A universal biomolecular integral feedback controller for robust perfect adaptation

Synthetic microbial ecology: engineering habitats for modular consortia

Microbiomes, the complex networks of micro-organisms and the molecules through which they interact, play a crucial role in health and ecology. Over at least the past two decades, engineering biology has made significant progress, impacting the bio-based industry, health, and environmental sectors; but has only recently begun to explore the engineering of microbial ecosystems. The creation of synthetic microbial communities presents opportunities to help us understand the dynamics of wild ecosystems, learn how to manipulate and interact with existing microbiomes for therapeutic and other purposes, and to create entirely new microbial communities capable of undertaking tasks for industrial biology. Here, we describe how synthetic ecosystems can be constructed and controlled, focusing on how the available methods and interaction mechanisms facilitate the regulation of community composition and output. While experimental decisions are dictated by intended applications, the vast number of tools available suggests great opportunity for researchers to develop a diverse array of novel microbial ecosystems.

Context-dependent redesign of robust synthetic gene circuits

Cells provide dynamic platforms for executing exogenous genetic programs in synthetic biology, resulting in highly context-dependent circuit performance. Recent years have seen an increasing interest in understanding the intricacies of circuit-host relationships, their influence on the synthetic bioengineering workflow, and in devising strategies to alleviate undesired effects. We provide an overview of how emerging circuit-host interactions, such as growth feedback and resource competition, impact both deterministic and stochastic circuit behaviors. We also emphasize control strategies for mitigating these unwanted effects. This review summarizes the latest advances and the current state of host-aware and resource-aware design of synthetic gene circuits.

Inteins: A Swiss army knife for synthetic biology

Inteins are proteins found in nature that execute protein splicing. Among them, split inteins stand out for their versatility and adaptability, presenting creative solutions for addressing intricate challenges in various biological applications. Their exquisite attributes, including compactness, reliability, orthogonality, low toxicity, and irreversibility, make them of interest to various fields including synthetic biology, biotechnology and biomedicine. In this review, we delve into the inherent challenges of using inteins, present approaches for overcoming these challenges, and detail their reliable use for specific cellular tasks. We will discuss the use of conditional inteins in areas like cancer therapy, drug screening, patterning, infection treatment, diagnostics and biocontainment. Additionally, we will underscore the potential of inteins in executing basic logical operations with practical implications. We conclude by showcasing their potential in crafting complex genetic circuits for performing computations and feedback control that achieves robust perfect adaptation.

Stochastic Gene Expression in Proliferating Cells: Differing Noise Intensity in Single-Cell and Population Perspectives

Random fluctuations (noise) in gene expression can be studied from two complementary perspectives: following expression in a single cell over time or comparing expression between cells in a proliferating population at a given time. Here, we systematically investigated scenarios where both perspectives lead to different levels of noise in a given gene product. We first consider a stable protein, whose concentration is diluted by cellular growth, and the protein inhibits growth at high concentrations, establishing a positive feedback loop. For a stochastic model with molecular bursting of gene products, we analytically predict and contrast the steady-state distributions of protein concentration in both frameworks. Although positive feedback amplifies the noise in expression, this amplification is much higher in the population framework compared to following a single cell over time. We also study other processes that lead to different noise levels even in the absence of such dilution-based feedback. When considering randomness in the partitioning of molecules between daughters during mitosis, we find that in the single-cell perspective, the noise in protein concentration is independent of noise in the cell cycle duration. In contrast, partitioning noise is amplified in the population perspective by increasing randomness in cell-cycle time. Overall, our results show that the commonly used single-cell framework that does not account for proliferating cells can, in some cases, underestimate the noise in gene product levels. These results have important implications for studying the inter-cellular variation of different stress-related expression programs across cell types that are known to inhibit cellular growth.

Accelerating Genetic Sensor Development, Scale-up, and Deployment Using Synthetic Biology

Living cells are exquisitely tuned to sense and respond to changes in their environment. Repurposing these systems to create engineered biosensors has seen growing interest in the field of synthetic biology and provides a foundation for many innovative applications spanning environmental monitoring to improved biobased production. In this review, we present a detailed overview of currently available biosensors and the methods that have supported their development, scale-up, and deployment. We focus on genetic sensors in living cells whose outputs affect gene expression. We find that emerging high-throughput experimental assays and evolutionary approaches combined with advanced bioinformatics and machine learning are establishing pipelines to produce genetic sensors for virtually any small molecule, protein, or nucleic acid. However, more complex sensing tasks based on classifying compositions of many stimuli and the reliable deployment of these systems into real-world settings remain challenges. We suggest that recent advances in our ability to precisely modify nonmodel organisms and the integration of proven control engineering principles (e.g., feedback) into the broader design of genetic sensing systems will be necessary to overcome these hurdles and realize the immense potential of the field.

Homeostasis in networks with multiple inputs

Homeostasis, also known as adaptation, refers to the ability of a system to counteract persistent external disturbances and tightly control the output of a key observable. Existing studies on homeostasis in network dynamics have mainly focused on 'perfect adaptation' in deterministic single-input single-output networks where the disturbances are scalar and affect the network dynamics via a pre-specified input node. In this paper we provide a full classification of all possible network topologies capable of generating infinitesimal homeostasis in arbitrarily large and complex multiple inputs networks. Working in the framework of 'infinitesimal homeostasis' allows us to make no assumption about how the components are interconnected and the functional form of the associated differential equations, apart from being compatible with the network architecture. Remarkably, we show that there are just three distinct 'mechanisms' that generate infinitesimal homeostasis. Each of these three mechanisms generates a rich class of well-defined network topologies-called homeostasis subnetworks. More importantly, we show that these classes of homeostasis subnetworks provides a topological basis for the classification of 'homeostasis types': the full set of all possible multiple inputs networks can be uniquely decomposed into these special homeostasis subnetworks. We illustrate our results with some simple abstract examples and a biologically realistic model for the co-regulation of calcium ( Ca ) and phosphate ( PO 4 ) in the rat. Furthermore, we identify a new phenomenon that occurs in the multiple input setting, that we call homeostasis mode interaction, in analogy with the well-known characteristic of multiparameter bifurcation theory.

Advanced methods for gene network identification and noise decomposition from single-cell data

Central to analyzing noisy gene expression systems is solving the Chemical Master Equation (CME), which characterizes the probability evolution of the reacting species' copy numbers. Solving CMEs for high-dimensional systems suffers from the curse of dimensionality. Here, we propose a computational method for improved scalability through a divide-and-conquer strategy that optimally decomposes the whole system into a leader system and several conditionally independent follower subsystems. The CME is solved by combining Monte Carlo estimation for the leader system with stochastic filtering procedures for the follower subsystems. We demonstrate this method with high-dimensional numerical examples and apply it to identify a yeast transcription system at the single-cell resolution, leveraging mRNA time-course experimental data. The identification results enable an accurate examination of the heterogeneity in rate parameters among isogenic cells. To validate this result, we develop a noise decomposition technique exploiting time-course data but requiring no supplementary components, e.g., dual-reporters.

Lattice ultrasensitivity produces large gain in E. coli chemosensing

E. coli use a regular lattice of receptors and attached kinases to detect and amplify faint chemical signals. Kinase output is characterized by precise adaptation to a wide range of background ligand levels and large gain in response to small relative changes in ligand concentration. These characteristics are well described by models which achieve their gain through equilibrium cooperativity. But these models are challenged by two experimental results. First, neither adaptation nor large gain are present in receptor binding assays. Second, in cells lacking adaptation machinery, fluctuations can sometimes be enormous, with essentially all kinases transitioning together. Here we introduce a far-from equilibrium model in which receptors gate the spread of activity between neighboring kinases. This model achieves large gain through a mechanism we term lattice ultrasensitivity (LU). In our LU model, kinase and receptor states are separate degrees of freedom, and kinase kinetics are dominated by chemical rates far-from-equilibrium rather than by equilibrium allostery. The model recapitulates the successes of past models, but also matches the challenging experimental findings. Importantly, unlike past lattice critical models, our LU model does not require parameters to be fine tuned for function.

Noise Reduction in Resource-Coupled Multi-Module Gene Circuits through Antithetic Feedback Control

Gene circuits within the same host cell often experience coupling, stemming from the competition for limited resources during transcriptional and translational processes. This resource competition introduces an additional layer of noise to gene expression. Here we present three multi-module antithetic control strategies: negatively competitive regulation (NCR) controller, alongside local and global controllers, aimed at reducing the gene expression noise within the context of resource competition. Through stochastic simulations and fluctuation-dissipation theorem (FDT) analysis, our findings highlight the superior performance of the NCR antithetic controller in reducing noise levels. Our research provides an effective control strategy for attenuating resource-driven noise and offers insight into the development of robust gene circuits.

Signal integration and integral feedback control with biochemical reaction networks

Biochemical reaction networks perform a variety of signal processing functions, one of which is computing the integrals of signal values. This is often used in integral feedback control, where it enables a system's output to respond to changing inputs, but to then return exactly back to some pre-determined setpoint value afterward. To gain a deeper understanding of how biochemical networks are able to both integrate signals and perform integral feedback control, we investigated these abilities for several simple reaction networks. We found imperfect overlap between these categories, with some networks able to perform both tasks, some able to perform integration but not integral feedback control, and some the other way around. Nevertheless, networks that could either integrate or perform integral feedback control shared key elements. In particular, they included a chemical species that was neutrally stable in the open loop system (no feedback), meaning that this species does not have a unique stable steady-state concentration. Neutral stability could arise from zeroth order decay reactions, binding to a partner that was produced at a constant rate (which occurs in antithetic control), or through a long chain of covalent cycles. Mathematically, it arose from rate equations for the reaction network that were underdetermined when evaluated at steady-state.

Design and Model-Driven Analysis of Synthetic Circuits with the Staphylococcus aureus Dead-Cas9 (sadCas9) as a Programmable Transcriptional Regulator in Bacteria

Synthetic circuit design is crucial for engineering microbes that process environmental cues and provide biologically relevant outputs. To reliably scale-up circuit complexity, the availability of parts toolkits is central. Streptococcus pyogenes (sp)-derived CRISPR interference/dead-Cas9 (CRISPRi/spdCas9) is widely adopted for implementing programmable regulations in synthetic circuits, and alternative CRISPRi systems will further expand our toolkits of orthogonal components. Here, we showcase the potential of CRISPRi using the engineered dCas9 from Staphylococcus aureus (sadCas9), not previously used in bacterial circuits, that is attractive for its low size and high specificity. We designed a collection of ∼20 increasingly complex circuits and variants in Escherichia coli, including circuits with static function like one-/two-input logic gates (NOT, NAND), circuits with dynamic behavior like incoherent feedforward loops (iFFLs), and applied sadCas9 to fix a T7 polymerase-based cascade. Data demonstrated specific and efficient target repression (100-fold) and qualitatively successful functioning for all circuits. Other advantageous features included low sadCas9-borne cell load and orthogonality with spdCas9. However, different circuit variants showed quantitatively unexpected and previously unreported steady-state responses: the dynamic range, switch point, and slope of NOT/NAND gates changed for different output promoters, and a multiphasic behavior was observed in iFFLs, differing from the expected bell-shaped or sigmoidal curves. Model analysis explained the observed curves by complex interplays among components, due to reporter gene-borne cell load and regulator competition. Overall, CRISPRi/sadCas9 successfully expanded the available toolkit for bacterial engineering. Analysis of our circuit collection depicted the impact of generally neglected effects modulating the shape of component dose-response curves, to avoid drawing wrong conclusions on circuit functioning.

A coarse-grained bacterial cell model for resource-aware analysis and design of synthetic gene circuits

Within a cell, synthetic and native genes compete for expression machinery, influencing cellular process dynamics through resource couplings. Models that simplify competitive resource binding kinetics can guide the design of strategies for countering these couplings. However, in bacteria resource availability and cell growth rate are interlinked, which complicates resource-aware biocircuit design. Capturing this interdependence requires coarse-grained bacterial cell models that balance accurate representation of metabolic regulation against simplicity and interpretability. We propose a coarse-grained E. coli cell model that combines the ease of simplified resource coupling analysis with appreciation of bacterial growth regulation mechanisms and the processes relevant for biocircuit design. Reliably capturing known growth phenomena, it provides a unifying explanation to disparate empirical relations between growth and synthetic gene expression. Considering a biomolecular controller that makes cell-wide ribosome availability robust to perturbations, we showcase our model's usefulness in numerically prototyping biocircuits and deriving analytical relations for design guidance.

Design patterns of biological cells

Design patterns are generalized solutions to frequently recurring problems. They were initially developed by architects and computer scientists to create a higher level of abstraction for their designs. Here, we extend these concepts to cell biology to lend a new perspective on the evolved designs of cells' underlying reaction networks. We present a catalog of 21 design patterns divided into three categories: creational patterns describe processes that build the cell, structural patterns describe the layouts of reaction networks, and behavioral patterns describe reaction network function. Applying this pattern language to the E. coli central metabolic reaction network, the yeast pheromone response signaling network, and other examples lends new insights into these systems.

Analysis and design of antithetic proportional-integral-derivative biocontrol-systems with species dilution

The nonlinearity and non-separability of the antithetic PID (aPID) controller have provided greater flexibility in the design of biochemical reaction networks (BCRNs), resulting in significant impacts on biocontrol-systems. Nevertheless, the dilution of control species is disregarded in designs of aPID controllers, which would lead to the failure of inhibition mechanism in the controller and loss of robust perfect adaptation (RPA)-the biological counterpart of robust steady-state tracking. Here, the impact of dilution processes on the structure of aPID is investigated in this study. It is discovered that the proportional and low-pass filters are altered when the dilution processes is present in control species, which increases the coupling between the controller parameters. Moreover, additional integrations for the reference signal and control output generated by control species dilution further leads to the loss of RPA. Subsequently, a novel aPID controller represented by BCRNs, termed quasi-aPID, has been designed to eliminate the detrimental effects of the dilution processes. In an effort to ameliorate the interdependencies among controller parameters, a degradation inhibition mechanism is employed within this controller. Furthermore, this work establishes the limiting relationship between the controller's reaction rates in order to guarantee RPA, while abstaining from the introduction of supplementary species and biochemical reactions. By using the quasi-aPID controller in both the Escherichia coli gene expression model and the whole-body cholesterol metabolism model, its effectiveness is confirmed. Simulation results demonstrate that, the quasi-aPID exhibits a smaller absolute steady-state error in both models and guarantees the RPA property.

Realizing Antithetic Integral Feedback Control in Mammalian Cells

Genetic circuit engineering has emerged as a powerful methodology to program the behavior of mammalian cells to respond to internal and external cues. This approach is now used to develop new therapeutics and improve production processes. However, genetic interaction networks are complex and hard to engineer rationally. Moreover, a design may fail, and it may not be possible to identify the root cause of its breakdown. Introducing designated regulatory circuitry in the form of integral feedback can introduce performance guarantees by ensuring robust and precise operation.

Repeated Decision Stumping Distils Simple Rules from Single-Cell Data

Single-cell data afford unprecedented insights into molecular processes. But the complexity and size of these data sets have proved challenging and given rise to a large armory of statistical and machine learning approaches. The majority of approaches focuses on either describing features of these data, or making predictions and classifying unlabeled samples. In this study, we introduce repeated decision stumping (ReDX) as a method to distill simple models from single-cell data. We develop decision trees of depth one-hence "stumps"-to identify in an inductive manner, gene products involved in driving cell fate transitions, and in applications to published data we are able to discover the key players involved in these processes in an unbiased manner without prior knowledge. Our algorithm is deliberately targeting the simplest possible candidate hypotheses that can be extracted from complex high-dimensional data. There are three reasons for this: (1) the predictions become straightforwardly testable hypotheses; (2) the identified candidates form the basis for further mechanistic model development, for example, for engineering and synthetic biology interventions; and (3) this approach complements existing descriptive modeling approaches and frameworks. The approach is computationally efficient, has remarkable predictive power, including in simulation studies where the ground truth is known, and yields robust and statistically stable predictors; the same set of candidates is generated by applying the algorithm to different subsamples of experimental data.

Customizing cellular signal processing by synthetic multi-level regulatory circuits

As synthetic biology permeates society, the signal processing circuits in engineered living systems must be customized to meet practical demands. Towards this mission, novel regulatory mechanisms and genetic circuits with unprecedented complexity have been implemented over the past decade. These regulatory mechanisms, such as transcription and translation control, could be integrated into hybrid circuits termed "multi-level circuits". The multi-level circuit design will tremendously benefit the current genetic circuit design paradigm, from modifying basic circuit dynamics to facilitating real-world applications, unleashing our capabilities to customize cellular signal processing and address global challenges through synthetic biology.

Competition and evolutionary selection among core regulatory motifs in gene expression control

Gene products that are beneficial in one environment may become burdensome in another, prompting the emergence of diverse regulatory schemes that carry their own bioenergetic cost. By ensuring that regulators are only expressed when needed, we demonstrate that autoregulation generally offers an advantage in an environment combining mutation and time-varying selection. Whether positive or negative feedback emerges as dominant depends primarily on the demand for the target gene product, typically to ensure that the detrimental impact of inevitable mutations is minimized. While self-repression of the regulator curbs the spread of these loss-of-function mutations, self-activation instead facilitates their propagation. By analyzing the transcription network of multiple model organisms, we reveal that reduced bioenergetic cost may contribute to the preferential selection of autoregulation among transcription factors. Our results not only uncover how seemingly equivalent regulatory motifs have fundamentally different impact on population structure, growth dynamics, and evolutionary outcomes, but they can also be leveraged to promote the design of evolutionarily robust synthetic gene circuits.

Steering and controlling evolution - from bioengineering to fighting pathogens

Control interventions steer the evolution of molecules, viruses, microorganisms or other cells towards a desired outcome. Applications range from engineering biomolecules and synthetic organisms to drug, therapy and vaccine design against pathogens and cancer. In all these instances, a control system alters the eco-evolutionary trajectory of a target system, inducing new functions or suppressing escape evolution. Here, we synthesize the objectives, mechanisms and dynamics of eco-evolutionary control in different biological systems. We discuss how the control system learns and processes information about the target system by sensing or measuring, through adaptive evolution or computational prediction of future trajectories. This information flow distinguishes pre-emptive control strategies by humans from feedback control in biotic systems. We establish a cost-benefit calculus to gauge and optimize control protocols, highlighting the fundamental link between predictability of evolution and efficacy of pre-emptive control.

Prevalence of and gene regulatory constraints on transcriptional adaptation in single cells

Cells and tissues have a remarkable ability to adapt to genetic perturbations via a variety of molecular mechanisms. Nonsense-induced transcriptional compensation, a form of transcriptional adaptation, has recently emerged as one such mechanism, in which nonsense mutations in a gene can trigger upregulation of related genes, possibly conferring robustness at cellular and organismal levels. However, beyond a handful of developmental contexts and curated sets of genes, to date, no comprehensive genome-wide investigation of this behavior has been undertaken for mammalian cell types and contexts. Moreover, how the regulatory-level effects of inherently stochastic compensatory gene networks contribute to phenotypic penetrance in single cells remains unclear. Here we combine computational analysis of existing datasets with stochastic mathematical modeling and machine learning to uncover the widespread prevalence of transcriptional adaptation in mammalian systems and the diverse single-cell manifestations of minimal compensatory gene networks. Regulon gene expression analysis of a pooled single-cell genetic perturbation dataset recapitulates important model predictions. Our integrative approach uncovers several putative hits-genes demonstrating possible transcriptional adaptation-to follow up on experimentally, and provides a formal quantitative framework to test and refine models of transcriptional adaptation.

Diya - A universal light illumination platform for multiwell plate cultures

Recent progress in protein engineering has established optogenetics as one of the leading external non-invasive stimulation strategies, with many optogenetic tools being designed for in vivo operation. Characterization and optimization of these tools require a high-throughput and versatile light delivery system targeting micro-titer culture volumes. Here, we present a universal light illumination platform - Diya, compatible with a wide range of cell culture plates and dishes. Diya hosts specially designed features ensuring active thermal management, homogeneous illumination, and minimal light bleedthrough. It offers light induction programming via a user-friendly custom-designed GUI. Through extensive characterization experiments with multiple optogenetic tools in diverse model organisms (bacteria, yeast, and human cell lines), we show that Diya maintains viable conditions for cell cultures undergoing light induction. Finally, we demonstrate an optogenetic strategy for in vivo biomolecular controller operation. With a custom-designed antithetic integral feedback circuit, we exhibit robust perfect adaptation and light-controlled set-point variation using Diya.

Advances in automated and reactive flow cytometry for synthetic biotechnology

Automated flow cytometry (FC) has been initially considered for bioprocess monitoring and optimization. More recently, new physical and software interfaces have been made available, facilitating the access to this technology for labs and industries. It also comes with new capabilities, such as being able to act on the cultivation conditions based on population data. This approach, known as reactive FC, extended the range of applications of automated FC to bioprocess control and the stabilization of cocultures, but also to the broad field of synthetic and systems biology for the characterization of gene circuits. However, several issues must be addressed before automated and reactive FC can be considered standard and modular technologies.

Robust homeostasis of cellular cholesterol is a consequence of endogenous antithetic integral control

Although cholesterol is essential for cellular viability and proliferation, it is highly toxic in excess. The concentration of cellular cholesterol must therefore be maintained within tight tolerances, and is thought to be subject to a stringent form of homeostasis known as Robust Perfect Adaptation (RPA). While much is known about the cellular signalling interactions involved in cholesterol regulation, the specific chemical reaction network structures that might be responsible for the robust homeostatic regulation of cellular cholesterol have been entirely unclear until now. In particular, the molecular mechanisms responsible for sensing excess whole-cell cholesterol levels have not been identified previously, and no mathematical models to date have been able to capture an integral control implementation that could impose RPA on cellular cholesterol. Here we provide a detailed mathematical description of cholesterol regulation pathways in terms of biochemical reactions, based on an extensive review of experimental and clinical literature. We are able to decompose the associated chemical reaction network structures into several independent subnetworks, one of which is responsible for conferring RPA on several intracellular forms of cholesterol. Remarkably, our analysis reveals that RPA in the cholesterol concentration in the endoplasmic reticulum (ER) is almost certainly due to a well-characterised control strategy known as antithetic integral control which, in this case, involves the high-affinity binding of a multi-molecular transcription factor complex with cholesterol molecules that are excluded from the ER membrane. Our model provides a detailed framework for exploring the necessary biochemical conditions for robust homeostatic control of essential and tightly regulated cellular molecules such as cholesterol.

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.

Unbalanced response to growth variations reshapes the cell fate decision landscape

The global regulation of cell growth rate on gene expression perturbs the performance of gene networks, which would impose complex variations on the cell-fate decision landscape. Here we use a simple synthetic circuit of mutual repression that allows a bistable landscape to examine how such global regulation would affect the stability of phenotypic landscape and the accompanying dynamics of cell-fate determination. We show that the landscape experiences a growth-rate-induced bifurcation between monostability and bistability. Theoretical and experimental analyses reveal that this bifurcating deformation of landscape arises from the unbalanced response of gene expression to growth variations. The path of growth transition across the bifurcation would reshape cell-fate decisions. These results demonstrate the importance of growth regulation on cell-fate determination processes, regardless of specific molecular signaling or regulation.

A portable regulatory RNA array design enables tunable and complex regulation across diverse bacteria

A lack of composable and tunable gene regulators has hindered efforts to engineer non-model bacteria and consortia. Toward addressing this, we explore the broad-host potential of small transcription activating RNA (STAR) and propose a design strategy to achieve tunable gene control. First, we demonstrate that STARs optimized for E. coli function across different Gram-negative species and can actuate using phage RNA polymerase, suggesting that RNA systems acting at the level of transcription are portable. Second, we explore an RNA design strategy that uses arrays of tandem and transcriptionally fused RNA regulators to precisely alter regulator concentration from 1 to 8 copies. This provides a simple means to predictably tune output gain across species and does not require access to large regulatory part libraries. Finally, we show RNA arrays can be used to achieve tunable cascading and multiplexing circuits across species, analogous to the motifs used in artificial neural networks.

Coherent feedback leads to robust background compensation in oscillatory and non-oscillatory homeostats

When in a reaction kinetic integral controller a step perturbation is applied besides a constant background, the concentration of a controlled variable (described as A) will generally respond with decreased response amplitudes ΔA as backgrounds increase. The controller variable E will at the same time provide the necessary compensatory flux to move A back to its set-point. A typical example of decreased response amplitudes at increased backgrounds is found in retinal light adaptation. Due to remarks in the literature that retinal light adaptation would also involve a compensation of backgrounds we became interested in conditions how background compensation could occur. In this paper we describe novel findings how background influences can be robustly eliminated. When such a background compensation is active, oscillatory controllers will respond to a defined perturbation with always the same (damped or undamped) frequency profile, or in the non-oscillatory case, with the same response amplitude ΔA, irrespective of the background level. To achieve background compensation we found that two conditions need to apply: (i) an additional set of integral controllers (here described as I1 and I2) have to be employed to keep the manipulated variable E at a defined set-point, and (ii), I1 and I2 need to feed back to the A-E signaling axis directly through the controlled variable A. In analogy to a similar feedback applied in quantum control theory, we term these feedback conditions as 'coherent feedback'. When analyzing retinal light adaptations in more detail, we find no evidence of the presence of background compensation mechanisms. Although robust background compensation, as described theoretically here, appears to be an interesting regulatory property, relevant biological or biochemical examples still need to be identified.

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.

Structural identifiability of biomolecular controller motifs with and without flow measurements as model output

Controller motifs are simple biomolecular reaction networks with negative feedback. They can explain how regulatory function is achieved and are often used as building blocks in mathematical models of biological systems. In this paper we perform an extensive investigation into structural identifiability of controller motifs, specifically the so-called basic and antithetic controller motifs. Structural identifiability analysis is a useful tool in the creation and evaluation of mathematical models: it can be used to ensure that model parameters can be determined uniquely and to examine which measurements are necessary for this purpose. This is especially useful for biological models where parameter estimation can be difficult due to limited availability of measureable outputs. Our aim with this work is to investigate how structural identifiability is affected by controller motif complexity and choice of measurements. To increase the number of potential outputs we propose two methods for including flow measurements and show how this affects structural identifiability in combination with, or in the absence of, concentration measurements. In our investigation, we analyze 128 different controller motif structures using a combination of flow and/or concentration measurements, giving a total of 3648 instances. Among all instances, 34% of the measurement combinations provided structural identifiability. Our main findings for the controller motifs include: i) a single measurement is insufficient for structural identifiability, ii) measurements related to different chemical species are necessary for structural identifiability. Applying these findings result in a reduced subset of 1568 instances, where 80% are structurally identifiable, and more complex/interconnected motifs appear easier to structurally identify. The model structures we have investigated are commonly used in models of biological systems, and our results demonstrate how different model structures and measurement combinations affect structural identifiability of controller motifs.

Effects of growth feedback on gene circuits: A dynamical understanding

The successful integration of engineered gene circuits into host cells remains a significant challenge in synthetic biology due to circuit-host interactions, such as growth feedback, where the circuit influences cell growth and vice versa. Understanding the dynamics of circuit failures and identifying topologies resilient to growth feedback are crucial for both fundamental and applied research. Utilizing transcriptional regulation circuits with adaptation as a paradigm, we systematically study 435 distinct topological structures and uncover six categories of failures. Three dynamical mechanisms of circuit failures are identified: continuous deformation of the response curve, strengthened or induced oscillations, and sudden switching to coexisting attractors. Our extensive computations also uncover a scaling law between a circuit robustness measure and the strength of growth feedback. Despite the negative effects of growth feedback on the majority of circuit topologies, we identify a few circuits that maintain optimal performance as designed, a feature important for applications.

A blueprint for a synthetic genetic feedback optimizer

Biomolecular control enables leveraging cells as biomanufacturing factories. Despite recent advancements, we currently lack genetically encoded modules that can be deployed to dynamically fine-tune and optimize cellular performance. Here, we address this shortcoming by presenting the blueprint of a genetic feedback module to optimize a broadly defined performance metric by adjusting the production and decay rate of a (set of) regulator species. We demonstrate that the optimizer can be implemented by combining available synthetic biology parts and components, and that it can be readily integrated with existing pathways and genetically encoded biosensors to ensure its successful deployment in a variety of settings. We further illustrate that the optimizer successfully locates and tracks the optimum in diverse contexts when relying on mass action kinetics-based dynamics and parameter values typical in Escherichia coli.

Universal structures for adaptation in biochemical reaction networks

At the molecular level, the evolution of life is driven by the generation and diversification of adaptation mechanisms. A universal description of adaptation-capable chemical reaction network (CRN) structures has remained elusive until now, since currently-known criteria for adaptation apply only to a tiny subset of possible CRNs. Here we identify the definitive structural requirements that characterize all adaptation-capable collections of interacting molecules, however large or complex. We show that these network structures implement a form of integral control in which multiple independent integrals can collaborate to confer the capacity for adaptation on specific molecules. Using an algebraic algorithm informed by these findings, we demonstrate the existence of embedded integrals in a variety of biologically important CRNs that have eluded previous methods, and for which adaptation has been observed experimentally. This definitive picture of biological adaptation at the level of intermolecular interactions represents a blueprint for adaptation-capable signaling networks across all domains of life, and for the design of synthetic biosystems.

Recent advances, opportunities and challenges in cybergenetic identification and control of biomolecular networks

Cybergenetics is a new area of research aimed at developing digital and biological controllers for living systems. Synthetic biologists have begun exploiting cybergenetic tools and platforms to both accelerate the development of mathematical models and develop control strategies for complex biological phenomena. Here, we review the state of the art in cybergenetic identification and control. Our aim is to lower the entry barrier to this field and foster the adoption of methods and technologies that will accelerate the pace at which Synthetic Biology progresses toward applications.

A cybergenetic framework for engineering intein-mediated integral feedback control systems

The ability of biological systems to tightly regulate targeted variables, despite external and internal disturbances, is known as Robust Perfect Adaptation (RPA). Achieved frequently through biomolecular integral feedback controllers at the cellular level, RPA has important implications for biotechnology and its various applications. In this study, we identify inteins as a versatile class of genetic components suitable for implementing these controllers and present a systematic approach for their design. We develop a theoretical foundation for screening intein-based RPA-achieving controllers and a simplified approach for modeling them. We then genetically engineer and test intein-based controllers using commonly used transcription factors in mammalian cells and demonstrate their exceptional adaptation properties over a wide dynamic range. The small size, flexibility, and applicability of inteins across life forms allow us to create a diversity of genetic RPA-achieving integral feedback control systems that can be used in various applications, including metabolic engineering and cell-based therapy.

Protein circuit design using de novo proteins

Protein-based biological circuits enable customized control of cellular functions, and de novo protein design enables circuit functionalities that are not possible by repurposing natural proteins. Here, I highlight recent progress in protein circuit design, including CHOMP, developed by Gao et al., and SPOC, developed by Fink et al.

A portable regulatory RNA array design enables tunable and complex regulation across diverse bacteria

A lack of composable and tunable gene regulators has hindered efforts to engineer non-model bacteria and consortia. To address this, we explore the broad-host potential of small transcription activating RNA (STAR) and propose a novel design strategy to achieve tunable gene control. First, we demonstrate that STARs optimized for E. coli function across different Gram-negative species and can actuate using phage RNA polymerase, suggesting that RNA systems acting at the level of transcription are portable. Second, we explore a novel RNA design strategy that uses arrays of tandem and transcriptionally fused RNA regulators to precisely alter regulator concentration from 1 to 8 copies. This provides a simple means to predictably tune output gain across species and does not require access to large regulatory part libraries. Finally, we show RNA arrays can be used to achieve tunable cascading and multiplexing circuits across species, analogous to the motifs used in artificial neural networks.

Biomolecular feedback controllers: from theory to applications

Billions of years of evolution have led to the creation of sophisticated genetic regulatory mechanisms that control various biological processes in a timely and precise fashion, despite their uncertain and noisy environments. Understanding such naturally existing mechanisms and even designing novel ones will have direct implications in various fields such as biotechnology, medicine, and synthetic biology. In particular, many studies have revealed that feedback-based control mechanisms inside the living cells endow the overall system with multiple attractive features, including homeostasis, noise reduction, and high dynamic performance. The remarkable interdisciplinary nature of these studies has brought together disparate disciplines such as systems/synthetic biology and control theory in an effort to design and build more powerful and reliable biomolecular control systems. Here, we review various biomolecular feedback controllers, highlight their characteristics, and point out their promising impact.

A split ribozyme that links detection of a native RNA to orthogonal protein outputs

Individual RNA remains a challenging signal to synthetically transduce into different types of cellular information. Here, we describe Ribozyme-ENabled Detection of RNA (RENDR), a plug-and-play strategy that uses cellular transcripts to template the assembly of split ribozymes, triggering splicing reactions that generate orthogonal protein outputs. To identify split ribozymes that require templating for splicing, we use laboratory evolution to evaluate the activities of different split variants of the Tetrahymena thermophila ribozyme. The best design delivers a 93-fold dynamic range of splicing with RENDR controlling fluorescent protein production in response to an RNA input. We further resolve a thermodynamic model to guide RENDR design, show how input signals can be transduced into diverse outputs, demonstrate portability across different bacteria, and use RENDR to detect antibiotic-resistant bacteria. This work shows how transcriptional signals can be monitored in situ and converted into different types of biochemical information using RNA synthetic biology.

Protein-protein complexes can undermine ultrasensitivity-dependent biological adaptation

Robust perfect adaptation (RPA) is a ubiquitously observed signalling response across all scales of biological organization. A major class of network architectures that drive RPA in complex networks is the Opposer module-a feedback-regulated network into which specialized integral-computing 'opposer node(s)' are embedded. Although ultrasensitivity-generating chemical reactions have long been considered a possible mechanism for such adaptation-conferring opposer nodes, this hypothesis has relied on simplified Michaelian models, which neglect the presence of protein-protein complexes. Here we develop complex-complete models of interlinked covalent-modification cycles with embedded ultrasensitivity, explicitly capturing all molecular interactions and protein complexes. Strikingly, we demonstrate that the presence of protein-protein complexes thwarts the network's capacity for RPA in any 'free' active protein form, conferring RPA capacity instead on the concentration of a larger protein pool consisting of two distinct forms of a single protein. We further show that the presence of enzyme-substrate complexes, even at comparatively low concentrations, play a crucial and previously unrecognized role in controlling the RPA response-significantly reducing the range of network inputs for which RPA can obtain, and imposing greater parametric requirements on the RPA response. These surprising results raise fundamental new questions as to the biochemical requirements for adaptation-conferring Opposer modules within complex cellular networks.

Homeostasis at different backgrounds: The roles of overlayed feedback structures in vertebrate photoadaptation

We have studied the resetting behavior of eight basic integral controller motifs with respect to different but constant backgrounds. We found that the controllers split symmetrically into two classes: one class, based on derepression of the compensatory flux, leads to more rapid resetting kinetics as backgrounds increase. The other class, which directly activates the compensatory flux, shows a slowing down in the resetting at increased backgrounds. We found a striking analogy between the resetting kinetics of vertebrate photoreceptors and controllers based on derepression, i.e. vertebrate rod or cone cells show decreased sensitivities and accelerated response kinetics as background illuminations increase. The central molecular model of vertebrate photoadaptation consists of an overlay of three negative feedback loops with cytosolic calcium ([Formula: see text]), cyclic guanosine monophosphate (cGMP) and cyclic nucleotide-gated (CNG) channels as components. While in one of the feedback loops the extrusion of [Formula: see text] by potassium-dependent sodium-calcium exchangers (NCKX) can lead to integral control with cGMP as the controlled variable, the expected robust perfect adaptation of cGMP is lost, because of the two other feedback loops. They avoid that [Formula: see text] levels become too high and toxic. Looking at psychophysical laws, we found that in all of the above mentioned basic controllers Weber's law is followed when a "just noticeable difference" (threshold) of 1% of the controlled variable's set-point was considered. Applying comparable threshold pulses or steps to the photoadaptation model we find, in agreement with experimental results, that Weber's law is followed for relatively high backgrounds, while Stephens' power law gives a better description when backgrounds are low. Limitations of our photoadaption model, in particular with respect to potassium/sodium homeostasis, are discussed. Finally, we discuss possible implication of background perturbations in biological controllers when compensatory fluxes are based on activation.

Design Principles Underlying Robust Adaptation of Complex Biochemical Networks

Biochemical networks are often characterized by tremendous complexity-both in terms of the sheer number of interacting molecules ("nodes") and in terms of the varied and incompletely understood interactions among these molecules ("interconnections" or "edges"). Strikingly, the vast and intricate networks of interacting proteins that exist within each living cell have the capacity to perform remarkably robustly, and reproducibly, despite significant variations in concentrations of the interacting components from one cell to the next and despite mutability over time of biochemical parameters. Here we consider the ubiquitously observed and fundamentally important signalling response known as robust perfect adaptation (RPA). We have recently shown that all RPA-capable networks, even the most complex ones, must satisfy an extremely rigid set of design principles, and are modular, being decomposable into just two types of network building-blocks-opposer modules and balancer modules. Here we present an overview of the design principles that characterize all RPA-capable network topologies through a detailed examination of a collection of simple examples. We also introduce a diagrammatic method for studying the potential of a network to exhibit RPA, which may be applied without a detailed knowledge of the complex mathematical principles governing RPA.

Evolution of self-organised division of labour driven by stigmergy in leaf-cutter ants

Social insects owe their widespread success to their ability to efficiently coordinate behaviour to carry out complex tasks. Several leaf-cutter ant species employ an advanced type of division of labour known as task partitioning, where the task of retrieving leaves is distributed between workers that cut and drop and those that collect the fallen leaves. It is not entirely clear how such highly coordinated behaviour can evolve, as it would seem to require the simultaneous mutations of multiple traits during the same generation. Here, we use an agent-based simulation model to show how task partitioning in leaf-cutter ants can gradually evolve by exploiting stigmergy (indirect coordination through the environment) through gravity (leaves falling from the treetop on the ground forming a cache). Our simple model allows independent variation in two core behavioural dimensions: the tendency to drop leaves and the tendency to pick up dropped leaves. Task partitioning readily evolves even under these minimal assumptions through adaptation to an arboreal environment where traveling up and down the tree is costly. Additionally, we analyse ant movement dynamics to demonstrate how the ants achieve efficient task allocation through task switching and negative feedback control.

Synthetic biology by controller design

Natural biological systems display complex regulation and synthetic biomolecular systems have been used to understand their natural counterparts and to parse sophisticated regulations into core design principles. At the same time, the engineering of biomolecular systems has unarguable potential to transform current and to enable new, yet-to-be-imagined, biotechnology applications. In this review, we discuss the progression of control systems design in synthetic biology, from the purpose of understanding the function of naturally occurring regulatory motifs to that of creating genetic circuits whose function is sufficiently robust for biotechnology applications.

Inducible plasmid copy number control for synthetic biology in commonly used E. coli strains

The ability to externally control gene expression has been paradigm shifting for all areas of biological research, especially for synthetic biology. Such control typically occurs at the transcriptional and translational level, while technologies enabling control at the DNA copy level are limited by either (i) relying on a handful of plasmids with fixed and arbitrary copy numbers; or (ii) require multiple plasmids for replication control; or (iii) are restricted to specialized strains. To overcome these limitations, we present TULIP (TUnable Ligand Inducible Plasmid): a self-contained plasmid with inducible copy number control, designed for portability across various Escherichia coli strains commonly used for cloning, protein expression, and metabolic engineering. Using TULIP, we demonstrate through multiple application examples that flexible plasmid copy number control accelerates the design and optimization of gene circuits, enables efficient probing of metabolic burden, and facilitates the prototyping and recycling of modules in different genetic contexts.

Toward predictive engineering of gene circuits

Many synthetic biology applications rely on programming living cells using gene circuits - the assembly and wiring of genetic elements to control cellular behaviors. Extensive progress has been made in constructing gene circuits with diverse functions and applications. For many circuit functions, however, it remains challenging to ensure that the circuits operate in a predictable manner. Although the notion of predictability may appear intuitive, close inspection suggests that it is not always clear what constitutes predictability. We dissect this concept and how it can be confounded by the complexity of a circuit, the complexity of the context, and the interplay between the two. We discuss circuit engineering strategies, in both computation and experiment, that have been used to improve the predictability of gene circuits.

Universal structural requirements for maximal robust perfect adaptation in biomolecular networks

Adaptation is a running theme in biology. It allows a living system to survive and thrive in the face of unpredictable environments by maintaining key physiological variables at their desired levels through tight regulation. When one such variable is maintained at a certain value at the steady state despite perturbations to a single input, this property is called robust perfect adaptation (RPA). Here we address and solve the fundamental problem of maximal RPA (maxRPA), whereby, for a designated output variable, RPA is achieved with respect to perturbations in virtually all network parameters. In particular, we show that the maxRPA property imposes certain structural constraints on the network. We then prove that these constraints are fully characterized by simple linear algebraic stoichiometric conditions which differ between deterministic and stochastic descriptions of the dynamics. We use our results to derive a new internal model principle (IMP) for biomolecular maxRPA networks, akin to the celebrated IMP in control theory. We exemplify our results through several known biological examples of robustly adapting networks and construct examples of such networks with the aid of our linear algebraic characterization. Our results reveal the universal requirements for maxRPA in all biological systems, and establish a foundation for studying adaptation in general biomolecular networks, with important implications for both systems and synthetic biology.

Synthetic neuromorphic computing in living cells

Computational properties of neuronal networks have been applied to computing systems using simplified models comprising repeated connected nodes, e.g., perceptrons, with decision-making capabilities and flexible weighted links. Analogously to their revolutionary impact on computing, neuro-inspired models can transform synthetic gene circuit design in a manner that is reliable, efficient in resource utilization, and readily reconfigurable for different tasks. To this end, we introduce the perceptgene, a perceptron that computes in the logarithmic domain, which enables efficient implementation of artificial neural networks in Escherichia coli cells. We successfully modify perceptgene parameters to create devices that encode a minimum, maximum, and average of analog inputs. With these devices, we create multi-layer perceptgene circuits that compute a soft majority function, perform an analog-to-digital conversion, and implement a ternary switch. We also create a programmable perceptgene circuit whose computation can be modified from OR to AND logic using small molecule induction. Finally, we show that our approach enables circuit optimization via artificial intelligence algorithms.