Relaxation oscillations and hierarchy of feedbacks in MAPK signaling.
ABSTRACT: We formulated a computational model for a MAPK signaling cascade downstream of the EGF receptor to investigate how interlinked positive and negative feedback loops process EGF signals into ERK pulses of constant amplitude but dose-dependent duration and frequency. A positive feedback loop involving RAS and SOS, which leads to bistability and allows for switch-like responses to inputs, is nested within a negative feedback loop that encompasses RAS and RAF, MEK, and ERK that inhibits SOS via phosphorylation. This negative feedback, operating on a longer time scale, changes switch-like behavior into oscillations having a period of 1?hour or longer. Two auxiliary negative feedback loops, from ERK to MEK and RAF, placed downstream of the positive feedback, shape the temporal ERK activity profile but are dispensable for oscillations. Thus, the positive feedback introduces a hierarchy among negative feedback loops, such that the effect of a negative feedback depends on its position with respect to the positive feedback loop. Furthermore, a combination of the fast positive feedback involving slow-diffusing membrane components with slower negative feedbacks involving faster diffusing cytoplasmic components leads to local excitation/global inhibition dynamics, which allows the MAPK cascade to transmit paracrine EGF signals into spatially non-uniform ERK activity pulses.
Project description:Cell signaling is the process by which extracellular information is transmitted into the cell to perform useful biological functions. The ERK (extracellular-signal-regulated kinase) signaling controls several cellular processes such as cell growth, proliferation, differentiation and apoptosis. The ERK signaling pathway considered in this work starts with an extracellular stimulus and ends with activated (double phosphorylated) ERK which gets translocated into the nucleus. We model and analyze this complex pathway by decomposing it into three functional subsystems. The first subsystem spans the initial part of the pathway from the extracellular growth factor to the formation of the SOS complex, ShC-Grb2-SOS. The second subsystem includes the activation of Ras which is mediated by the SOS complex. This is followed by the MAPK subsystem (or the Raf-MEK-ERK pathway) which produces the double phosphorylated ERK upon being activated by Ras. Although separate models exist in the literature at the subsystems level, a comprehensive model for the complete system including the important regulatory feedback loops is missing. Our dynamic model combines the existing subsystem models and studies their steady-state and dynamic interactions under feedback. We establish conditions under which bistability and oscillations exist for this important pathway. In particular, we show how the negative and positive feedback loops affect the dynamic characteristics that determine the cellular outcome.
Project description:Ligand-induced homo- and hetero-dimer formation of ErbB receptors results in different biological outcomes irrespective of recruitment and activation of similar effector proteins. Earlier experimental research indicated that cells expressing both EGFR (epidermal growth factor receptor) and the ErbB4 receptor (E1/4 cells) induced E1/4 cell-specific B-Raf activation and higher extracellular signal-regulated kinase (ERK) activation, followed by cellular transformation, than cells solely expressing EGFR (E1 cells) in Chinese hamster ovary (CHO) cells. Since our experimental data revealed the presence of positive feedback by ERK on upstream pathways, it was estimated that the cross-talk/feedback pathway structure of the Raf-MEK-ERK cascade might affect ERK activation dynamics in our cell system. To uncover the regulatory mechanism concerning the ERK dynamics, we used topological models and performed parameter estimation for all candidate structures that possessed ERK-mediated positive feedback regulation of Raf. The structure that reliably reproduced a series of experimental data regarding signal amplitude and duration of the signaling molecules was selected as a solution. We found that the pathway structure is characterized by ERK-mediated positive feedback regulation of B-Raf and B-Raf-mediated negative regulation of Raf-1. Steady-state analysis of the estimated structure indicated that the amplitude of Ras activity might critically affect ERK activity through ERK-B-Raf positive feedback coordination with sustained B-Raf activation in E1/4 cells. However, Rap1 that positively regulates B-Raf activity might be less effective concerning ERK and B-Raf activity. Furthermore, we investigated how such Ras activity in E1/4 cells can be regulated by EGFR/ErbB4 heterodimer-mediated signaling. From a sensitivity analysis of the detailed upstream model for Ras activation, we concluded that Ras activation dynamics is dominated by heterodimer-mediated signaling coordination with a large initial speed of dimerization when the concentration of the ErbB4 receptor is considerably high. Such characteristics of the signaling cause the preferential binding of the Grb2-SOS complex to heterodimer-mediated signaling molecules.
Project description:Son of sevenless (SOS) is a guanine nucleotide exchange factor that regulates cell behavior by activating the small GTPase RAS. Recent <i>in vitro</i> studies have suggested that an interaction between SOS and the GTP-bound active form of RAS generates a positive feedback loop that propagates RAS activation. However, it remains unclear how the multiple domains of SOS contribute to the regulation of the feedback loop in living cells. Here, we observed single molecules of SOS in living cells to analyze the kinetics and dynamics of SOS behavior. The results indicate that the histone fold and Grb2-binding domains of SOS concertedly produce an intermediate state of SOS on the cell surface. The fraction of the intermediated state was reduced in positive feedback mutants, suggesting that the feedback loop functions during the intermediate state. Translocation of RAF, recognizing the active form of RAS, to the cell surface was almost abolished in the positive feedback mutants. Thus, the concerted functions of multiple membrane-associating domains of SOS governed the positive feedback loop, which is crucial for cell fate decision regulated by RAS.
Project description:Epithelial-mesenchymal transition (EMT) is a key event in the generation of invasive tumor cells. A hallmark of EMT is the repression of E-cadherin expression, which is regulated by various signal transduction pathways including extracellular signal-regulated kinase (ERK) and Wnt. These pathways are highly interconnected via multiple coupled feedback loops (CFL). As the function of such coupled feedback regulations is difficult to analyze experimentally, we used a systems biology approach where computational models were designed to predict biological effects that result from the complex interplay of CFLs. Using epidermal growth factor (EGF) and Wnt as input and E-cadherin transcriptional regulation as output, we established an ordinary differential equation model of the ERK and Wnt signaling network containing six feedback links and used extensive computer simulations to analyze the effects of these feedback links in isolation and different combinations. The results show that the feedbacks can generate a rich dynamic behavior leading to various dose-response patterns and have a decisive role in determining network responses to EGF and Wnt. In particular, we made two important findings: first, that coupled positive feedback loops composed of phosphorylation of Raf kinase inhibitor RKIP by ERK and transcriptional repression of RKIP by Snail have an essential role in causing a switch-like behavior of E-cadherin expression; and second, that RKIP expression inhibits EMT progression by preventing E-cadherin suppression. Taken together, our findings provide us with a system-level understanding of how RKIP can regulate EMT progression and may explain why RKIP is downregulated in so many metastatic cancer cells.
Project description:EGF-induced activation of ERK has been extensively studied by both experimental and theoretical approaches. Here, we used a simulation model based mostly on experimentally determined parameters to study the ERK-mediated negative feedback regulation of the Ras guanine nucleotide exchange factor, son of sevenless (SOS). Because SOS1 is phosphorylated at multiple serine residues upon stimulation, we evaluated the role of the multiplicity by building two simulation models, which we termed the decisive and cooperative phosphorylation models. The two models were constrained by the duration of Ras activation and basal phosphorylation level of SOS1. Possible solutions were found only in the decisive model wherein at least three, and probably more than four, phosphorylation sites decisively suppress the SOS activity. Thus, the combination of experimental approaches and the model analysis has suggested an unexpected role of multiple phosphorylations of SOS1 in the negative regulation.
Project description:Chemical inhibition and genetic knockdown of enzymes are not equivalent in cells, but network-level mechanisms that cause discrepancies between knockdown and inhibitor perturbations are not understood. Here we report that enzymes regulated by negative feedback are robust to knockdown but susceptible to inhibition. Using the Raf-MEK-ERK kinase cascade as a model system, we find that ERK activation is resistant to genetic knockdown of MEK but susceptible to a comparable degree of chemical MEK inhibition. We demonstrate that negative feedback from ERK to Raf causes this knockdown-versus-inhibitor discrepancy in vivo. Exhaustive mathematical modeling of three-tiered enzyme cascades suggests that this result is general: negative autoregulation or feedback favors inhibitor potency, whereas positive autoregulation or feedback favors knockdown potency. Our findings provide a rationale for selecting pharmacologic versus genetic perturbations in vivo and point out the dangers of using knockdown approaches in search of drug targets.
Project description:It is well known that noise is inevitable in gene regulatory networks due to the low-copy numbers of molecules and local environmental fluctuations. The prediction of noise effects is a key issue in ensuring reliable transmission of information. Interlinked positive and negative feedback loops are essential signal transduction motifs in biological networks. Positive feedback loops are generally believed to induce a switch-like behavior, whereas negative feedback loops are thought to suppress noise effects. Here, by using the signal sensitivity (susceptibility) and noise amplification to quantify noise propagation, we analyze an abstract model of the Myc/E2F/MiR-17-92 network that is composed of a coupling between the E2F/Myc positive feedback loop and the E2F/Myc/miR-17-92 negative feedback loop. The role of the feedback loop on noise effects is found to depend on the dynamic properties of the system. When the system is in monostability or bistability with high protein concentrations, noise is consistently suppressed. However, the negative feedback loop reduces this suppression ability (or improves the noise propagation) and enhances signal sensitivity. In the case of excitability, bistability, or monostability, noise is enhanced at low protein concentrations. The negative feedback loop reduces this noise enhancement as well as the signal sensitivity. In all cases, the positive feedback loop acts contrary to the negative feedback loop. We also found that increasing the time scale of the protein module or decreasing the noise autocorrelation time can enhance noise suppression; however, the systems sensitivity remains unchanged. Taken together, our results suggest that the negative/positive feedback mechanisms in coupled feedback loop dynamically buffer noise effects rather than only suppressing or amplifying the noise.
Project description:Cell growth critically depends on signalling pathways whose regulation is the focus of intense research. Without utilizing a priori knowledge of the relative importance of pathway components, we have applied in silico computational methods to the EGF-induced MAPK cascade. Specifically, we systematically perturbed the entire parameter space, including initial conditions, using a Monte Carlo approach, and investigate which protein components or kinetic reaction steps contribute to the differentiation of ERK responses. The model, based on previous work by Brightman and Fell (2000), is composed of 28 reactions, 27 protein molecules, and 48 parameters from both mass action and Michaelis-Menten kinetics. Our multi-parametric systems analysis confirms that Raf inactivation is one of the key steps regulating ERK responses to be either transient or sustained. Furthermore, the results of amplitude-differential ERK phosphorylations within the transient case are mainly attributed to the balance between activation and inactivation of Ras while duration-differential ERK responses for the sustained case are, in addition to Ras, markedly affected by dephospho-/phosphorylation of both MEK and ERK. Our sub-module perturbations showed that MEK and ERK's contribution to this differential ERK activation originates from fluctuations in intermediate pathway module components such as Ras and Raf, implicating a cooperative regulatory mode among the key components. The initial protein concentrations of corresponding reactions such as Ras, GAP, and Raf also influence the distinct signalling outputs of ERK activation. We then compare these results with those obtained from a single-parametric perturbation approach using an overall state sensitivity (OSS) analysis. The OSS findings indicate a more pronounced role of ERK's inhibitory feedback effect on catalysing the dissociation of the SOS complex. Both approaches reveal the presence of multiple specific reactions involved in the distinct dynamics of ERK responses and the cell fate decisions they trigger. This work adds a mechanistic insight of the contribution of key pathway components, thus may support the identification of biomarkers for pharmaceutical drug discovery processes.
Project description:Feedback modules, which appear ubiquitously in biological regulations, are often subject to disturbances from the input, leading to fluctuations in the output. Thus, the question becomes how a feedback system can produce a faithful response with a noisy input. We employed multiple time scale analysis, Fluctuation Dissipation Theorem, linear stability, and numerical simulations to investigate a module with one positive feedback loop driven by an external stimulus, and we obtained a critical quantity in noise attenuation, termed as "signed activation time". We then studied the signed activation time for a system of two positive feedback loops, a system of one positive feedback loop and one negative feedback loop, and six other existing biological models consisting of multiple components along with positive and negative feedback loops. An inverse relationship is found between the noise amplification rate and the signed activation time, defined as the difference between the deactivation and activation time scales of the noise-free system, normalized by the frequency of noises presented in the input. Thus, the combination of fast activation and slow deactivation provides the best noise attenuation, and it can be attained in a single positive feedback loop system. An additional positive feedback loop often leads to a marked decrease in activation time, decrease or slight increase of deactivation time and allows larger kinetic rate variations for slow deactivation and fast activation. On the other hand, a negative feedback loop may increase the activation and deactivation times. The negative relationship between the noise amplification rate and the signed activation time also holds for the six other biological models with multiple components and feedback loops. This principle may be applicable to other feedback systems.
Project description:BRAF(V600E) drives tumors by dysregulating ERK signaling. In these tumors, we show that high levels of ERK-dependent negative feedback potently suppress ligand-dependent mitogenic signaling and Ras function. BRAF(V600E) activation is Ras independent and it signals as a RAF-inhibitor-sensitive monomer. RAF inhibitors potently inhibit RAF monomers and ERK signaling, causing relief of ERK-dependent feedback, reactivation of ligand-dependent signal transduction, increased Ras-GTP, and generation of RAF-inhibitor-resistant RAF dimers. This results in a rebound in ERK activity and culminates in a new steady state, wherein ERK signaling is elevated compared to its initial nadir after RAF inhibition. In this state, ERK signaling is RAF inhibitor resistant, and MEK inhibitor sensitive, and combined inhibition results in enhancement of ERK pathway inhibition and antitumor activity.