Dimerization and bifunctionality confer robustness to the isocitrate dehydrogenase regulatory system in Escherichia coli

Bifunctional enzyme provides absolute concentration robustness in multisite covalent modification networks

Biochemical covalent modification networks exhibit a remarkable suite of steady state and dynamical properties such as multistationarity, oscillations, ultrasensitivity and absolute concentration robustness. This paper focuses on conditions required for a network of this type to have a species with absolute concentration robustness. We find that the robustness in a substrate is endowed by its interaction with a bifunctional enzyme, which is an enzyme that has different roles when isolated versus when bound as a substrate-enzyme complex. When isolated, the bifunctional enzyme promotes production of more molecules of the robust species while when bound, the same enzyme facilitates degradation of the robust species. These dual actions produce robustness in the large class of covalent modification networks. For each network of this type, we find the network conditions for the presence of robustness, the species that has robustness, and its robustness value. The unified approach of simultaneously analyzing a large class of networks for a single property, i.e. absolute concentration robustness, reveals the underlying mechanism of the action of bifunctional enzyme while simultaneously providing a precise mathematical description of bifunctionality.

Chemical Reaction Models in Synthetic Promoter Design in Bacteria

We discuss the formalism of chemical reaction networks (CRNs) as a computer-aided design interface for using formal methods in engineering living technologies. We set out by reviewing formal methods within a broader view of synthetic biology. Based on published results, we illustrate, step by step, how mathematical and computational techniques on CRNs can be used to study the structural and dynamic properties of the designed systems. As a case study, we use an E. coli two-component system that relays the external inorganic phosphate concentration signal to genetic components. We show how CRN models can scan and explore phenotypic regimes of synthetic promoters with varying detection thresholds, thereby providing a means for fine-tuning the promoter strength to match the specification.

Foundations of static and dynamic absolute concentration robustness

Absolute Concentration Robustness (ACR) was introduced by Shinar and Feinberg (Science 327:1389-1391, 2010) as robustness of equilibrium species concentration in a mass action dynamical system. Their aim was to devise a mathematical condition that will ensure robustness in the function of the biological system being modeled. The robustness of function rests on what we refer to as empirical robustness-the concentration of a species remains unvarying, when measured in the long run, across arbitrary initial conditions. Even simple examples show that the ACR notion introduced in Shinar and Feinberg (Science 327:1389-1391, 2010) (here referred to as static ACR) is neither necessary nor sufficient for empirical robustness. To make a stronger connection with empirical robustness, we define dynamic ACR, a property related to long-term, global dynamics, rather than only to equilibrium behavior. We discuss general dynamical systems with dynamic ACR properties as well as parametrized families of dynamical systems related to reaction networks. We find necessary and sufficient conditions for dynamic ACR in complex balanced reaction networks, a class of networks that is central to the theory of reaction networks.

Model-based robustness and bistability analysis for methylation-based, epigenetic memory systems

In recent years, epigenetic memory systems have been developed based on DNA methylation and positive feedback systems. Achieving a robust design for these systems is generally a challenging and multifactorial task. We developed and validated a novel mathematical model to describe methylation-based epigenetic memory systems that capture switching dynamics of methylation levels and methyltransferase amounts induced by different inputs. A bifurcation analysis shows that the system operates in the bistable range, but in its current setup is not robust to changes in parameters. An expansion of the model captures heterogeneity of cell populations by accounting for distributed cell division rates. Simulations predict that the system is highly sensitive to variations in temperature, which affects cell division and the efficiency of the zinc finger repressor. A moderate decrease in temperature leads to a highly heterogeneous response to input signals and bistability on a single-cell level. The predictions of our model were confirmed by flow cytometry experiments conducted in this study. Overall, the results of our study give insights into the functional mechanisms of methylation-based memory systems and demonstrate that the switching dynamics can be highly sensitive to experimental conditions.

Absolutely robust controllers for chemical reaction networks

In this work, we design a type of controller that consists of adding a specific set of reactions to an existing mass-action chemical reaction network in order to control a target species. This set of reactions is effective for both deterministic and stochastic networks, in the latter case controlling the mean as well as the variance of the target species. We employ a type of network property called absolute concentration robustness (ACR). We provide applications to the control of a multisite phosphorylation model as well as a receptor-ligand signalling system. For this framework, we use the so-called deficiency zero theorem from chemical reaction network theory as well as multiscaling model reduction methods. We show that the target species has approximately Poisson distribution with the desired mean. We further show that ACR controllers can bring robust perfect adaptation to a target species and are complementary to a recently introduced antithetic feedback controller used for stochastic chemical reactions.

Quantifying dynamic mechanisms of auto-regulation in Escherichia coli with synthetic promoter in response to varying external phosphate levels

Escherichia coli have developed one of the most efficient regulatory response mechanisms to phosphate starvation. The machinery involves a cascade with a two-component system (TCS) that relays the external signal to the genetic circuit, resulting in a feedback response. Achieving a quantitative understanding of this system has implications in synthetic biology and biotechnology, for example, in applications for wastewater treatment. To this aim, we present a computational model and experimental results with a detailed description of the TCS, consisting of PhoR and PhoB, together with the mechanisms of gene expression. The model is parameterised within the feasible range, and fitted to the dynamic response of our experimental data on PhoB as well as PhoA, the product of this network that is used in alkaline phosphatase production. Deterministic and stochastic simulations with our model predict the regulation dynamics in higher external phosphate concentrations while reproducing the experimental observations. In a cycle of simulations and experimental verification, our model predicts and explores phenotypes with various synthetic promoter designs that can optimise the inorganic phosphate intake in E. coli. Sensitivity analysis demonstrates that the Pho-controlled genes have a significant influence over the phosphate response. Together with experimental findings, our model should thus provide insights for the investigations on engineering new sensors and regulators for living technologies.

Lack of evidence for substrate channeling or flux between wildtype and mutant isocitrate dehydrogenase to produce the oncometabolite 2-hydroxyglutarate

Monoallelic point mutations in the gene encoding the cytosolic, NADP⁺-dependent enzyme isocitrate dehydrogenase 1 (IDH1) cause increased production of the oncometabolite 2-hydroxyglutarate (2-HG) in multiple cancers. Most IDH1 mutant tumors retain one wildtype (WT) IDH1 allele. Several studies have proposed that retention of this WT allele is protumorigenic by facilitating substrate channeling through a WT-mutant IDH1 heterodimer, with the WT subunit generating a local supply of α-ketoglutarate and NADPH that is then consumed by the mutant subunit to produce 2-HG. Here, we confirmed that coexpression of WT and mutant IDH1 subunits leads to formation of WT-mutant hetero-oligomers and increases 2-HG production. An analysis of a recently reported crystal structure of the WT-R132H IDH1 heterodimer and of in vitro kinetic parameters for 2-HG production, however, indicated that substrate channeling between the subunits is biophysically implausible. We also found that putative carbon-substrate flux between WT and mutant IDH1 subunits is inconsistent with the results of isotope tracing experiments in cancer cells harboring an endogenous monoallelic IDH1 mutation. Finally, using a mathematical model of WT-mutant IDH1 heterodimers, we estimated that the NADPH:NADP⁺ ratio is higher in the cytosol than in the mitochondria, suggesting that NADPH is unlikely to be limiting for 2-HG production in the cytosol. These findings argue against supply of either substrate being limiting for 2-HG production by a cytosolic IDH1 mutant and suggest that the retention of a WT allele in IDH1 mutant tumors is not due to a requirement for carbon or cofactor flux between WT and mutant IDH1.

Thermodynamic analysis of computed pathways integrated into the metabolic networks of E. coli and Synechocystis reveals contrasting expansion potential

Introducing biosynthetic pathways into an organism is both reliant on and challenged by endogenous biochemistry. Here we compared the expansion potential of the metabolic network in the photoautotroph Synechocystis with that of the heterotroph E. coli using the novel workflow POPPY (Prospecting Optimal Pathways with PYthon). First, E. coli and Synechocystis metabolomic and fluxomic data were combined with metabolic models to identify thermodynamic constraints on metabolite concentrations (NET analysis). Then, thousands of automatically constructed pathways were placed within each network and subjected to a network-embedded variant of the max-min driving force analysis (NEM). We found that the networks had different capabilities for imparting thermodynamic driving forces toward certain compounds. Key metabolites were constrained differently in Synechocystis due to opposing flux directions in glycolysis and carbon fixation, the forked tri-carboxylic acid cycle, and photorespiration. Furthermore, the lysine biosynthesis pathway in Synechocystis was identified as thermodynamically constrained, impacting both endogenous and heterologous reactions through low 2-oxoglutarate levels. Our study also identified important yet poorly covered areas in existing metabolomics data and provides a reference for future thermodynamics-based engineering in Synechocystis and beyond. The POPPY methodology represents a step in making optimal pathway-host matches, which is likely to become important as the practical range of host organisms is diversified.

Analysis of network motifs in cellular regulation: Structural similarities, input-output relations and signal integration

Much of the complexity of regulatory networks derives from the necessity to integrate multiple signals and to avoid malfunction due to cross-talk or harmful perturbations. Hence, one may expect that the input-output behavior of larger networks is not necessarily more complex than that of smaller network motifs which suggests that both can, under certain conditions, be described by similar equations. In this review, we illustrate this approach by discussing the similarities that exist in the steady state descriptions of a simple bimolecular reaction, covalent modification cycles and bacterial two-component systems. Interestingly, in all three systems fundamental input-output characteristics such as thresholds, ultrasensitivity or concentration robustness are described by structurally similar equations. Depending on the system the meaning of the parameters can differ ranging from protein concentrations and affinity constants to complex parameter combinations which allows for a quantitative understanding of signal integration in these systems. We argue that this approach may also be extended to larger regulatory networks.

Transient absolute robustness in stochastic biochemical networks

Absolute robustness allows biochemical networks to sustain a consistent steady-state output in the face of protein concentration variability from cell to cell. This property is structural and can be determined from the topology of the network alone regardless of rate parameters. An important question regarding these systems is the effect of discrete biochemical noise in the dynamical behaviour. In this paper, a variable freezing technique is developed to show that under mild hypotheses the corresponding stochastic system has a transiently robust behaviour. Specifically, after finite time the distribution of the output approximates a Poisson distribution, centred around the deterministic mean. The approximation becomes increasingly accurate, and it holds for increasingly long finite times, as the total protein concentrations grow to infinity. In particular, the stochastic system retains a transient, absolutely robust behaviour corresponding to the deterministic case. This result contrasts with the long-term dynamics of the stochastic system, which eventually must undergo an extinction event that eliminates robustness and is completely different from the deterministic dynamics. The transiently robust behaviour may be sufficient to carry out many forms of robust signal transduction and cellular decision-making in cellular organisms.

A network property necessary for concentration robustness

Maintenance of functionality of complex cellular networks and entire organisms exposed to environmental perturbations often depends on concentration robustness of the underlying components. Yet, the reasons and consequences of concentration robustness in large-scale cellular networks remain largely unknown. Here, we derive a necessary condition for concentration robustness based only on the structure of networks endowed with mass action kinetics. The structural condition can be used to design targeted experiments to study concentration robustness. We show that metabolites satisfying the necessary condition are present in metabolic networks from diverse species, suggesting prevalence of this property across kingdoms of life. We also demonstrate that our predictions about concentration robustness of energy-related metabolites are in line with experimental evidence from Escherichia coli. The necessary condition is applicable to mass action biological systems of arbitrary size, and will enable understanding the implications of concentration robustness in genetic engineering strategies and medical applications.

Absolute concentration robustness (ACR), independence of the steady-state concentration of a molecule from the environment, is difficult to predict. Here, the authors derive a network structure-based necessary condition for ACR, and suggest that metabolites satisfying the condition are prevalent.

Invariants reveal multiple forms of robustness in bifunctional enzyme systems

Experimental and theoretical studies have suggested that bifunctional enzymes catalyzing opposing modification and demodification reactions can confer steady-state concentration robustness to their substrates. However, the types of robustness and the biochemical basis for them have remained elusive. Here we report a systematic study of the most general biochemical reaction network for a bifunctional enzyme acting on a substrate with one modification site, along with eleven sub-networks with more specialized biochemical assumptions. We exploit ideas from computational algebraic geometry, introduced in previous work, to find a polynomial expression (an invariant) between the steady state concentrations of the modified and unmodified substrate for each network. We use these invariants to identify five classes of robust behavior: robust upper bounds on concentration, robust two-sided bounds on concentration ratio, hybrid robustness, absolute concentration robustness (ACR), and robust concentration ratio. This analysis demonstrates that robustness can take a variety of forms and that the type of robustness is sensitive to many biochemical details, with small changes in biochemistry leading to very different steady-state behaviors. In particular, we find that the widely-studied ACR requires highly specialized assumptions in addition to bifunctionality. An unexpected result is that the robust bounds derived from invariants are strictly tighter than those derived by ad hoc manipulation of the underlying differential equations, confirming the value of invariants as a tool to gain insight into biochemical reaction networks. Furthermore, invariants yield multiple experimentally testable predictions and illuminate new strategies for inferring enzymatic mechanisms from steady-state measurements.

Robust network structure of the Sln1-Ypd1-Ssk1 three-component phospho-relay prevents unintended activation of the HOG MAPK pathway in Saccharomyces cerevisiae

BACKGROUND

The yeast Saccharomyces cerevisiae relies on the high-osmolarity glycerol (HOG) signaling pathway to respond to increases in external osmolarity. The HOG pathway is rapidly activated under conditions of elevated osmolarity and regulates transcriptional and metabolic changes within the cell. Under normal growth conditions, however, a three-component phospho-relay consisting of the histidine kinase Sln1, the transfer protein Ypd1, and the response regulator Ssk1 represses HOG pathway activity by phosphorylation of Ssk1. This inhibition of the HOG pathway is essential for cellular fitness in normal osmolarity. Nevertheless, the extent to and mechanisms by which inhibition is robust to fluctuations in the concentrations of the phospho-relay components has received little attention.

RESULTS

We established that the Sln1-Ypd1-Ssk1 phospho-relay is robust-it is able to maintain inhibition of the HOG pathway even after significant changes in the levels of its three components. We then developed a biochemically realistic mathematical model of the phospho-relay, which suggested that robustness is due to buffering by a large excess pool of Ypd1. We confirmed experimentally that depletion of the Ypd1 pool results in inappropriate activation of the HOG pathway.

CONCLUSIONS

We identified buffering by an intermediate component in excess as a novel mechanism through which a phospho-relay can achieve robustness. This buffering requires multiple components and is therefore unavailable to two-component systems, suggesting one important advantage of multi-component relays.

Sensitivity and robustness in covalent modification cycles with a bifunctional converter enzyme

Regulation by covalent modification is a common mechanism to transmit signals in biological systems. The modifying reactions are catalyzed either by two distinct converter enzymes or by a single bifunctional enzyme (which may employ either one or two catalytic sites for its opposing activities). The reason for this diversification is unclear, but contemporary theoretical models predict that systems with distinct converter enzymes can exhibit enhanced sensitivity to input signals whereas bifunctional enzymes with two catalytic sites are believed to generate robustness against variations in system's components. However, experiments indicate that bifunctional enzymes can also exhibit enhanced sensitivity due to the zero-order effect, raising the question whether both phenomena could be understood within a common mechanistic model. Here, I argue that this is, indeed, the case. Specifically, I show that bifunctional enzymes with two catalytic sites can exhibit both ultrasensitivity and concentration robustness, depending on the kinetic operating regime of the enzyme's opposing activities. The model predictions are discussed in the context of experimental observations of ultrasensitivity and concentration robustness in the uridylylation cycle of the PII protein, and in the phosphorylation cycle of the isocitrate dehydrogenase, respectively.

Transcriptional and proteomic responses to carbon starvation in Paracoccidioides

Background

The genus Paracoccidioides comprises human thermal dimorphic fungi, which cause paracoccidioidomycosis (PCM), an important mycosis in Latin America. Adaptation to environmental conditions is key to fungal survival during human host infection. The adaptability of carbon metabolism is a vital fitness attribute during pathogenesis.

Methodology/Principal Findings

The fungal pathogen Paracoccidioides spp. is exposed to numerous adverse conditions, such as nutrient deprivation, in the human host. In this study, a comprehensive response of Paracoccidioides, Pb01, under carbon starvation was investigated using high-resolution transcriptomic (RNAseq) and proteomic (NanoUPLC-MS^E) approaches. A total of 1,063 transcripts and 421 proteins were differentially regulated, providing a global view of metabolic reprogramming during carbon starvation. The main changes were those related to cells shifting to gluconeogenesis and ethanol production, supported by the degradation of amino acids and fatty acids and by the modulation of the glyoxylate and tricarboxylic cycles. This proposed carbon flow hypothesis was supported by gene and protein expression profiles assessed using qRT-PCR and western blot analysis, respectively, as well as using enzymatic, cell dry weight and fungus-macrophage interaction assays. The carbon source provides a survival advantage to Paracoccidioides inside macrophages.

Conclusions/Significance

For a complete understanding of the physiological processes in an organism, the integration of approaches addressing different levels of regulation is important. To the best of our knowledge, this report presents the first description of the responses of Paracoccidioides spp. to host-like conditions using large-scale expression approaches. The alternative metabolic pathways that could be adopted by the organism during carbon starvation can be important for a better understanding of the fungal adaptation to the host, because systems for detecting and responding to carbon sources play a major role in adaptation and persistence in the host niche.

The species of the Paracoccidioides genus, a neglected human pathogen, represent the causative agents of paracoccidioidomycosis (PCM), one of the most frequent systemic mycoses in Latin America. Despite being phagocytosed, the fungus conidia differentiate into the parasitic yeast form that subverts the normally harsh intraphagosomal environment and survives and replicates into murine and human macrophages. It has been suggested that alternative carbon metabolism plays a role in the survival and virulence of Paracoccidioides spp. within host cells. We used large-scale transcriptome and proteome approaches to better characterize the responses of Paracoccidioides, Pb01, yeast parasitic cells, to carbon starvation. We aimed to identify important molecules used by the fungus to adapt to these hostile conditions. The shift to a starvation mode, including gluconeogenesis and ethanol increases, activation of fatty acids, and amino acid degradation are the strategies used by the pathogen to persist under this stress. Our study provides a detailed map of Paracoccidioides spp. responses under carbon starvation conditions and contributes to further investigations of the importance of alternative carbon adaptation during fungus pathogenesis.

A fundamental trade-off in covalent switching and its circumvention by enzyme bifunctionality in glucose homeostasis

Covalent modification provides a mechanism for modulating molecular state and regulating physiology. A cycle of competing enzymes that add and remove a single modification can act as a molecular switch between "on" and "off" and has been widely studied as a core motif in systems biology. Here, we exploit the recently developed "linear framework" for time scale separation to determine the general principles of such switches. These methods are not limited to Michaelis-Menten assumptions, and our conclusions hold for enzymes whose mechanisms may be arbitrarily complicated. We show that switching efficiency improves with increasing irreversibility of the enzymes and that the on/off transition occurs when the ratio of enzyme levels reaches a value that depends only on the rate constants. Fluctuations in enzyme levels, which habitually occur due to cellular heterogeneity, can cause flipping back and forth between on and off, leading to incoherent mosaic behavior in tissues, that worsens as switching becomes sharper. This trade-off can be circumvented if enzyme levels are correlated. In particular, if the competing catalytic domains are on the same protein but do not influence each other, the resulting bifunctional enzyme can switch sharply while remaining coherent. In the mammalian liver, the switch between glycolysis and gluconeogenesis is regulated by the bifunctional 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase (PFK-2/FBPase-2). We suggest that bifunctionality of PFK-2/FBPase-2 complements the metabolic zonation of the liver by ensuring coherent switching in response to insulin and glucagon.

Evidence for hysteretic substrate channeling in the proline dehydrogenase and Δ1-pyrroline-5-carboxylate dehydrogenase coupled reaction of proline utilization A (PutA)

PutA (proline utilization A) is a large bifunctional flavoenzyme with proline dehydrogenase (PRODH) and Δ(1)-pyrroline-5-carboxylate dehydrogenase (P5CDH) domains that catalyze the oxidation of l-proline to l-glutamate in two successive reactions. In the PRODH active site, proline undergoes a two-electron oxidation to Δ(1)-pyrroline-5-carboxlylate, and the FAD cofactor is reduced. In the P5CDH active site, l-glutamate-γ-semialdehyde (the hydrolyzed form of Δ(1)-pyrroline-5-carboxylate) undergoes a two-electron oxidation in which a hydride is transferred to NAD(+)-producing NADH and glutamate. Here we report the first kinetic model for the overall PRODH-P5CDH reaction of a PutA enzyme. Global analysis of steady-state and transient kinetic data for the PRODH, P5CDH, and coupled PRODH-P5CDH reactions was used to test various models describing the conversion of proline to glutamate by Escherichia coli PutA. The coupled PRODH-P5CDH activity of PutA is best described by a mechanism in which the intermediate is not released into the bulk medium, i.e., substrate channeling. Unexpectedly, single-turnover kinetic experiments of the coupled PRODH-P5CDH reaction revealed that the rate of NADH formation is 20-fold slower than the steady-state turnover number for the overall reaction, implying that catalytic cycling speeds up throughput. We show that the limiting rate constant observed for NADH formation in the first turnover increases by almost 40-fold after multiple turnovers, achieving half of the steady-state value after 15 turnovers. These results suggest that EcPutA achieves an activated channeling state during the approach to steady state and is thus a new example of a hysteretic enzyme. Potential underlying causes of activation of channeling are discussed.

Circles within circles: crosstalk between protein Ser/Thr/Tyr-phosphorylation and Met oxidation

BACKGROUND

Reversible posttranslational protein modifications such as phosphorylation of Ser/Thr/Tyr and Met oxidation are critical for both metabolic regulation and cellular signalling. Although these modifications are typically studied individually, herein we describe the potential for cross-talk and hierarchical regulation.

RESULTS

The proximity of Met to Ser/Thr/Tyr within the proteome has not previously been addressed. In order to consider the possibility of a generalized interaction, we performed a trans-kingdom sequence analysis of known phosphorylation sites in proteins from bacteria, fungi, plants, and animals. The proportion of phosphorylation sites that include a Met within a 13-residue window centered upon Ser/Thr/Tyr is significantly less than the occurrence of Met in proximity to all Ser/Thr/Tyr residues. Met residues are present at all positions (-6 to +6, inclusive) within the 13-residue window that we have considered. Detailed analysis of sequences from eight disparate plant taxa revealed that many conserved phosphorylation sites have a Met residue in the proximity. Results from GO enrichment analysis indicated that the potential for phosphorylation and Met oxidation crosstalk is most prevalent in kinases and proteins involved in signalling.

CONCLUSION

The large proportion of known phosphorylation sites with Met in the proximity fulfils the necessary condition for cross-talk. Kinases/signalling proteins are enriched for Met around phosphorylation sites. These proteins/sites are likely candidates for cross-talk between oxidative signalling and reversible phosphorylation.