extended to rigorously analyse the robustness of this class of system. We show that parametric uncertainty in the system affects the location of its equilibrium, and that this must be taken into account in the analysis. We also show that the parameterisation of the system can be scaled for experimental feasibility without affecting its robustness properties, and that a statistical analysis via Monte Carlo simulation fails to uncover the worst-case uncertainty combination found by μ-analysis.</p

Robust mixing in self-consistent linearized augmented planewave calculations

We devise a mixing algorithm for full-potential (FP) all-electron calculations in the linearized augmented planewave (LAPW) method. Pulay's direct inversion in the iterative subspace is complemented with the Kerker preconditioner and further improvements to achieve smooth convergence, avoiding charge sloshing and noise in the exchange-correlation potential. As the Kerker preconditioner was originally designed for the planewave basis, we have adapted it to the FP-LAPW method and implemented in the exciting code. Applications to the $2\times 2$ Au(111) surface with a vacancy and to the Pd(111) surface demonstrate that this approach and our implementation work reliably with both density and potential mixing