Bistability from double phosphorylation in signal transduction. Kinetic and structural requirements

Previous studies have suggested that positive feedback loops and ultrasensitivity are prerequisites for bistability in covalent modification cascades. However, it was recently shown that bistability and hysteresis can also arise solely from multisite phosphorylation. Here we analytically demonstrate that double phosphorylation of a protein (or other covalent modification) generates bistability only if: (a) the two phosphorylation (or the two dephosphorylation) reactions are catalyzed by the same enzyme; (b) the kinetics operate at least partly in the zero-order region; and (c) the ratio of the catalytic constants of the phosphorylation and dephosphorylation steps in the first modification cycle is less than this ratio in the second cycle. We also show that multisite phosphorylation enlarges the region of kinetic parameter values in which bistability appears, but does not generate multistability. In addition, we conclude that a cascade of phosphorylation/dephosphorylation cycles generates multiple steady states in the absence of feedback or feedforward loops. Our results show that bistable behavior in covalent modification cascades relies not only on the structure and regulatory pattern of feedback/feedforward loops, but also on the kinetic characteristics of their component proteins.     

Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades

Mitogen-activated protein kinase (MAPK) cascades can operate as bistable switches residing in either of two different stable states. MAPK cascades are often embedded in positive feedback loops, which are considered to be a prerequisite for bistable behavior. Here we demonstrate that in the absence of any imposed feedback regulation, bistability and hysteresis can arise solely from a distributive kinetic mechanism of the two-site MAPK phosphorylation and dephosphorylation. Importantly, the reported kinetic properties of the kinase (MEK) and phosphatase (MKP3) of extracellular signal-regulated kinase (ERK) fulfill the essential requirements for generating a bistable switch at a single MAPK cascade level. Likewise, a cycle where multisite phosphorylations are performed by different kinases, but dephosphorylation reactions are catalyzed by the same phosphatase, can also exhibit bistability and hysteresis. Hence, bistability induced by multisite covalent modification may be a widespread mechanism of the control of protein activity.     

Competing docking interactions can bring about bistability in the MAPK cascade

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

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.     

Split Histidine Kinases Enable Ultrasensitivity and Bistability in Two-Component Signaling Networks

Bacteria sense and respond to their environment through signaling cascades generally referred to as two-component signaling networks. These networks comprise histidine kinases and their cognate response regulators. Histidine kinases have a number of biochemical activities: ATP binding, autophosphorylation, the ability to act as a phosphodonor for their response regulators, and in many cases the ability to catalyze the hydrolytic dephosphorylation of their response regulator. Here, we explore the functional role of “split kinases” where the ATP binding and phosphotransfer activities of a conventional histidine kinase are split onto two distinct proteins that form a complex. We find that this unusual configuration can enable ultrasensitivity and bistability in the signal-response relationship of the resulting system. These dynamics are displayed under a wide parameter range but only when specific biochemical requirements are met. We experimentally show that one of these requirements, namely segregation of the phosphatase activity predominantly onto the free form of one of the proteins making up the split kinase, is met in Rhodobacter sphaeroides. These findings indicate split kinases as a bacterial alternative for enabling ultrasensitivity and bistability in signaling networks. Genomic analyses reveal that up 1.7% of all identified histidine kinases have the potential to be split and bifunctional.     

Steady state and (bi-) stability evaluation of simple protease signalling networks

Signal transduction networks are complex, as are their mathematical models. Gaining a deeper understanding requires a system analysis. Important aspects are the number, location and stability of steady states. In particular, bistability has been recognised as an important feature to achieve molecular switching. This paper compares different model structures and analysis methods particularly useful for bistability analysis.The biological applications include proteolytic cascades as, for example, encountered in the apoptotic signalling pathway or in the blood clotting system. We compare three model structures containing zero-order, inhibitor and cooperative ultrasensitive reactions, all known to achieve bistability. The combination of phase plane and bifurcation analysis provides an illustrative and comprehensive understanding of how bistability can be achieved and indicates how robust this behaviour is.Experimentally, some so-called “inactive” components were shown to have a residual activity. This has been mostly ignored in mathematical models. Our analysis reveals that bistability is only mildly affected in the case of zero-order or inhibitor ultrasensitivity. However, the case where bistability is achieved by cooperative ultrasensitivity is severely affected by this perturbation.     

Steady state and (bi-) stability evaluation of simple protease signalling networks

Signal transduction networks are complex, as are their mathematical models. Gaining a deeper understanding requires a system analysis. Important aspects are the number, location and stability of steady states. In particular, bistability has been recognised as an important feature to achieve molecular switching. This paper compares different model structures and analysis methods particularly useful for bistability analysis.

The biological applications include proteolytic cascades as, for example, encountered in the apoptotic signalling pathway or in the blood clotting system. We compare three model structures containing zero-order, inhibitor and cooperative ultrasensitive reactions, all known to achieve bistability. The combination of phase plane and bifurcation analysis provides an illustrative and comprehensive understanding of how bistability can be achieved and indicates how robust this behaviour is.

Experimentally, some so-called “inactive” components were shown to have a residual activity. This has been mostly ignored in mathematical models. Our analysis reveals that bistability is only mildly affected in the case of zero-order or inhibitor ultrasensitivity. However, the case where bistability is achieved by cooperative ultrasensitivity is severely affected by this perturbation.     

Multisite phosphorylation and network dynamics of cyclin-dependent kinase signaling in the eukaryotic cell cycle

Multisite phosphorylation of regulatory proteins has been proposed to underlie ultrasensitive responses required to generate nontrivial dynamics in complex biological signaling networks. We used a random search strategy to analyze the role of multisite phosphorylation of key proteins regulating cyclin-dependent kinase (CDK) activity in a model of the eukaryotic cell cycle. We show that multisite phosphorylation of either CDK, CDC25, wee1, or CDK-activating kinase is sufficient to generate dynamical behaviors including bistability and limit cycles. Moreover, combining multiple feedback loops based on multisite phosphorylation do not destabilize the cell cycle network by inducing complex behavior, but rather increase the overall robustness of the network. In this model we find that bistability is the major dynamical behavior of the CDK signaling network, and that negative feedback converts bistability into limit cycle behavior. We also compare the dynamical behavior of several simplified models of CDK regulation to the fully detailed model. In summary, our findings suggest that multisite phosphorylation of proteins is a critical biological mechanism in generating the essential dynamics and ensuring robust behavior of the cell cycle.     

On the number of steady states in a multiple futile cycle

The multisite phosphorylation-dephosphorylation cycle is a motif repeatedly used in cell signaling. This motif itself can generate a variety of dynamic behaviors like bistability and ultrasensitivity without direct positive feedbacks. In this paper, we study the number of positive steady states of a general multisite phosphorylation–dephosphorylation cycle, and how the number of positive steady states varies by changing the biological parameters. We show analytically that (1) for some parameter ranges, there are at least n + 1 (if n is even) or n (if n is odd) steady states; (2) there never are more than 2n − 1 steady states (in particular, this implies that for n = 2, including single levels of MAPK cascades, there are at most three steady states); (3) for parameters near the standard Michaelis–Menten quasi-steady state conditions, there are at most n + 1 steady states; and (4) for parameters far from the standard Michaelis–Menten quasi-steady state conditions, there is at most one steady state.      

Dynamics of the cell cycle: checkpoints, sizers, and timers

We have developed a generic mathematical model of a cell cycle signaling network in higher eukaryotes that can be used to simulate both the G1/S and G2/M transitions. In our model, the positive feedback facilitated by CDC25 and wee1 causes bistability in cyclin-dependent kinase activity, whereas the negative feedback facilitated by SKP2 or anaphase-promoting-complex turns this bistable behavior into limit cycle behavior. The cell cycle checkpoint is a Hopf bifurcation point. These behaviors are coordinated by growth and division to maintain normal cell cycle and size homeostasis. This model successfully reproduces sizer, timer, and the restriction point features of the eukaryotic cell cycle, in addition to other experimental findings.     

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.     

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.     

Plant mitogen-activated protein kinase signaling cascades

Mitogen-activated protein kinase (MAPK) cascades have emerged as a universal signal transduction mechanism that connects diverse receptors/sensors to cellular and nuclear responses in eukaryotes. Recent studies in plants indicate that MAPK cascades are vital to fundamental physiological functions involved in hormonal responses, cell cycle regulation, abiotic stress signaling, and defense mechanisms. New findings have revealed the complexity and redundancy of the signaling components, the antagonistic nature of distinct pathways, and the use of both positive and negative regulatory mechanisms.     

A quantitative model of the effect of unreplicated DNA on cell cycle progression in frog egg extracts

A critical goal in cell biology is to develop a systems-level perspective of eukaryotic cell cycle controls. Among these controls, a complex signaling network (called ‘checkpoints’) arrests progression through the cell cycle when there is a threat to genomic integrity such as unreplicated or damaged DNA. Understanding the regulatory principles of cell cycle checkpoints is important because loss of checkpoint regulation may be a requisite step on the roadway to cancer. Mathematical modeling has proved to be a useful guide to cell cycle regulation by revealing the importance of bistability, hysteresis and time lags in governing cell cycle transitions and checkpoint mechanisms. In this report, we propose a mathematical model of the frog egg cell cycle including effects of unreplicated DNA on progression into mitosis. By a stepwise approach utilizing parameter estimation tools, we build a model that is grounded in fundamental behaviors of the cell cycle engine (hysteresis and time lags), includes new elements in the signaling network (Myt1 and Chk1 kinases), and fits a large and diverse body of data from the experimental literature. The model provides a validated framework upon which to build additional aspects of the cell cycle checkpoint signaling network, including those control signals in the mammalian cell cycle that are commonly mutated in cancer.     

植物MPK信号通路与信号分子H2O2和NO之间的相互关系

促分裂原活化蛋白激酶(MPK)级联途径是真核细胞中普遍存在且保守的信号传导通路,广泛参与植物生长发育和植物抵抗生物和非生物胁迫的防御反应。过氧化氢(H2O2)和一氧化氮(NO)作为重要的信使分子也广泛参与植物生长发育和防御反应的信号传导。近年来,研究也表明MPK信号通路与信号分子H2O2和NO之间存在着多种复杂的关系。一方面,在一些刺激的信号传递过程中,MPK信号通路参与了信号分子H2O2和NO的产生、清除或其信号的向下传递等过程;另一方面,在有些刺激的信号传递过程中,它们位于不同的信号传递途经中,行使不同的功能。本文就目前植物MPK信号通路与H2O2和NO之间相互关系的研究现状进行了综述和分析,并指出了该研究领域存在的问题。     

PYK2 signaling is required for PDGF-dependent vascular smooth muscle cell proliferation

Aberrant vascular smooth muscle cell (VSMC) growth is associated with many vascular diseases including atherosclerosis, hypertension, and restenosis. Platelet-derived growth factor-BB (PDGF) induces VSMC proliferation through control of cell cycle progression and protein and DNA synthesis. Multiple signaling cascades control VSMC growth, including members of the mitogen-activated protein kinase (MAPK) family as well as phosphatidylinositol 3-kinase (PI3K) and its downstream effector AKT/protein kinase B (PKB). Little is known about how these signals are integrated by mitogens and whether there are common receptor-proximal signaling control points that synchronize the execution of physiological growth functions. The nonreceptor proline-rich tyrosine kinase 2 (PYK2) is activated by a variety of growth factors and G protein receptor agonists in VSMC and lies upstream of both PI3K and MAPK cascades. The present study investigated the role of PYK2 in PDGF signaling in cultured rat aortic VSMC. PYK2 downregulation attenuated PDGF-dependent protein and DNA synthesis, which correlated with inhibition of AKT and extracellular signal-regulated kinases 1 and 2 (ERK1/2) but not p38 MAPK activation. Inhibition of PDGF-dependent protein kinase B (AKT) and ERK1/2 signaling by inhibitors of upstream kinases PI3K and MEK, respectively, as well as downregulation of PYK2 resulted in modulation of the G(1)/S phase of the cell cycle through inhibition of retinoblastoma protein (Rb) phosphorylation and cyclin D(1) expression, as well as p27(Kip) upregulation. Cell division kinase 2 (cdc2) phosphorylation at G(2)/M was also contingent on PDGF-dependent PI3K-AKT and ERK1/2 signaling. These data suggest that PYK2 is an important upstream mediator in PDGF-dependent signaling cascades that regulate VSMC proliferation.     

Conserved cAMP signaling cascades regulate fungal development and virulence

Two well characterized signal transduction cascades regulating fungal development and virulence are the MAP kinase and cAMP signaling cascades. Here we review the current state of knowledge on cAMP signaling cascades in fungi. While the processes regulated by cAMP signaling in fungi are as diverse as the fungi themselves, the components involved in signal transduction are remarkably conserved. Fungal cAMP signaling cascades are also quite versatile, which is apparent from the differential regulation of similar biological processes. In this review we compare and contrast cAMP signaling pathways that regulate development in the budding yeast Saccharomyces cerevisiae, the fission yeast Schizosaccharomyces pombe, and differentiation and virulence in the human pathogen Cryptococcus neoformans and the plant pathogen Ustilago maydis. We also present examples of interaction between the cAMP and MAP kinase signaling cascades in the regulation of fungal development and virulence.