Perfect adaptation in biology

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.

A multiscale sensorimotor model of experience-dependent behavior in a minimal organism

To survive in ever-changing environments, living organisms need to continuously combine the ongoing external inputs they receive, representing present conditions, with their dynamical internal state, which includes influences of past experiences. It is still unclear in general, however 1) how this happens at the molecular and cellular levels and 2) how the corresponding molecular and cellular processes are integrated with the behavioral responses of the organism. Here, we address these issues by modeling mathematically a particular behavioral paradigm in a minimal model organism, namely chemotaxis in the nematode C. elegans. Specifically, we use a long-standing collection of elegant experiments on salt chemotaxis in this animal, in which the migration direction varies depending on its previous experience. Our model integrates the molecular, cellular, and organismal levels to reproduce the experimentally observed experience-dependent behavior. The model proposes specific molecular mechanisms for the encoding of current conditions and past experiences in key neurons associated with this response, predicting the behavior of various mutants associated with those molecular circuits.

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.

Design Principles for Biological Adaptation: A Systems and Control-Theoretic Treatment

Establishing a mapping between (from and to) the functionality of interest and the underlying network structure (design principles) remains a crucial step toward understanding and design of bio-systems. Perfect adaptation is one such crucial functionality that enables every living organism to regulate its essential activities in the presence of external disturbances. Previous approaches to deducing the design principles for adaptation have either relied on computationally burdensome brute-force methods or rule-based design strategies detecting only a subset of all possible adaptive network structures. This chapter outlines a scalable and generalizable method inspired by systems theory that unravels an exhaustive set of adaptation-capable structures. We first use the well-known performance parameters to characterize perfect adaptation. These performance parameters are then mapped back to a few parameters (poles, zeros, gain) characteristic of the underlying dynamical system constituted by the rate equations. Therefore, the performance parameters evaluated for the scenario of perfect adaptation can be expressed as a set of precise mathematical conditions involving the system parameters. Finally, we use algebraic graph theory to translate these abstract mathematical conditions to certain structural requirements for adaptation. The proposed algorithm does not assume any particular dynamics and is applicable to networks of any size. Moreover, the results offer a significant advancement in the realm of understanding and designing complex biochemical networks.

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.

Modulating Biological Rhythms: A Noncomputational Strategy Harnessing Nonlinearity and Decoupling Frequency and Amplitude

Understanding and achieving concurrent modulation of amplitude and frequency, particularly adjusting one quantity and simultaneously sustaining the other at an invariant level, are of paramount importance for complex biophysical systems, including the signal pathway where different frequency indicates different upstream signal yielding a certain downstream physiological function while different amplitude further determines different efficacy of a downstream output. However, such modulators with clearly described and universally valid mechanisms are still lacking. Here, we rigorously propose an easy-to-use control strategy containing only one or two steps, leveraging the nonlinearity in the modulated systems to decouple frequency and amplitude in a noncomputational manner. The strategy's efficacy is demonstrated using representative biochemical systems and, thus, it could be potentially applicable to modulating rhythms in experiments of biochemistry and synthetic biology.

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.

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.

Upf3a but not Upf1 mediates the genetic compensation response induced by leg1 deleterious mutations in an H3K4me3-independent manner

Genetic compensation responses (GCRs) can be induced by deleterious mutations in living organisms in order to maintain genetic robustness. One type of GCRs, homology-dependent GCR (HDGCR), involves transcriptional activation of one or more homologous genes related to the mutated gene. In zebrafish, ~80% of the genetic mutants produced by gene editing technology failed to show obvious phenotypes. The HDGCR has been proposed to be one of the main reasons for this phenomenon. It is triggered by mutant mRNA bearing a premature termination codon and has been suggested to depend on components of both the nonsense mRNA-mediated degradation (NMD) pathway and the complex of proteins associated with Set1 (COMPASS). However, exactly which specific NMD factor is required for HDGCR remains disputed. Here, zebrafish leg1 deleterious mutants are adopted as a model to distinguish the role of the NMD factors Upf1 and Upf3a in HDGCR. Four single mutant lines and three double mutant lines were produced. The RNA-seq data from 71 samples and the ULI-NChIP-seq data from 8 samples were then analyzed to study the HDGCR in leg1 mutants. Our results provide strong evidence that Upf3a, but not Upf1, is essential for the HDGCR induced by nonsense mutations in leg1 genes where H3K4me3 enrichment appears not to be a prerequisite. We also show that Upf3a is responsible for correcting the expression of hundreds of genes that would otherwise be dysregulated in the leg1 deleterious mutant.

Evolutionary Stability of Small Molecular Regulatory Networks That Exhibit Near-Perfect Adaptation

Large-scale protein regulatory networks, such as signal transduction systems, contain small-scale modules ('motifs') that carry out specific dynamical functions. Systematic characterization of the properties of small network motifs is therefore of great interest to molecular systems biologists. We simulate a generic model of three-node motifs in search of near-perfect adaptation, the property that a system responds transiently to a change in an environmental signal and then returns near-perfectly to its pre-signal state (even in the continued presence of the signal). Using an evolutionary algorithm, we search the parameter space of these generic motifs for network topologies that score well on a pre-defined measure of near-perfect adaptation. We find many high-scoring parameter sets across a variety of three-node topologies. Of all possibilities, the highest scoring topologies contain incoherent feed-forward loops (IFFLs), and these topologies are evolutionarily stable in the sense that, under 'macro-mutations' that alter the topology of a network, the IFFL motif is consistently maintained. Topologies that rely on negative feedback loops with buffering (NFLBs) are also high-scoring; however, they are not evolutionarily stable in the sense that, under macro-mutations, they tend to evolve an IFFL motif and may-or may not-lose the NFLB motif.

A plausible identifiable model of the canonical NF-κB signaling pathway

An overwhelming majority of mathematical models of regulatory pathways, including the intensively studied NF-κB pathway, remains non-identifiable, meaning that their parameters may not be determined by existing data. The existing NF-κB models that are capable of reproducing experimental data contain non-identifiable parameters, whereas simplified models with a smaller number of parameters exhibit dynamics that differs from that observed in experiments. Here, we reduced an existing model of the canonical NF-κB pathway by decreasing the number of equations from 15 to 6. The reduced model retains two negative feedback loops mediated by IκBα and A20, and in response to both tonic and pulsatile TNF stimulation exhibits dynamics that closely follow that of the original model. We carried out the sensitivity-based linear analysis and Monte Carlo-based analysis to demonstrate that the resulting model is both structurally and practically identifiable given measurements of 5 model variables from a simple TNF stimulation protocol. The reduced model is capable of reproducing different types of responses that are characteristic to regulatory motifs controlled by negative feedback loops: nearly-perfect adaptation as well as damped and sustained oscillations. It can serve as a building block of more comprehensive models of the immune response and cancer, where NF-κB plays a decisive role. Our approach, although may not be automatically generalized, suggests that models of other regulatory pathways can be transformed to identifiable, while retaining their dynamical features.

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.

On biological networks capable of robust adaptation in the presence of uncertainties: A linear systems-theoretic approach

Biological adaptation, the tendency of every living organism to regulate its essential activities in environmental fluctuations, is a well-studied functionality in systems and synthetic biology. In this work, we present a generic methodology inspired by systems theory to discover the design principles for robust adaptation, perfect and imperfect, in two different contexts: (1) in the presence of deterministic external and parametric disturbances and (2) in a stochastic setting. In all the cases, firstly, we translate the necessary qualitative conditions for adaptation to mathematical constraints using the language of systems theory, which we then map back as design requirements for the underlying networks. Thus, contrary to the existing approaches, the proposed methodologies provide an exhaustive set of admissible network structures without resorting to computationally burdensome brute-force techniques. Further, the proposed frameworks do not assume prior knowledge about the particular rate kinetics, thereby validating the conclusions for a large class of biological networks. In the deterministic setting, we show that unlike the incoherent feed-forward network structures (IFFLP or opposer modules), the modules containing negative feedback with buffer action (NFBLB or balancer modules) are robust to parametric fluctuations when a specific part of the network is assumed to remain unaffected. To this end, we propose a sufficient condition for imperfect adaptation and show that adding negative feedback in an IFFLP topology improves the robustness concerning parametric fluctuations. Further, we propose a stricter set of necessary conditions for imperfect adaptation. Turning to the stochastic scenario, we adopt a Wiener-Kolmogorov filter strategy to tune the parameters of a given network structure towards minimum output variance. We show that both NFBLB and IFFLP can be used as a reduced-order W-K filter. Further, we define the notion of nearest neighboring motifs to compare the output variances across different network structures. We argue that the NFBLB achieves adaptation at the cost of a variance higher than its nearest neighboring motifs whereas the IFFLP topology produces locally minimum variance while compared with its nearest neighboring motifs. We present numerical simulations to support the theoretical results. Overall, our results present a generic, systematic, and robust framework for advancing the understanding of complex biological 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.

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.

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.

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.

Sequential and additive expression of miR-9 precursors control timing of neurogenesis

MicroRNAs (miRs) have an important role in tuning dynamic gene expression. However, the mechanism by which they are quantitatively controlled is unknown. We show that the amount of mature miR-9, a key regulator of neuronal development, increases during zebrafish neurogenesis in a sharp stepwise manner. We characterize the spatiotemporal profile of seven distinct microRNA primary transcripts (pri-mir)-9s that produce the same mature miR-9 and show that they are sequentially expressed during hindbrain neurogenesis. Expression of late-onset pri-mir-9-1 is added on to, rather than replacing, the expression of early onset pri-mir-9-4 and -9-5 in single cells. CRISPR/Cas9 mutation of the late-onset pri-mir-9-1 prevents the developmental increase of mature miR-9, reduces late neuronal differentiation and fails to downregulate Her6 at late stages. Mathematical modelling shows that an adaptive network containing Her6 is insensitive to linear increases in miR-9 but responds to stepwise increases of miR-9. We suggest that a sharp stepwise increase of mature miR-9 is created by sequential and additive temporal activation of distinct loci. This may be a strategy to overcome adaptation and facilitate a transition of Her6 to a new dynamic regime or steady state.

Vertex results for the robust analysis of uncertain biochemical systems

We consider the problem of assessing the sensitivity of uncertain biochemical systems in the presence of input perturbations (either constant or periodic) around a stable steady state. In particular, we propose approaches for the robust sensitivity analysis of systems with uncertain parameters assumed to take values in a hyper-rectangle. We highlight vertex results, which allow us to check whether a property is satisfied for all parameter choices in the hyper-rectangle by simply checking whether it is satisfied for all parameter choices at the vertices of the hyper-rectangle. We show that, for a vast class of systems, including (bio)chemical reaction networks with mass-action kinetics, the system Jacobian has a totally multiaffine structure (namely, all minors of the Jacobian matrix are multiaffine functions of the uncertain parameters), which can be exploited to obtain several vertex results. We consider different problems: robust non-singularity; robust stability of the steady-state; robust steady-state sensitivity analysis, in the case of constant perturbations; robust frequency-response sensitivity analysis, in the presence of periodic perturbations; and robust adaptation analysis. The developed theory is then applied to gain insight into some examples of uncertain biochemical systems, including the incoherent feed-forward loop, the coherent feed-forward loop, the Brusselator oscillator and the Goldbeter oscillator.

Kinetics and mechanisms of catalyzed dual-E (antithetic) controllers

Homeostasis plays a central role in our understanding how cells and organisms are able to oppose environmental disturbances and thereby maintain an internal stability. During the last two decades there has been an increased interest in using control engineering methods, especially integral control, in the analysis and design of homeostatic networks. Several reaction kinetic mechanisms have been discovered which lead to integral control. In two of them integral control is achieved, either by the removal of a single control species E by zero-order kinetics (“single-E controllers”), or by the removal of two control species by second-order kinetics (“antithetic or dual-E control”). In this paper we show results when the control species E₁ and E₂ in antithetic control are removed enzymatically by ping-pong or ternary-complex mechanisms. Our findings show that enzyme-catalyzed dual-E controllers can work in two control modes. In one mode, one of the two control species is active, but requires zero-order kinetics in its removal. In the other mode, both controller species are active and both are removed enzymatically. Conditions for the two control modes are put forward and biochemical examples with the structure of enzyme-catalyzed dual-E controllers are discussed.

A genetic mammalian proportional-integral feedback control circuit for robust and precise gene regulation

To survive in the harsh environments they inhabit, cells have evolved sophisticated regulatory mechanisms that can maintain a steady internal milieu or homeostasis. This robustness, however, does not generally translate to engineered genetic circuits, such as the ones studied by synthetic biology. Here, we introduce an implementation of a minimal and universal gene regulatory motif that produces robust perfect adaptation for mammalian cells, and we improve on it by enhancing the precision of its regulation.

The processes that keep a cell alive are constantly challenged by unpredictable changes in its environment. Cells manage to counteract these changes by employing sophisticated regulatory strategies that maintain a steady internal milieu. Recently, the antithetic integral feedback motif has been demonstrated to be a minimal and universal biological regulatory strategy that can guarantee robust perfect adaptation for noisy gene regulatory networks in Escherichia coli. Here, we present a realization of the antithetic integral feedback motif in a synthetic gene circuit in mammalian cells. We show that the motif robustly maintains the expression of a synthetic transcription factor at tunable levels even when it is perturbed by increased degradation or its interaction network structure is perturbed by a negative feedback loop with an RNA-binding protein. We further demonstrate an improved regulatory strategy by augmenting the antithetic integral motif with additional negative feedback to realize antithetic proportional–integral control. We show that this motif produces robust perfect adaptation while also reducing the variance of the regulated synthetic transcription factor. We demonstrate that the integral and proportional–integral feedback motifs can mitigate the impact of gene expression burden, and we computationally explore their use in cell therapy. We believe that the engineering of precise and robust perfect adaptation will enable substantial advances in industrial biotechnology and cell-based therapeutics.

A hierarchy of biomolecular proportional-integral-derivative feedback controllers for robust perfect adaptation and dynamic performance

Proportional-Integral-Derivative (PID) feedback controllers are the most widely used controllers in industry. Recently, the design of molecular PID-controllers has been identified as an important goal for synthetic biology and the field of cybergenetics. In this paper, we consider the realization of PID-controllers via biomolecular reactions. We propose an array of topologies offering a compromise between simplicity and high performance. We first demonstrate that different biomolecular PI-controllers exhibit different performance-enhancing capabilities. Next, we introduce several derivative controllers based on incoherent feedforward loops acting in a feedback configuration. Alternatively, we show that differentiators can be realized by placing molecular integrators in a negative feedback loop, which can be augmented by PI-components to yield PID-controllers. We demonstrate that PID-controllers can enhance stability and dynamic performance, and can also reduce stochastic noise. Finally, we provide an experimental demonstration using a hybrid setup where in silico PID-controllers regulate a genetic circuit in single yeast cells.

Designing Biological Circuits: From Principles to Applications

Genetic circuit design is a well-studied problem in synthetic biology. Ever since the first genetic circuits─the repressilator and the toggle switch─were designed and implemented, many advances have been made in this area of research. The current review systematically organizes a number of key works in this domain by employing the versatile framework of generalized morphological analysis. Literature in the area has been mapped on the basis of (a) the design methodologies used, ranging from brute-force searches to control-theoretic approaches, (b) the modeling techniques employed, (c) various circuit functionalities implemented, (d) key design characteristics, and (e) the strategies used for the robust design of genetic circuits. We conclude our review with an outlook on multiple exciting areas for future research, based on the systematic assessment of key research gaps that have been readily unravelled by our analysis framework.

Synthetic robust perfect adaptation achieved by negative feedback coupling with linear weak positive feedback

Unlike their natural counterparts, synthetic genetic circuits are usually fragile in the face of environmental perturbations and genetic mutations. Several theoretical robust genetic circuits have been designed, but their performance under real-world conditions has not yet been carefully evaluated. Here, we designed and synthesized a new robust perfect adaptation circuit composed of two-node negative feedback coupling with linear positive feedback on the buffer node. As a key feature, the linear positive feedback was fine-tuned to evaluate its necessity. We found that the desired function was robustly achieved when genetic parameters were varied by systematically perturbing all interacting parts within the topology, and the necessity of the completeness of the topological structures was evaluated by destroying key circuit features. Furthermore, different environmental perturbances were imposed onto the circuit by changing growth rates, carbon metabolic strategies and even chassis cells, and the designed perfect adaptation function was still achieved under all conditions. The successful design of a robust perfect adaptation circuit indicated that the top-down design strategy is capable of predictably guiding bottom-up engineering for robust genetic circuits. This robust adaptation circuit could be integrated as a motif into more complex circuits to robustly implement more sophisticated and critical biological functions.

DOPA Homeostasis by Dopamine: A Control-Theoretic View

Dopamine (DA) is an important signal mediator in the brain as well as in the periphery. The term "dopamine homeostasis" occasionally found in the literature refers to the fact that abnormal DA levels can be associated with a variety of neuropsychiatric disorders. An analysis of the negative feedback inhibition of tyrosine hydroxylase (TH) by DA indicates, with support from the experimental data, that the TH-DA negative feedback loop has developed to exhibit 3,4-dihydroxyphenylalanine (DOPA) homeostasis by using DA as a derepression regulator. DA levels generally decline when DOPA is removed, for example, by increased oxidative stress. Robust DOPA regulation by DA further implies that maximum vesicular DA levels are established, which appear necessary for a reliable translation of neural activity into a corresponding chemical transmitter signal. An uncontrolled continuous rise (windup) in DA occurs when Levodopa treatment exceeds a critical dose. Increased oxidative stress leads to the successive breakdown of DOPA homeostasis and to a corresponding reduction in DA levels. To keep DOPA regulation robust, the vesicular DA loading requires close to zero-order kinetics combined with a sufficiently high compensatory flux provided by TH. The protection of DOPA and DA due to a channeling complex is discussed.

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.