Even though synchronization in autonomous systems has been observed for over three centuries, reports of systematic experimental studies on synchronized oscillators are limited. Here, we report on observations of internal synchronization in coupled silicon micromechanical oscillators associated with a reduction in the relative phase random walk that is modulated by the magnitude of the reactive coupling force between the oscillators. Additionally, for the first time, a significant improvement in the frequency stability of synchronized micromechanical oscillators is reported. The concept presented here is scalable and could be suitably engineered to establish the basis for a new class of highly precise miniaturized clocks and frequency references.

Precise control over the nucleation, growth, and termination of self-assembly processes is a fundamental tool for controlling product yield and assembly dynamics. Mechanisms for altering these processes programmatically could allow the use of simple components to self-assemble complex final products or to design processes allowing for dynamic assembly or reconfiguration. Here we use DNA tile self-assembly to develop general design principles for building complexes that can bind to a growing biomolecular assembly and terminate its growth by systematically characterizing how different DNA origami nanostructures interact with the growing ends of DNA tile nanotubes. We find that nanostructures that present binding interfaces for all of the binding sites on a growing facet can bind selectively to growing ends and stop growth when these interfaces are presented on either a rigid or floppy scaffold. In contrast, nucleation of nanotubes requires the presentation of binding sites in an arrangement that matches the shape of the structure's facet. As a result, it is possible to build nanostructures that can terminate the growth of existing nanotubes but cannot nucleate a new structure. The resulting design principles for constructing structures that direct nucleation and termination of the growth of one-dimensional nanostructures can also serve as a starting point for programmatically directing two- and three-dimensional crystallization processes using nanostructure design.

An essential motif for the assembly of biological materials such as actin at the scale of hundreds of nanometers and beyond is a network of one-dimensional fibers with well-defined geometry. Here, we demonstrate the programmed organization of DNA filaments into micron-scale architectures where component filaments are oriented at preprogrammed angles. We assemble L-, T-, and Y-shaped DNA origami junctions that nucleate two or three micron length DNA nanotubes at high yields. The angles between the nanotubes mirror the angles between the templates on the junctions, demonstrating that nanoscale structures can control precisely how micron-scale architectures form. The ability to precisely program filament orientation could allow the assembly of complex filament architectures in two and three dimensions, including circuit structures, bundles, and extended materials.

Feedback allows biological systems to control gene expression precisely and reliably, even in the presence of uncertainty, by sensing and processing environmental changes. Taking inspiration from natural architectures, synthetic biologists have engineered feedback loops to tune the dynamics and improve the robustness and predictability of gene expression. However, experimental implementations of biomolecular control systems are still far from satisfying performance specifications typically achieved by electrical or mechanical control systems. To address this gap, we present mathematical models of biomolecular controllers that enable reference tracking, disturbance rejection, and tuning of the temporal response of gene expression. These controllers employ RNA transcriptional regulators to achieve closed loop control where feedback is introduced via molecular sequestration. Sensitivity analysis of the models allows us to identify which parameters influence the transient and steady state response of a target gene expression process, as well as which biologically plausible parameter values enable perfect reference tracking. We quantify performance using typical control theory metrics to characterize response properties and provide clear selection guidelines for practical applications. Our results indicate that RNA regulators are well-suited for building robust and precise feedback controllers for gene expression. Additionally, our approach illustrates several quantitative methods useful for assessing the performance of biomolecular feedback control systems.

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We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.

To build complex genetic networks with predictable behaviors, synthetic biologists use libraries of modular parts that can be characterized in isolation and assembled together to create programmable higher‐order functions. Characterization experiments and computational models for gene regulatory parts operating in isolation are routinely used to predict the dynamics of interconnected parts and guide the construction of new synthetic devices. Here, we individually characterize two modes of RNA‐based transcriptional regulation, using small transcription activating RNAs (STARs) and clustered regularly interspaced short palindromic repeats interference (CRISPRi), and show how their distinct regulatory timescales can be used to engineer a composed feedforward loop that creates a pulse of gene expression. We use a cell‐free transcription‐translation system (TXTL) to rapidly characterize the system, and we apply Bayesian inference to extract kinetic parameters for an ordinary differential equation‐based mechanistic model. We then demonstrate in simulation and verify with TXTL experiments that the simultaneous regulation of a single gene target with STARs and CRISPRi leads to a pulse of gene expression. Our results suggest the modularity of the two regulators in an integrated genetic circuit, and we anticipate that construction and modeling frameworks that can leverage this modularity will become increasingly important as synthetic circuits increase in complexity.

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 gene circuits, biological engineers have proposed various designs that 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 synthetic biomolecular controller executed in vitro. The controller ensures that gene expression rate tracks an externally imposed reference level, and achieves this goal even in the presence of certain kinds 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 system, which allows rapid prototyping and implementation. Modeling and theory guide experimental implementation with well-defined operational predictability.