Oscillatory dynamics arising from competitive inhibition and multisite phosphorylation

Design patterns of biological cells

Design patterns are generalized solutions to frequently recurring problems. They were initially developed by architects and computer scientists to create a higher level of abstraction for their designs. Here, we extend these concepts to cell biology to lend a new perspective on the evolved designs of cells' underlying reaction networks. We present a catalog of 21 design patterns divided into three categories: creational patterns describe processes that build the cell, structural patterns describe the layouts of reaction networks, and behavioral patterns describe reaction network function. Applying this pattern language to the E. coli central metabolic reaction network, the yeast pheromone response signaling network, and other examples lends new insights into these systems.

First-order ultrasensitivity in phosphorylation cycles

Cellular signal transduction takes place through a network of phosphorylation cycles. These pathways take the form of a multi-layered cascade of cycles. This work focuses on the sensitivity of single, double and n length cycles. Cycles that operate in the zero-order regime can become sensitive to changes in signal, resulting in zero-order ultrasensitivity (ZOU). Using frequency analysis, we confirm previous efforts that cascades can act as noise filters by computing the bandwidth. We show that n length cycles display what we term first-order ultrasensitivity which occurs even when the cycles are not operating in the zero-order regime. The magnitude of the sensitivity, however, has an upper bound equal to the number of cycles. It is known that ZOU can be significantly reduced in the presence of retroactivity. We show that the first-order ultrasensitivity is immune to retroactivity and that the ZOU and first-order ultrasensitivity can be blended to create systems with constant sensitivity over a wider range of signal. We show that the ZOU in a double cycle is only modestly higher compared with a single cycle. We therefore speculate that the double cycle has evolved to enable amplification even in the face of retroactivity.

Tethered particle motion of the adaptation enzyme CheR in bacterial chemotaxis

Bacteria perform chemotactic adaptation by sequential modification of multiple modifiable sites on chemoreceptors through stochastic action of tethered adaptation enzymes (CheR and CheB). To study the molecular kinetics of this process, we measured the response to different concentrations of MeAsp for the Tar-only Escherichia coli strain. We found a strong dependence of the methylation rate on the methylation level and established a new mechanism of adaptation kinetics due to tethered particle motion of the methylation enzyme CheR. Experiments with various lengths of the C-terminal flexible chain in the Tar receptor further validated this mechanism. The tethered particle motion resulted in a CheR concentration gradient that ensures encounter-rate matching of the sequential modifiable sites. An analytical model of multisite catalytic reaction showed that this enables robustness of methylation to fluctuations in receptor activity or cell-to-cell variations in the expression of adaptation enzymes and reduces the variation in methylation level among individual receptors.

Sensitivity and Frequency Response of Biochemical Cascades

Signal transduction from a cell's surface to cytoplasmic and nuclear targets takes place through a complex network of interconnected pathways. Phosphorylation cycles are common components of many pathways and may take the form of a multi-layered cascade of cycles or incorporate species with multiple phosphorylation sites that effectively create a sequence of cycles with increasing states of phosphorylation. This work focuses on the frequency response and sensitivity of such systems, two properties that have not been thoroughly examined. Starting with a singularly phosphorylated single-cycle system, we compare the sensitivity to perturbation at steady-state across a range of input signal strengths. This is followed by a frequency response analysis focusing on the gain and associated bandwidth. Next, we consider a two-layer cascade of single phosphorylation cycles and focus on how the two cycles interact to produce various effects on the bandwidth and damping properties. Then we consider the (ultra)sensitivity of a doubly phosphorylated system, where we describe in detail first-order ultrasensitivity, a unique property of these systems, which can be blended with zero-order ultrasensitivity to create systems with relatively constant gain over a range of signal input. Finally, we give an in-depth analysis of the sensitivity of an n-phosphorylated system.

Dynamics and Sensitivity of Signaling Pathways

Purpose of Review

Signaling pathways serve to communicate information about extracellular conditions into the cell, to both the nucleus and cytoplasmic processes to control cell responses. Genetic mutations in signaling network components are frequently associated with cancer and can result in cells acquiring an ability to divide and grow uncontrollably. Because signaling pathways play such a significant role in cancer initiation and advancement, their constituent proteins are attractive therapeutic targets. In this review, we discuss how signaling pathway modeling can assist with identifying effective drugs for treating diseases, such as cancer. An achievement that would facilitate the use of such models is their ability to identify controlling biochemical parameters in signaling pathways, such as molecular abundances and chemical reaction rates, because this would help determine effective points of attack by therapeutics.

Recent Findings

We summarize the current state of understanding the sensitivity of phosphorylation cycles with and without sequestration. We also describe some basic properties of regulatory motifs including feedback and feedforward regulation.

Summary

Although much recent work has focused on understanding the dynamics and particularly the sensitivity of signaling networks in eukaryotic systems, there is still an urgent need to build more scalable models of signaling networks that can appropriately represent their complexity across different cell types and tumors.

CRYPTOCHROMES confer robustness, not rhythmicity, to circadian timekeeping

Circadian rhythms are a pervasive property of mammalian cells, tissues and behaviour, ensuring physiological adaptation to solar time. Models of cellular timekeeping revolve around transcriptional feedback repression, whereby CLOCK and BMAL1 activate the expression of PERIOD (PER) and CRYPTOCHROME (CRY), which in turn repress CLOCK/BMAL1 activity. CRY proteins are therefore considered essential components of the cellular clock mechanism, supported by behavioural arrhythmicity of CRY-deficient (CKO) mice under constant conditions. Challenging this interpretation, we find locomotor rhythms in adult CKO mice under specific environmental conditions and circadian rhythms in cellular PER2 levels when CRY is absent. CRY-less oscillations are variable in their expression and have shorter periods than wild-type controls. Importantly, we find classic circadian hallmarks such as temperature compensation and period determination by CK1δ/ε activity to be maintained. In the absence of CRY-mediated feedback repression and rhythmic Per2 transcription, PER2 protein rhythms are sustained for several cycles, accompanied by circadian variation in protein stability. We suggest that, whereas circadian transcriptional feedback imparts robustness and functionality onto biological clocks, the core timekeeping mechanism is post-translational.

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

Exploring cyclic networks of multisite modification reveals origins of information processing characteristics

Multisite phosphorylation (and generally multisite modification) is a basic way of encoding substrate function and circuits/networks of post-translational modifications (PTM) are ubiquitous in cell signalling. The information processing characteristics of PTM systems are a focal point of broad interest. The ordering of modifications is a key aspect of multisite modification, and a broad synthesis of the impact of ordering of modifications is still missing. We focus on a basic class of multisite modification circuits: the cyclic mechanism, which corresponds to the same ordering of phosphorylation and dephosphorylation, and examine multiple variants involving common/separate kinases and common/separate phosphatases. This is of interest both because it is encountered in concrete cellular contexts, and because it serves as a bridge between ordered (sequential) mechanisms (representing one type of ordering) and random mechanisms (which have no ordering). We show that bistability and biphasic dose response curves of the maximally modified phosphoform are ruled out for basic structural reasons independent of parameters, while oscillations can result with even just one shared enzyme. We then examine the effect of relaxing some basic assumptions about the ordering of modification. We show computationally and analytically how bistability, biphasic responses and oscillations can be generated by minimal augmentations to the cyclic mechanism even when these augmentations involved reactions operating in the unsaturated limit. All in all, using this approach we demonstrate (1) how the cyclic mechanism (with single augmentations) represents a modification circuit using minimal ingredients (in terms of shared enzymes and sequestration of enzymes) to generate bistability and oscillations, when compared to other mechanisms, (2) new design principles for rationally designing PTM systems for a variety of behaviour, (3) a basis and a necessary step for understanding the origins and robustness of behaviour observed in basic multisite modification systems.

Exploring the intrinsic behaviour of multisite phosphorylation systems as part of signalling pathways

Multisite phosphorylation is a basic way of chemically encoding substrate function and a recurring feature of cell signalling pathways. A number of studies have explored information processing characteristics of multisite phosphorylation, through studies of the intrinsic kinetics. Many of these studies focus on the module in isolation. In this paper, we build a bridge to connect the behaviour of multisite modification in isolation to that as part of pathways. We study the effect of activation of the enzymes (which are basic ways in which the module may be regulated), as well the effects of the modified substrates being involved in further modifications or exiting reaction compartments. We find that these effects can induce multiple kinds of transitions, including to behaviour not seen intrinsically in the multisite modification module. We then build on these insights to investigate how these multisite modification systems can be tuned by enzyme activation to realize a range of information processing outcomes for the design of synthetic phosphorylation circuits. Connecting the complexity of multisite modification kinetics, with the pathways in which they are embedded, serves as a basis for teasing out many aspects of their interaction, providing insights of relevance in systems biology, synthetic biology/chemistry and chemical information processing.

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.

Minimal oscillating subnetwork in the Huang-Ferrell model of the MAPK cascade

Prompted by the recent growing evidence of oscillatory behavior involving MAPK cascades we present a systematic approach of analyzing models and elucidating the nature of biochemical oscillations based on reaction network theory. In particular, we formulate a minimal biochemically consistent mass action subnetwork of the Huang-Ferrell model of the MAPK signalling that provides an oscillatory response when a parameter controlling the activation of the top-tier kinase is varied. Such dynamics are either intertwined with or separated from the earlier found bistable/hysteretic behavior in this model. Using the theory of stability of stoichiometric networks, we reduce the original MAPK model, convert kinetic to convex parameters and examine those properties of the minimal subnetwork that underlie the oscillatory dynamics. We also use the methods of classification of chemical oscillatory networks to explain the rhythmic behavior in physicochemical terms, i.e., we identify of the role of individual biochemical species in positive and negative feedback loops and describe their coordinated action leading to oscillations. Our approach provides an insight into dynamics without the necessity of knowing rate coefficients and thus is useful prior the statistical evaluation of parameters.

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.

Quorum Sensing Communication Modules for Microbial Consortia

The power of a single engineered organism is limited by its capacity for genetic modification. To circumvent the constraints of any singular microbe, a new frontier in synthetic biology is emerging: synthetic ecology, or the engineering of microbial consortia. Here we develop communication systems for such consortia in an effort to allow for complex social behavior across different members of a community. We posit that such communities will outpace monocultures in their ability to perform complicated tasks if communication among and between members of the community is well regulated. Quorum sensing was identified as the most promising candidate for precise control of engineered microbial ecosystems, due to its large diversity and established utility in synthetic biology. Through promoter and protein modification, we engineered two quorum sensing systems (rpa and tra) to add to the extensively used lux and las systems. By testing the cross-talk between all systems, we thoroughly characterized many new inducible systems for versatile control of engineered communities. Furthermore, we've identified several system pairs that exhibit useful types of orthogonality. Most notably, the tra and rpa systems were shown to have neither signal crosstalk nor promoter crosstalk for each other, making them completely orthogonal in operation. Overall, by characterizing the interactions between all four systems and their components, these circuits should lend themselves to higher-level genetic circuitry for use in microbial consortia.

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.

Enzyme Sequestration as a Tuning Point in Controlling Response Dynamics of Signalling Networks

Signalling networks result from combinatorial interactions among many enzymes and scaffolding proteins. These complex systems generate response dynamics that are often essential for correct decision-making in cells. Uncovering biochemical design principles that underpin such response dynamics is a prerequisite to understand evolved signalling networks and to design synthetic ones. Here, we use in silico evolution to explore the possible biochemical design space for signalling networks displaying ultrasensitive and adaptive response dynamics. By running evolutionary simulations mimicking different biochemical scenarios, we find that enzyme sequestration emerges as a key mechanism for enabling such dynamics. Inspired by these findings, and to test the role of sequestration, we design a generic, minimalist model of a signalling cycle, featuring two enzymes and a single scaffolding protein. We show that this simple system is capable of displaying both ultrasensitive and adaptive response dynamics. Furthermore, we find that tuning the concentration or kinetics of the sequestering protein can shift system dynamics between these two response types. These empirical results suggest that enzyme sequestration through scaffolding proteins is exploited by evolution to generate diverse response dynamics in signalling networks and could provide an engineering point in synthetic biology applications.

Receptor Level Mechanisms Are Required for Epidermal Growth Factor (EGF)-stimulated Extracellular Signal-regulated Kinase (ERK) Activity Pulses

In both physiological and cell culture systems, EGF-stimulated ERK activity occurs in discrete pulses within individual cells. Many feedback loops are present in the EGF receptor (EGFR)-ERK network, but the mechanisms driving pulsatile ERK kinetics are unknown. Here, we find that in cells that respond to EGF with frequency-modulated pulsatile ERK activity, stimulation through a heterologous TrkA receptor system results in non-pulsatile, amplitude-modulated activation of ERK. We further dissect the kinetics of pulse activity using a combination of FRET- and translocation-based reporters and find that EGFR activity is required to maintain ERK activity throughout the 10-20-minute lifetime of pulses. Together, these data indicate that feedbacks operating within the core Ras-Raf-MEK-ERK cascade are insufficient to drive discrete pulses of ERK activity and instead implicate mechanisms acting at the level of EGFR.

Visualization of the spatial and temporal dynamics of MAPK signaling using fluorescence imaging techniques

Conserved mitogen-activated protein kinase (MAPK) signaling pathways are major mechanisms through which cells perceive and respond properly to their surrounding environment. Such homeostatic responses maintain the life of the organism. Since errors in MAPK signaling pathways can lead to cancers and to defects in immune responses, in the nervous system and metabolism, these pathways have been extensively studied as potential therapeutic targets. Although much has been studied about the roles of MAPKs in various cellular functions, less is known regarding regulation of MAPK in living organisms. This review will focus on the latest understanding of the dynamic regulation of MAPK signaling in intact cells that was revealed by using novel fluorescence imaging techniques and advanced systems-analytical methods. These techniques allowed quantitative analyses of signal transduction in situ with high spatio-temporal resolution and have revealed the nature of the molecular dynamics that determine cellular responses and fates.

Enhancement of tunability of MAPK cascade due to coexistence of processive and distributive phosphorylation mechanisms

The processive phosphorylation mechanism becomes important when there is macromolecular crowding in the cytoplasm. Integrating the processive phosphorylation mechanism with the traditional distributive one, we propose a mixed dual-site phosphorylation (MDP) mechanism in a single-layer phosphorylation cycle. Further, we build a degree model by applying the MDP mechanism to a three-layer mitogen-activated protein kinase (MAPK) cascade. By bifurcation analysis, our study suggests that the crowded-environment-induced pseudoprocessive mechanism can qualitatively change the response of this biological network. By adjusting the degree of processivity in our model, we find that the MAPK cascade is able to switch between the ultrasensitivity, bistability, and oscillatory dynamical states. Sensitivity analysis shows that the theoretical results remain unchanged within a reasonably chosen variation of parameter perturbation. By scaling the reaction rates and also introducing new connections into the kinetic scheme, we further construct a proportion model of the MAPK cascade to validate our findings. Finally, it is illustrated that the spatial propagation of the activated MAPK signal can be improved (or attenuated) by increasing the degree of processivity of kinase (or phosphatase). Our research implies that the MDP mechanism makes the MAPK cascade become a flexible signal module, and the coexistence of processive and distributive phosphorylation mechanisms enhances the tunability of the MAPK cascade.

Phosphate sink containing two-component signaling systems as tunable threshold devices

Synthetic biology aims to design de novo biological systems and reengineer existing ones. These efforts have mostly focused on transcriptional circuits, with reengineering of signaling circuits hampered by limited understanding of their systems dynamics and experimental challenges. Bacterial two-component signaling systems offer a rich diversity of sensory systems that are built around a core phosphotransfer reaction between histidine kinases and their output response regulator proteins, and thus are a good target for reengineering through synthetic biology. Here, we explore the signal-response relationship arising from a specific motif found in two-component signaling. In this motif, a single histidine kinase (HK) phosphotransfers reversibly to two separate output response regulator (RR) proteins. We show that, under the experimentally observed parameters from bacteria and yeast, this motif not only allows rapid signal termination, whereby one of the RRs acts as a phosphate sink towards the other RR (i.e. the output RR), but also implements a sigmoidal signal-response relationship. We identify two mathematical conditions on system parameters that are necessary for sigmoidal signal-response relationships and define key parameters that control threshold levels and sensitivity of the signal-response curve. We confirm these findings experimentally, by in vitro reconstitution of the one HK-two RR motif found in the Sinorhizobium meliloti chemotaxis pathway and measuring the resulting signal-response curve. We find that the level of sigmoidality in this system can be experimentally controlled by the presence of the sink RR, and also through an auxiliary protein that is shown to bind to the HK (yielding Hill coefficients of above 7). These findings show that the one HK-two RR motif allows bacteria and yeast to implement tunable switch-like signal processing and provides an ideal basis for developing threshold devices for synthetic biology applications.

Two-component signaling systems are found in bacteria, fungi and plants. Their modular structures make them ideal targets for de novo engineering through synthetic biology. Here, we explore the signal-response relationship arising from a common two-component system, where a single HK phosphotransfers reversibly to two separate output RRs. We show that under the experimentally observed parameters, this motif implements a sigmoidal signal-response relationship, whereby one of the RRs acts as a phosphate sink towards the other. We identify two mathematical conditions on the system parameters that are necessary for sigmoidality and define key parameters that control threshold levels and sensitivity. We confirm these findings experimentally by in vitro reconstitution of the “one HK-two RR” motif found in S. meliloti. Particularly, we show that the level of sigmoidality in this system can be experimentally controlled by the amount of sink RR and also through an auxiliary protein, CheS. These findings show that the one HK-two RR motif can open the way to the design of novel threshold systems in synthetic biology.

Graph-theoretic analysis of a model for the coupling between photosynthesis and photorespiration

We develop and analyze a mathematical model based on a previously enunciated hypothesis regarding the origin of rapid, irregular oscillations observed in photosynthetic variables when a leaf is transferred to a low-CO2atmosphere. This model takes the form of a set of differential equations with two delays. We review graph-theoretical methods of analysis based on the bipartite graph representation of mass-action models, including models with delays. We illustrate the use of these methods by showing that our model is capable of delay-induced oscillations. We present some numerical examples confirming this possibility, including the possibility of complex transient oscillations. We then use the structure of the identified oscillophore, the part of the reaction network responsible for the oscillations, along with our knowledge of the plausible range of values for one of the delays, to rule out this hypothetical mechanism.

The Goodwin model: behind the Hill function

The Goodwin model is a 3-variable model demonstrating the emergence of oscillations in a delayed negative feedback-based system at the molecular level. This prototypical model and its variants have been commonly used to model circadian and other genetic oscillators in biology. The only source of non-linearity in this model is a Hill function, characterizing the repression process. It was mathematically shown that to obtain limit-cycle oscillations, the Hill coefficient must be larger than 8, a value often considered unrealistic. It is indeed difficult to explain such a high coefficient with simple cooperative dynamics. We present here molecular models of the standard Goodwin model, based on single or multisite phosphorylation/dephosphorylation processes of a transcription factor, which have been previously shown to generate switch-like responses. We show that when the phosphorylation/dephosphorylation processes are fast enough, the limit-cycle obtained with a multisite phosphorylation-based mechanism is in very good quantitative agreement with the oscillations observed in the Goodwin model. Conditions in which the detailed mechanism is well approximated by the Goodwin model are given. A variant of the Goodwin model which displays sharp thresholds and relaxation oscillations is also explained by a double phosphorylation/dephosphorylation-based mechanism through a bistable behavior. These results not only provide rational support for the Goodwin model but also highlight the crucial role of the speed of post-translational processes, whose response curve are usually established at a steady state, in biochemical oscillators.

In vivo, in vitro, and in silico studies suggest a conserved immune module that regulates malaria parasite transmission from mammals to mosquitoes

Human malaria can be caused by the parasite Plasmodium falciparum that is transmitted by female Anopheles mosquitoes. "Immunological crosstalk" between the mammalian and anopheline hosts for Plasmodium functions to control parasite numbers. Key to this process is the mammalian cytokine transforming growth factor-β1 (TGF-β1). In mammals, TGF-β1 regulates inducible nitric oxide (NO) synthase (iNOS) both positively and negatively. In some settings, high levels of NO activate latent TGF-β1, which in turn suppresses iNOS expression. In the mosquito, ingested TGF-β1 induces A. stephensi NOS (AsNOS), which limits parasite development and which in turn is suppressed by activation of the mosquito homolog of the mitogen-activated protein kinases MEK and ERK. Computational models linking TGF-β1, AsNOS, and MEK/ERK were developed to provide insights into this complex biology. An initial Boolean model suggested that, as occurs in mammalian cells, MEK/ERK and AsNOS would oscillate upon ingestion of TGF-β1. An ordinary differential equation (ODE) model further supported the hypothesis of TGF-β1-induced multiphasic behavior of MEK/ERK and AsNOS. To achieve this multiphasic behavior, the ODE model was predicated on the presence of constant levels of TGF-β1 in the mosquito midgut. Ingested TGF-β1, however, did not exhibit this behavior. Accordingly, we hypothesized and experimentally verified that ingested TGF-β1 induces the expression of the endogenous mosquito TGF-β superfamily ligand As60A. Computational simulation of these complex, cross-species interactions suggested that TGF-β1 and NO-mediated induction of As60A expression together may act to maintain multiphasic AsNOS expression via MEK/ERK-dependent signaling. We hypothesize that multiphasic behavior as represented in this model allows the mosquito to balance the conflicting demands of parasite killing and metabolic homeostasis in the face of damaging inflammation.

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.

Oscillations in MAPK cascade triggered by two distinct designs of coupled positive and negative feedback loops

BACKGROUND

Feedback loops, both positive and negative are embedded in the Mitogen Activated Protein Kinase (MAPK) cascade. In the three layer MAPK cascade, both feedback loops originate from the terminal layer and their sites of action are either of the two upstream layers. Recent studies have shown that the cascade uses coupled positive and negative feedback loops in generating oscillations. Two plausible designs of coupled positive and negative feedback loops can be elucidated from the literature; in one design the positive feedback precedes the negative feedback in the direction of signal flow and vice-versa in another. But it remains unexplored how the two designs contribute towards triggering oscillations in MAPK cascade. Thus it is also not known how amplitude, frequency, robustness or nature (analogous/digital) of the oscillations would be shaped by these two designs.

RESULTS

We built two models of MAPK cascade that exhibited oscillations as function of two underlying designs of coupled positive and negative feedback loops. Frequency, amplitude and nature (digital/analogous) of oscillations were found to be differentially determined by each design. It was observed that the positive feedback emerging from an oscillating MAPK cascade and functional in an external signal processing module can trigger oscillations in the target module, provided that the target module satisfy certain parametric requirements. The augmentation of the two models was done to incorporate the nuclear-cytoplasmic shuttling of cascade components followed by induction of a nuclear phosphatase. It revealed that the fate of oscillations in the MAPK cascade is governed by the feedback designs. Oscillations were unaffected due to nuclear compartmentalization owing to one design but were completely abolished in the other case.

CONCLUSION

The MAPK cascade can utilize two distinct designs of coupled positive and negative feedback loops to trigger oscillations. The amplitude, frequency and robustness of the oscillations in presence or absence of nuclear compartmentalization were differentially determined by two designs of coupled positive and negative feedback loops. A positive feedback from an oscillating MAPK cascade was shown to induce oscillations in an external signal processing module, uncovering a novel regulatory aspect of MAPK signal processing.

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.

Invariants and other structural properties of biochemical models as a constraint satisfaction problem

BACKGROUND

We present a way to compute the minimal semi-positive invariants of a Petri net representing a biological reaction system, as resolution of a Constraint Satisfaction Problem. The use of Petri nets to manipulate Systems Biology models and make available a variety of tools is quite old, and recently analyses based on invariant computation for biological models have become more and more frequent, for instance in the context of module decomposition.

RESULTS

In our case, this analysis brings both qualitative and quantitative information on the models, in the form of conservation laws, consistency checking, etc. thanks to finite domain constraint programming. It is noticeable that some of the most recent optimizations of standard invariant computation techniques in Petri nets correspond to well-known techniques in constraint solving, like symmetry-breaking. Moreover, we show that the simple and natural encoding proposed is not only efficient but also flexible enough to encompass sub/sur-invariants, siphons/traps, etc., i.e., other Petri net structural properties that lead to supplementary insight on the dynamics of the biochemical system under study.

CONCLUSIONS

A simple implementation based on GNU-Prolog's finite domain solver, and including symmetry detection and breaking, was incorporated into the BIOCHAM modelling environment and in the independent tool Nicotine. Some illustrative examples and benchmarks are provided.

Evolutionary principles underlying structure and response dynamics of cellular networks

The network view in systems biology, in conjunction with the continuing development of experimental technologies, is providing us with the key structural and dynamical features of both cell-wide and pathway-level regulatory, signaling and metabolic systems. These include for example modularity and presence of hub proteins at the structural level and ultrasensitivity and feedback control at the level of dynamics. The uncovering of such features, and the seeming commonality of some of them, makes many systems biologists believe that these could represent design principles that underpin cellular systems across organisms. Here, we argue that such claims on any observed feature requires an understanding of how it has emerged in evolution and how it can shape subsequent evolution. We review recent and past studies that aim to achieve such evolutionary understanding for observed features of cellular networks. We argue that this evolutionary framework could lead to deciphering evolutionary origin and relevance of proposed design principles, thereby allowing to predict their presence or absence in an organism based on its environment and biochemistry and their effect on its future evolution.

Synthesis of robust tunable oscillators using mitogen activated protein kinase cascades

Mitogen activated protein kinase (MAPK) cascade is evolutionally preserved in all eukaryotic cells, and regulates various cellular activities such as gene expression, mitosis, differentiation, and apoptosis. Recently, Bashor et al. have shown that Ste5 scaffold protein can be used to reshape the MAPK cascade through engineered feedback loops, and have used heuristic tuning mechanisms to synthesize the feedback. A problem of interest is to determine whether information regarding the underlying biochemical reactions can be used to synthesize robust feedback that will ensure that the resultant circuit has the desired properties. In this paper, we consider the problem of engineering feedback in MAPK cascade to synthesize an oscillator of the desired frequency. Our approach builds on the MAPK cascade model derived by Chikarmane et al. who have exploited the existence of a Hopf bifurcation point in the Markevich model of the MAPK cascade to synthesize the exciting kinase as a function of the doubly phosphorylated protein. We show how the [Formula: see text]-control theory can be used for a robust synthesis of the oscillator and present the simulation results.

CONSTRUCTION AND CUSTOMIZATION OF STABLE OSCILLATION MODELS IN BIOLOGY

Oscillations exist at all levels of biological systems and are often crucial for their proper functioning. Among the various types of oscillations, limit cycles have received particular attention for more than one hundred years. Specifically, theorems have been established that characterize whether a system might have the capability of exhibiting limit cycles. However, the practical application of these theorems is usually cumbersome and there are hardly any guidelines for devising de novo models that exhibit limit cycles of a desired form. In this paper, we propose a simple method for constructing and customizing stable limit cycles in two-dimensional systems according to desired features, including frequency, amplitude, and phase shift between system variables. The method is based on "inverting" a criterion proposed by Lewis for characterizing oscillations in two-dimensional S-system models. First, we execute comprehensive simulations that result in a set of over 2000 prototype limit cycles. Second, we show with examples how these prototypes can be further customized to adhere to predetermined specifications. This two-step process is fast and efficacious, especially when one considers the paucity of alternative methods. Finally, we illustrate how one may create systems with more complex dynamics by modulating the prototypes with external input signals.

Minimum protein oscillator based on multisite phosphorylation∕dephosphorylation

The authors propose a novel minimum oscillator whereby a protein with multiple phosphorylation sites directly embedded in a negative feedback loop can exhibit oscillation. They demonstrate that if the fully phosphorylated substrate inhibits the first phosphorylation step in a cooperative manner, multisite substrates can exhibit oscillatory behaviour at the presence of a kinase and phosphatase. With a fixed number of sites, the non-linearity of the negative feedback and the substrate∕enzyme ratio must be above certain threshold values to generate undamped oscillation. There is an inverse relationship between the number of phosphorylation sites and the minimum non-linearity of the negative feedback required for oscillation; that is, the ultrasensitivity and time delay rooted in multisite phosphorylation compensate for the explicit non-linearity in the negative feedback. The period and amplitude of oscillation are mainly determined by the number of phosphorylation sites and the substrate∕enzyme ratio. The authors' results suggest that a multisite protein can be exploited for the construction of a synthetic protein oscillator featuring simplicity, robustness and tunability.

Four-dimensional dynamics of MAPK information processing systems

Mitogen activated protein kinase (MAPK) cascades process a myriad of stimuli received by cell-surface receptors and generate precise spatio-temporal guidance for multiple target proteins, dictating receptor-specific cellular outcomes. Computational modelling reveals that the intrinsic topology of MAPK cascades enables them to amplify signal sensitivity and amplitude, reduce noise and display intricate dynamic properties, which include toggle switches, excitation pulses and oscillations. Specificity of signaling responses can be brought about by signal-induced feedback and feedforward wiring imposed on the MAPK cascade backbone. Intracellular gradients of protein activities arise from the spatial separation of opposing reactions in kinase-phosphatase cycles. The membrane confinement of the initiating kinase in MAPK cascades and cytosolic localization of phosphatases can result in precipitous gradients of phosphorylated signal-transducers if they spread solely by diffusion. Endocytotic trafficking of active kinases driven by molecular motors and traveling waves of protein phosphorylation can propagate phosphorylation signals from the plasma membrane to the nucleus, especially in large cells, such as Xenopus eggs.

A combination of multisite phosphorylation and substrate sequestration produces switchlike responses

The phosphorylation of a protein on multiple sites has been proposed to promote the switchlike regulation of protein activity. Recent theoretical work, however, indicates that multisite phosphorylation, by itself, is less effective at creating switchlike responses than had been previously thought. The phosphorylation of a protein often alters its spatial localization, or its association with other proteins, and this sequestration can alter the accessibility of the substrate to the relevant kinases and phosphatases. Sequestration thus has the potential to interact with multisite phosphorylation to modulate ultrasensitivity and threshold. Here, using simple ordinary differential equations to represent phosphorylation, dephosphorylation, and binding/sequestration, we demonstrate that the combination of multisite phosphorylation and regulated substrate sequestration can produce a response that is both a good threshold and a good switch. Several strategies are explored, including both stronger and weaker sequestration with successive phosphorylations, as well as combinations that are more elaborate. In some strategies, such as when phosphorylation and dephosphorylation are segregated, a near-optimal switch is possible, where the effective Hill number equals the number of phosphorylation sites.

Mathematical modeling: bridging the gap between concept and realization in synthetic biology

Mathematical modeling plays an important and often indispensable role in synthetic biology because it serves as a crucial link between the concept and realization of a biological circuit. We review mathematical modeling concepts and methodologies as relevant to synthetic biology, including assumptions that underlie a model, types of modeling frameworks (deterministic and stochastic), and the importance of parameter estimation and optimization in modeling. Additionally we expound mathematical techniques used to analyze a model such as sensitivity analysis and bifurcation analysis, which enable the identification of the conditions that cause a synthetic circuit to behave in a desired manner. We also discuss the role of modeling in phenotype analysis such as metabolic and transcription network analysis and point out some available modeling standards and software. Following this, we present three case studies—a metabolic oscillator, a synthetic counter, and a bottom-up gene regulatory network—which have incorporated mathematical modeling as a central component of synthetic circuit design.

On the mechanism of oscillations in neutrophils

We have investigated the regulation of the oscillatory generation of H(2)O(2) and oscillations in shape and size in neutrophils in suspension. The oscillations are independent of cell density and hence do not represent a collective phenomena. Furthermore, the oscillations are independent of the external glucose concentration and the oscillations in H(2)O(2) production are 180 degrees out of phase with the oscillations in NAD(P)H. Cytochalasin B blocked the oscillations in shape and size whereas it increased the period of the oscillations in H(2)O(2) production. 1- and 2-butanol also blocked the oscillations in shape and size, but only 1-butanol inhibited the oscillations in H(2)O(2) production. We conjecture that the oscillations are likely to be due to feedback regulations in the signal transduction cascade involving phosphoinositide 3-kinases (PI3K). We have tested this using a simple mathematical model, which explains most of our experimental observations.

Employing a Mechanistic Model for the MAPK Pathway to Examine the Impact of Cellular all or None Behavior on Overall Tissue Response

The mitogen activated protein kinase (MAPK) cascade is a three-tiered phosphorylation cascade that is ubiquitously expressed among eukaryotic cells. Its primary function is to propagate signals from cell surface receptors to various cytosolic and nuclear targets. Recent studies have demonstrated that the MAPK cascade exhibits an all-or-none response to graded stimuli. This study quantitatively investigates MAPK activation in Xenopus oocytes using both empirical and biologically-based mechanistic models. Empirical models can represent overall tissue MAPK activation in the oocytes. However, these models lack description of key biological processes and therefore give no insight into whether the cellular response occurs in a graded or all-or-none fashion. To examine the propagation of cellular MAPK all-or-none activation to overall tissue response, mechanistic models in conjunction with Monte Carlo simulations are employed. An adequate description of the dose response relationship of MAPK activation in Xenopus oocytes is achieved. Furthermore, application of these mechanistic models revealed that the initial receptor-ligand binding rate contributes to the cells' ability to exhibit an all-or-none MAPK activation response, while downstream activation parameters contribute more to the magnitude of activation. These mechanistic models enable us to identify key biological events which quantitatively impact the shape of the dose response curve, especially at low environmentally relevant doses.

Spatio-temporal correlations can drastically change the response of a MAPK pathway

Multisite covalent modification of proteins is omnipresent in eukaryotic cells. A well-known example is the mitogen-activated protein kinase (MAPK) cascade where, in each layer of the cascade, a protein is phosphorylated at two sites. It has long been known that the response of a MAPK pathway strongly depends on whether the enzymes that modify the protein act processively or distributively. A distributive mechanism, in which the enzyme molecules have to release the substrate molecules in between the modification of the two sites, can generate an ultrasensitive response and lead to hysteresis and bistability. We study by Green's Function Reaction Dynamics (GFRD), a stochastic scheme that makes it possible to simulate biochemical networks at the particle level in time and space, a dual phosphorylation cycle in which the enzymes act according to a distributive mechanism. We find that the response of this network can differ dramatically from that predicted by a mean-field analysis based on the chemical rate equations. In particular, rapid rebindings of the enzyme molecules to the substrate molecules after modification of the first site can markedly speed up the response and lead to loss of ultrasensitivity and bistability. In essence, rapid enzyme-substrate rebindings can turn a distributive mechanism into a processive mechanism. We argue that slow ADP release by the enzymes can protect the system against these rapid rebindings, thus enabling ultrasensitivity and bistability.

Rapid and sustained nuclear-cytoplasmic ERK oscillations induced by epidermal growth factor

Although the ERK pathway has a central role in the response of cells to growth factors, its regulatory structure and dynamics are incompletely understood. To investigate ERK activation in real time, we expressed an ERK–GFP fusion protein in human mammary epithelial cells. On EGF stimulation, we observed sustained oscillations of the ERK–GFP fusion protein between the nucleus and cytoplasm with a periodicity of ∼15 min. The oscillations were persistent (>45 cycles), independent of cell cycle phase, and were highly dependent on cell density, essentially disappearing at confluency. Oscillations occurred even at ligand doses that elicited very low levels of ERK phosphorylation, and could be detected biochemically in both transfected and nontransfected cells. Mathematical modeling revealed that negative feedback from phosphorylated ERK to the cascade input was necessary to match the robustness of the oscillation characteristics observed over a broad range of ligand concentrations. Our characterization of single-cell ERK dynamics provides a quantitative foundation for understanding the regulatory structure of this signaling cascade.

Frustrated bistability as a means to engineer oscillations in biological systems

Oscillations play an important physiological role in a variety of biological systems. For example, respiration and carbohydrate synthesis are coupled to the circadian clock in cyanobacteria (Ishiura et al 1998 Science 281 1519) and ultradian oscillations with time periods of a few hours have been observed in immune response (NF-kappaB, Hoffmann et al 2002 Science 298 1241, Neson et al 2004 Science 306 704), apoptosis (p53, Lahav et al 2004 Nat. Genet. 36 53), development (Hes, Hirata et al 2002 Science 298 840) and growth hormone secretion (Plotsky and Vale 1985 Science 230 461, Zeitler et al 1991 Proc. Natl. Acad. Sci. USA 88 8920). Here we discuss how any bistable system can be 'frustrated' to produce oscillations of a desired nature--we use the term frustration, in analogy to frustrated spins in antiferromagnets, to refer to the addition of a negative feedback loop that destabilizes the bistable system. We show that the molecular implementation can use a wide variety of methods ranging from translation regulation, using small non-coding RNAs, to targeted protein modification to transcriptional regulation. We also introduce a simple graphical method for determining whether a particular implementation will produce oscillations. The shape of the resulting oscillations can be readily tuned to produce spiky and asymmetric oscillations--quite different from the shapes produced by synthetic oscillators (Elowitz and Leibler 2000 Nature 403 335, Fung et al 2005 Nature 435 118). The time period and amplitude can also be manipulated and these oscillators are easy to reset or switch on and off using a tunable external input. The mechanism of frustrated bistability could thus prove to be an easily implementable way to synthesize flexible, designable oscillators.

Biological switches and clocks

To introduce this special issue on biological switches and clocks, we review the historical development of mathematical models of bistability and oscillations in chemical reaction networks. In the 1960s and 1970s, these models were limited to well-studied biochemical examples, such as glycolytic oscillations and cyclic AMP signalling. After the molecular genetics revolution of the 1980s, the field of molecular cell biology was thrown wide open to mathematical modellers. We review recent advances in modelling the gene-protein interaction networks that control circadian rhythms, cell cycle progression, signal processing and the design of synthetic gene networks.

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.

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.

Bistable MAP kinase activity: a plausible mechanism contributing to maintenance of late long-term potentiation

Bistability of MAP kinase (MAPK) activity has been suggested to contribute to several cellular processes, including differentiation and long-term synaptic potentiation. A recent model (Markevich NI, Hoek JB, Kholodenko BN. J Cell Biol 164: 353–359, 2004) predicts bistability due to interactions of the kinases and phosphatases in the MAPK pathway, without feedback from MAPK to earlier reactions. Using this model and enzyme concentrations appropriate for neurons, we simulated bistable MAPK activity, but bistability was present only within a relatively narrow range of activity of Raf, the first pathway kinase. Stochastic fluctuations in molecule numbers eliminated bistability for small molecule numbers, such as are expected in the volume of a dendritic spine. However, positive-feedback loops have been posited from MAPK up to Raf activation. One proposed loop in which MAPK directly activates Raf was incorporated into the model. We found that such feedback greatly enhanced the robustness of both stable states of MAPK activity to stochastic fluctuations and to parameter variations. Bistability was robust for molecule numbers plausible for a dendritic spine volume. The upper state of MAPK activity was resistant to inhibition of MEK activation for >1 h, which suggests that inhibitor experiments have not sufficed to rule out a role for persistent MAPK activity in the maintenance of long-term potentiation (LTP). These simulations suggest that persistent MAPK activity and consequent upregulation of translation may contribute to LTP maintenance and to long-term memory. Experiments using a fluorescent MAPK substrate may further test this hypothesis.

Functions of bifans in context of multiple regulatory motifs in signaling networks

Representation of intracellular signaling networks as directed graphs allows for the identification of regulatory motifs. Regulatory motifs are groups of nodes with the same connectivity structure, capable of processing information. The bifan motif, made of two source nodes directly crossregulating two target nodes, is an overrepresented motif in a mammalian cell signaling network and in transcriptional networks. One example of a bifan is the two MAP-kinases, p38, and JNK that phosphorylate and activate the two transcription factors ATF2 and Elk-1. We have used a system of coupled ordinary differential equations to analyze the regulatory capability of this bifan motif by itself, and when it interacts with other motifs such as positive and negative feedback loops. Our results indicate that bifans provide temporal regulation of signal propagation and act as signal sorters, filters, and synchronizers. Bifans that have OR gate configurations show rapid responses whereas AND gate bifans can introduce delays and allow prolongation of signal outputs. Bifans that have AND gates can filter noisy signal inputs. The p38/JNK-ATF2/Elk-1bifan synchronizes the output of activated transcription factors. Synchronization is a robust property of bifans and is exhibited even when the bifan is adjacent to a positive feedback loop. The presence of the bifan promotes the transcription and translation of the dual specificity protein phosphatase MKP-1 that inhibits p38 and JNK thus enabling a negative feedback loop. These results indicate that bifan motifs in cell signaling networks can contribute to signal processing capability both intrinsically and by enabling the functions of other regulatory motifs.

A sequential program of dual phosphorylation of KaiC as a basis for circadian rhythm in cyanobacteria

The circadian phosphorylation cycle of the cyanobacterial clock protein KaiC has been reconstituted in vitro. The phosphorylation profiles of two phosphorylation sites in KaiC, serine 431 (S431) and threonine 432 (T432), revealed that the phosphorylation cycle contained four steps: (i) T432 phosphorylation; (ii) S431 phosphorylation to generate the double-phosphorylated form of KaiC; (iii) T432 dephosphorylation; and (iv) S431 dephosphorylation. We then examined the effects of mutations introduced at one KaiC phosphorylation site on the intact phosphorylation site. We found that the product of each step in the phosphorylation cycle regulated the reaction in the next step, and that double phosphorylation converted KaiC from an autokinase to an autophosphatase, whereas complete dephosphorylation had the opposite effect. These mechanisms serve as the basis for cyanobacterial circadian rhythm generation. We also found that associations among KaiA, KaiB, and KaiC result from S431 phosphorylation, and these interactions would maintain the amplitude of the rhythm.

Thymosin beta 4 suppression of corneal NFkappaB: a potential anti-inflammatory pathway

The purpose of this study was to determine the effect of thymosin beta 4 (Tbeta4) on NFkappaB protein levels, activation, phosphorylation, and nuclear translocation in a model of tumor necrosis factor (TNF)-alpha-mediated corneal inflammation. Transformed and primary (HCET and HCEC) human corneal epithelial cells were stimulated with the pro-inflammatory cytokine TNF-alpha and treated or not with Tbeta4. Nuclear NFkappaB p65 subunit protein levels were assayed using ELISA, and activity was measured by determining NFkappaB binding to consensus oligonucleotides. NFkappaB p65 protein phosphorylation was also measured by ELISA. Nuclear translocation of NFkappaB p65 subunit was assayed by immunofluorescence microscopy. Compared to non-treated controls, Tbeta4 treatment significantly decreased nuclear NFkappaB protein levels, NFkappaB activity and p65 subunit phosphorylation in corneal epithelial cells after TNF-alpha stimulation. In TNF-alpha-stimulated corneal epithelial cells, NFkappaB p65 subunit translocation to the nucleus was observed using immunofluorescence microscopy. In contrast, Tbeta4 blocked nuclear translocation of the NFkappaB p65 subunit in TNF-alpha-stimulated corneal epithelial cells. TNF-alpha initiates cell signaling pathways that converge on the activation of NFkappaB, thus both are known mediators of the inflammatory process. Tbeta4, a protein with diverse cellular functions including wound healing and suppression of inflammation, inhibits the activation of NFkappaB in TNF-alpha-stimulated cells. These results have important clinical implications for the potential role of Tbeta4 as a corneal anti-inflammatory agent.