(Im)Perfect robustness and adaptation of metabolic networks subject to metabolic and gene-expression regulation: marrying control engineering with metabolic control analysis

Control Theory and Systems Biology: Potential Applications in Neurodegeneration and Search for Therapeutic Targets

Control theory, a well-established discipline in engineering and mathematics, has found novel applications in systems biology. This interdisciplinary approach leverages the principles of feedback control and regulation to gain insights into the complex dynamics of cellular and molecular networks underlying chronic diseases, including neurodegeneration. By modeling and analyzing these intricate systems, control theory provides a framework to understand the pathophysiology and identify potential therapeutic targets. Therefore, this review examines the most widely used control methods in conjunction with genomic-scale metabolic models in the steady state of the multi-omics type. According to our research, this approach involves integrating experimental data, mathematical modeling, and computational analyses to simulate and control complex biological systems. In this review, we find that the most significant application of this methodology is associated with cancer, leaving a lack of knowledge in neurodegenerative models. However, this methodology, mainly associated with the Minimal Dominant Set (MDS), has provided a starting point for identifying therapeutic targets for drug development and personalized treatment strategies, paving the way for more effective therapies.

On paradoxes between optimal growth, metabolic control analysis, and flux balance analysis

In Microbiology it is often assumed that growth rate is maximal. This may be taken to suggest that the dependence of the growth rate on every enzyme activity is at the top of an inverse-parabolic function, i.e. that all flux control coefficients should equal zero. This might seem to imply that the sum of these flux control coefficients equals zero. According to the summation law of Metabolic Control Analysis (MCA) the sum of flux control coefficients should equal 1 however. And in Flux Balance Analysis (FBA) catabolism is often limited by a hard bound, causing catabolism to fully control the fluxes, again in apparent contrast with a flux control coefficient of zero. Here we resolve these paradoxes (apparent contradictions) in an analysis that uses the 'Edinburgh pathway', the 'Amsterdam pathway', as well as a generic metabolic network providing the building blocks or Gibbs energy for microbial growth. We review and show that (i) optimization depends on so-called enzyme control coefficients rather than the 'catalytic control coefficients' of MCA's summation law, (ii) when optimization occurs at fixed total protein, the former differ from the latter to the extent that they may all become equal to zero in the optimum state, (iii) in more realistic scenarios of optimization where catalytically inert biomass is compensating or maintenance metabolism is taken into consideration, the optimum enzyme concentrations should not be expected to equal those that maximize the specific growth rate, (iv) optimization may be in terms of yield rather than specific growth rate, which resolves the paradox because the sum of catalytic control coefficients on yield equals 0, (v) FBA effectively maximizes growth yield, and for yield the summation law states 0 rather than 1, thereby removing the paradox, (vi) furthermore, FBA then comes more often to a 'hard optimum' defined by a maximum catabolic flux and a catabolic-enzyme control coefficient of 1. The trade-off between maintenance metabolism and growth is highlighted as worthy of further analysis.

Trade-Offs in Biosensor Optimization for Dynamic Pathway Engineering

Recent progress in synthetic biology allows the construction of dynamic control circuits for metabolic engineering. This technology promises to overcome many challenges encountered in traditional pathway engineering, thanks to its ability to self-regulate gene expression in response to bioreactor perturbations. The central components in these control circuits are metabolite biosensors that read out pathway signals and actuate enzyme expression. However, the construction of metabolite biosensors is a major bottleneck for strain design, and a key challenge is to understand the relation between biosensor dose-response curves and pathway performance. Here we employ multiobjective optimization to quantify performance trade-offs that arise in the design of metabolite biosensors. Our approach reveals strategies for tuning dose-response curves along an optimal trade-off between production flux and the cost of an increased expression burden on the host. We explore properties of control architectures built in the literature and identify their advantages and caveats in terms of performance and robustness to growth conditions and leaky promoters. We demonstrate the optimality of a control circuit for glucaric acid production in Escherichia coli, which has been shown to increase the titer by 2.5-fold as compared to static designs. Our results lay the groundwork for the automated design of control circuits for pathway engineering, with applications in the food, energy, and pharmaceutical sectors.

Robust adaptation of PKCζ-IRS1 insulin signaling pathways through integral feedback control

Insulin signaling pathways in muscle tissue play a major role in maintaining glucose homeostasis. Dysregulation in these pathways results in the onset of serious metabolic disorders like type 2 diabetes. Robustness is an essential characteristic of insulin signaling pathways that ensures reliable signal transduction in the presence of perturbations as a result of several feedback mechanisms. Integral control, according to control engineering, provides reliable setpoint tracking and disturbance rejection. The presence of negative feedback and integrating process is crucial for biological processes to achieve integral control. The existence of an integral controller leads to the rejection of perturbations which resulted in the robust regulation of biochemical entities within acceptable levels. In the presentin silicoresearch work, the presence of integral control in the protein kinase Cζ- insulin receptor substrate-1 (PKCζ-IRS1) pathway is identified, verified mathematically and model is simulated in Cell Designer. The data is exported to Minitab software and robustness analysis is carried out statistically using the Mann-Whitney test. The p-value of the results obtained with given parameters perturbed by ±1% is greater than the significance level of 0.05 (0.2132 for 1% error in k7(rate constant of IRS1 phosphorylation), 0.2096 for -1% error in k7, 0.9037 for both ±1% error in insulin and 0.9037 for ±1% error in k1(association rate constant of the first molecule of insulin to bind the insulin receptor), indicated that our hypothesis is proved The results satisfactorily indicate that even when perturbations are present, glucose homeostasis in muscle tissue is robust due to the presence of integral regulation in the PKCζ-IRS1 insulin signaling pathways. In this paper, we have analysed the findings from the framework of robust control theory, which has allowed us to examine that how PKCζ-IRS1 insulin signaling pathways produces desired output in presence of perturbations.

Pareto optimality between growth-rate and lag-time couples metabolic noise to phenotypic heterogeneity in Escherichia coli

Despite mounting evidence that in clonal bacterial populations, phenotypic variability originates from stochasticity in gene expression, little is known about noise-shaping evolutionary forces and how expression noise translates to phenotypic differences. Here we developed a high-throughput assay that uses a redox-sensitive dye to couple growth of thousands of bacterial colonies to their respiratory activity and show that in Escherichia coli, noisy regulation of lower glycolysis and citric acid cycle is responsible for large variations in respiratory metabolism. We found that these variations are Pareto optimal to maximization of growth rate and minimization of lag time, two objectives competing between fermentative and respiratory metabolism. Metabolome-based analysis revealed the role of respiratory metabolism in preventing the accumulation of toxic intermediates of branched chain amino acid biosynthesis, thereby supporting early onset of cell growth after carbon starvation. We propose that optimal metabolic tradeoffs play a key role in shaping and preserving phenotypic heterogeneity and adaptation to fluctuating environments.

Quantifying Dynamic Regulation in Metabolic Pathways with Nonparametric Flux Inference

One of the central tasks in systems biology is to understand how cells regulate their metabolism. Hierarchical regulation analysis is a powerful tool to study this regulation at the metabolic, gene-expression, and signaling levels. It has been widely applied to study steady-state regulation, but analysis of the metabolic dynamics remains challenging because it is difficult to measure time-dependent metabolic flux. Here, we develop a nonparametric method that uses Gaussian processes to accurately infer the dynamics of a metabolic pathway based only on metabolite measurements; from this, we then go on to obtain a dynamical view of the hierarchical regulation processes invoked over time to control the activity in a pathway. Our approach allows us to use hierarchical regulation analysis in a dynamic setting but without the need for explicitly time-dependent flux measurements.

Metabolic Responses to Polymyxin Treatment in Acinetobacter baumannii ATCC 19606: Integrating Transcriptomics and Metabolomics with Genome-Scale Metabolic Modeling

Multidrug-resistant (MDR) Acinetobacter baumannii has emerged as a very problematic pathogen over the past decades, with a high incidence in nosocomial infections. Discovered in the late 1940s but abandoned in the 1970s, polymyxins (i.e., polymyxin B and colistin) have been revived as the last-line therapy against Gram-negative "superbugs," including MDR A. baumannii. Worryingly, resistance to polymyxins in A. baumannii has been increasingly reported, urging the development of novel antimicrobial therapies to rescue this last-line class of antibiotics. In the present study, we integrated genome-scale metabolic modeling with multiomics data to elucidate the mechanisms of cellular responses to colistin treatment in A. baumannii. A genome-scale metabolic model, iATCC19606, was constructed for strain ATCC 19606 based on the literature and genome annotation, containing 897 genes, 1,270 reactions, and 1,180 metabolites. After extensive curation, prediction of growth on 190 carbon sources using iATCC19606 achieved an overall accuracy of 84.3% compared to Biolog experimental results. Prediction of gene essentiality reached a high accuracy of 86.1% and 82.7% compared to two transposon mutant libraries of AB5075 and ATCC 17978, respectively. Further integrative modeling with our correlative transcriptomics and metabolomics data deciphered the complex regulation on metabolic responses to colistin treatment, including (i) upregulated fluxes through gluconeogenesis, the pentose phosphate pathway, and amino acid and nucleotide biosynthesis; (ii) downregulated TCA cycle and peptidoglycan and lipopolysaccharide biogenesis; and (iii) altered fluxes over respiratory chain. Our results elucidated the interplay of multiple metabolic pathways under colistin treatment in A. baumannii and provide key mechanistic insights into optimizing polymyxin combination therapy. IMPORTANCE Combating antimicrobial resistance has been highlighted as a critical global health priority. Due to the drying drug discovery pipeline, polymyxins have been employed as the last-line therapy against Gram-negative "superbugs"; however, the detailed mechanisms of antibacterial killing remain largely unclear, hampering the improvement of polymyxin therapy. Our integrative modeling using the constructed genome-scale metabolic model iATCC19606 and the correlative multiomics data provide the fundamental understanding of the complex metabolic responses to polymyxin treatment in A. baumannii at the systems level. The model iATCC19606 may have a significant potential in antimicrobial systems pharmacology research in A. baumannii.

Variable setpoint as a relaxing component in physiological control

Setpoints in physiology have been a puzzle for decades, and especially the notion of fixed or variable setpoints have received much attention. In this paper, we show how previously presented homeostatic controller motifs, extended with saturable signaling kinetics, can be described as variable setpoint controllers. The benefit of a variable setpoint controller is that an observed change in the concentration of the regulated biochemical species (the controlled variable) is fully characterized, and is not considered a deviation from a fixed setpoint. The variation in this biochemical species originate from variation in the disturbances (the perturbation), and thereby in the biochemical species representing the controller (the manipulated variable). Thus, we define an operational space which is spanned out by the combined high and low levels of the variations in (1) the controlled variable, (2) the manipulated variable, and (3) the perturbation. From this operational space, we investigate whether and how it imposes constraints on the different motif parameters, in order for the motif to represent a mathematical model of the regulatory system. Further analysis of the controller's ability to compensate for disturbances reveals that a variable setpoint represents a relaxing component for the controller, in that the necessary control action is reduced compared to that of a fixed setpoint controller. Such a relaxing component might serve as an important property from an evolutionary point of view. Finally, we illustrate the principles using the renal sodium and aldosterone regulatory system, where we model the variation in plasma sodium as a function of salt intake. We show that the experimentally observed variations in plasma sodium can be interpreted as a variable setpoint regulatory system.

A biomolecular proportional integral controller based on feedback regulations of protein level and activity

Homeostasis is the capacity of living organisms to keep internal conditions regulated at a constant level, despite environmental fluctuations. Integral feedback control is known to play a key role in this behaviour. Here, I show that a feedback system involving transcriptional and post-translational regulations of the same executor protein acts as a proportional integral (PI) controller, leading to enhanced transient performances in comparison with a classical integral loop. Such a biomolecular controller-which I call a level and activity-PI controller (LA-PI)-is involved in the regulation of ammonium uptake by Escherichia coli through the transporter AmtB. The P _II molecules, which reflect the nitrogen status of the cell, inhibit both the production of AmtB and its activity (via the NtrB-NtrC system and the formation of a complex with GlnK, respectively). Other examples of LA-PI controller include copper and zinc transporters, and the redox regulation in photosynthesis. This scheme has thus emerged through evolution in many biological systems, surely because of the benefits it offers in terms of performances (rapid and perfect adaptation) and economy (protein production according to needs).

Criticality and Adaptivity in Enzymatic Networks

The contrast between the stochasticity of biochemical networks and the regularity of cellular behavior suggests that biological networks generate robust behavior from noisy constituents. Identifying the mechanisms that confer this ability on biological networks is essential to understanding cells. Here we show that queueing for a limited shared resource in broad classes of enzymatic networks in certain conditions leads to a critical state characterized by strong and long-ranged correlations between molecular species. An enzymatic network reaches this critical state when the input flux of its substrate is balanced by the maximum processing capacity of the network. We then consider enzymatic networks with adaptation, when the limiting resource (enzyme or cofactor) is produced in proportion to the demand for it. We show that the critical state becomes an attractor for these networks, which points toward the onset of self-organized criticality. We suggest that the adaptive queueing motif that leads to significant correlations between multiple species may be widespread in biological systems.

Calcium Oscillation Frequency-Sensitive Gene Regulation and Homeostatic Compensation in Pancreatic β-Cells

Pancreatic islet [Formula: see text]-cells are electrically excitable cells that secrete insulin in an oscillatory fashion when the blood glucose concentration is at a stimulatory level. Insulin oscillations are the result of cytosolic [Formula: see text] oscillations that accompany bursting electrical activity of [Formula: see text]-cells and are physiologically important. ATP-sensitive [Formula: see text] channels (K(ATP) channels) play the key role in setting the overall activity of the cell and in driving bursting, by coupling cell metabolism to the membrane potential. In humans, when there is a defect in K(ATP) channel function, [Formula: see text]-cells fail to respond appropriately to changes in the blood glucose level, and electrical and [Formula: see text] oscillations are lost. However, mice compensate for K(ATP) channel defects in islet [Formula: see text]-cells by employing alternative mechanisms to maintain electrical and [Formula: see text] oscillations. In a recent study, we showed that in mice islets in which K(ATP) channels are genetically knocked out another [Formula: see text] current, provided by inward-rectifying [Formula: see text] channels, is increased. With mathematical modeling, we demonstrated that a sufficient upregulation in these channels can account for the paradoxical electrical bursting and [Formula: see text] oscillations observed in these [Formula: see text]-cells. However, the question of determining the correct level of upregulation that is necessary for this compensation remained unanswered, and this question motivates the current study. [Formula: see text] is a well-known regulator of gene expression, and several examples have been shown of genes that are sensitive to the frequency of the [Formula: see text] signal. In this mathematical modeling study, we demonstrate that a [Formula: see text] oscillation frequency-sensitive gene transcription network can adjust the gene expression level of a compensating [Formula: see text] channel so as to rescue electrical bursting and [Formula: see text] oscillations in a model [Formula: see text]-cell in which the key K(ATP) current is removed. This is done without the prescription of a target [Formula: see text] level, but evolves naturally as a consequence of the feedback between the [Formula: see text]-dependent enzymes and the cell's electrical activity. More generally, the study indicates how [Formula: see text] can provide the link between gene expression and cellular electrical activity that promotes wild-type behavior in a cell following gene knockout.

System wide cofactor turnovers can propagate metabolic stability between pathways

Metabolic homeostasis, or low-level metabolic steady state, has long been taken for granted in metabolic engineering, and research priority has always been given to understand metabolic flux control and regulation of the reaction network. In the past, this has not caused concerns because the metabolic networks studied were invariably associated with living cells. Nowadays, there are needs to reconstruct metabolic networks, and so metabolic homeostasis cannot be taken for granted. For metabolic steady state, enzyme feedback control has been known to explain why metabolites in metabolic pathways can avoid accumulation. However, we reasoned that there are further contributing mechanisms. As a new methodology developed, we separated cofactor intermediates (CIs) from non-cofactor intermediates, and identified an appropriate type of open systems for operating putative reaction topologies. Furthermore, we elaborated the criteria to tell if a multi-enzyme over-all reaction path is of in vivo nature or not at the metabolic level. As new findings, we discovered that there are interactions between the enzyme feedback inhibition and the CI turnover, and such interactions may well lead to metabolic homeostasis, an emergent property of the system. To conclude, this work offers a new perspective for understanding the role of CIs and the presence of metabolic homeostasis in the living cell. In perspective, this work might provide clues for constructing non-natural metabolic networks using multi-enzyme reactions or by degenerating metabolic reaction networks from the living cell.

Design of a Synthetic Integral Feedback Circuit: Dynamic Analysis and DNA Implementation

The design and implementation of regulation motifs ensuring robust perfect adaptation are challenging problems in synthetic biology. Indeed, the design of high-yield robust metabolic pathways producing, for instance, drug precursors and biofuels, could be easily imagined to rely on such a control strategy in order to optimize production levels and reduce production costs, despite the presence of environmental disturbance and model uncertainty. We propose here a motif that ensures tracking and robust perfect adaptation for the controlled reaction network through integral feedback. Its metabolic load on the host is fully tunable and can be made arbitrarily close to the constitutive limit, the universal minimal metabolic load of all possible controllers. A DNA implementation of the controller network is finally provided. Computer simulations using realistic parameters demonstrate the good agreement between the DNA implementation and the ideal controller dynamics.

Law of Localization in Chemical Reaction Networks

In living cells, chemical reactions are connected by sharing their products and substrates, and form complex networks, e.g., metabolic pathways. Here we developed a theory to predict the sensitivity, i.e., the responses of concentrations and fluxes to perturbations of enzymes, from network structure alone. Nonzero response patterns turn out to exhibit two characteristic features, localization and hierarchy. We present a general theorem connecting sensitivity with network topology that explains these characteristic patterns. Our results imply that network topology is an origin of biological robustness. Finally, we suggest a strategy to determine real networks from experimental measurements.

Synthetic biology and regulatory networks: where metabolic systems biology meets control engineering

Metabolic pathways can be engineered to maximize the synthesis of various products of interest. With the advent of computational systems biology, this endeavour is usually carried out through in silico theoretical studies with the aim to guide and complement further in vitro and in vivo experimental efforts. Clearly, what counts is the result in vivo, not only in terms of maximal productivity but also robustness against environmental perturbations. Engineering an organism towards an increased production flux, however, often compromises that robustness. In this contribution, we review and investigate how various analytical approaches used in metabolic engineering and synthetic biology are related to concepts developed by systems and control engineering. While trade-offs between production optimality and cellular robustness have already been studied diagnostically and statically, the dynamics also matter. Integration of the dynamic design aspects of control engineering with the more diagnostic aspects of metabolic, hierarchical control and regulation analysis is leading to the new, conceptual and operational framework required for the design of robust and productive dynamic pathways.

Modeling energy intake by adding homeostatic feedback and drug intervention

Energy intake (EI) is a pivotal biomarker used in quantification approaches to metabolic disease processes such as obesity, diabetes, and growth disorders. Eating behavior is however under both short-term and long-term control. This control system manifests itself as tolerance and rebound phenomena in EI, when challenged by drug treatment or diet restriction. The paper describes a model with the capability to capture physiological counter-regulatory feedback actions triggered by energy imbalances. This feedback is general as it handles tolerance to both increases and decreases in EI, and works in both acute and chronic settings. A drug mechanism function inhibits (or stimulates) EI. The deviation of EI relative to a reference level (set-point) serves as input to a non-linear appetite control signal which in turn impacts EI in parallel to the drug intervention. Three examples demonstrate the potential usefulness of the model in both acute and chronic dosing situations. The model shifts the predicted concentration-response relationship rightwardly at lower concentrations, in contrast to models that do not handle functional adaptation. A fourth example further shows that the model may qualitatively explain differences in rate and extent of adaptation in observed EI and its concomitants in both rodents and humans.

Macromolecular networks and intelligence in microorganisms

Living organisms persist by virtue of complex interactions among many components organized into dynamic, environment-responsive networks that span multiple scales and dimensions. Biological networks constitute a type of information and communication technology (ICT): they receive information from the outside and inside of cells, integrate and interpret this information, and then activate a response. Biological networks enable molecules within cells, and even cells themselves, to communicate with each other and their environment. We have become accustomed to associating brain activity - particularly activity of the human brain - with a phenomenon we call "intelligence." Yet, four billion years of evolution could have selected networks with topologies and dynamics that confer traits analogous to this intelligence, even though they were outside the intercellular networks of the brain. Here, we explore how macromolecular networks in microbes confer intelligent characteristics, such as memory, anticipation, adaptation and reflection and we review current understanding of how network organization reflects the type of intelligence required for the environments in which they were selected. We propose that, if we were to leave terms such as "human" and "brain" out of the defining features of "intelligence," all forms of life - from microbes to humans - exhibit some or all characteristics consistent with "intelligence." We then review advances in genome-wide data production and analysis, especially in microbes, that provide a lens into microbial intelligence and propose how the insights derived from quantitatively characterizing biomolecular networks may enable synthetic biologists to create intelligent molecular networks for biotechnology, possibly generating new forms of intelligence, first in silico and then in vivo.