Substrate-dependent control of ERK phosphorylation can lead to oscillations

Kinetics of diffusion-influenced multisite phosphorylation with enzyme reactivation

The simplest way to account for the influence of diffusion on the kinetics of multisite phosphorylation is to modify the rate constants in the conventional rate equations of chemical kinetics. We have previously shown that this is not enough and new transitions between the reactants must also be introduced. Here we extend our results by considering enzymes that are inactive after modifying the substrate and need time to become active again. This generalization leads to a surprising result. The introduction of enzyme reactivation results in a diffusion-modified kinetic scheme with a new transition that has a negative rate constant. The reason for this is that mapping non-Markovian rate equations onto Markovian ones with time-independent rate constants is not a good approximation at short times. We then developed a non-Markovian theory that involves memory kernels instead of rate constants. This theory is now valid at short times, but is more challenging to use. As an example, the diffusion-modified kinetic scheme with new connections was used to calculate kinetics of double phosphorylation and steady-state response in a phosphorylation-dephosphorylation cycle. We have reproduced the loss of bistability in the phosphorylation-dephosphorylation cycle when the enzyme reactivation time decreases, which was obtained by particle-based computer simulations.

A nested bistable module within a negative feedback loop ensures different types of oscillations in signaling systems

In this article, we consider a double phosphorylation cycle, a ubiquitous signaling component, having the ability to display bistability, a behavior strongly related to the existence of positive feedback loops. If this component is connected to other signaling elements, it very likely undergoes some sort of protein-protein interaction. In several cases, these interactions result in a non-explicit negative feedback effect, leading to interlinked positive and negative feedbacks. This combination was studied in the literature as a way to generate relaxation-type oscillations. Here, we show that the two feedbacks together ensure two types of oscillations, the relaxation-type ones and a smoother type of oscillations functioning in a very narrow range of frequencies, in such a way that outside that range, the amplitude of the oscillations is severely compromised. Even more, we show that the two feedbacks are essential for both oscillatory types to emerge, and it is their hierarchy what determines the type of oscillation at work. We used bifurcation analyses and amplitude vs. frequency curves to characterize and classify the oscillations. We also applied the same ideas to another simple model, with the goal of generalizing what we learned from signaling models. The results obtained display the wealth of oscillatory dynamics that exists in a system with a bistable module nested within a negative feedback loop, showing how to transition between different types of oscillations and other dynamical behaviors such as excitability. Our work provides a framework for the study of other oscillatory systems based on bistable modules, from simple two-component models to more complex examples like the MAPK cascade and experimental cases like cell cycle oscillators.

Harnessing conserved signaling and metabolic pathways to enhance the maturation of functional engineered tissues

The development of induced-pluripotent stem cell (iPSC)-derived cell types offers promise for basic science, drug testing, disease modeling, personalized medicine, and translatable cell therapies across many tissue types. However, in practice many iPSC-derived cells have presented as immature in physiological function, and despite efforts to recapitulate adult maturity, most have yet to meet the necessary benchmarks for the intended tissues. Here, we summarize the available state of knowledge surrounding the physiological mechanisms underlying cell maturation in several key tissues. Common signaling consolidators, as well as potential synergies between critical signaling pathways are explored. Finally, current practices in physiologically relevant tissue engineering and experimental design are critically examined, with the goal of integrating greater decision paradigms and frameworks towards achieving efficient maturation strategies, which in turn may produce higher-valued iPSC-derived tissues.

A design principle for posttranslational chaotic oscillators

Chaos behavior has been observed in various cellular and molecular processes. Here, we modeled reversible phosphorylation dynamics to elucidate a design principle for autonomous chaos generation that may arise from generic enzymatic reactions. A comprehensive parameter search demonstrated that the reaction system composed of a set of kinases and phosphatases and two substrates with two modification sites exhibits chaos behavior. All reactions are described according to the Michaelis-Menten reaction scheme without exotic functions being applied to enzymes and substrates. Clustering analysis of parameter sets that can generate chaos behavior revealed the existence of motif structures. These chaos motifs allow the two-substrate species to interact via enzyme availability and constrain the two substrates' dynamic changes in phosphorylation status so that they occur at different timescales. This chaos motif structure is found in several enzymatic reactions, suggesting that chaos behavior may underlie cellular autonomy in a variety of biochemical systems.

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Two substrates with reversible two-site phosphorylation can exhibit chaos behavior

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The chaos does not require autocatalysis or allosteric regulation of enzymes

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The chaos is a result of the coupling of two substrates via enzyme availability

Targeting ERK beyond the boundaries of the kinase active site in melanoma

Extracellular signal-regulated kinase 1/2 (ERK1/2) constitute a point of convergence for complex signaling events that regulate essential cellular processes, including proliferation and survival. As such, dysregulation of the ERK signaling pathway is prevalent in many cancers. In the case of BRAF-V600E mutant melanoma, ERK inhibition has emerged as a viable clinical approach to abrogate signaling through the ERK pathway, even in cases where MEK and Raf inhibitor treatments fail to induce tumor regression due to resistance mechanisms. Several ERK inhibitors that target the active site of ERK have reached clinical trials, however, many critical ERK interactions occur at other potentially druggable sites on the protein. Here we discuss the role of ERK signaling in cell fate, in driving melanoma, and in resistance mechanisms to current BRAF-V600E melanoma treatments. We explore targeting ERK via a distinct site of protein-protein interaction, known as the D-recruitment site (DRS), as an alternative or supplementary mode of ERK pathway inhibition in BRAF-V600E melanoma. Targeting the DRS with inhibitors in melanoma has the potential to not only disrupt the catalytic apparatus of ERK but also its noncatalytic functions, which have significant impacts on spatiotemporal signaling dynamics and cell fate.

Outstanding questions in developmental ERK signaling

The extracellular signal-regulated kinase (ERK) pathway leads to activation of the effector molecule ERK, which controls downstream responses by phosphorylating a variety of substrates, including transcription factors. Crucial insights into the regulation and function of this pathway came from studying embryos in which specific phenotypes arise from aberrant ERK activation. Despite decades of research, several important questions remain to be addressed for deeper understanding of this highly conserved signaling system and its function. Answering these questions will require quantifying the first steps of pathway activation, elucidating the mechanisms of transcriptional interpretation and measuring the quantitative limits of ERK signaling within which the system must operate to avoid developmental defects.

A novel interaction perturbation analysis reveals a comprehensive regulatory principle underlying various biochemical oscillators

Background

Biochemical oscillations play an important role in maintaining physiological and cellular homeostasis in biological systems. The frequency and amplitude of oscillations are regulated to properly adapt to environments by numerous interactions within biomolecular networks. Despite the advances in our understanding of biochemical oscillators, the relationship between the network structure of an oscillator and its regulatory function still remains unclear. To investigate such a relationship in a systematic way, we have developed a novel analysis method called interaction perturbation analysis that enables direct modulation of the strength of every interaction and evaluates its consequence on the regulatory function. We have applied this new method to the analysis of three representative types of oscillators.

Results

The results of interaction perturbation analysis showed different regulatory features according to the network structure of the oscillator: (1) both frequency and amplitude were seldom modulated in simple negative feedback oscillators; (2) frequency could be tuned in amplified negative feedback oscillators; (3) amplitude could be modulated in the incoherently amplified negative feedback oscillators. A further analysis of naturally-occurring biochemical oscillator models supported such different regulatory features according to their network structures.

Conclusions

Our results provide a clear evidence that different network structures have different regulatory features in modulating the oscillation frequency and amplitude. Our findings may help to elucidate the fundamental regulatory roles of network structures in biochemical oscillations.

Electronic supplementary material

The online version of this article (10.1186/s12918-017-0472-7) contains supplementary material, which is available to authorized users.

Two faces of competition: target-mediated reverse signalling in microRNA and mitogen-activated protein kinase regulatory networks

Biomolecular regulatory networks are organised around hubs, which can interact with a large number of targets. These targets compete with each other for access to their common hubs, but whether the effect of this competition would be significant in magnitude and in function is not clear. In this review, the authors discuss recent in vivo studies that analysed the system level retroactive effects induced by target competition in microRNA and mitogen-activated protein kinase regulatory networks. The results of these studies suggest that downstream targets can regulate the overall state of their upstream regulators, and thus cannot be ignored in analysing biomolecular networks.

Systems Biology-Derived Discoveries of Intrinsic Clocks

A systems approach to studying biology uses a variety of mathematical, computational, and engineering tools to holistically understand and model properties of cells, tissues, and organisms. Building from early biochemical, genetic, and physiological studies, systems biology became established through the development of genome-wide methods, high-throughput procedures, modern computational processing power, and bioinformatics. Here, we highlight a variety of systems approaches to the study of biological rhythms that occur with a 24-h period-circadian rhythms. We review how systems methods have helped to elucidate complex behaviors of the circadian clock including temperature compensation, rhythmicity, and robustness. Finally, we explain the contribution of systems biology to the transcription-translation feedback loop and posttranslational oscillator models of circadian rhythms and describe new technologies and "-omics" approaches to understand circadian timekeeping and neurophysiology.

Sustained oscillations in the MAP kinase cascade

The MAP kinase cascade is a network of enzymatic reactions arranged in layers. In each layer occurs a multiple futile cycle of phosphorylations. The fully phosphorylated substrate then serves as an enzyme for the layer below. This paper focusses on the existence of parameters for which Hopf bifurcations occur and generate periodic orbits. Furthermore it is explained how geometric singular perturbation theory allows to generalize results from simple models to more complex ones.

A mathematical model of endothelial nitric oxide synthase activation with time delay exhibiting Hopf bifurcation and oscillations

Nitric oxide (NO) is a gaseous compound that serves as a signaling molecule in cellular interactions. In the vasculature, NO is synthesized from endogenous agents by endothelial nitric oxide synthase (eNOS) where it plays key roles in several functions related to homeostasis, adaptation, and development. Recent experimental studies have revealed cycles of increasing and decreasing NO production when eNOS is stimulated by factors such as glucose or insulin. We offer a mathematical model of a generic amino acid receptor site on eNOS wherein this species is subject to activation/deactivation by a pair of interactive kinase and phosphatase species. The enzyme kinetic model is presented as a system of ordinary differential equations including time delay to allow for various intermediate, unspecified complexes. We show that under conditions on the model parameters, varying the delay time may give rise to a Hopf bifurcation. Properties of the bifurcating solutions are explored via a center manifold reduction, and a numerical illustration is provided.

Multi-Compartmentalisation in the MAPK Signalling Pathway Contributes to the Emergence of Oscillatory Behaviour and to Ultrasensitivity

Signal transduction through the Mitogen Activated Protein Kinase (MAPK) pathways is evolutionarily highly conserved. Many cells use these pathways to interpret changes to their environment and respond accordingly. The pathways are central to triggering diverse cellular responses such as survival, apoptosis, differentiation and proliferation. Though the interactions between the different MAPK pathways are complex, nevertheless, they maintain a high level of fidelity and specificity to the original signal. There are numerous theories explaining how fidelity and specificity arise within this complex context; spatio-temporal regulation of the pathways and feedback loops are thought to be very important. This paper presents an agent based computational model addressing multi-compartmentalisation and how this influences the dynamics of MAPK cascade activation. The model suggests that multi-compartmentalisation coupled with periodic MAPK kinase (MAPKK) activation may be critical factors for the emergence of oscillation and ultrasensitivity in the system. Finally, the model also establishes a link between the spatial arrangements of the cascade components and temporal activation mechanisms, and how both contribute to fidelity and specificity of MAPK mediated signalling.

Long-term dynamics of multisite phosphorylation

A systematic framework for exploring the long-term dynamics of a reaction network is applied to a minimal model of ERK regulation that distinguishes both monophosphorylated forms and allows for nonzero enzyme processivity. Bistability and oscillations can be observed at high levels of processivity.

Multisite phosphorylation cycles are ubiquitous in cell regulation systems and are studied at multiple levels of complexity, from molecules to organisms, with the ultimate goal of establishing predictive understanding of the effects of genetic and pharmacological perturbations of protein phosphorylation in vivo. Achieving this goal is essentially impossible without mathematical models, which provide a systematic framework for exploring dynamic interactions of multiple network components. Most of the models studied to date do not discriminate between the distinct partially phosphorylated forms and focus on two limiting reaction regimes, distributive and processive, which differ in the number of enzyme–substrate binding events needed for complete phosphorylation or dephosphorylation. Here we use a minimal model of extracellular signal-related kinase regulation to explore the dynamics of a reaction network that includes all essential phosphorylation forms and arbitrary levels of reaction processivity. In addition to bistability, which has been studied extensively in distributive mechanisms, this network can generate periodic oscillations. Both bistability and oscillations can be realized at high levels of reaction processivity. Our work provides a general framework for systematic analysis of dynamics in multisite phosphorylation systems.

Network Architecture Predisposes an Enzyme to Either Pharmacologic or Genetic Targeting

Chemical inhibition and genetic knockdown of enzymes are not equivalent in cells, but network-level mechanisms that cause discrepancies between knockdown and inhibitor perturbations are not understood. Here we report that enzymes regulated by negative feedback are robust to knockdown but susceptible to inhibition. Using the Raf-MEK-ERK kinase cascade as a model system, we find that ERK activation is resistant to genetic knockdown of MEK but susceptible to a comparable degree of chemical MEK inhibition. We demonstrate that negative feedback from ERK to Raf causes this knockdown-versus-inhibitor discrepancy in vivo. Exhaustive mathematical modeling of three-tiered enzyme cascades suggests that this result is general: negative autoregulation or feedback favors inhibitor potency, whereas positive autoregulation or feedback favors knockdown potency. Our findings provide a rationale for selecting pharmacologic versus genetic perturbations in vivo and point out the dangers of using knockdown approaches in search of drug targets.

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.

Determinants of cell-to-cell variability in protein kinase signaling

Cells reliably sense environmental changes despite internal and external fluctuations, but the mechanisms underlying robustness remain unclear. We analyzed how fluctuations in signaling protein concentrations give rise to cell-to-cell variability in protein kinase signaling using analytical theory and numerical simulations. We characterized the dose-response behavior of signaling cascades by calculating the stimulus level at which a pathway responds (‘pathway sensitivity’) and the maximal activation level upon strong stimulation. Minimal kinase cascades with gradual dose-response behavior show strong variability, because the pathway sensitivity and the maximal activation level cannot be simultaneously invariant. Negative feedback regulation resolves this trade-off and coordinately reduces fluctuations in the pathway sensitivity and maximal activation. Feedbacks acting at different levels in the cascade control different aspects of the dose-response curve, thereby synergistically reducing the variability. We also investigated more complex, ultrasensitive signaling cascades capable of switch-like decision making, and found that these can be inherently robust to protein concentration fluctuations. We describe how the cell-to-cell variability of ultrasensitive signaling systems can be actively regulated, e.g., by altering the expression of phosphatase(s) or by feedback/feedforward loops. Our calculations reveal that slow transcriptional negative feedback loops allow for variability suppression while maintaining switch-like decision making. Taken together, we describe design principles of signaling cascades that promote robustness. Our results may explain why certain signaling cascades like the yeast pheromone pathway show switch-like decision making with little cell-to-cell variability.

Cells sense their surroundings and respond to soluble factors in the extracellular space. Extracellular factors frequently induce heterogeneous responses, thereby restricting the biological outcome to a fraction of the cell population. However, the question arises how such cell-to-cell variability can be controlled, because some cellular systems show a very homogenous response at a defined level of an extracellular stimulus. We derived an analytical framework to systematically characterize the cell-to-cell variability of intracellular signaling pathways which transduce external signals. We analyzed how heterogeneity arises from fluctuations in the total concentrations of signaling proteins because this is the main source of variability in eukaryotic systems. We find that signaling pathways can be highly variable or inherently invariant, depending on the kinetic parameters and the structural features of the cascade. Our results indicate that the cell-to-cell variability can be reduced by negative feedback in the cascade or by signaling crosstalk between parallel pathways. We precisely define the role of negative feedback loops in variability suppression, and show that different aspects of the dose-response curve can be controlled, depending on the feedback kinetics and site of action in the cascade. This work constitutes a first step towards a systematic understanding of cell-to-cell variability in signal transduction.

A design principle for a posttranslational biochemical oscillator

Multisite phosphorylation plays an important role in biological oscillators such as the circadian clock. Its general role, however, has been elusive. In this theoretical study, we show that a simple substrate with two modification sites acted upon by two opposing enzymes (e.g., a kinase and a phosphatase) can show oscillations in its modification state. An unbiased computational analysis of this oscillator reveals two common characteristics: a unidirectional modification cycle and sequestering of an enzyme by a specific modification state. These two motifs cause a substrate to act as a coupled system in which a unidirectional cycle generates single-molecule oscillators, whereas sequestration synchronizes the population by limiting the available enzyme under conditions in which substrate is in excess. We also demonstrate the conditions under which the oscillation period is temperature compensated, an important feature of the circadian clock. This theoretical model will provide a framework for analyzing and synthesizing posttranslational oscillators.