Biased Agonism as a Mechanism for Differential Signaling by Chemokine Receptors

Chemokines display considerable promiscuity with multiple ligands and receptors shared in common, a phenomenon that is thought to underlie their biochemical “redundancy.” Their receptors are part of a larger seven-transmembrane receptor superfamily, commonly referred to as G protein-coupled receptors, which have been demonstrated to be able to signal with different efficacies to their multiple downstream signaling pathways, a phenomenon referred to as biased agonism. Biased agonism has been primarily reported as a phenomenon of synthetic ligands, and the biologic prevalence and importance of such signaling are unclear. Here, to assess the presence of biased agonism that may underlie differential signaling by chemokines targeting the same receptor, we performed a detailed pharmacologic analysis of a set of chemokine receptors with multiple endogenous ligands using assays for G protein signaling, β-arrestin recruitment, and receptor internalization. We found that chemokines targeting the same receptor can display marked differences in their efficacies for G protein- or β-arrestin-mediated signaling or receptor internalization. This ligand bias correlates with changes in leukocyte migration, consistent with different mechanisms underlying the signaling downstream of these receptors induced by their ligands. These findings demonstrate that biased agonism is a common and likely evolutionarily conserved biological mechanism for generating qualitatively distinct patterns of signaling via the same receptor in response to different endogenous ligands.     

Silencing of ErbB3/ErbB2 Signaling by Immunoglobulin-like Necl-2

ErbB2 and ErbB3, members of the EGF receptor/ErbB family, form a heterodimer upon binding of a ligand, inducing the activation of Rac small G protein and Akt protein kinase for cell movement and survival, respectively. The enhanced ErbB3/ErbB2 signaling causes tumorigenesis, invasion, and metastasis. We found here that the ErbB3/ErbB2 signaling is regulated by immunoglobulin-like Necl-2, which is down-regulated in various cancer cells and serves as a tumor suppressor. The extracellular region of ErbB3, but not ErbB2, interacted in cis with that of Necl-2. This interaction reduced the ligand-induced, ErbB2-catalyzed tyrosine phosphorylation of ErbB3 and inhibited the consequent ErbB3-mediated activation of Rac and Akt, resulting in the inhibition of cancer cell movement and survival. These inhibitory effects of Necl-2 were mediated by the protein-tyrosine phosphatase PTPN13 which interacted with the cytoplasmic tail of Necl-2. We describe here this novel mechanism for silencing of the ErbB3/ErbB2 signaling by Necl-2.ErbB2 and ErbB3 are members of the EGF receptor/ErbB family, which has ErbB1 and ErbB4 as additional members (1). ErbB2 and ErbB3 are also known as HER2/Neu and HER3, respectively. No ligands binding directly to ErbB2 have been identified yet, whereas heregulin (HRG)³-α and -β, also known as neuregulin-1 and -2, respectively, directly bind to ErbB3. ErbB2 and ErbB3 have kinase domains in their cytoplasmic tails, but that of ErbB3 lacks kinase activity. Therefore, the homodimer of ErbB3 formed by binding of HRG does not transduce any intracellular signaling. By contrast, ErbB2 heterophilically interacts in cis with HRG-occupied ErbB3 and phosphorylates nine tyrosine residues of ErbB3, causing recruitment and activation of the p85 subunit of phosphoinositide 3-kinase (PI3K) and the subsequent activation of Rac small G protein and Akt protein kinase (2). The activation of Rac enhances cell movement and that of Akt prevents cell apoptosis (3).ErbB2 serves as an oncogenic protein (4), and amplification of the ErbB2 gene is observed in many types of cancers. For instance, it is amplified in ∼3% of lung cancers, ∼30% of breast cancers, ∼20% of gastric cancers, and ∼60% of ovarian cancers (5). Moreover, mutation of the ErbB2 gene is found in many types of cancers, namely, ∼10% of lung cancers, ∼4% of breast cancers, ∼5% of gastric cancers, and ∼3% of colorectal cancers (6). This gene amplification or mutation causes enhanced signaling for cell movement and survival, eventually resulting in tumorigenesis, invasiveness, and metastasis. On the basis of these properties of ErbB2, it has been recognized as a good target for cancer therapy; indeed, ErbB2-targeting drugs have already been developed and used clinically (7, 8). However, it remains unknown whether ErbB2 is involved in oncogenesis in cancers in which its gene is not amplified or mutated. In addition, it was recently reported that overexpression of ErbB3 is also involved in tumor malignancy (9), but it remains unknown how ErbB3 serves as an oncogenic protein in cancers in which it is not overexpressed.The nectin-like molecule (Necl) family consists of five members, Necl-1, Necl-2, Necl-3, Necl-4, and Necl-5, and comprises a superfamily with the nectin family, which consists of four members, nectin-1, nectin-2, nectin-3, and nectin-4 (10). All members of this superfamily have similar domain structures: they have one extracellular region with three Ig-like loops, one transmembrane segment, and one cytoplasmic tail. We recently found that the extracellular region of Necl-5 directly interacts in cis with that of the platelet-derived growth factor (PDGF) receptor and that this interaction enhances the PDGF-induced cell proliferation and movement (11–14). Necl-5 is up-regulated in many types of cancer cells and causes at least partly enhanced movement and proliferation of cancer cells (11, 12). These earlier findings prompted us to study the potential interaction of other Necls with other growth factor receptors. Consequently, we found here that the extracellular region of Necl-2 directly interacts in cis with that of ErbB3, but not ErbB2, and reduces the HRG-induced signaling pathways of the ErbB3/ErbB2 heterodimer for cell movement and survival.Necl-2 is known by many names: IgSF4a, RA175, SgIGSF, TSLC1, and SynCAM1 (15–19). Necl-2 was directly reported in GenBank^TM in 1998; IgSF4a was identified as a candidate for a tumor suppressor gene in the loss of heterozygosity region of chromosome 11q23.2 (16); RA175 was identified as a gene highly expressed during the neuronal differentiation of embryonic carcinoma cells (19); SgIGSF was identified as a gene expressed in spermatogenic cells during the early stages of spermatogenesis (18); TSLC1 was identified as a tumor suppressor in human non-small cell lung cancer (17); and SynCAM1 was identified as a brain-specific synaptic adhesion molecule (15). In this study, we use the name “Necl-2,” because it was first reported.Necl-2 shows Ca²⁺-independent homophilic cell-cell adhesion activity and Ca²⁺-independent heterophilic cell-cell adhesion activity with other members of the nectin and Necl families, Necl-1 and nectin-3, and another Ig-like molecule with two Ig-like loops, CRTAM (20–22). These cell-cell adhesion activities are mediated by their extracellular regions. Necl-2 is associated with many peripheral membrane proteins through its cytoplasmic tail. The juxtamembrane region of the cytoplasmic tail contains a band 4.1-binding motif and binds the tumor suppressor DAL-1, a band 4.1 family member, which connects Necl-2 to the actin cytoskeleton (23). In addition, the cytoplasmic tail contains a PDZ domain-binding motif in its C-terminal region and binds Pals2, Dlg3/MPP3, and CASK, which are MAGUK subfamily members having an L27 domain (15, 20, 24, 25). However, the exact roles of the binding of these molecules to Necl-2 remain unknown.Necl-2 is widely expressed in various tissues and organs, and abundantly expressed in epithelial cells (20, 26). Its expression is down-regulated in many types of cancer cells owing to hypermethylation of the Necl-2 gene promoter and/or loss of heterozygosity of 11q23.2 (26). Its expression is also undetectable in fibroblasts, such as NIH3T3, Swiss3T3, and L cells (20). Necl-2 has been shown to be a tumor suppressor in human non-small cell lung cancer (17), but it remains unknown how it fulfills this role. The relationship between Necl-2 and the ErbB family remains unknown, either. In addition, the heterophilic interaction of Necl-2 with CRTAM enhances the cytotoxicity of NK cells and the secretion of γ-interferon from CD8⁺ T cells to attack the Necl-2-expressing cells (22, 27). Studies using Necl-2-deficient mice have revealed that Necl-2 in Sertoli cells is an important cell adhesion molecule for Sertoli-spermatid junctions during spermatogenesis (28–30). In the seminiferous tubules of Necl-2-deficient mice, round and elongating spermatids with a distorted shape are generated owing to failure of contact with Sertoli cells, resulting in male-specific infertility. In the present study, we focused on the role of Necl-2 as a tumor suppressor and clarified its mode of action.     

Differential Release of Estradiol from Immobilized Estrogen Receptors by p-Sec-Amylphenol: Evidence for a Functional Microheterogeneity of Estrogen Receptors

Abstract

³H-Estradiol-estrogen receptor complexes were adsorbed on a column of heparin-agarose and subjected to a gradient of increasing concentrations of p-sec-amylphenol. At least five peaks of released ³H-estradiol were observed—demonstrating the existence of subsets of heparin-immobilized receptors with different affinities for estradiol. This finding is presented as further evidence for a functional microheterogeneity among estrogen receptors. The origin of the observed differences in estrogen receptors and possible relevance of the findings to receptor-mediated responses are discussed.     

Differential Activation of Dual Signaling Responses by Human H1 and H2 Histamine Receptors

Abstract

Stimulation of human H₁ and H₂‐histamine receptors (HRs) primarily activates signaling pathways to increase intracellular calcium [Ca²⁺]_i and cyclic AMP (cAMP), respectively. Activation of H₂‐HR in human embryonic kidney (HEK) cells by histamine and dimaprit increases both cAMP formation and [Ca²⁺]_i, as determined by cAMP‐scintillation proximity assays and fluorescence imaging plate reader (FLIPR) assays. In HEK cells expressing relatively high levels of H₂‐HR (B_max = 26 pmol/mg protein), histamine and dimaprit are full agonists in eliciting cAMP responses with pEC₅₀ values of 9.30 and 7.72 that are 1000‐fold more potent than their respective pEC₅₀ values of 6.13 and 4.91 for increasing [Ca²⁺]_i. The agonist potencies decrease for both responses at lower H₂‐HR density (5 pmol/mg protein) and dimaprit exhibits partial agonist behavior for the [Ca²⁺]_i response. The inverse agonists ranitidine and cimetidine more potently inhibit cAMP production in the higher expressing H₂‐HR line. Histamine also activated both signaling pathways via human H₁‐HRs highly expressed (B_max = 17 pmol/mg protein) in HEK cells, with a 1000‐fold greater potency for [Ca²⁺]_i vs. cAMP responses (pEC₅₀ = 7.86 and 4.82, respectively). These studies demonstrate a markedly different potency for activation of multiple signaling pathways by H₁‐ and H₂‐HRs that may contribute to the selectivity of histamine responses in vivo.     

Multiplex Detection of Homo- and Heterodimerization of G Protein-Coupled Receptors by Proximity Biotinylation

Dimerization of G protein-coupled receptors (GPCRs) represents a potential mechanism by which GPCR functions are regulated. Several resonance energy transfer (RET)-based methods have revealed GPCR homo- and heterodimerization. However, interpretation of an increase in FRET efficiency could be attributed to either dimerization/oligomerization events or conformational changes within an already dimerized/oligomerized receptor complex. Furthermore, RET-based methods can only measure pairwise dimerization, and cannot easily achieve multiplex detection. In this study, we applied proximity-based biotinylation for detecting receptor dimerization by utilizing a specific enzyme-substrate pair that are fused to GPCRs. The biotin ligase BirA is fused to CXCR4 and site-specifically biotinylates an acceptor peptide (AP) in the presence of biotin. As a test case for our newly developed assay, we have characterized the homo-dimerization of chemokine receptor CXCR4 and heterodimerization of CXCR4 with CCR2 or CCR5. The degree of biotinylation varies with the amount of GPCR-AP as well as biotinylation time. Using enzyme/substrate receptor pairs and measuring receptor biotinylation, we demonstrate that CXCR4 can homo-dimerize and hetero-dimerize with CCR2 and CCR5. The effect of CXCL12, agonist for CXCR4, was found to decrease surface biotinylation of CXCR4-AP. This effect is due to a combination of CXCR4 endocytosis and stabilization of CXCR4 homodimers. Finally, when CXCR4-AP, CCR2-AP, and CCR5-AP were expressed together, we observed CXCR4-CXCR4 homodimers and CXCR4-CCR2 and CXCR4-CCR5 heterodimers. The newly developed assay opens new opportunity for multiplex detection for GPCR homo- and heterodimerization within the same cellular context.     

Structure-Function Analysis of Nucleolin and ErbB Receptors Interactions

Background

The ErbB receptor tyrosine kinases and nucleolin are major contributors to malignant transformation. Recently we have found that cell-surface ErbB receptors interact with nucleolin via their cytoplasmic tail. Overexpression of ErbB1 and nucleolin leads to receptor phosphorylation, dimerization and anchorage independent growth.

Methodology/Principal Findings

In the present study we explored the regions of nucleolin and ErbB responsible for their interaction. Using mutational analyses, we addressed the structure–function relationship of the interaction between ErbB1 and nucleolin. We identified the ErbB1 nuclear localization domain as nucleolin interacting region. This region is important for nucleolin-associated receptor activation. Notably, though the tyrosine kinase domain is important for nucleolin-associated receptor activation, it is not involved in nucleolin/ErbB interactions. In addition, we demonstrated that the 212 c-terminal portion of nucleolin is imperative for the interaction with ErbB1 and ErbB4. This region of nucleolin is sufficient to induce ErbB1 dimerization, phosphorylation and growth in soft agar.

Conclusions/Significance

The oncogenic potential of ErbB depends on receptor levels and activation. Nucleolin affects ErbB dimerization and activation leading to enhanced cell growth. The C-terminal region of nucleolin and the ErbB1 NLS-domain mediate this interaction. Moreover, when the C-terminal 212 amino acids region of nucleolin is expressed with ErbB1, it can enhance anchorage independent cell growth. Taken together these results offer new insight into the role of ErbB1 and nucleolin interaction in malignant cells.     

Kinase Activator-Receiver Preference in ErbB Heterodimers Is Determined by Intracellular Regions and Is Not Coupled to Extracellular Asymmetry

The EGF receptor (EGFR) family comprises four homologs in humans collectively known as the ErbB or HER proteins. ErbB proteins are receptor tyrosine kinases that become activated when ligands bind to their extracellular regions and promote formation of specific homo- and heterodimers with enhanced tyrosine kinase activity. An essential feature of ErbB activation is formation of an asymmetric kinase dimer in which the C-terminal lobe of one kinase serves as the activator or donor kinase by binding the N-terminal lobe of a receiver or acceptor kinase and stabilizing its active conformation. ErbB extracellular regions are also thought to form active asymmetric dimers in which only one subunit binds ligand. The observation that the unliganded ErbB2 kinase preferentially serves as the activator kinase when paired with EGFR/ErbB1 implied that extracellular asymmetry in ErbB proteins might be coupled to intracellular asymmetry with unliganded partners favoring the activator kinase position. Using cell-based stimulation assays and chimeric ErbB proteins, we show that extracellular asymmetry is not coupled to intracellular asymmetry and that ErbB intracellular regions are sufficient to determine relative kinase activator-receiver orientation. We further show a hierarchy of activator-receiver preferences among ErbB proteins, with EGFR/ErbB1 being the strongest receiver, followed by ErbB2 and then ErbB4, and that cis-phosphorylation of EGFR and ErbB2 appears to be negligible. This hierarchy shapes the nature of signaling responses to different ligands in cells expressing multiple ErbB proteins.     

Differential cytoskeletal association of ErbB1 and ErbB2 during keratinocyte differentiation

ErbB1 and ErbB2 display differential subcellular localization in human skin and cultured keratinocytes. To determine whether ErbB1 and ErbB2 also differ in cytoskeletal binding properties, normal human keratinocytes grown under conditions favoring a basal or differentiated phenotype were repeatedly extracted in a non-ionic detergent buffer. In basaloid keratinocytes, cytoskeletal association of ErbB1 and ErbB2 was limited. ErbB1 ( approximately 5%) was tightly associated with the cytoskeleton, compared to <1% of ErbB2 (p=0.004). After EGF stimulation, activated ErbB1 and ERK associated with the cytoskeleton to a greater extent than did total ErbB1 and total ERK. Association of ErbB2 increased markedly in differentiated keratinocytes, whereas association of ErbB1 was similar in basaloid and differentiated cells. Cytoskeletal association of ErbB2 correlated with plasma membrane localization. These results suggest that ErbB1 and ErbB2 employ different mechanisms of plasma membrane targeting during keratinocyte differentiation, and that cytoskeletal association may facilitate the coupling of activated ErbB1 and ERK.     

Differential Functions of ApoER2 and Very Low Density Lipoprotein Receptor in Reelin Signaling Depend on Differential Sorting of the Receptors

ApoER2 and very low density lipoprotein (VLDL) receptor transmit the Reelin signal into target cells of the central nervous system. To a certain extent, both receptors can compensate for each other, and only the loss of both receptors results in the reeler phenotype, which is characterized by a gross defect in the architecture of laminated brain structures. Nevertheless, both receptors also have specific distinct functions, as corroborated by analyses of the subtle phenotypes displayed in mice lacking either ApoER2 or VLDL receptor. The differences in their function(s), however, have not been defined at the cellular level. Here, using a panel of chimeric receptors, we demonstrate that endocytosis of Reelin and the fate of the individual receptors upon stimulation are linked to their specific sorting to raft versus non-raft domains of the plasma membrane. VLDL receptor residing in the non-raft domain endocytoses and destines Reelin for degradation via the clathrin-coated pit/clathrin-coated vesicle/endosome pathway without being degraded to a significant extent. Binding of Reelin to ApoER2, a resident of rafts, leads to the production of specific receptor fragments with specific functions of their own and to degradation of ApoER2 via lysosomes. These features contribute to a receptor-specific fine tuning of the Reelin signal, leading to a novel model that emphasizes negative feedback loops specifically mediated by ApoER2 and VLDL receptor, respectively.     

Signaling of Ankle Joint Position by Receptors in Different Muscles

Plots were made of multiunit activity versus ankle joint position for receptors in each of the 12 muscles crossing the cat ankle joint, except peroneus tertius, by recording from populations of afferent fibers in muscle nerves. The discharge was measured 15 or 30 sec after terminating the movements that altered the position of the joint. These recordings were dominated by large-spike activity that would be expected to originate mainly from primary spindle endings. Seven of the 12 muscles also cross other joints. Their responses at a given ankle joint position were so altered by changes in the position of the knee or toe joints that they could not reliably signal the position of the ankle joint. As judged from multiunit recording, receptors in each of the five muscles specific to the ankle joint were influenced by more than one axis of ankle joint displacement.

Single-unit recording from dorsal root filaments was used to determine whether primary or secondary spindle receptors in soleus and tibialis anterior could selectively signal one axis of ankle joint rotation. Individual soleus receptors were tested both on the flexion extension axis and with a combined adduction–eversion movement.

For 38 of the 70 soleus receptors examined (54%), firm adduction–eversion produced a level of activity greater than that caused by 10° of flexion, and for 77% the level of activity was greater than that caused by 5° of flexion. For 168 of the 184 tibialis anterior receptors studied (91%), firm abduction inversion produced a level of activity greater than that caused by 10° of extension. Thus few receptors were found that responded exclusively to one axis of rotation.

One way in which the position of the ankle joint could be specified in the face of multiaxial receptor activity is by examining the receptor discharge from more than one muscle. A suggestion for how the nervous system might do this is given in the discussion.     

Proliferation of Colorectal Cancer Is Promoted by Two Signaling Transduction Expression Patterns: ErbB2/ErbB3/AKT and MET/ErbB3/MAPK

One of the recent breakthroughs in cancer research is the identification of activating mutations in various receptor tyrosine kinase(RTK) pathways in many cancers including colorectal cancer(CRC). We hypothesize that, alternative to mutations, overexpression of various oncogenic RTKs may also underpin CRC pathogenesis, and different RTK may couple with distinct downstream signaling pathways in different subtypes of human CRC. By immunohistochemistry, we show here that RTK members ErbB2, ErbB3 and c-Met were in deed differentially overexpressed in colorectal cancer patient samples leading to constitutive activation of RTK signaling pathways. Using ErbB2 specific inhibitor Lapatinib and c-Met specific inhibitor PHA-665752, we further demonstrated that this constitutive activation of RTK signaling is necessary for the survival of colorectal cancer cells. Furthermore, we show that RTK overexpression pattern dictates the use of downstream AKT and/or MAPK pathways. Our data are important additions to current oncogenic mutation models, and further explain the clinical variation in therapeutic responses of colorectal cancer. Our findings advocate for more personalized therapy tailored to individual patients based on their type of RTK expression in addition to their mutation status.     

Toll样受体(TLRs)的信号转导与免疫调节

Toll样受体(Toll-like receptors,TLRs)是进化中比较保守的一个受体家族,至少包括10个成员.TLRs能特异地识别病原相关的分子模式(PAMPs),不仅在激活天然免疫中发挥重要的作用,而且还调节获得性免疫,是连接天然免疫和获得性免疫的桥梁.近年来,TLRs信号转导的研究,特别是在负调控研究领域,进展非常迅速.对TLRs信号通路新进展以及TLRs在抗感染免疫中的作用进行了综述.     

Dysregulation of ErbB Receptor Trafficking and Signaling in Demyelinating Charcot-Marie-Tooth Disease

Charcot-Marie-Tooth (CMT) disease is the most common inherited peripheral neuropathy with the majority of cases involving demyelination of peripheral nerves. The pathogenic mechanisms of demyelinating CMT remain unclear, and no effective therapy currently exists for this disease. The discovery that mutations in different genes can cause a similar phenotype of demyelinating peripheral neuropathy raises the possibility that there may be convergent mechanisms leading to demyelinating CMT pathogenesis. Increasing evidence indicates that ErbB receptor-mediated signaling plays a major role in the control of Schwann cell-axon communication and myelination in the peripheral nervous system. Recent studies reveal that several demyelinating CMT-linked proteins are novel regulators of endocytic trafficking and/or phosphoinositide metabolism that may affect ErbB receptor signaling. Emerging data have begun to suggest that dysregulation of ErbB receptor trafficking and signaling in Schwann cells may represent a common pathogenic mechanism in multiple subtypes of demyelinating CMT. In this review, we focus on the roles of ErbB receptor trafficking and signaling in regulation of peripheral nerve myelination and discuss the emerging evidence supporting the potential involvement of altered ErbB receptor trafficking and signaling in demyelinating CMT pathogenesis and the possibility of modulating these trafficking and signaling processes for treating demyelinating peripheral neuropathy.     

Quantitation of the Effect of ErbB2 on Epidermal Growth Factor Receptor Binding and Dimerization

The epidermal growth factor (EGF) receptor is a member of the ErbB family of receptors that also includes ErbB2, ErbB3, and ErbB4. These receptors form homo- and heterodimers in response to ligand with ErbB2 being the preferred dimerization partner. Here we use (125)I-EGF binding to quantitate the interaction of the EGF receptor with ErbB2. We show that the EGFR/ErbB2 heterodimer binds EGF with a 7-fold higher affinity than the EGFR homodimer. Because it cannot bind a second ligand, the EGFR/ErbB2 heterodimer is not subject to ligand-induced dissociation caused by the negatively cooperative binding of EGF to the second site on the EGFR homodimer. This increases the stability of the heterodimer relative to the homodimer and is associated with enhanced and prolonged EGF receptor autophosphorylation. These effects are independent of the kinase activity of ErbB2 but require back-to-back dimerization of the EGF receptor with ErbB2. Back-to-back dimerization is also required for phosphorylation of ErbB2. These findings provide a molecular explanation for the apparent preference of the EGF receptor for dimerizing with ErbB2 and suggest that the phosphorylation of ErbB2 occurs largely in the context of the EGFR/ErbB2 heterodimer, rather than through lateral phosphorylation of isolated ErbB2 subunits.     

A Model of Cell Biological Signaling Predicts a Phase Transition of Signaling and Provides Mathematical Formulae

A biological signal is transmitted by interactions between signaling molecules in the cell. To date, there have been extensive studies regarding signaling pathways using numerical simulation of kinetic equations that are based on equations of continuity and Fick’s law. To obtain a mathematical formulation of cell signaling, we propose a stability kinetic model of cell biological signaling of a simple two-parameter model based on the kinetics of the diffusion-limiting step. In the present model, the signaling is regulated by the binding of a cofactor, such as ATP. Non-linearity of the kinetics is given by the diffusion fluctuation in the interaction between signaling molecules, which is different from previous works that hypothesized autocatalytic reactions. Numerical simulations showed the presence of a critical concentration of the cofactor beyond which the cell signaling molecule concentration is altered in a chaos-like oscillation with frequency, which is similar to a discontinuous phase transition in physics. Notably, we found that the frequency is given by the logarithm function of the difference of the outside cofactor concentration from the critical concentration. This implies that the outside alteration of the cofactor concentration is transformed into the oscillatory alteration of cell inner signaling. Further, mathematical stability kinetic analysis predicted a discontinuous dynamic phase transition in the critical state at which the cofactor concentration is equivalent to the critical concentration. In conclusion, the present model illustrates a unique feature of cell signaling, and the stability analysis may provide an analytical framework of the cell signaling system and a novel formulation of biological signaling.