A generic model for open signaling cascades with forward activation

In this work, cellular signal transduction in an open cascade with forward activation was studied. By proposing a generic model which captures the common features of major existing models in the literature, it is showed how signaling profile changes during the propagation along the cascade. In particular, a typical OFF-ON-OFF switch-like transient behavior with prolonged temporary ON state is revealed, where OFF and ON represent the states of low level and high level concentrations, respectively. Analytically this phenomenon is closely related to uniform convergence of the active protein concentration of downstream cycles in the finite time range and its failure in the entire time domain. Consequently a classification of open signaling cascade which can sustain OFF-ON-OFF behavior in the far downstream cycles is accessible. Relevant biological issues, such as delayed activation of downstream reaction cycles, signal amplification and prolonged signal duration, to the generic model is discussed.     

Retroactive signaling in short signaling pathways

In biochemical signaling pathways without explicit feedback connections, the core signal transduction is usually described as a one-way communication, going from upstream to downstream in a feedforward chain or network of covalent modification cycles. In this paper we explore the possibility of a new type of signaling called retroactive signaling, offered by the recently demonstrated property of retroactivity in signaling cascades. The possibility of retroactive signaling is analysed in the simplest case of the stationary states of a bicyclic cascade of signaling cycles. In this case, we work out the conditions for which variables of the upstream cycle are affected by a change of the total amount of protein in the downstream cycle, or by a variation of the phosphatase deactivating the same protein. Particularly, we predict the characteristic ranges of the downstream protein, or of the downstream phosphatase, for which a retroactive effect can be observed on the upstream cycle variables. Next, we extend the possibility of retroactive signaling in short but nonlinear signaling pathways involving a few covalent modification cycles.     

Long signaling cascades tend to attenuate retroactivity

Signaling pathways consisting of phosphorylation/dephosphorylation cycles with no explicit feedback allow signals to propagate not only from upstream to downstream but also from downstream to upstream due to retroactivity at the interconnection between phosphorylation/dephosphorylation cycles. However, the extent to which a downstream perturbation can propagate upstream in a signaling cascade and the parameters that affect this propagation are presently unknown. Here, we determine the downstream-to-upstream steady-state gain at each stage of the signaling cascade as a function of the cascade parameters. This gain can be made smaller than 1 (attenuation) by sufficiently fast kinase rates compared to the phosphatase rates and/or by sufficiently large Michaelis-Menten constants and sufficiently low amounts of total stage protein. Numerical studies performed on sets of biologically relevant parameters indicated that ∼50% of these parameters could give rise to amplification of the downstream perturbation at some stage in a three-stage cascade. In an n-stage cascade, the percentage of parameters that lead to an overall attenuation from the last stage to the first stage monotonically increases with the cascade length n and reaches 100% for cascades of length at least 6.     

The effects of time delays in a phosphorylation-dephosphorylation pathway

Complex signaling cascades involve many interlocked positive and negative feedback loops which have inherent delays. Modeling these complex cascades often requires a large number of variables and parameters. Delay differential equation models have been helpful in describing inherent time lags and also in reducing the number of governing equations. However the consequences of model reduction via delay differential equations have not been fully explored. In this paper we systematically examine the effect of delays in a complex network of phosphorylation-dephosphorylation cycles (described by Gonze and Goldbeter, J. Theor. Biol., 210, (2001) 167-186), which commonly occur in many biochemical pathways. By introducing delays in the positive and negative regulatory interactions, we show that a delay differential model can indeed reduce the number of cycles actually required to describe the phosphorylation-dephosphorylation pathway. In addition, we find some of the unique properties of the network and a quantitative measure of the minimum number of delay variables required to model the network. These results can be extended for modeling complex signalling cascades.     

The effects of reversibility and noise on stochastic phosphorylation cycles and cascades

The phosphorylation-dephosphorylation cycle is a common motif in cellular signaling networks. Previous work has revealed that, when driven by a noisy input signal, these cycles may exhibit bistable behavior. Here, a recently introduced theorem on network bistability is applied to prove that the existence of bistability is dependent on the stochastic nature of the system. Furthermore, the thermodynamics of simple cycles and cascades is investigated in the stochastic setting. Because these cycles are driven by the ATP hydrolysis potential, they may operate far from equilibrium. It is shown that sufficient high ATP hydrolysis potential is necessary for the existence of a bistable steady state. For the single-cycle system, the ensemble average behavior follows the ultrasensitive response expected from analysis of the corresponding deterministic system, but with significant fluctuations. For the two-cycle cascade, the average behavior begins to deviate from the expected response of the deterministic system. Examination of a two-cycle cascade reveals that the bistable steady state may be either propagated or abolished along a cascade, depending on the parameters chosen. Likewise, the variance in the response can be maximized or minimized by tuning the number of enzymes in the second cycle.     

Intrinsic fluctuations, robustness, and tunability in signaling cycles

Covalent modification cycles (e.g., phosphorylation-dephosphorylation) underlie most cellular signaling and control processes. Low molecular copy number, arising from compartmental segregation and slow diffusion between compartments, potentially renders these cycles vulnerable to intrinsic chemical fluctuations. How can a cell operate reliably in the presence of this inherent stochasticity? How do changes in extrinsic parameters lead to variability of response? Can cells exploit these parameters to tune cycles to different ranges of stimuli? We study the dynamics of an isolated phosphorylation cycle. Our model shows that the cycle transmits information reliably if it is tuned to an optimal parameter range, despite intrinsic fluctuations and even for small input signal amplitudes. At the same time, the cycle is sensitive to changes in the concentration and activity of kinases and phosphatases. This sensitivity can lead to significant cell-to-cell response variability. It also provides a mechanism to tune the cycle to transmit signals in various amplitude ranges. Our results show that signaling cycles possess a surprising combination of robustness and tunability. This combination makes them ubiquitous in eukaryotic signaling, optimizing signaling in the presence of fluctuations using their inherent flexibility. On the other hand, cycles tuned to suppress intrinsic fluctuations can be vulnerable to changes in the number and activity of kinases and phosphatases. Such trade-offs in robustness to intrinsic and extrinsic fluctuations can influence the evolution of signaling cascades, making them the weakest links in cellular circuits.     

Bistability in the JNK cascade

BACKGROUND: Important signaling properties, like adaptation, oscillations, and bistability, can emerge at the level of relatively simple systems of signaling proteins. Here, we have examined the quantitative properties of one well-studied signaling system, the JNK cascade. We experimentally assessed the response of JNK to a physiological stimulus (progesterone) and a pathological stress (hyperosmolar sorbitol) in Xenopus laevis oocytes, a cell type that is well-suited to the quantitative analysis of cell signaling. Our aim was to determine whether JNK responses are graded (Michaelian) in character; ultrasensitive in character, resembling the responses of cooperative enzymes; or bistable and all-or-none in character. RESULTS: The responses of JNK to both progesterone and sorbitol were found to be essentially all-or-none. Individual oocytes had either very high or very low JNK activities, with few oocytes possessing intermediate levels of JNK activity. Moreover, JNK activation was autocatalytic, indicating that the JNK cascade is either embedded in or downstream of a positive feedback loop. JNK also exhibited hysteresis, a form of biochemical memory, in its response to sorbitol. These findings indicate that the JNK cascade is part of a bistable signaling system in oocytes. CONCLUSIONS: In Xenopus oocytes, JNK responds to physiological and pathological stimuli in an all-or-none manner. The JNK response shows all the hallmarks of a bistable response, including strong positive feedback and hysteresis. Bistability is a recurring theme in the biochemistry of oocyte maturation and early embryogenesis; the Mos/MEK/p42 MAPK cascade also exhibits bistable responses, and the Cdc2/cyclin B system is hypothesized to be bistable as well. However, the mechanisms underpinning the positive feedback and bistability in the three cases are different, suggesting that evolution has repeatedly converged upon bistability as a way of producing digital responses.     

Hardware (DNA) circuits

A scheme is presented whereby a new genetic control circuit can be introduced into an organism, permitting the experimenter to turn the expression of a given gene (or set of genes) on or off at will. The proposed scheme involves a positive feedback loop--here, a positive regulator, the CII protein of phage lambda, with its structural gene engineered so as to require CII for its expression. This feedback loop creates the possibility of two stable steady states, with gene cII ON or OFF. Genes added downstream of cII and lacking a promoter will follow the same expression as cII. Two additional circuits allow the experimenter to switch at will between the ON and OFF states.     

A kinetic model of ERK cyclic pathway on substrate control

Extracellular signal-regulated kinase (ERK) is a key factor in the widely used signaling cascade of phosphorylation-dephosphorylation cycles and plays pivotal roles in many aspects of biological processes. Experimental studies in yeast and in Drosophila embryo have suggested that the phosphorylation and spatial localization of ERK are influenced by the level of its downstream substrates. However, the mechanism, through which these substrates control properties of ERK signaling, has been unclear. I propose a mass-action kinetic model of ERK cycle with its substrate, and demonstrate that the substrate can modulate the ERK activity by directly interacting with ERK. The model shows that the addition of substrate controls the level of ERK phosphorylation positively or negatively, depending on the balance between dissociation constants of ERK-substrate interaction and properties of ERK cyclic signaling in the absence of the substrate. In addition, by considering cellular compartments, cytosol and nucleus, the substrate can lead to nuclear accumulation of ERK, suggesting that the substrate can act as a nuclear anchor of ERK. The model gives a possible mechanism that can account for substrate-mediated modulation of ERK signaling.     

Kinase inhibitors can produce off-target effects and activate linked pathways by retroactivity

Background

It has been shown in experimental and theoretical work that covalently modified signaling cascades naturally exhibit bidirectional signal propagation via a phenomenon known as retroactivity. An important consequence of retroactivity, which arises due to enzyme sequestration in covalently modified signaling cascades, is that a downstream perturbation can produce a response in a component upstream of the perturbation without the need for explicit feedback connections. Retroactivity may, therefore, play an important role in the cellular response to a targeted therapy. Kinase inhibitors are a class of targeted therapies designed to interfere with a specific kinase molecule in a dysregulated signaling pathway. While extremely promising as anti-cancer agents, kinase inhibitors may produce undesirable off-target effects by non-specific interactions or pathway cross-talk. We hypothesize that targeted therapies such as kinase inhibitors can produce off-target effects as a consequence of retroactivity alone.

Results

We used a computational model and a series of simple signaling motifs to test the hypothesis. Our results indicate that within physiologically and therapeutically relevant ranges for all parameters, a targeted inhibitor can naturally induce an off-target effect via retroactivity. The kinetics governing covalent modification cycles in a signaling network were more important for propagating an upstream off-target effect in our models than the kinetics governing the targeted therapy itself. Our results also reveal the surprising and crucial result that kinase inhibitors have the capacity to turn "on" an otherwise "off" parallel cascade when two cascades share an upstream activator.

Conclusions

A proper and detailed characterization of a pathway's structure is important for identifying the optimal protein to target as well as what concentration of the targeted therapy is required to modulate the pathway in a safe and effective manner. We believe our results support the position that such characterizations should consider retroactivity as a robust potential source of off-target effects induced by kinase inhibitors and other targeted therapies.

     

Trade-offs and Noise Tolerance in Signal Detection by Genetic Circuits

Genetic circuits can implement elaborated tasks of amplitude or frequency signal detection. What type of constraints could circuits experience in the performance of these tasks, and how are they affected by molecular noise? Here, we consider a simple detection process–a signal acting on a two-component module–to analyze these issues. We show that the presence of a feedback interaction in the detection module imposes a trade-off on amplitude and frequency detection, whose intensity depends on feedback strength. A direct interaction between the signal and the output species, in a type of feed-forward loop architecture, greatly modifies these trade-offs. Indeed, we observe that coherent feed-forward loops can act simultaneously as good frequency and amplitude noise-tolerant detectors. Alternatively, incoherent feed-forward loop structures can work as high-pass filters improving high frequency detection, and reaching noise tolerance by means of noise filtering. Analysis of experimental data from several specific coherent and incoherent feed-forward loops shows that these properties can be realized in a natural context. Overall, our results emphasize the limits imposed by circuit structure on its characteristic stimulus response, the functional plasticity of coherent feed-forward loops, and the seemingly paradoxical advantage of improving signal detection with noisy circuit components.     

Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades.

Functional organization of signal transduction into protein phosphorylation cascades, such as the mitogen-activated protein kinase (MAPK) cascades, greatly enhances the sensitivity of cellular targets to external stimuli. The sensitivity increases multiplicatively with the number of cascade levels, so that a tiny change in a stimulus results in a large change in the response, the phenomenon referred to as ultrasensitivity. In a variety of cell types, the MAPK cascades are imbedded in long feedback loops, positive or negative, depending on whether the terminal kinase stimulates or inhibits the activation of the initial level. Here we demonstrate that a negative feedback loop combined with intrinsic ultrasensitivity of the MAPK cascade can bring about sustained oscillations in MAPK phosphorylation. Based on recent kinetic data on the MAPK cascades, we predict that the period of oscillations can range from minutes to hours. The phosphorylation level can vary between the base level and almost 100% of the total protein. The oscillations of the phosphorylation cascades and slow protein diffusion in the cytoplasm can lead to intracellular waves of phospho-proteins.     

Effect of the MAPK cascade structure, nuclear translocation and regulation of transcription factors on gene expression

The mitogen activated protein kinase (MAP kinase) cascade system represents a highly conserved prototype of signal transduction by enzyme cascades. One of the best-studied properties of the MAPK system is its ability to convert graded input stimulus to switch-like all-or-none responses. Previous theoretical studies have centered on quantifying dual phosphorylated MAPK as a final output response and have not incorporated its influence on the regulation of gene expression. The main objective of the current work is to understand the regulatory effect of positive feedback loop embedded in the MAPK cascade, nuclear translocation of active MAPK, phosphorylation and activation of nuclear target proteins on the regulation of specific gene expression. To achieve this objective, we have simulated the MAPK cascade system, which resembles Hog1p activation pathway in yeast, at steady state. Thus, the input signal to the MAPK system is correlated with gene expression as a final system-level output response. The steady state simulation results suggest that other than regulating the signal propagation through cascades, the nuclear translocation of activated MAPK and subsequent regulation of gene expression represent one of the key modes to control the threshold level of response. This work proposes that, it is essential to consider the compartmental distributions of signaling species and the corresponding regulatory mechanisms of gene expression to study the system-level performance of signaling modules such as the MAPK cascade. Such an analysis will relate the extracellular cues to the final phenotypic response by capturing the mechanistic details of the signaling pathway.     

Feed-Forward versus Feedback Inhibition in a Basic Olfactory Circuit

Inhibitory interneurons play critical roles in shaping the firing patterns of principal neurons in many brain systems. Despite difference in the anatomy or functions of neuronal circuits containing inhibition, two basic motifs repeatedly emerge: feed-forward and feedback. In the locust, it was proposed that a subset of lateral horn interneurons (LHNs), provide feed-forward inhibition onto Kenyon cells (KCs) to maintain their sparse firing—a property critical for olfactory learning and memory. But recently it was established that a single inhibitory cell, the giant GABAergic neuron (GGN), is the main and perhaps sole source of inhibition in the mushroom body, and that inhibition from this cell is mediated by a feedback (FB) loop including KCs and the GGN. To clarify basic differences in the effects of feedback vs. feed-forward inhibition in circuit dynamics we here use a model of the locust olfactory system. We found both inhibitory motifs were able to maintain sparse KCs responses and provide optimal odor discrimination. However, we further found that only FB inhibition could create a phase response consistent with data recorded in vivo. These findings describe general rules for feed-forward versus feedback inhibition and suggest GGN is potentially capable of providing the primary source of inhibition to the KCs. A better understanding of how inhibitory motifs impact post-synaptic neuronal activity could be used to reveal unknown inhibitory structures within biological networks.     

Goldbeter–Koshland model for open signaling cascades: a mathematical study

A modified Goldbeter–Koshland (GK) type model is proposed to study the open signaling cascade with forward activation. Three different regimes related to the ultrasensitivity are clearly defined. When the cascade is sufficiently long, the steady states in the downstream cycles exhibit a limiting behavior. Meanwhile, a temporal switch-like behavior is revealed in the pre-ultrasensitivity regime without any feedback circuitry. A detailed analysis of this phenomenon is provided.     

The potential for signal integration and processing in interacting MAP kinase cascades

The cellular response to environmental stimuli requires biochemical information processing through which sensory inputs and cellular status are integrated and translated into appropriate responses by way of interacting networks of enzymes. One such network, the mitogen-activated protein (MAP) kinase cascade is a highly conserved signal transduction module that propagates signals from cell surface receptors to various cytosolic and nuclear targets by way of a phosphorylation cascade. We have investigated the potential for signal processing within a network of interacting feed-forward kinase cascades typified by the MAP kinase cascade. A genetic algorithm was used to search for sets of kinetic parameters demonstrating representative key input-output patterns of interest. We discuss two of the networks identified in our study, one implementing the exclusive-or function (XOR) and another implementing what we refer to as an in-band detector (IBD) or two-sided threshold. These examples confirm the potential for logic and amplitude-dependent signal processing in interacting MAP kinase cascades demonstrating limited cross-talk. Specifically, the XOR function allows the network to respond to either one, but not both signals simultaneously, while the IBD permits the network to respond exclusively to signals within a given range of strength, and to suppress signals below as well as above this range. The solution to the XOR problem is interesting in that it requires only two interacting pathways, crosstalk at only one layer, and no feedback or explicit inhibition. These types of responses are not only biologically relevant but constitute signal processing modules that can be combined to create other logical functions and that, in contrast to amplification, cannot be achieved with a single cascade or with two non-interacting cascades. Our computational results revealed surprising similarities between experimental data describing the JNK/MKK4/MKK7 pathway and the solution for the IBD that evolved from the genetic algorithm. The evolved IBD not only exhibited the required non-monotonic signal strength-response, but also demonstrated transient and sustained responses that properly reflected the input signal strength, dependence on both of the MAPKKs for signaling, phosphorylation site preferences by each of the MAPKKs, and both activation and inhibition resulting from the overexpression of one of the MAPKKs.     

MAP Kinase Pathways in the Yeast Saccharomyces cerevisiae

A cascade of three protein kinases known as a mitogen-activated protein kinase (MAPK) cascade is commonly found as part of the signaling pathways in eukaryotic cells. Almost two decades of genetic and biochemical experimentation plus the recently completed DNA sequence of the Saccharomyces cerevisiae genome have revealed just five functionally distinct MAPK cascades in this yeast. Sexual conjugation, cell growth, and adaptation to stress, for example, all require MAPK-mediated cellular responses. A primary function of these cascades appears to be the regulation of gene expression in response to extracellular signals or as part of specific developmental processes. In addition, the MAPK cascades often appear to regulate the cell cycle and vice versa. Despite the success of the gene hunter era in revealing these pathways, there are still many significant gaps in our knowledge of the molecular mechanisms for activation of these cascades and how the cascades regulate cell function. For example, comparison of different yeast signaling pathways reveals a surprising variety of different types of upstream signaling proteins that function to activate a MAPK cascade, yet how the upstream proteins actually activate the cascade remains unclear. We also know that the yeast MAPK pathways regulate each other and interact with other signaling pathways to produce a coordinated pattern of gene expression, but the molecular mechanisms of this cross talk are poorly understood. This review is therefore an attempt to present the current knowledge of MAPK pathways in yeast and some directions for future research in this area.     

Allosteric interactions and bifunctionality make the response of glutamine synthetase cascade system of Escherichia coli robust and ultrasensitive

Glutamine synthetase (GS) regulation in Escherichia coli by reversible covalent modification cycles is a prototype of signal transduction by enzyme cascades. Such enzyme cascades are known to exhibit ultrasensitive response to primary stimuli and act as signal integration systems. Here, we have quantified GS bicyclic cascade based on steady state analysis by evaluating Hill coefficient. We demonstrate that adenylylation of GS with glutamine as input is insensitive to total enzyme concentrations of GS, uridylyltransferase/uridylyl-removing enzyme, regulatory protein PII, and adenylyltransferase/adenylyl-removing enzyme. This robust response of GS adenylylation is also observed for change in system parameters. From numerical analyses, we show that the robust ultrasensitive response of bicyclic cascade is because of allosteric interactions of glutamine and 2-ketoglutarate, bifunctionality of converter enzymes, and closed loop bicyclic cascade structure. By system level quantification of the GS bicyclic cascade, we conclude that such a robust response may help the cell in adapting to different carbon and nitrogen status.     

A computational study of feedback effects on signal dynamics in a mitogen-activated protein kinase (MAPK) pathway model

Exploiting signaling pathways for the purpose of controlling cell function entails identifying and manipulating the information content of intracellular signals. As in the case of the ubiquitously expressed, eukaryotic mitogen-activated protein kinase (MAPK) signaling pathway, this information content partly resides in the signals' dynamical properties. Here, we utilize a mathematical model to examine mechanisms that govern MAPK pathway dynamics, particularly the role of putative negative feedback mechanisms in generating complete signal adaptation, a term referring to the reset of a signal to prestimulation levels. In addition to yielding adaptation of its direct target, feedback mechanisms implemented in our model also indirectly assist in the adaptation of signaling components downstream of the target under certain conditions. In fact, model predictions identify conditions yielding ultra-desensitization of signals in which complete adaptation of target and downstream signals culminates even while stimulus recognition (i.e., receptor-ligand binding) continues to increase. Moreover, the rate at which signal decays can follow first-order kinetics with respect to signal intensity, so that signal adaptation is achieved in the same amount of time regardless of signal intensity or ligand dose. All of these features are consistent with experimental findings recently obtained for the Chinese hamster ovary (CHO) cell lines (Asthagiri et al., J. Biol. Chem. 1999, 274, 27119-27127). Our model further predicts that although downstream effects are independent of whether an enzyme or adaptor protein is targeted by negative feedback, adaptor-targeted feedback can "back-propagate" effects upstream of the target, specifically resulting in increased steady-state upstream signal. Consequently, where these upstream components serve as nodes within a signaling network, feedback can transfer signaling through these nodes into alternate pathways, thereby promoting the sort of signaling cross-talk that is becoming more widely appreciated.