Ultrasensitization: switch-like regulation of cellular signaling by transcriptional induction

ANPELA: analysis and performance assessment of the label-free quantification workflow for metaproteomic studies

Label-free quantification (LFQ) with a specific and sequentially integrated workflow of acquisition technique, quantification tool and processing method has emerged as the popular technique employed in metaproteomic research to provide a comprehensive landscape of the adaptive response of microbes to external stimuli and their interactions with other organisms or host cells. The performance of a specific LFQ workflow is highly dependent on the studied data. Hence, it is essential to discover the most appropriate one for a specific data set. However, it is challenging to perform such discovery due to the large number of possible workflows and the multifaceted nature of the evaluation criteria. Herein, a web server ANPELA (https://idrblab.org/anpela/) was developed and validated as the first tool enabling performance assessment of whole LFQ workflow (collective assessment by five well-established criteria with distinct underlying theories), and it enabled the identification of the optimal LFQ workflow(s) by a comprehensive performance ranking. ANPELA not only automatically detects the diverse formats of data generated by all quantification tools but also provides the most complete set of processing methods among the available web servers and stand-alone tools. Systematic validation using metaproteomic benchmarks revealed ANPELA's capabilities in 1 discovering well-performing workflow(s), (2) enabling assessment from multiple perspectives and (3) validating LFQ accuracy using spiked proteins. ANPELA has a unique ability to evaluate the performance of whole LFQ workflow and enables the discovery of the optimal LFQs by the comprehensive performance ranking of all 560 workflows. Therefore, it has great potential for applications in metaproteomic and other studies requiring LFQ techniques, as many features are shared among proteomic studies.

Multiple random phosphorylations in clock proteins provide long delays and switches

Theory predicts that self-sustained oscillations require robust delays and nonlinearities (ultrasensitivity). Delayed negative feedback loops with switch-like inhibition of transcription constitute the core of eukaryotic circadian clocks. The kinetics of core clock proteins such as PER2 in mammals and FRQ in Neurospora crassa is governed by multiple phosphorylations. We investigate how multiple, slow and random phosphorylations control delay and molecular switches. We model phosphorylations of intrinsically disordered clock proteins (IDPs) using conceptual models of sequential and distributive phosphorylations. Our models help to understand the underlying mechanisms leading to delays and ultrasensitivity. The model shows temporal and steady state switches for the free kinase and the phosphoprotein. We show that random phosphorylations and sequestration mechanisms allow high Hill coefficients required for self-sustained oscillations.

Finding the positive feedback loops underlying multi-stationarity

BACKGROUND

Bistability is ubiquitous in biological systems. For example, bistability is found in many reaction networks that involve the control and execution of important biological functions, such as signaling processes. Positive feedback loops, composed of species and reactions, are necessary for bistability, and generally for multi-stationarity, to occur. These loops are therefore often used to illustrate and pinpoint the parts of a multi-stationary network that are relevant ('responsible') for the observed multi-stationarity. However positive feedback loops are generally abundant in reaction networks but not all of them are important for understanding the network's dynamics.

RESULTS

We present an automated procedure to determine the relevant positive feedback loops of a multi-stationary reaction network. The procedure only reports the loops that are relevant for multi-stationarity (that is, when broken multi-stationarity disappears) and not all positive feedback loops of the network. We show that the relevant positive feedback loops must be understood in the context of the network (one loop might be relevant for one network, but cannot create multi-stationarity in another). Finally, we demonstrate the procedure by applying it to several examples of signaling processes, including a ubiquitination and an apoptosis network, and to models extracted from the Biomodels database. The procedure is implemented in Maple.

CONCLUSIONS

We have developed and implemented an automated procedure to find relevant positive feedback loops in reaction networks. The results of the procedure are useful for interpretation and summary of the network's dynamics.

Positive feedback promotes oscillations in negative feedback loops

A simple three-component negative feedback loop is a recurring motif in biochemical oscillators. This motif oscillates as it has the three necessary ingredients for oscillations: a three-step delay, negative feedback, and nonlinearity in the loop. However, to oscillate, this motif under the common Goodwin formulation requires a high degree of cooperativity (a measure of nonlinearity) in the feedback that is biologically “unlikely.” Moreover, this recurring negative feedback motif is commonly observed augmented by positive feedback interactions. Here we show that these positive feedback interactions promote oscillation at lower degrees of cooperativity, and we can thus unify several common kinetic mechanisms that facilitate oscillations, such as self-activation and Michaelis-Menten degradation. The positive feedback loops are most beneficial when acting on the shortest lived component, where they function by balancing the lifetimes of the different components. The benefits of multiple positive feedback interactions are cumulative for a majority of situations considered, when benefits are measured by the reduction in the cooperativity required to oscillate. These positive feedback motifs also allow oscillations with longer periods than that determined by the lifetimes of the components alone. We can therefore conjecture that these positive feedback loops have evolved to facilitate oscillations at lower, kinetically achievable, degrees of cooperativity. Finally, we discuss the implications of our conclusions on the mammalian molecular clock, a system modeled extensively based on the three-component negative feedback loop.

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.

Simplifying biochemical models with intermediate species

Mathematical models are increasingly being used to understand complex biochemical systems, to analyse experimental data and make predictions about unobserved quantities. However, we rarely know how robust our conclusions are with respect to the choice and uncertainties of the model. Using algebraic techniques, we study systematically the effects of intermediate, or transient, species in biochemical systems and provide a simple, yet rigorous mathematical classification of all models obtained from a core model by including intermediates. Main examples include enzymatic and post-translational modification systems, where intermediates often are considered insignificant and neglected in a model, or they are not included because we are unaware of their existence. All possible models obtained from the core model are classified into a finite number of classes. Each class is defined by a mathematically simple canonical model that characterizes crucial dynamical properties, such as mono- and multistationarity and stability of steady states, of all models in the class. We show that if the core model does not have conservation laws, then the introduction of intermediates does not change the steady-state concentrations of the species in the core model, after suitable matching of parameters. Importantly, our results provide guidelines to the modeller in choosing between models and in distinguishing their properties. Further, our work provides a formal way of comparing models that share a common skeleton.

Employing the metabolic "branch point effect" to generate an all-or-none, digital-like response in enzymatic outputs and enzyme-based sensors

Here, we demonstrate a strategy to convert the graded Michaelis-Menten response typical of unregulated enzymes into a sharp, effectively all-or-none response. We do so using an approach analogous to the "branch point effect", a mechanism observed in naturally occurring metabolic networks in which two or more enzymes compete for the same substrate. As a model system, we used the enzymatic reaction of glucose oxidase (GOx) and coupled it to a second, nonsignaling reaction catalyzed by the higher affinity enzyme hexokinase (HK) such that, at low substrate concentrations, the second enzyme outcompetes the first, turning off the latter's response. Above an arbitrarily selected "threshold" substrate concentration, the nonsignaling HK enzyme saturates leading to a "sudden" activation of the first signaling GOx enzyme and a far steeper dose-response curve than that observed for simple Michaelis-Menten kinetics. Using the well-known GOx-based amperometric glucose sensor to validate our strategy, we have steepen the normally graded response of this enzymatic sensor into a discrete yes/no output similar to that of a multimeric cooperative enzyme with a Hill coefficient above 13. We have also shown that, by controlling the HK reaction we can precisely tune the threshold target concentration at which we observe the enzyme output. Finally, we demonstrate the utility of this strategy for achieving effective noise attenuation in enzyme logic gates. In addition to supporting the development of biosensors with digital-like output, we envisage that the use of all-or-none enzymatic responses will also improve our ability to engineer efficient enzyme-based catalysis reactions in synthetic biology applications.

An algebraic approach to signaling cascades with N layers

Posttranslational modification of proteins is key in transmission of signals in cells. Many signaling pathways contain several layers of modification cycles that mediate and change the signal through the pathway. Here, we study a simple signaling cascade consisting of n layers of modification cycles such that the modified protein of one layer acts as modifier in the next layer. Assuming mass-action kinetics and taking the formation of intermediate complexes into account, we show that the steady states are solutions to a polynomial in one variable and in fact that there is exactly one steady state for any given total amounts of substrates and enzymes.We demonstrate that many steady-state concentrations are related through rational functions that can be found recursively. For example, stimulus-response curves arise as inverse functions to explicit rational functions. We show that the stimulus-response curves of the modified substrates are shifted to the left as we move down the cascade. Further, our approach allows us to study enzyme competition, sequestration, and how the steady state changes in response to changes in the total amount of substrates.Our approach is essentially algebraic and follows recent trends in the study of posttranslational modification systems.

Protein sequestration generates a flexible ultrasensitive response in a genetic network

Ultrasensitive responses are crucial for cellular regulation. Protein sequestration, where an active protein is bound in an inactive complex by an inhibitor, can potentially generate ultrasensitivity. Here, in a synthetic genetic circuit in budding yeast, we show that sequestration of a basic leucine zipper transcription factor by a dominant-negative inhibitor converts a graded transcriptional response into a sharply ultrasensitive response, with apparent Hill coefficients up to 12. A simple quantitative model for this genetic network shows that both the threshold and the degree of ultrasensitivity depend upon the abundance of the inhibitor, exactly as we observed experimentally. The abundance of the inhibitor can be altered by simple mutation; thus, ultrasensitive responses mediated by protein sequestration are easily tuneable. Gene duplication of regulatory homodimers and loss-of-function mutations can create dominant negatives that sequester and inactivate the original regulator. The generation of flexible ultrasensitive responses is an unappreciated adaptive advantage that could explain the frequent evolutionary emergence of dominant negatives.

Regulating the total level of a signaling protein can vary its dynamics in a range from switch like ultrasensitivity to adaptive responses

Biological signaling networks can exhibit rich response dynamics including ultrasensitivity, adaptation to persistent stimuli and oscillations. Previous modeling efforts have considered the proteins in these networks as two-state entities and their total levels as fixed quantities. However, inside the cell, most molecules are in constant flux because of various processes such as degradation, synthesis, binding of scaffold proteins and release from vesicles. The resulting freedom in the amount of signaling protein that is available for signaling has not been explored. Here, we analyze the response dynamics of a signaling protein when it enters the signaling pool in one state (modified or unmodified) and exits in both states. When the exit rates of these two states are comparable, a persistent stimulus results in step responses and can produce ultrasensitivity, as shown previously. However, we find that when the exit rates are imbalanced, the signaling protein gives transient responses to persistent stimuli even though the system does not have any explicit feedback. Further, these rates determine the signal range over which the system is responsive. Building small networks from signaling proteins with different exit rates, we show that these systems can exhibit rich behavior. Taken together, these findings indicate that altering the total level of signaling proteins can significantly change their response and provide additional richness in system dynamics. We discuss relevant biological examples in which regulating total protein levels could be exploited to alter signaling behavior.

Molecular titration and ultrasensitivity in regulatory networks

Protein sequestration occurs when an active protein is sequestered by a repressor into an inactive complex. Using mathematical and computational modeling, we show how this regulatory mechanism (called "molecular titration") can generate ultrasensitive or "all-or-none" responses that are equivalent to highly cooperative processes. The ultrasensitive nature of the input-output response is mainly determined by two parameters: the dimer dissociation constant and the repressor concentration. Because in vivo concentrations are tunable through a variety of mechanisms, molecular titration represents a flexible mechanism for generating ultrasensitivity. Using physiological parameters, we report how details of in vivo protein degradation affect the strength of the ultrasensitivity at steady state. Given that developmental systems often transduce signals into cell-fate decisions on timescales incompatible with steady state, we further examine whether molecular titration can produce ultrasensitive responses within physiologically relevant time intervals. Using Drosophila somatic sex determination as a developmental paradigm, we demonstrate that molecular titration can generate ultrasensitivity on timescales compatible with most cell-fate decisions. Gene duplication followed by loss-of-function mutations can create dominant negatives that titrate and compete with the original protein. Dominant negatives are abundant in gene regulatory circuits, and our results suggest that molecular titration might be generating an ultrasensitive response in these networks.

Positive receptor feedback during lineage commitment can generate ultrasensitivity to ligand and confer robustness to a bistable switch

Cytokines and lineage-specific transcription factors are critical molecular effectors for terminal differentiation during hematopoiesis. Intrinsic transcription factor activity is often believed to drive commitment and differentiation, whereas cytokine receptor signals have been implicated in the regulation of cell proliferation, survival, and differentiation. In erythropoiesis, recent experimental findings provide direct evidence that erythropoietin (Epo) can generate commitment cues via the erythropoietin receptor (EpoR); specifically, EpoR signaling leads to activation of the transcription factor GATA-1, which then triggers transcription of erythrocyte-specific genes. In particular, activated GATA-1 induces two positive feedback loops in the system through the enhanced expression of both inactive GATA-1 and EpoR, the latter of which is externally regulatable by Epo. Based upon this network architecture, we present a mathematical model of GATA-1 activation by EpoR, which bidirectionally links a lineage-specific receptor and transcription factor. Our deterministic model offers insight into stimulus-response relationships between Epo and several downstream effectors. In addition to the survival signals that EpoR provides, steady-state analysis of our model suggests that receptor upregulation during lineage commitment can also generate ultrasensitivity to Epo and bistability in GATA-1 activity. These system-level properties can induce a switch-like characteristic during differentiation and provide robustness to the mature state. The topology also suggests a novel mechanism for achieving robust bistability in a purely deterministic manner without molecular cooperativity. The analytical solution of a generalized, minimal model is provided and the significance of each of the two positive feedback loops is elucidated through bifurcation analysis. This network topology, or variations thereof, may link other receptor-transcription factor pairs and may therefore be of general relevance in cellular decision-making.

Operating regimes of signaling cycles: statics, dynamics, and noise filtering

A ubiquitous building block of signaling pathways is a cycle of covalent modification (e.g., phosphorylation and dephosphorylation in MAPK cascades). Our paper explores the kind of information processing and filtering that can be accomplished by this simple biochemical circuit. Signaling cycles are particularly known for exhibiting a highly sigmoidal (ultrasensitive) input–output characteristic in a certain steady-state regime. Here, we systematically study the cycle's steady-state behavior and its response to time-varying stimuli. We demonstrate that the cycle can actually operate in four different regimes, each with its specific input–output characteristics. These results are obtained using the total quasi–steady-state approximation, which is more generally valid than the typically used Michaelis-Menten approximation for enzymatic reactions. We invoke experimental data that suggest the possibility of signaling cycles operating in one of the new regimes. We then consider the cycle's dynamic behavior, which has so far been relatively neglected. We demonstrate that the intrinsic architecture of the cycles makes them act—in all four regimes—as tunable low-pass filters, filtering out high-frequency fluctuations or noise in signals and environmental cues. Moreover, the cutoff frequency can be adjusted by the cell. Numerical simulations show that our analytical results hold well even for noise of large amplitude. We suggest that noise filtering and tunability make signaling cycles versatile components of more elaborate cell-signaling pathways.

A cell is subjected to constantly changing environments and time-varying stimuli. Signals sensed at the cell surface are transmitted inside the cell by signaling pathways. Such pathways can transform signals in diverse ways and perform some preliminary information processing. A ubiquitous building block of signaling pathways is a simple biochemical cycle involving covalent modification of an enzyme–substrate pair. Our paper is devoted to fully characterizing the static and dynamic behavior of this simple cycle, an essential first step in understanding the behavior of interconnections of such cycles. It is known that a signaling cycle can function as a static switch, with the steady-state output being an “ultrasensitive” function of the input, i.e., changing from a low to high value for only a small change in the input. We show that there are in fact precisely four major regimes of static and dynamic operation (with ultrasensitive being one of the static regimes). Each regime has its own input–output characteristics. Despite the distinctive features of these four regimes, they all respond to time-varying stimuli by filtering out high-frequency fluctuations or noise in their inputs, while passing through the lower-frequency information-bearing variations. A cell can select the regime and tune the noise-filtering characteristics of the individual cycles in a specific signaling pathway. This tunability makes signaling cycles versatile components of elaborate cell-signaling pathways.

An ultrasensitive sorting mechanism for EGF receptor endocytosis

Background

The Epidermal Growth Factor (EGF) receptor has been shown to internalize via clathrin-independent endocytosis (CIE) in a ligand concentration dependent manner. From a modeling point of view, this resembles an ultrasensitive response, which is the ability of signaling networks to suppress a response for low input values and to increase to a pre-defined level for inputs exceeding a certain threshold. Several mechanisms to generate this behaviour have been described theoretically, the underlying assumptions of which, however, have not been experimentally demonstrated for the EGF receptor internalization network.

Results

Here, we present a mathematical model of receptor sorting into alternative pathways that explains the EGF-concentration dependent response of CIE. The described mechanism involves a saturation effect of the dominant clathrin-dependent endocytosis pathway and implies distinct steady-states into which the system is forced for low vs high EGF stimulations. The model is minimal since no experimentally unjustified reactions or parameter assumptions are imposed. We demonstrate the robustness of the sorting effect for large parameter variations and give an analytic derivation for alternative steady-states that are reached. Further, we describe extensibility of the model to more than two pathways which might play a role in contexts other than receptor internalization.

Conclusion

Our main result is that a scenario where different endocytosis routes consume the same form of receptor corroborates the observation of a clear-cut, stimulus dependent sorting. This is especially important since a receptor modification discriminating between the pathways has not been found experimentally. The model is not restricted to EGF receptor internalization and might account for ultrasensitivity in other cellular contexts.

Modeling and analyzing gene co-expression in hepatocellular carcinoma using actor-semiotic networks and centrality signatures

Primary hepatocellular carcinoma (HCC) is currently the fifth most common malignancy and the third most common cause of cancer mortality worldwide. Because of its high prevalence in developing nations, there have been numerous efforts made in the molecular characterization of primary HCC. However, a better understanding into the pathology of HCC required software-assisted network modeling and analysis. In this paper, the author presented his first attempt in exploring the biological implication of gene co-expression in HCC using actor-semiotic network modeling and analysis. The network was first constructed by integrating inter-actor relationships, e.g. gene co-expression, microRNA-to-gene, and protein interactions, with semiotic relationships, e.g. gene-to-Gene Ontology Process. Topological features that are highly discriminative of the HCC phenotype were identified by visual inspection. Finally, the author devised a graph signature-based analysis method to supplement the network exploration.

HAUSP-regulated switch from auto- to p53 ubiquitination by Mdm2 (in silico discovery)

Stability of the 'guardian of the genome' tumor suppressor protein p53 is regulated predominantly through its ubiquitination. The ubiquitin-specific protease HAUSP plays an important role in this process. Recent experiments showed that p53 demonstrates a differential response to changes in HAUSP which nature and significance are not understood yet. Here a data-driven mathematical model of the Mdm2-mediated p53 ubiquitination network is presented which offers an explanation for the cause of such a response. The model predicts existence of the HAUSP-regulated switch from auto- to p53 ubiquitination by Mdm2. This switch suggests a potential role of HAUSP as a downstream target of stress signals in cells. The model accounts for a significant amount of experimental data, makes predictions for some rate constants, and can serve as a building block for the larger model describing a complex dynamic response of p53 to cellular stresses.

Competing docking interactions can bring about bistability in the MAPK cascade

Mitogen-activated protein kinases are crucial regulators of various cell fate decisions including proliferation, differentiation, and apoptosis. Depending on the cellular context, the Raf-Mek-Erk mitogen-activated protein kinase cascade responds to extracellular stimuli in an all-or-none manner, most likely due to bistable behavior. Here, we describe a previously unrecognized positive-feedback mechanism that emerges from experimentally observed sequestration effects in the core Raf-Mek-Erk cascade. Unphosphorylated/monophosphorylated Erk sequesters Mek into Raf-inaccessible complexes upon weak stimulation, and thereby inhibits cascade activation. Mek, once phosphorylated by Raf, triggers Erk phosphorylation, which in turn induces dissociation of Raf-inaccessible Mek-Erk heterodimers, and thus further amplifies Mek phosphorylation. We show that this positive circuit can bring about bistability for parameter values measured experimentally in living cells. Previous studies revealed that bistability can also arise from enzyme depletion effects in the Erk double (de)phosphorylation cycle. We demonstrate that the feedback mechanism proposed in this article synergizes with such enzyme depletion effects to bring about a much larger bistable range than either mechanism alone. Our results show that stable docking interactions and competition effects, which are common in protein kinase cascades, can result in sequestration-based feedback, and thus can have profound effects on the qualitative behavior of signaling pathways.

Competition Effects Shape the Response Sensitivity and Kinetics of Phosphorylation Cycles in Cell Signaling

Phosphorylation cycles are a core component of cell signaling networks. The response sensitivity and kinetics of these cycles are controlled by thermodynamic, kinetic, and structural factors, including binding affinities, catalytic activities, and the phosphorylation order of multiple sites. Based on mathematical models, we interpret the role of these factors in terms of competition effects. For the regulation of a single phosphorylation site, two kinds of competition effects turn out to shape behavior: the competition between kinase and phosphatase to bind the substrate, and the competition between the distinct phosphorylation forms of the substrate for binding to either enzyme. Depending on the concentrations and mutual affinities of the enzymes and the target, the response function can be graded, ultrasensitive, or biphasic. In multiply phosphorylatable proteins, additional factors generating competition effects are present and more complex responses can be obtained. For example, the combination of a cooperative kinetics with the conditions for zero-order ultrasensitivity may yield a bistable response. We show that a repeated competition between kinase and phosphatase for binding the substrate and/or between the phosphorylation and dephosphorylation reactions at each phosphorylation site generally result in a threshold response. The phosphorylation time is also strongly affected by the kinetic design of the cycle. In particular, threshold responses are generally associated with very long phosphorylation times. We also argue here that a description in terms of elementary binding and reaction steps is required for an appropriate analysis of these cycles in cell signaling.

Effects of sequestration on signal transduction cascades

The building blocks of most signal transduction pathways are pairs of enzymes, such as kinases and phosphatases, that control the activity of protein targets by covalent modification. It has previously been shown [Goldbeter A & Koshland DE (1981) Proc Natl Acad Sci USA 78, 6840-6844] that these systems can be highly sensitive to changes in stimuli if their catalysing enzymes are saturated with their target protein substrates. This mechanism, termed zero-order ultrasensitivity, may set thresholds that filter out subthreshold stimuli. Experimental data on protein abundance suggest that the enzymes and their target proteins are present in comparable concentrations. Under these conditions a large fraction of the target protein may be sequestrated by the enzymes. This causes a reduction in ultrasensitivity so that the proposed mechanism is unlikely to account for ultrasensitivity under the conditions present in most in vivo signalling cascades. Furthermore, we show that sequestration changes the dynamics of a covalent modification cycle and may account for signal termination and a sign-sensitive delay. Finally, we analyse the effect of sequestration on the dynamics of a complex signal transduction cascade: the mitogen-activated protein kinase (MAPK) cascade with negative feedback. We show that sequestration limits ultrasensitivity in this cascade and may thereby abolish the potential for oscillations induced by negative feedback.