Mathematical Modeling of RNA-Based Architectures for Closed Loop Control of Gene Expression

Developing, characterizing and modeling CRISPR-based point-of-use pathogen diagnostics

Recent years have seen intense interest in the development of point-of-care nucleic acid diagnostic technologies to address the scaling limitations of laboratory-based approaches. Chief among these are combinations of isothermal amplification approaches with CRISPR-based detection and readouts of target products. Here, we contribute to the growing body of rapid, programmable point-of-care pathogen tests by developing and optimizing a one-pot NASBA-Cas13a nucleic acid detection assay. This test uses the isothermal amplification technique NASBA to amplify target viral nucleic acids, followed by Cas13a-based detection of amplified sequences. We first demonstrate an in-house formulation of NASBA that enables optimization of individual NASBA components. We then present design rules for NASBA primer sets and LbuCas13a guide RNAs for fast and sensitive detection of SARS-CoV-2 viral RNA fragments, resulting in 20 - 200 aM sensitivity without any specialized equipment. Finally, we explore the combination of high-throughput assay condition screening with mechanistic ordinary differential equation modeling of the reaction scheme to gain a deeper understanding of the NASBA-Cas13a system. This work presents a framework for developing a mechanistic understanding of reaction performance and optimization that uses both experiments and modeling, which we anticipate will be useful in developing future nucleic acid detection technologies.

Noise properties of adaptation-conferring biochemical control modules

A key goal of synthetic biology is to develop functional biochemical modules with network-independent properties. Antithetic integral feedback (AIF) is a recently developed control module in which two control species perfectly annihilate each other's biological activity. The AIF module confers robust perfect adaptation to the steady-state average level of a controlled intracellular component when subjected to sustained perturbations. Recent work has suggested that such robustness comes at the unavoidable price of increased stochastic fluctuations around average levels. We present theoretical results that support and quantify this trade-off for the commonly analyzed AIF variant in the idealized limit with perfect annihilation. However, we also show that this trade-off is a singular limit of the control module: Even minute deviations from perfect adaptation allow systems to achieve effective noise suppression as long as cells can pay the corresponding energetic cost. We further show that a variant of the AIF control module can achieve significant noise suppression even in the idealized limit with perfect adaptation. This atypical configuration may thus be preferable in synthetic biology applications.

Regulation strategies for two-output biomolecular networks

Feedback control theory facilitates the development of self-regulating systems with desired performance which are predictable and insensitive to disturbances. Feedback regulatory topologies are found in many natural systems and have been of key importance in the design of reliable synthetic bio-devices operating in complex biological environments. Here, we study control schemes for biomolecular processes with two outputs of interest, expanding previously described concepts based on single-output systems. Regulation of such processes may unlock new design possibilities but can be challenging due to coupling interactions; also potential disturbances applied on one of the outputs may affect both. We therefore propose architectures for robustly manipulating the ratio/product and linear combinations of the outputs as well as each of the outputs independently. To demonstrate their characteristics, we apply these architectures to a simple process of two mutually activated biomolecular species. We also highlight the potential for experimental implementation by exploring synthetic realizations both in vivo and in vitro. This work presents an important step forward in building bio-devices capable of sophisticated functions.

Variability in cell-free expression reactions can impact qualitative genetic circuit characterization

Cell-free expression systems provide a suite of tools that are used in applications from sensing to biomanufacturing. One of these applications is genetic circuit prototyping, where the lack of cloning is required and a high degree of control over reaction components and conditions enables rapid testing of design candidates. Many studies have shown utility in the approach for characterizing genetic regulation elements, simple genetic circuit motifs, protein variants or metabolic pathways. However, variability in cell-free expression systems is a known challenge, whether between individuals, laboratories, instruments, or batches of materials. While the issue of variability has begun to be quantified and explored, little effort has been put into understanding the implications of this variability. For genetic circuit prototyping, it is unclear when and how significantly variability in reaction activity will impact qualitative assessments of genetic components, e.g. relative activity between promoters. Here, we explore this question by assessing DNA titrations of seven genetic circuits of increasing complexity using reaction conditions that ostensibly follow the same protocol but vary by person, instrument and material batch. Although the raw activities vary widely between the conditions, by normalizing within each circuit across conditions, reasonably consistent qualitative performance emerges for the simpler circuits. For the most complex case involving expression of three proteins, we observe a departure from this qualitative consistency, offering a provisional cautionary line where normal variability may disrupt reliable reuse of prototyping results. Our results also suggest that a previously described closed loop controller circuit may help to mitigate such variability, encouraging further work to design systems that are robust to variability. Graphical Abstract.

Model-Based Investigation of the Relationship between Regulation Level and Pulse Property of I1-FFL Gene Circuits

Mathematical models are powerful tools in guiding the construction of synthetic biological circuits, given their capability of accurately capturing and predicting circuit dynamics. Recent innovations in RNA technology have enabled the development of a variety of new tools for regulating gene expression at both the transcription and translation levels. However, the effects of different regulation levels on the circuit dynamics remain largely unexplored. In this study, we focus on the type 1 incoherent feed-forward loop (I1-FFL) gene circuit with four different variations (TX, TL, HY-1, HY-2), to investigate how regulation at the transcription and translation levels affect the circuit dynamics. We develop a mechanistic model for each of the four circuits and deploy sensitivity analysis to investigate the circuits' dynamics in terms of pulse generation. Based on the analysis, we observe that the repression regulation mechanism dominates the characteristics of the pulse as compared to the activation regulation mechanism and find that the I1-FFL with transcription repression has a higher chance of generating a pulse meeting the desired criteria. The experimental results in Escherichia coli also confirm our findings from the computational analysis. We expect our findings to facilitate future experimental construction of gene circuits with insights on the selection of appropriate transcription and translation regulation tools.

Controlling the Effects of External Perturbations on a Gene Regulatory Network Using Proportional-Integral-Derivative Controller

Gene regulatory networks are biologically robust, which imparts resilience to living systems against most external perturbations affecting them. However, there is a limit to this and disturbances beyond this limit can impart unwanted signalling on one or more master regulators in a network. Certain disturbances may affect the functioning of other constituent genes of the same network. In most cases, this phenomenon can have some effect on the functioning of the living organism. In this investigation, we have proposed a methodology to mitigate the effects of external perturbations on a genetic network using a proportional-integral-derivative controller. The proposed controller has been used to perturb one or more of the other unaffected master regulators such that the most affected gene/s of the network revert to their normal state. The only required condition of such type of manoeuvring is that there should be multiple master regulators in a network. The proposed technique has been experimented on a 10-gene DREAM4 benchmark network and also on a larger 20-gene network, where only downregulation has been considered due to data constraints. Simulation results indicate that the most vulnerable genes can be reverted to their normal expression levels in 10 out of the 16 simulations performed.

Dichotomous feedback: a signal sequestration-based feedback mechanism for biocontroller design

We introduce a new design framework for implementing negative feedback regulation in synthetic biology, which we term ‘dichotomous feedback’. Our approach is different from current methods, in that it sequesters existing fluxes in the process to be controlled, and in this way takes advantage of the process’s architecture to design the control law. This signal sequestration mechanism appears in many natural biological systems and can potentially be easier to realize than ‘molecular sequestration’ and other comparison motifs that are nowadays common in biomolecular feedback control design. The loop is closed by linking the strength of signal sequestration to the process output. Our feedback regulation mechanism is motivated by two-component signalling systems, where a second response regulator could be competing with the natural response regulator thus sequestering kinase activity. Here, dichotomous feedback is established by increasing the concentration of the second response regulator as the level of the output of the natural process increases. Extensive analysis demonstrates how this type of feedback shapes the signal response, attenuates intrinsic noise while increasing robustness and reducing crosstalk.

GAMES: A Dynamic Model Development Workflow for Rigorous Characterization of Synthetic Genetic Systems

Mathematical modeling is invaluable for advancing understanding and design of synthetic biological systems. However, the model development process is complicated and often unintuitive, requiring iteration on various computational tasks and comparisons with experimental data. Ad hoc model development can pose a barrier to reproduction and critical analysis of the development process itself, reducing the potential impact and inhibiting further model development and collaboration. To help practitioners manage these challenges, we introduce the Generation and Analysis of Models for Exploring Synthetic Systems (GAMES) workflow, which includes both automated and human-in-the-loop processes. We systematically consider the process of developing dynamic models, including model formulation, parameter estimation, parameter identifiability, experimental design, model reduction, model refinement, and model selection. We demonstrate the workflow with a case study on a chemically responsive transcription factor. The generalizable workflow presented in this tutorial can enable biologists to more readily build and analyze models for various applications.

Control of mammalian cell-based devices with genetic programming

Synthetic biology increasingly enables the construction of sophisticated functions in mammalian cells. A particularly promising frontier combines concepts drawn from industrial process control engineering-which is used to confer and balance properties such as stability and efficiency-with understanding as to how living systems have evolved to perform similar tasks with biological components. In this review, we first survey the state-of-the-art for both technologies and strategies available for genetic programming in mammalian cells. We then discuss recent progress in implementing programming objectives inspired by engineered and natural control mechanisms. Finally, we consider the transformative role of model-guided design in the present and future construction of customized mammalian cell functions for applications in biotechnology, medicine, and fundamental research.

Systematic Quantification of Sequence and Structural Determinants Controlling mRNA stability in Bacterial Operons

mRNA degradation is a central process that affects all gene expression levels, and yet, the determinants that control mRNA decay rates remain poorly characterized. Here, we applied a synthetic biology, learn-by-design approach to elucidate the sequence and structural determinants that control mRNA stability in bacterial operons. We designed, constructed, and characterized 82 operons in Escherichia coli, systematically varying RNase binding site characteristics, translation initiation rates, and transcriptional terminator efficiencies in the 5' untranslated region (UTR), intergenic, and 3' UTR regions, followed by measuring their mRNA levels using reverse transcription quantitative polymerase chain reaction (RT-qPCR) assays during exponential growth. We show that introducing long single-stranded RNA into 5' UTRs reduced mRNA levels by up to 9.4-fold and that lowering translation rates reduced mRNA levels by up to 11.8-fold. We also found that RNase binding sites in intergenic regions had much lower effects on mRNA levels. Surprisingly, changing the transcriptional termination efficiency or introducing long single-stranded RNA into 3' UTRs had no effect on upstream mRNA levels. From these measurements, we developed and validated biophysical models of ribosome protection and RNase activity with excellent quantitative agreement. We also formulated design rules to rationally control a mRNA's stability, facilitating the automated design of engineered genetic systems with desired functionalities.

Ultrasensitive molecular controllers for quasi-integral feedback

Feedback control has enabled the success of automated technologies by mitigating the effects of variability, unknown disturbances, and noise. While it is known that biological feedback loops reduce the impact of noise and help shape kinetic responses, many questions remain about how to design molecular integral controllers. Here, we propose a modular strategy to build molecular quasi-integral feedback controllers, which involves following two design principles. The first principle is to utilize an ultrasensitive response, which determines the gain of the controller and influences the steady-state error. The second is to use a tunable threshold of the ultrasensitive response, which determines the equilibrium point of the system. We describe a reaction network, named brink controller, that satisfies these conditions by combining molecular sequestration and an activation/deactivation cycle. With computational models, we examine potential biological implementations of brink controllers, and we illustrate different example applications.

Multidimensional Characterization of Parts Enhances Modeling Accuracy in Genetic Circuits

Mathematical models can aid the design of genetic circuits, but may yield inaccurate results if individual parts are not modeled at the appropriate resolution. To illustrate the importance of this concept, we study transcriptional cascades consisting of two inducible synthetic transcription factors connected in series. Despite the simplicity of this design, we find that accurate prediction of circuit behavior requires mapping the dose responses of each circuit component along the dimensions of both its expression level and its inducer concentration. Using this multidimensional characterization, we were able to computationally explore the behavior of 16 different circuit designs. We experimentally verified a subset of these predictions and found substantial agreement. This method of biological part characterization enables the use of models to identify (un)desired circuit behaviors prior to experimental implementation, thus shortening the design-build-test cycle for more complex circuits.

Modeling Cell-Free Protein Synthesis Systems-Approaches and Applications

In vitro systems are ideal setups to investigate the basic principles of biochemical reactions and subsequently the bricks of life. Cell-free protein synthesis (CFPS) systems mimic the transcription and translation processes of whole cells in a controlled environment and allow the detailed study of single components and reaction networks. In silico studies of CFPS systems help us to understand interactions and to identify limitations and bottlenecks in those systems. Black-box models laid the foundation for understanding the production and degradation dynamics of macromolecule components such as mRNA, ribosomes, and proteins. Subsequently, more sophisticated models revealed shortages in steps such as translation initiation and tRNA supply and helped to partially overcome these limitations. Currently, the scope of CFPS modeling has broadened to various applications, ranging from the screening of kinetic parameters to the stochastic analysis of liposome-encapsulated CFPS systems and the assessment of energy supply properties in combination with flux balance analysis (FBA).

Guidelines for designing the antithetic feedback motif

Integral feedback control is commonly used in mechanical and electrical systems to achieve zero steady-state error following an external disturbance. Equivalently, in biological systems, a property known as robust perfect adaptation guarantees robustness to environmental perturbations and return to the pre-disturbance state. Previously, Briat et al proposed a biomolecular design for integral feedback control (robust perfect adaptation) called the antithetic feedback motif. The antithetic feedback controller uses the sequestration binding reaction of two biochemical species to record the integral of the error between the current and the desired output of the network it controls. The antithetic feedback motif has been successfully built using synthetic components in vivo in Escherichia coli and Saccharomyces cerevisiae cells. However, these previous synthetic implementations of antithetic feedback have not produced perfect integral feedback control due to the degradation and dilution of the two controller species. Furthermore, previous theoretical results have cautioned that integral control can only be achieved under stability conditions that not all antithetic feedback motifs necessarily fulfill. In this paper, we study how to design antithetic feedback motifs that simultaneously achieve good stability and small steady-state error properties, even as the controller species are degraded and diluted. We provide simple tuning guidelines to achieve flexible and practical synthetic biological implementations of antithetic feedback control. We use several tools and metrics from control theory to design antithetic feedback networks, paving the path for the systematic design of synthetic biological controllers.

Cell-Free Systems: A Proving Ground for Rational Biodesign

Cell-free gene expression systems present an alternative approach to synthetic biology, where biological gene expression is harnessed inside non-living, in vitro biochemical reactions. Taking advantage of a plethora of recent experimental innovations, they easily overcome certain challenges for computer-aided biological design. For instance, their open nature renders all their components directly accessible, greatly facilitating model construction and validation. At the same time, these systems present their own unique difficulties, such as limited reaction lifetimes and lack of homeostasis. In this Perspective, I propose that cell-free systems are an ideal proving ground to test rational biodesign strategies, as demonstrated by a small but growing number of examples of model-guided, forward engineered cell-free biosystems. It is likely that advances gained from this approach will contribute to our efforts to more reliably and systematically engineer both cell-free as well as living cellular systems for useful applications.

Mathematical Models of Protease-Based Enzymatic Biosensors

An important goal of synthetic biology is to build biosensors and circuits with well-defined input-output relationships that operate at speeds found in natural biological systems. However, for molecular computation, most commonly used genetic circuit elements typically involve several steps from input detection to output signal production: transcription, translation, and post-translational modifications. These multiple steps together require up to several hours to respond to a single stimulus, and this limits the overall speed and complexity of genetic circuits. To address this gap, molecular frameworks that rely exclusively on post-translational steps to realize reaction networks that can process inputs at a time scale of seconds to minutes have been proposed. Here, we build mathematical models of fast biosensors capable of producing Boolean logic functionality. We employ protease-based chemical and light-induced switches, investigate their operation, and provide selection guidelines for their use as on-off switches. As a proof of concept, we implement a rapamycin-induced switch in vitro and demonstrate that its response qualitatively agrees with the predictions from our models. We then use these switches as elementary blocks, developing models for biosensors that can perform OR and XOR Boolean logic computation while using reaction conditions as tuning parameters. We use sensitivity analysis to determine the time-dependent sensitivity of the output to proteolytic and protein-protein binding reaction parameters. These fast protease-based biosensors can be used to implement complex molecular circuits with a capability of processing multiple inputs controllably and algorithmically. Our framework for evaluating and optimizing circuit performance can be applied to other molecular logic circuits.

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

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.

Low-Burden Biological Feedback Controllers for Near-Perfect Adaptation

The robustness and reliability of synthetic biological systems can be substantially improved by the introduction of feedback control architectures that parallel those employed in traditional engineering disciplines. One common control goal is adaptation (or disturbance rejection), which refers to a system's ability to maintain a constant output despite variation in some of its constituent processes (as frequently occurs in noisy cellular environments) or external perturbations. In this paper, we propose and analyze a control architecture that employs integrase and excisionase proteins to invert regions of DNA and an mRNA-mRNA annihilation reaction. Combined, these components approximate the functionality of a switching controller (as employed in classical control engineering) with three distinct operational modes. We demonstrate that this system is capable of near-perfect adaptation to variation in rates of both transcription and translation and can also operate without excessive consumption of cellular resources. The system's steady-state behavior is analyzed, and limits on its operating range are derived. Deterministic simulations of its dynamics are presented and are then extended to the stochastic case, which treats biochemical reactions as discrete events.

Synthetic negative feedback circuits using engineered small RNAs

Negative feedback is known to enable biological and man-made systems to perform reliably in the face of uncertainties and disturbances. To date, synthetic biological feedback circuits have primarily relied upon protein-based, transcriptional regulation to control circuit output. Small RNAs (sRNAs) are non-coding RNA molecules that can inhibit translation of target messenger RNAs (mRNAs). In this work, we modelled, built and validated two synthetic negative feedback circuits that use rationally-designed sRNAs for the first time. The first circuit builds upon the well characterised tet-based autorepressor, incorporating an externally-inducible sRNA to tune the effective feedback strength. This allows more precise fine-tuning of the circuit output in contrast to the sigmoidal, steep input–output response of the autorepressor alone. In the second circuit, the output is a transcription factor that induces expression of an sRNA, which inhibits translation of the mRNA encoding the output, creating direct, closed-loop, negative feedback. Analysis of the noise profiles of both circuits showed that the use of sRNAs did not result in large increases in noise. Stochastic and deterministic modelling of both circuits agreed well with experimental data. Finally, simulations using fitted parameters allowed dynamic attributes of each circuit such as response time and disturbance rejection to be investigated.

Hard Limits and Performance Tradeoffs in a Class of Antithetic Integral Feedback Networks

Feedback regulation is pervasive in biology at both the organismal and cellular level. In this article, we explore the properties of a particular biomolecular feedback mechanism called antithetic integral feedback, which can be implemented using the binding of two molecules. Our work develops an analytic framework for understanding the hard limits, performance tradeoffs, and architectural properties of this simple model of biological feedback control. Using tools from control theory, we show that there are simple parametric relationships that determine both the stability and the performance of these systems in terms of speed, robustness, steady-state error, and leakiness. These findings yield a holistic understanding of the behavior of antithetic integral feedback and contribute to a more general theory of biological control systems.

Architectural Principles for Characterizing the Performance of Antithetic Integral Feedback Networks

As we begin to design increasingly complex synthetic biomolecular systems, it is essential to develop rational design methodologies that yield predictable circuit performance. Here we apply mathematical tools from the theory of control and dynamical systems to yield practical insights into the architecture and function of a particular class of biological feedback circuit. Specifically, we show that it is possible to analytically characterize both the operating regime and performance tradeoffs of an antithetic integral feedback circuit architecture. Furthermore, we demonstrate how these principles can be applied to inform the design process of a particular synthetic feedback circuit.

Cell-machine interfaces for characterizing gene regulatory network dynamics

Gene regulatory networks and the dynamic responses they produce offer a wealth of information about how biological systems process information about their environment. Recently, researchers interested in dissecting these networks have been outsourcing various parts of their experimental workflow to computers. Here we review how, using microfluidic or optogenetic tools coupled with fluorescence imaging, it is now possible to interface cells and computers. These platforms enable scientists to perform informative dynamic stimulations of genetic pathways and monitor their reaction. It is also possible to close the loop and regulate genes in real time, providing an unprecedented view of how signals propagate through the network. Finally, we outline new tools that can be used within the framework of cell-machine interfaces.

A quasi-integral controller for adaptation of genetic modules to variable ribosome demand

The behavior of genetic circuits is often poorly predictable. A gene’s expression level is not only determined by the intended regulators, but also affected by changes in ribosome availability imparted by expression of other genes. Here we design a quasi-integral biomolecular feedback controller that enables the expression level of any gene of interest (GOI) to adapt to changes in available ribosomes. The feedback is implemented through a synthetic small RNA (sRNA) that silences the GOI’s mRNA, and uses orthogonal extracytoplasmic function (ECF) sigma factor to sense the GOI’s translation and to actuate sRNA transcription. Without the controller, the expression level of the GOI is reduced by 50% when a resource competitor is activated. With the controller, by contrast, gene expression level is practically unaffected by the competitor. This feedback controller allows adaptation of genetic modules to variable ribosome demand and thus aids modular construction of complicated circuits.

Competition for shared cellular resources often renders genetic circuits poorly predictable. Here the authors design a biomolecular quasi-integral controller that allows gene expression to adapt to variable demand in translation resources.