Perfect Adaptation and Optimal Equilibrium Productivity in a Simple Microbial Biofuel Metabolic Pathway Using Dynamic Integral Control

Single cell technologies for monitoring protein secretion heterogeneity

Cell-to-cell heterogeneity presents challenges across various fields, from biomedicine to bioproduction, where precise cellular responses are vital. While single cell technologies have significantly enhanced our understanding of population heterogeneity, the predominant focus has been on monitoring intracellular compounds. Recognizing the added complexity introduced by the secretion system, in this review, we first provide a systematic overview of the distinct steps necessary for driving protein secretion. We discuss the various sources of noise acting from the synthesized preprotein to the secretory protein released based on a Gram-positive cellular system as a model. We next explore the applicability of single cell technologies for monitoring protein secretion throughout these functional stages. We also emphasize the importance of applying these single cell technologies for monitoring protein secretion during bioproduction.

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.

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.

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.

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.

Exploiting Information and Control Theory for Directing Gene Expression in Cell Populations

Microbial populations can adapt to adverse environmental conditions either by appropriately sensing and responding to the changes in their surroundings or by stochastically switching to an alternative phenotypic state. Recent data point out that these two strategies can be exhibited by the same cellular system, depending on the amplitude/frequency of the environmental perturbations and on the architecture of the genetic circuits involved in the adaptation process. Accordingly, several mitigation strategies have been designed for the effective control of microbial populations in different contexts, ranging from biomedicine to bioprocess engineering. Technically, such control strategies have been made possible by the advances made at the level of computational and synthetic biology combined with control theory. However, these control strategies have been applied mostly to synthetic gene circuits, impairing the applicability of the approach to natural circuits. In this review, we argue that it is possible to expand these control strategies to any cellular system and gene circuits based on a metric derived from this information theory, i.e., mutual information (MI). Indeed, based on this metric, it should be possible to characterize the natural frequency of any gene circuits and use it for controlling gene circuits within a population of cells.

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

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

Stabilization of antithetic control via molecular buffering

A key goal in synthetic biology is the construction of molecular circuits that robustly adapt to perturbations. Although many natural systems display perfect adaptation, whereby stationary molecular concentrations are insensitive to perturbations, its de novo engineering has proven elusive. The discovery of the antithetic control motif was a significant step towards a universal mechanism for engineering perfect adaptation. Antithetic control provides perfect adaptation in a wide range of systems, but it can lead to oscillatory dynamics due to loss of stability; moreover, it can lose perfect adaptation in fast growing cultures. Here, we introduce an extended antithetic control motif that resolves these limitations. We show that molecular buffering, a widely conserved mechanism for homeostatic control in Nature, stabilizes oscillations and allows for near-perfect adaptation during rapid growth. We study multiple buffering topologies and compare their performance in terms of their stability and adaptation properties. We illustrate the benefits of our proposed strategy in exemplar models for biofuel production and growth rate control in bacterial cultures. Our results provide an improved circuit for robust control of biomolecular systems.

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.

A protocol for dynamic model calibration

Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and nonmeasurable parameters, which have to be determined by fitting the model to experimental data. In order to perform this task, known as parameter estimation or model calibration, the modeller faces challenges such as poor parameter identifiability, lack of sufficiently informative experimental data and the existence of local minima in the objective function landscape. These issues tend to worsen with larger model sizes, increasing the computational complexity and the number of unknown parameters. An incorrectly calibrated model is problematic because it may result in inaccurate predictions and misleading conclusions. For nonexpert users, there are a large number of potential pitfalls. Here, we provide a protocol that guides the user through all the steps involved in the calibration of dynamic models. We illustrate the methodology with two models and provide all the code required to reproduce the results and perform the same analysis on new models. Our protocol provides practitioners and researchers in biological modelling with a one-stop guide that is at the same time compact and sufficiently comprehensive to cover all aspects of the problem.

Reducing phenotypic instabilities of a microbial population during continuous cultivation based on cell switching dynamics

Predicting the fate of individual cells among a microbial population (i.e., growth and gene expression) remains a challenge, especially when this population is exposed to very dynamic environmental conditions, such as those encountered during continuous cultivation. Indeed, the dynamic nature of a continuous cultivation process implies the potential diversification of the microbial population resulting in genotypic and phenotypic heterogeneity. The present work focused on the induction of the arabinose operon in Escherichia coli as a model system to study this diversification process in continuous cultivations. As a preliminary step, the green fluorescent protein (GFP) level triggered by an arabinose-inducible ParaBAD promoter was tracked by flow cytometry in chemostat cultivations with glucose-arabinose co-feeding. For a wide range of glucose-arabinose co-feeding concentrations in the chemostats, the simultaneous occurrence of GFP positive and negative subpopulation was observed. In the second set of experiments, continuous cultivation was performed by adding glucose continuously and arabinose based on the capability of individual cells to switch from low GFP to high GFP expression states, performed with a technology setup called segregostat. In the segregostat cultivation mode, on-line flow cytometry analysis was used for adjusting the arabinose/glucose transitions based on the phenotypic switching profiles of the microbial population. This strategy allowed finding an appropriate arabinose pulsing frequency, leading to prolonged maintenance of the induction level with a limited increase in the phenotypic diversity for more than 60 generations. The results suggest that the steady forcing of individual cells into a given phenotypic trajectory may not be the best strategy for controlling cell populations. Instead, allowing individual cells to switch periodically around a predefined threshold seems to be a more robust strategy leading to oscillations, but within a predictable cell population behavior range.

Perfect adaptation in biology

A distinctive feature of many biological systems is their ability to adapt to persistent stimuli or disturbances that would otherwise drive them away from a desirable steady state. The resulting stasis enables organisms to function reliably while being subjected to very different external environments. This perspective concerns a stringent type of biological adaptation, robust perfect adaptation (RPA), that is resilient to certain network and parameter perturbations. As in engineered control systems, RPA requires that the regulating network satisfy certain structural constraints that cannot be avoided. We elucidate these ideas using biological examples from systems and synthetic biology. We then argue that understanding the structural constraints underlying RPA allows us to look past implementation details and offers a compelling means to unravel regulatory biological complexity.

Ultrasensitive molecular controllers for quasi-integral feedback

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

Autonomous and Assisted Control for Synthetic Microbiology

The control of microbes and microbial consortia to achieve specific functions requires synthetic circuits that can reliably cope with internal and external perturbations. Circuits that naturally evolved to regulate biological functions are frequently robust to alterations in their parameters. As the complexity of synthetic circuits increases, synthetic biologists need to implement such robust control "by design". This is especially true for intercellular signaling circuits for synthetic consortia, where robustness is highly desirable, but its mechanisms remain unclear. Cybergenetics, the interface between synthetic biology and control theory, offers two approaches to this challenge: external (computer-aided) and internal (autonomous) control. Here, we review natural and synthetic microbial systems with robustness, and outline experimental approaches to implement such robust control in microbial consortia through population-level cybergenetics. We propose that harnessing natural intercellular circuit topologies with robust evolved functions can help to achieve similar robust control in synthetic intercellular circuits. A "hybrid biology" approach, where robust synthetic microbes interact with natural consortia and-additionally-with external computers, could become a useful tool for health and environmental applications.

Extended Metabolic Biosensor Design for Dynamic Pathway Regulation of Cell Factories

Transcription factor-based biosensors naturally occur in metabolic pathways to maintain cell growth and to provide a robust response to environmental fluctuations. Extended metabolic biosensors, i.e., the cascading of a bio-conversion pathway and a transcription factor (TF) responsive to the downstream effector metabolite, provide sensing capabilities beyond natural effectors for implementing context-aware synthetic genetic circuits and bio-observers. However, the engineering of such multi-step circuits is challenged by stability and robustness issues. In order to streamline the design of TF-based biosensors in metabolic pathways, here we investigate the response of a genetic circuit combining a TF-based extended metabolic biosensor with an antithetic integral circuit, a feedback controller that achieves robustness against environmental fluctuations. The dynamic response of an extended biosensor-based regulated flavonoid pathway is analyzed in order to address the issues of biosensor tuning of the regulated pathway under industrial biomanufacturing operating constraints.

Transporter Engineering for Microbial Manufacturing

Microbes play an important role in biotransformation and biosynthesis of biofuels, natural products, and polymers. Therefore, microbial manufacturing has been widely used in medicine, industry, and agriculture. However, common strategies including enzyme engineering, pathway optimization, and host engineering are generally inadequate to obtain an efficient microbial production system. Transporter engineering provides an alternative strategy to promote the transmembrane transfer of substrates, intermediates, and final products in microbial cells and thus enhances production by alleviating feedback inhibition and cytotoxicity caused by final products. According to the current studies in transport engineering, native transporters usually have low expression and poor transportation ability, resulting in inefficient transport processes and microbial production. In this review, current approaches for transporter mining, characterization, and verification are comprehensively summarized. Practical approaches to enhance the transport system in engineered cells, such as balancing transporter overexpression and cell growth, and evolution of native transporters are discussed. Furthermore, the applications of transporter engineering in microbial manufacturing, including enhancement of substrate utilization, concentration of metabolic flux to the target pathway, and acceleration of efflux and recovery of products, demonstrate its outstanding advantages and promising prospects.

Segregostat: a novel concept to control phenotypic diversification dynamics on the example of Gram-negative bacteria

Controlling and managing the degree of phenotypic diversification of microbial populations is a challenging task. This task not only requires detailed knowledge regarding diversification mechanisms but also advanced technical set-ups for the real-time analyses and control of population behaviour on single-cell level. In this work, set-up, design and operation of the so called segregostat are described which, in contrast to a traditional chemostat, allows the control of phenotypic diversification of microbial populations over time. Two exemplary case studies will be discussed, i.e. phenotypic diversification dynamics of Eschericia coli and Pseudomonas putida based on outer membrane permeabilization, emphasizing the applicability and versatility of the proposed approach. Upon nutrient limitation, cell population tends to diversify into several subpopulations exhibiting distinct phenotypic features (non-permeabilized and permeabilized cells). Online analysis leads to the determination of the ratio between cells in these two states, which in turn triggers the addition of glucose pulses in order to maintain a predefined diversification ratio. These results prove that phenotypic diversification can be controlled by means of defined pulse-frequency modulation within continuously running bioreactor set-ups. This lays the foundation for systematic studies, not only of phenotypic diversification but also for all processes where dynamics single-cell approaches are required, such as synthetic co-culture processes.

Analysis of primitive genetic interactions for the design of a genetic signal differentiator

We study the dynamic and static input-output behavior of several primitive genetic interactions and their effect on the performance of a genetic signal differentiator. In a simplified design, several requirements for the linearity and time-scales of processes like transcription, translation and competitive promoter binding were introduced. By experimentally probing simple genetic constructs in a cell-free experimental environment and fitting semi-mechanistic models to these data, we show that some of these requirements can be verified, while others are only met with reservations in certain operational regimes. Analyzing the linearized model of the resulting genetic network, we conclude that it approximates a differentiator with relative degree one. Taking also the discovered nonlinearities into account and using a describing function approach, we further determine the particular frequency and amplitude ranges where the genetic differentiator can be expected to behave as such.

Regulation of Gene Expression and Signaling Pathway Activity in Mammalian Cells by Automated Microfluidics Feedback Control

Gene networks and signaling pathways display complex topologies and, as a result, complex nonlinear behaviors. Accumulating evidence shows that both static (concentration) and dynamical (rate-of-change) features of transcription factors, ligands and environmental stimuli control downstream processes and ultimately cellular functions. Currently, however, methods to generate stimuli with the desired features to probe cell response are still lacking. Here, combining tools from Control Engineering and Synthetic Biology (cybergenetics), we propose a simple and cost-effective microfluidics-based platform to precisely regulate gene expression and signaling pathway activity in mammalian cells by means of real-time feedback control. We show that this platform allows (i) to automatically regulate gene expression from inducible promoters in different cell types, including mouse embryonic stem cells; (ii) to precisely regulate the activity of the mTOR signaling pathway in single cells; (iii) to build a biohybrid oscillator in single embryonic stem cells by interfacing biological parts with virtual in silico counterparts. Ultimately, this platform can be used to probe gene networks and signaling pathways to understand how they process static and dynamic features of specific stimuli, as well as for the rapid prototyping of synthetic circuits for biotechnology and biomedical purposes.

Computing with biological switches and clocks

The complex dynamics of biological systems is primarily driven by molecular interactions that underpin the regulatory networks of cells. These networks typically contain positive and negative feedback loops, which are responsible for switch-like and oscillatory dynamics, respectively. Many computing systems rely on switches and clocks as computational modules. While the combination of such modules in biological systems leads to a variety of dynamical behaviours, it is also driving development of new computing algorithms. Here we present a historical perspective on computation by biological systems, with a focus on switches and clocks, and discuss parallels between biology and computing. We also outline our vision for the future of biological computing.