Bistability in the isocitrate dehydrogenase reaction: an experimentally based theoretical study

Multisite Enzymes as a Mechanism for Bistability in Reaction Networks

Here, we focus on a common class of enzymes that have multiple substrate binding sites (multisite enzymes) and analyze their capacity to generate bistable dynamics in the reaction networks that they are embedded in. These networks include both substrate-product-substrate cycles and substrate-to-product conversion with subsequent product consumption. Using mathematical techniques, we show that the inherent binding and catalysis reactions arising from multiple substrate-enzyme complexes create a potential for bistable dynamics in such reaction networks. We construct a generic model of an enzyme with n-substrate binding sites and derive an analytical solution for the steady-state concentration of all enzyme-substrate complexes. By studying these expressions, we obtain a mechanistic understanding of bistability, derive parameter combinations that guarantee bistability, and show how changing specific enzyme kinetic parameters and enzyme levels can lead to bistability in reaction networks involving multisite enzymes. Thus, the presented findings provide a biochemical and mathematical basis for predicting and engineering bistability in multisite enzymes.

Bistability in cell signalling and its significance in identifying potential drug targets

MOTIVATION

Bistability is one of the salient dynamical features in various all-or-none kinds of decision-making processes. The presence of bistability in a cell signalling network plays a key role in input-output (I/O) relation. Our study is aiming to capture and emphasise the role of motif structure influencing the I/O relation between two nodes in the context of bistability. Here, a model-based analysis is made to investigate the critical conditions responsible for the emergence of different bistable protein-protein interaction (PPI) motifs and their possible applications to find the potential drug targets.

RESULTS

The global sensitivity analysis is used to identify sensitive parameters and their role in maintaining the bistability. Additionally, the bistable switching through hysteresis is explored to develop an understanding of the underlying mechanisms involved in the cell signalling processes, when significant motifs exhibiting bistability have emerged. Further, we elaborate the application of the results by the implication of the emerged PPI motifs to identify potential drug-targets in three cancer networks, which is validated with existing databases. The influence of stochastic perturbations that could hinder desired functionality of any signalling networks is also described here.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

The IDO Metabolic Trap Hypothesis for the Etiology of ME/CFS

Myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS) is a debilitating noncommunicable disease brandishing an enormous worldwide disease burden with some evidence of inherited genetic risk. Absence of measurable changes in patients' standard blood work has necessitated ad hoc symptom-driven therapies and a dearth of mechanistic hypotheses regarding its etiology and possible cure. A new hypothesis, the indolamine-2,3-dioxygenase (IDO) metabolic trap, was developed and formulated as a mathematical model. The historical occurrence of ME/CFS outbreaks is a singular feature of the disease and implies that any predisposing genetic mutation must be common. A database search for common damaging mutations in human enzymes produces 208 hits, including IDO2 with four such mutations. Non-functional IDO2, combined with well-established substrate inhibition of IDO1 and kinetic asymmetry of the large neutral amino acid transporter, LAT1, yielded a mathematical model of tryptophan metabolism that displays both physiological and pathological steady-states. Escape from the pathological one requires an exogenous perturbation. This model also identifies a critical point in cytosolic tryptophan abundance beyond which descent into the pathological steady-state is inevitable. If, however, means can be discovered to return cytosolic tryptophan below the critical point, return to the normal physiological steady-state is assured. Testing this hypothesis for any cell type requires only labelled tryptophan, a means to measure cytosolic tryptophan and kynurenine, and the standard tools of tracer kinetics.

Multi-rhythmicity generated by coupling two cellular rhythms

The cell cycle and the circadian clock represent two major cellular rhythms, which are coupled because the circadian clock governs the synthesis of several proteins of the network that drives the mammalian cell cycle. Analysis of a detailed model for these coupled cellular rhythms previously showed that the cell cycle can be entrained at the circadian period of 24 h, or at a period of 48 h, depending on the autonomous period of the cell cycle and on the coupling strength. We show by means of numerical simulations that multiple stable periodic regimes, i.e. multi-rhythmicity, may originate from the coupling of the two cellular rhythms. In these conditions, the cell cycle can evolve to any one of two (birhythmicity) or three stable periodic regimes (trirhythmicity). When applied at the right phase, transient perturbations of appropriate duration and magnitude can induce the switch between the different oscillatory states. Such switching is characterized by final state sensitivity, which originates from the complex structure of the attraction basins. By providing a novel instance of multi-rhythmicity in a realistic model for the coupling of two major cellular rhythms, the results throw light on the conditions in which multiple stable periodic regimes may coexist in biological systems.

Dissipative structures in biological systems: bistability, oscillations, spatial patterns and waves

The goal of this review article is to assess how relevant is the concept of dissipative structure for understanding the dynamical bases of non-equilibrium self-organization in biological systems, and to see where it has been applied in the five decades since it was initially proposed by Ilya Prigogine. Dissipative structures can be classified into four types, which will be considered, in turn, and illustrated by biological examples: (i) multistability, in the form of bistability and tristability, which involve the coexistence of two or three stable steady states, or in the form of birhythmicity, which involves the coexistence between two stable rhythms; (ii) temporal dissipative structures in the form of sustained oscillations, illustrated by biological rhythms; (iii) spatial dissipative structures, known as Turing patterns; and (iv) spatio-temporal structures in the form of propagating waves. Rhythms occur with widely different periods at all levels of biological organization, from neural, cardiac and metabolic oscillations to circadian clocks and the cell cycle; they play key roles in physiology and in many disorders. New rhythms are being uncovered while artificial ones are produced by synthetic biology. Rhythms provide the richest source of examples of dissipative structures in biological systems. Bistability has been observed experimentally, but has primarily been investigated in theoretical models in an increasingly wide range of biological contexts, from the genetic to the cell and animal population levels, both in physiological conditions and in disease. Bistable transitions have been implicated in the progression between the different phases of the cell cycle and, more generally, in the process of cell fate specification in the developing embryo. Turing patterns are exemplified by the formation of some periodic structures in the course of development and by skin stripe patterns in animals. Spatio-temporal patterns in the form of propagating waves are observed within cells as well as in intercellular communication. This review illustrates how dissipative structures of all sorts abound in biological systems.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

Endocytosis as a stabilizing mechanism for tissue homeostasis

Cells in tissues communicate by secreted growth factors (GF) and other signals. An important function of cell circuits is tissue homeostasis: maintaining proper balance between the amounts of different cell types. Homeostasis requires negative feedback on the GFs, to avoid a runaway situation in which cells stimulate each other and grow without control. Feedback can be obtained in at least two ways: endocytosis in which a cell removes its cognate GF by internalization and cross-inhibition in which a GF down-regulates the production of another GF. Here we ask whether there are design principles for cell circuits to achieve tissue homeostasis. We develop an analytically solvable framework for circuits with multiple cell types and find that feedback by endocytosis is far more robust to parameter variation and has faster responses than cross-inhibition. Endocytosis, which is found ubiquitously across tissues, can even provide homeostasis to three and four communicating cell types. These design principles form a conceptual basis for how tissues maintain a healthy balance of cell types and how balance may be disrupted in diseases such as degeneration and fibrosis.

Noise-induced transitions in a double-well excitable oscillator

The model of a double-well oscillator with nonlinear dissipation is studied. The self-sustained oscillation regime and the excitable one are described. The first regime consists of the coexistence of two stable limit cycles in the phase space, which correspond to self-sustained oscillations of the point mass in either potential well. The self-sustained oscillations do not occur in a noise-free system in the excitable regime, but appropriate conditions for coherence resonance in either potential well can be achieved. The stochastic dynamics in both regimes is researched by using numerical simulation and electronic circuit implementation of the considered system. Multiple qualitative changes of the probability density function caused by noise intensity varying are explained by using the phase-space structure of the deterministic system.

Noise-induced transitions in a double-well oscillator with nonlinear dissipation

We develop a model of bistable oscillator with nonlinear dissipation. Using a numerical simulation and an electronic circuit realization of this system we study its response to additive noise excitations. We show that depending on noise intensity the system undergoes multiple qualitative changes in the structure of its steady-state probability density function (PDF). In particular, the PDF exhibits two pitchfork bifurcations versus noise intensity, which we describe using an effective potential and corresponding normal form of the bifurcation. These stochastic effects are explained by the partition of the phase space by the nullclines of the deterministic oscillator.

Ultrasensitivity part II: multisite phosphorylation, stoichiometric inhibitors, and positive feedback

In this series of reviews, we are examining ultrasensitive responses, the switch-like input-output relationships that contribute to signal processing in a wide variety of signaling contexts. In the first part of this series, we explored one mechanism for generating ultrasensitivity, zero-order ultrasensitivity, where the saturation of two converting enzymes allows the output to switch from low to high over a tight range of input levels. In this second installment, we focus on three conceptually distinct mechanisms for ultrasensitivity: multisite phosphorylation, stoichiometric inhibitors, and positive feedback. We also examine several related mechanisms and concepts, including cooperativity, reciprocal regulation, coherent feed-forward regulation, and substrate competition, and provide several examples of signaling processes where these mechanisms are known or are suspected to be applicable.

The robustness of the Escherichia coli signal-transducing UTase/UR-PII covalent modification cycle to variation in the PII concentration requires very strong inhibition of the UTase activity of UTase/UR by glutamine

Uridylyltransferase/uridylyl-removing enzyme (UTase/UR) catalyzes uridylylation of PII and deuridylylation of PII-UMP, with both activities regulated by glutamine. In a reconstituted UTase/UR-PII cycle containing wild-type UTase/UR, the steady-state modification of PII varied from nearly complete modification to nearly complete demodification as glutamine was varied, whether the level of PII was saturating or unsaturating, but when a His-tagged version of UTase/UR was used, the robustness to variations in PII concentration was lost and the range of PII modification states in response to glutamine became smaller as the PII concentration increased. The presence of the His tag on UTase/UR did not alter PII substrate inhibition of the UT activity and had little effect on the level of the UT activity but resulted in a slight defect in UR activity. Importantly, at high PII concentrations, glutamine inhibition of the UT activity was incomplete. We hypothesized that binding of PII to the UR active site in the HD domain was responsible for PII substrate inhibition of the UT activity and, in the His-tagged enzyme, also weakened glutamine inhibition of the UT activity. Consistent with this, three different UTase/UR proteins with HD domain alterations lacked substrate inhibition of UT activity by PII; in one case, the HD alteration eliminated glutamine regulation of UT activity, while for the other two proteins, alterations of the HD domain partially compensated for the effect of the His tag in restoring glutamine regulation of UT activity. We conclude that very strong inhibition of UT activity was required for the UTase/UR-PII cycle to display robustness to the PII concentration, that in the wild-type enzyme PII brings about substrate inhibition of the UT activity by binding to the HD domain of the enzyme, and that addition of an N-terminal His tag resulted in an altered enzyme with subtle changes in the interactions between domains such that binding of PII to the HD domain interfered with glutamine regulation of the UT domain.

Characterization of the reconstituted UTase/UR-PII-NRII-NRI bicyclic signal transduction system that controls the transcription of nitrogen-regulated (Ntr) genes in Escherichia coli

A reconstituted UTase/UR-PII-NRII-NRI bicyclic cascade regulated PII uridylylation and NRI phosphorylation in response to glutamine. We examined the sensitivity and robustness of the responses of the individual cycles and of the bicyclic system. The sensitivity of the glutamine response of the upstream UTase/UR-PII monocycle depended upon the PII concentration, and we show that PII exerted substrate inhibition of the UTase activity of UTase/UR, potentially contributing to this dependence of sensitivity on PII. In the downstream NRII-NRI monocycle, PII controlled NRI phosphorylation state, and the response to PII was hyperbolic at both saturating and unsaturating NRI concentration. As expected from theory, the level of NRI∼P produced by the NRII-NRI monocycle was robust to changes in the NRII or NRI concentrations when NRI was in excess over NRII, as long as the NRII concentration was above a threshold value, an example of absolute concentration robustness (ACR). Because of the parameters of the system, at physiological protein levels and ratios of NRI to NRII, the level of NRI∼P depended upon both protein concentrations. In bicyclic UTase/UR-PII-NRII-NRI systems, the NRI phosphorylation state response to glutamine was always hyperbolic, regardless of the PII concentration or sensitivity of the upstream UTase/UR-PII cycle. In these bicyclic systems, NRI phosphorylation state was only robust to variation in the PII/NRII ratio within a narrow range; when PII was in excess NRI∼P was low, and when NRII was in excess NRI phosphorylation was elevated, throughout the physiological range of glutamine concentrations. Our results show that the bicyclic system produced a graded response of NRI phosphorylation to glutamine under a range of conditions, and that under most conditions the response of NRI phosphorylation state to glutamine levels depended on the concentrations of NRI, NRII, and PII.

Response to Comment on “‘Load-Induced Modulation of Signal Transduction Networks’: Reconciling Ultrasensitivity with Bifunctionality?”

Complex biochemical and regulatory properties of a bifunctional enzyme mean that its activity cannot be modeled as a simple bifunctional system with distinct and reciprocally regulated states.

Dynamic disorder-driven substrate inhibition and bistability in a simple enzymatic reaction

Conformations and catalytic rates of enzymes (biological catalysts) fluctuate over a wide range of time scales. Recent experimental and theoretical investigations demonstrated case studies where the enzymatic catalysis rate follows the Michaelis-Menten (MM) rate law despite molecular fluctuations. In this paper, we investigate deviations from MM law and their effects on the dynamical behavior of the enzymatic network. We consider a simple kinetic scheme for a single substrate enzymatic reaction in which the product release step is treated explicitly. We examine how conformational fluctuations affect the underlying rate law in the quasi-static limit when conformational dynamics is very slow in one of the states. Our numerical results and analytically solvable model indicate that slow conformational fluctuations of the enzyme-substrate complex lead to non-MM behavior, substrate inhibition, and possible bistability of the reaction network.

Sharp developmental thresholds defined through bistability by antagonistic gradients of retinoic acid and FGF signaling

The establishment of thresholds along morphogen gradients in the embryo is poorly understood. Using mathematical modeling, we show that mutually inhibitory gradients can generate and position sharp morphogen thresholds in the embryonic space. Taking vertebrate segmentation as a paradigm, we demonstrate that the antagonistic gradients of retinoic acid (RA) and Fibroblast Growth Factor (FGF) along the presomitic mesoderm (PSM) may lead to the coexistence of two stable steady states. Here, we propose that this bistability is associated with abrupt switches in the levels of FGF and RA signaling, which permit the synchronized activation of segmentation genes, such as mesp2, in successive cohorts of PSM cells in response to the segmentation clock, thereby defining the future segments. Bistability resulting from mutual inhibition of RA and FGF provides a molecular mechanism for the all-or-none transitions assumed in the "clock and wavefront" somitogenesis model. Given that mutually antagonistic signaling gradients are common in development, such bistable switches could represent an important principle underlying embryonic patterning.

NOX4 as an oxygen sensor to regulate TASK-1 activity

When oxygen sensing cells are excited by hypoxia, background K+ currents are inhibited. TASK-1, which is commonly expressed in oxygen sensing cells and makes a background K+ current, is inactivated by hypoxia. Thus TASK-1 is a candidate molecule responsible for hypoxic excitation. However, TASK-1 per se cannot sense oxygen and may require a regulatory protein that can. In the present study, we propose that the NADPH oxidase NOX4 functions as an oxygen-sensing partner and that it modulates the oxygen sensitivity of TASK-1. Confocal imaging revealed the co-localization of TASK-1 and NOX4 in the plasma membrane. In HEK293 cells expressing NOX4 endogenously, the activity of expressed TASK-1 was moderately inhibited by hypoxia, and this oxygen response was significantly augmented by NOX4. Moreover, the oxygen sensitivity of TASK-1 was abolished by NOX4 siRNA and NADPH oxidase inhibitors. These results suggest a novel function for NOX4 in the oxygen-dependent regulation of TASK-1 activity.

Impact of coenzyme regeneration on the performance of an enzyme-based optical biosensor: a computational study

A mathematical model of a reagent-less optical sensing scheme composed of an enzymatic reaction coupled to light-controlled photochemical coenzyme regeneration is described. The model is based on previous experimental work describing the regeneration of NADPH from NADP(+) by excited state thionine coupled to the oxidation of isocitrate by isocitrate dehydrogenase. The system is capable of repeated isocitrate measurements without the addition of exogenous coenzyme. The model is simulated using numerical integration to determine the effect of regeneration on the sensor sensitivity, response time and maximum sample throughput rate. Prediction of these effects without a model is difficult due to activation and inhibition of the dehydrogenase by both forms of the coenzyme. The regeneration parameters, including thionine concentration and thionine excitation pattern, are varied to determine optimal sensor conditions to maximize performance. A periodic regeneration approach is found to be superior to a continuous regeneration approach as the former maximizes sensitivity and minimizes response time in most cases. In addition periodic regeneration results in a maximum sample throughput frequency that is achieved at a single optimal thionine level and is independent of the analyte concentration. In contrast the optimal thionine concentration during continuous regeneration varies with the sample analyte concentration. These findings highlight the importance of designing controllable regeneration for dehydrogenase-based optical biosensors.

From simple to complex oscillatory behavior in metabolic and genetic control networks

We present an overview of mechanisms responsible for simple or complex oscillatory behavior in metabolic and genetic control networks. Besides simple periodic behavior corresponding to the evolution toward a limit cycle we consider complex modes of oscillatory behavior such as complex periodic oscillations of the bursting type and chaos. Multiple attractors are also discussed, e.g., the coexistence between a stable steady state and a stable limit cycle (hard excitation), or the coexistence between two simultaneously stable limit cycles (birhythmicity). We discuss mechanisms responsible for the transition from simple to complex oscillatory behavior by means of a number of models serving as selected examples. The models were originally proposed to account for simple periodic oscillations observed experimentally at the cellular level in a variety of biological systems. In a second stage, these models were modified to allow for complex oscillatory phenomena such as bursting, birhythmicity, or chaos. We consider successively (1) models based on enzyme regulation, proposed for glycolytic oscillations and for the control of successive phases of the cell cycle, respectively; (2) a model for intracellular Ca(2+) oscillations based on transport regulation; (3) a model for oscillations of cyclic AMP based on receptor desensitization in Dictyostelium cells; and (4) a model based on genetic regulation for circadian rhythms in Drosophila. Two main classes of mechanism leading from simple to complex oscillatory behavior are identified, namely (i) the interplay between two endogenous oscillatory mechanisms, which can take multiple forms, overt or more subtle, depending on whether the two oscillators each involve their own regulatory feedback loop or share a common feedback loop while differing by some related process, and (ii) self-modulation of the oscillator through feedback from the system's output on one of the parameters controlling oscillatory behavior. However, the latter mechanism may also be viewed as involving the interplay between two feedback processes, each of which might be capable of producing oscillations. Although our discussion primarily focuses on the case of autonomous oscillatory behavior, we also consider the case of nonautonomous complex oscillations in a model for circadian oscillations subjected to periodic forcing by a light-dark cycle and show that the occurrence of entrainment versus chaos in these conditions markedly depends on the wave form of periodic forcing. (c) 2001 American Institute of Physics.

Oscillations and bistability predicted by a model for a cyclical bienzymatic system involving the regulated isocitrate dehydrogenase reaction

We analyze the dynamics of a bienzymatic system consisting of isocitrate dehydrogenase (IDH, EC. 1.1.1.42), which transforms NADP+ into NADPH, and of diaphorase (DIA, EC 1.8.1.4), which catalyzes the reverse reaction. Experimental evidence as well as a theoretical model showed the possibility of a coexistence between two stable steady states in this reaction system G.M. Guidi et al. Biophys. J. 74 (1998) 1229-1240[, owing to the regulatory properties of IDH. Here we extend this analysis by considering the behavior of the model proposed for the IDH-DIA bienzymatic system in conditions where the system is open to an influx of its substrates isocitrate and NADP+ and to an efflux of all metabolic species. The analysis indicates that in addition to different modes of bistability (including mushrooms and isolas), sustained oscillations can be observed in such conditions. These results point to the isocitrate dehydrogenase reaction coupled to diaphorase as a suitable candidate for further experimental and theoretical studies of bistability and oscillations in biochemical systems. The results obtained in this particular bienzymatic system bear on other enzymatic systems possessing a cyclical nature, which are known to play significant roles in a variety of metabolic and cellular regulatory processes.

Multistability: a major means of differentiation and evolution in biological systems

Very simple biochemical systems regulated at the level of gene expression or protein function are capable of complex dynamic behaviour. Among the various patterns of regulation associated with non-linear kinetics, multistability, which corresponds to a true switch between alternate steady states, allows a graded signal to be turned into a discontinuous evolution of the system along several possible distinct pathways, which can be either reversible or irreversible. Multistability plays a significant role in some of the basic processes of life. It might account for maintenance of phenotypic differences in the absence of genetic or environmental differences, as has been demonstrated experimentally for the regulation of the lactose operon in Escherichia coli. Cell differentiation might also be explained as multistability.

From bistability to oscillations in a model for the isocitrate dehydrogenase reaction

Considered is a bienzymatic system consisting of isocitrate dehydrogenase (IDH, EC 1.1.1.42), which transforms NADP(+) into NADPH, and of diaphorase (DIA, EC 1.8.1.4), which catalyzes the reverse reaction. Experimental evidence as well as a theoretical model show the possibility of a coexistence between two stable steady states in this reaction system. The phenomenon originates from the regulatory properties of IDH. We extend the analysis of a theoretical model proposed for the IDH-DIA bienzymatic system and investigate the occurrence of different modes of bistability, with or without hysteresis, i.e. in the presence of two or only one limit point bounding the domain of multiple steady states. The analysis indicates that the two types of bistability may sometimes be observed sequentially as a given control parameter is progressively increased. We further obtain conditions in which sustained oscillations develop in the model. These results establish the isocitrate dehydrogenase reaction coupled to diaphorase as a suitable candidate for further experimental and theoretical studies of bistability and oscillations in biochemical systems.