Quantification of short term signaling by the epidermal growth factor receptor

Hyperdigraph-theoretic analysis of the EGFR signaling network: initial steps leading to GTP:Ras complex formation

We construct an algebraic-combinatorial model of the SOS compartment of the EGFR biochemical network. A Petri net is used to construct an initial representation of the biochemical decision making network, which in turn defines a hyperdigraph. We observe that the linear algebraic structure of each hyperdigraph admits a canonical set of algebraic-combinatorial invariants that correspond to the information flow conservation laws governing a molecular kinetic reaction network. The linear algebraic structure of the hyperdigraph and its sets of invariants can be generalized to define a discrete algebraic-geometric structure, which is referred to as an oriented matroid. Oriented matroids define a polyhedral optimization geometry that is used to determine optimal subpaths that span the nullspace of a set of kinetic chemical reaction equations. Sets of constrained submodular path optimizations on the hyperdigraph are objectively obtained as a spanning tree of minimum cycle paths. This complete set of subcircuits is used to identify the network pinch points and invariant flow subpaths. We demonstrate that this family of minimal circuits also characteristically identifies additional significant biochemical reaction pattern features. We use the SOS Compartment A of the EGFR biochemical pathway to develop and demonstrate the application of our algebraic-combinatorial mathematical modeling methodology.

Reconstruction of cellular signalling networks and analysis of their properties

The study of cellular signalling over the past 20 years and the advent of high-throughput technologies are enabling the reconstruction of large-scale signalling networks. After careful reconstruction of signalling networks, their properties must be described within an integrative framework that accounts for the complexity of the cellular signalling network and that is amenable to quantitative modelling.

Principles behind the multifarious control of signal transduction. ERK phosphorylation and kinase/phosphatase control

General and simple principles are identified that govern signal transduction. The effects of kinase and phosphatase inhibition on a MAP kinase pathway are first examined in silico. Quantitative measures for the control of signal amplitude, duration and integral strength are introduced. We then identify and prove new principles, such that total control on signal amplitude and on final signal strength must amount to zero, and total control on signal duration and on integral signal intensity must equal -1. Collectively, kinases control amplitudes more than duration, whereas phosphatases tend to control both. We illustrate and validate these principles experimentally: (a) a kinase inhibitor affects the amplitude of EGF-induced ERK phosphorylation much more than its duration and (b) a phosphatase inhibitor influences both signal duration and signal amplitude, in particular long after EGF administration. Implications for the cellular decision between growth and differentiation are discussed.

Inference of signaling and gene regulatory networks by steady-state perturbation experiments: structure and accuracy

One of the fundamental problems of cell biology is the understanding of complex regulatory networks. Such networks are ubiquitous in cells and knowledge of their properties is essential for the understanding of cellular behavior. In earlier work (Kholodenko et al. (PNAS 99: 12841), it was shown how the structure of biological networks can be quantified from experimental measurements of steady-state concentrations of key intermediates as a result of perturbations using a simple algorithm called "unravelling". Here, we study the effect of experimental uncertainty on the accuracy of the inferred structure (i.e. whether interactions are excitatory or inhibitory) of the networks determined using the unravelling algorithm. We show that the accuracy of the network structure depends not only on the noise level but on the strength of the interactions within the network. In particular, both very small and very large values of the connection strengths lead to large uncertainty in the inferred network. We describe a powerful geometric tool for the intuitive understanding of the effect of experimental error on the qualitative accuracy of the inferred network. In addition, we show that the use of additional data beyond that needed to minimally constrain the network not only improves the accuracy of the inferred network, but also may allow the detection of situations in which the initial assumptions of unravelling with respect to the network and the perturbations have been violated. Our ideas are illustrated using the mitogen-activated protein kinase (MAPK) signaling network as an example.

The kinetics of FGF-2 binding to heparan sulfate proteoglycans and MAP kinase signaling

Binding of growth factors to specific cell surface receptors is the first step in initiating cell signaling cascades that ultimately result in diverse activities such as proliferation, differentiation, and apoptosis. Dimerization and phosphorylation of tyrosine kinase transmembrane receptors is the typical paradigm for this activation but, for many growth factors, cell surface interactions are not limited to a single receptor type. In particular, heparin-binding growth factors, such as fibroblast growth factor-2 (FGF-2), bind to heparan sulfate proteoglycans (HSPG) on the cell surface and within the extracellular matrix (ECM), and these molecules have been viewed as accessory co-receptors serving to facilitate tyrosine kinase receptor binding. Recent studies, however, have indicated that HSPG can directly participate in signal transduction in response to FGF-2 binding. Thus, in the present study, we used mathematical modeling to examine whether the kinetics of formation of the various FGF-2 bound complexes on the cell surface correlate with the activation of the downstream mediators of FGF-2 response, Erk1/2. We find that FGF-2 binding to its receptor correlates well with Erk1/2 activation and that HSPG can modulate this response through its ability to stabilize these ligand receptor complexes. Moreover, we also observed that FGF-2 binding to HSPG correlates strongly with Erk1/2 activation under conditions where there is a loss of receptor activity, and we demonstrate that the relative amounts of signaling and non-signaling HSPG on the cell surface, as well as the presence of competing HSPG in the ECM, can impact the signal potential via this pathway. Thus, the selective regulation of specific HSPG might provide a mechanism for fine tuned modulation of heparin-binding growth factor signaling in cells where signal intensity and duration could direct cellular response toward growth, migration or differentiation.

Parsing ERK activation reveals quantitatively equivalent contributions from epidermal growth factor receptor and HER2 in human mammary epithelial cells

HER2, a member of the epidermal growth factor receptor (EGFR) tyrosine kinase family, functions as an accessory EGFR signaling component and alters EGFR trafficking by heterodimerization. HER2 overexpression leads to aberrant cell behavior including enhanced proliferation and motility. Here we applied a combination of computational modeling and quantitative experimental studies of the dynamic interactions between EGFR and HER2 and their downstream activation of ERK to understand this complex signaling system. Using cells expressing different levels of HER2 relative to the EGFR, we could separate relative contributions of EGFR and HER2 to signaling amplitude and duration. Based on our model calculations, we demonstrated that, in contrast with previous suggestions in the literature, the intrinsic capabilities of EGFR and HER2 to activate ERK were quantitatively equivalent. We found that HER2-mediated effects on EGFR dimerization and trafficking were sufficient to explain the observed HER2-mediated amplification of epidermal growth factor-induced ERK signaling. Our model suggests that transient amplification of ERK activity by HER2 arises predominantly from the 2-to-1 stoichiometry of receptor kinase to bound ligand in EGFR/HER2 heterodimers compared with the 1-to-1 stoichiometry of the EGFR homodimer, but alterations in receptor trafficking yielding increased EGFR sparing cause the sustained HER2-mediated enhancement of ERK signaling.

Continuous-time identification of gene expression models

One objective of systems biology is to create predictive, quantitative models of the transcriptional regulation networks that govern numerous cellular processes. Gene expression measurements, as provided by microarrays, are commonly used in studies that attempt to infer the regulation underlying these processes. At present, most gene expression models that have been derived from microarray data are based in discrete-time, which have limited applicability to common biological data sets, and may impede the integration of gene expression models with other models of biological processes that are formulated as ordinary differential equations (ODEs). To overcome these difficulties, a continuous-time approach for process identification to identify gene expression models based in ODEs was developed. The approach utilizes the modulating functions method of parameter identification. The method was applied to three simulated systems: (1) a linear gene expression model, (2) an autoregulatory gene expression model, and (3) simulated microarray data from a nonlinear transcriptional network. In general, the approach was well suited for identifying models of gene expression dynamics, capable of accurately identifying parameters for small numbers of data samples in the presence of modest experimental noise. Additionally, numerous insights about gene expression modeling were revealed by the case studies.

Quantitative analysis of signaling networks

The response of biological cells to environmental change is coordinated by protein-based signaling networks. These networks are to be found in both prokaryotes and eukaryotes. In eukaryotes, the signaling networks can be highly complex, some networks comprising of 60 or more proteins. The fundamental motif that has been found in all signaling networks is the protein phosphorylation/dephosphorylation cycle--the cascade cycle. At this time, the computational function of many of the signaling networks is poorly understood. However, it is clear that it is possible to construct a huge variety of control and computational circuits, both analog and digital from combinations of the cascade cycle. In this review, we will summarize the great versatility of the simple cascade cycle as a computational unit and towards the end give two examples, one prokaryotic chemotaxis circuit and the other, the eukaryotic MAPK cascade.

Mathematical modeling reveals threshold mechanism in CD95-induced apoptosis

Mathematical modeling is required for understanding the complex behavior of large signal transduction networks. Previous attempts to model signal transduction pathways were often limited to small systems or based on qualitative data only. Here, we developed a mathematical modeling framework for understanding the complex signaling behavior of CD95(APO-1/Fas)-mediated apoptosis. Defects in the regulation of apoptosis result in serious diseases such as cancer, autoimmunity, and neurodegeneration. During the last decade many of the molecular mechanisms of apoptosis signaling have been examined and elucidated. A systemic understanding of apoptosis is, however, still missing. To address the complexity of apoptotic signaling we subdivided this system into subsystems of different information qualities. A new approach for sensitivity analysis within the mathematical model was key for the identification of critical system parameters and two essential system properties: modularity and robustness. Our model describes the regulation of apoptosis on a systems level and resolves the important question of a threshold mechanism for the regulation of apoptosis.

On the cross-regulation of protein tyrosine phosphatases and receptor tyrosine kinases in intracellular signaling

Intracellular signaling proteins are very often regulated by site-specific phosphorylation. For example, growth factor receptors in eukaryotic cells contain intrinsic tyrosine kinase activity and use inter- and intra-molecular interactions to recruit and orient potential protein substrates for phosphorylation. Equally important in determining the magnitude and kinetics of such a response is protein dephosphorylation, catalysed by phosphatase enzymes. A growing body of evidence indicates that certain protein tyrosine phosphatases (PTPs), like tyrosine kinases, are affected by intermolecular interactions that alter the specific activity or localization of their catalytic domains. Using a detailed kinetic modeling framework, we theoretically explore the regulation of PTPs through their association with receptor tyrosine kinases, as noted for the Src homology 2-domain-containing PTPs, SHP-1 and -2. Receptor-PTP binding, in turn, is expected to influence the phosphorylation pattern of those receptors and proteins they associate with, and we show how PTPs might serve to co- or counter-regulate parallel pathways in a signaling network.

Self-organization of polarized cell signaling via autocrine circuits: computational model analysis

Recent studies have suggested that autocrine signaling through epidermal growth factor receptor (EGFR) might be involved in generating or maintaining an intrinsic polarity in tissue cells, possibly via spatial localization of EGFR-mediated signaling. The difficulty of experimental investigation of autocrine signaling makes especially valuable an application of computational modeling for critical hypotheses about the dynamic operation of the underlying signaling circuits, both intracellular and extracellular. Toward this end, we develop and analyze here a spatially distributed dynamic computational model of autocrine EGFR signaling. Under certain conditions, the model spontaneously evolves into a state wherein sustained signaling is spatially localized on smaller than cell dimension, conferring a polarity to the otherwise nonpolar model cell. Conditions of a sufficiently large rate of autocrine EGFR ligand release and of a sufficiently small exogenous ligand concentration are qualitatively consistent with experimental observations of EGFR-mediated migration. Thus, computational analysis supports the concept that autocrine EGFR signaling circuits could play a role in helping generate and/or maintain an intrinsic cell spatial polarity, possibly related to migration as well as tissue organization. We additionally offer particular suggestions for critical nodes in the EGFR signaling circuits governing this self-organization capability.

Synergistic activation of signalling to extracellular signal-regulated kinases 1 and 2 by epidermal growth factor and 4β-phorbol 12-myristate 13-acetate

Signal transduction pathways are often embedded in complex networks, which result from interactions between pathways and feedback circuitry. In order to understand such networks, qualitative information on which interactions take place and quantitative data on their strength become essential. Here, we have investigated how the multiple interactions between the mitogen-activated protein kinase cascade and protein kinase C (PKC) affect the time profile of extracellular signal-regulated kinase (ERK) phosphorylation upon epidermal growth factor (EGF) stimulation in normal rat kidney fibroblasts. This profile is a major determinant for the cellular response that is evoked. We found that EGF stimulation leads to a biphasic ERK-PP pattern, consisting of an initial peak and a relaxation to a low quasi-steady state-phase. Costimulation with the EGF and PKC activator, 4 beta-phorbol 12-myristate 13-acetate (PMA) resulted in a similar pattern, but the ERK-PP concentration in the quasi-steady state-phase was synergistically higher than after stimulation with either EGF or PMA only. This resulted in prolonged signalling to ERK. PMA increased the EGF concentration sufficient to obtain half-maximum ERK phosphorylation. These data suggest that PKC amplifies EGF-induced signalling to ERK, without increasing its sensitivity to low EGF concentrations. Furthermore, PKC inhibition did not affect the ERK-PP time profile upon EGF stimulation and a cellular phospholipase A2 (cPLA(2)) inhibitor did not decrease the synergistic effect of EGF and PMA. This indicates that the positive feedback loop from ERK to Raf via cPLA(2) and PKC does not contribute significantly to signalling from EGF to ERK in normal rat kidney cells. Taken together, we provide a quantitative description of which reported interactions in this network affect the time profile of ERK phosphorylation.

Intracoronary administration of FGF-2: a computational model of myocardial deposition and retention

This study uses a computational model to characterize the myocardial deposition and retention of basic fibroblast growth factor (FGF-2) at the cellular level after intracoronary (IC) administration of exogenous FGF-2. The model is applied to the in situ conditions present within the myocardium of a dog for which the plasma pharmacokinetics resulting from IC injection of FGF-2 were recorded. Our estimates show that the processes involved in FGF-2 signaling are not diffusion limited; rather, the response time is determined by the reaction time of FGF-2 binding to cell surface receptors. Additionally, the processes of receptor secretion and internalization are found to play crucial roles in the FGF-2 dynamics; future experiments are required to quantify these processes. The model predictions obtained in this study suggest that IC administration of FGF-2 via either a single bolus or repetitive injections causes a transient increase (time scale of hours) in myocardial FGF-2 concentration if the endogenous level of free interstitial FGF-2 is low enough to allow permeation of FGF-2 molecules from the microvascular to the interstitial spaces. The model shows that the majority (64%) of the extracellular FGF-2 ligands are located within the interstitium, and similar fractions are found in the basement membrane and extracellular matrix. Among the FGF-2 molecules found within the interstitium, 2% are free and 98% are bound to interstitial heparan sulfate proteoglycans. These results support the theory of extracellular control of the bioavailability of FGF-2 via dynamic storage of FGF-2 within the basement membrane and extracellular matrix.

The complexity of complexes in signal transduction

Many activities of cells are controlled by cell-surface receptors, which in response to ligands, trigger intracellular signaling reactions that elicit cellular responses. A hallmark of these signaling reactions is the reversible nucleation of multicomponent complexes, which typically begin to assemble when ligand-receptor binding allows an enzyme, often a kinase, to create docking sites for signaling molecules through chemical modifications, such as tyrosine phosphorylation. One function of such docking sites is the co-localization of enzymes with their substrates, which can enhance both enzyme activity and specificity. The directed assembly of complexes can also influence the sensitivity of cellular responses to ligand-receptor binding kinetics and determine whether a cellular response is up- or downregulated in response to a ligand stimulus. The full functional implications of ligand-stimulated complex formation are difficult to discern intuitively. Complex formation is governed by conditional interactions among multivalent signaling molecules and influenced by quantitative properties of both the components in a system and the system itself. Even a simple list of the complexes that can potentially form in response to a ligand stimulus is problematic because of the number of ways signaling molecules can be modified and combined. Here, we review the role of multicomponent complexes in signal transduction and advocate the use of mathematical models that incorporate detail at the level of molecular domains to study this important aspect of cellular signaling.

Model analysis of difference between EGF pathway and FGF pathway

The difference in time course of Ras and mitogen activated protein kinase (MAPK) cascade by different growth factors is considered to be the cause of different cellular responses. We have developed the computer simulation of Ras-MAPK signal transduction pathway containing newly identified negative feedback system, Sprouty, and adaptor molecules. Unexpectedly, negative feedback system did not profoundly affect time course of MAPK activation. We propose the key role of fibroblast growth factor receptor substrate 2 (FRS2) in NGF/FGF pathway for sustained MAPK activation. More Grb2-SOS complexes were recruited to the plasma membrane by binding to membrane-bound FRS2 in FGF pathway than in EGF pathway and caused sustained activation of ERK. The EGF pathway with high concentration of EGF receptor also induced sustained MAPK activation, which is consistent with the results in the PC12 cell overexpressing the EGF receptors. The simulated time courses of FRS2 knock-out cells were consistent with those of the reported experimental results.

Tyr-317 phosphorylation increases Shc structural rigidity and reduces coupling of domain motions remote from the phosphorylation site as revealed by molecular dynamics simulations

Activated receptor tyrosine kinases bind the Shc adaptor protein through its N-terminal phosphotyrosine-binding (PTB) and C-terminal Src homology 2 (SH2) domains. After binding, Shc is phosphorylated within the central collagen-homology (CH) linker region on Tyr-317, a residue remote to both the PTB and SH2 domains. Shc phosphorylation plays a pivotal role in the initiation of mitogenic signaling through the Ras/Raf/MEK/ERK pathway, but it is unclear if Tyr-317 phosphorylation affects Shc-receptor interactions through the PTB and SH2 domains. To investigate the structural impact of Shc phosphorylation, molecular dynamics simulations were carried out using special-purpose Molecular Dynamics Machine-Grape computers. After a 1-nanosecond equilibration, atomic motions in the structures of unphosphorylated Shc and Shc phosphorylated on Tyr-317 were calculated during a 2-nanosecond period. The results reveal larger phosphotyrosine-binding domain fluctuations and more structural flexibility of unphosphorylated Shc compared with phosphorylated Shc. Collective motions between the PTB-SH2, PTB-CH, and CH-SH2 domains were highly correlated only in unphosphorylated Shc. Dramatic changes in domain coupling and structural rigidity, induced by Tyr-317 phosphorylation, may alter Shc function, bringing about marked differences in the association of unphosphorylated and phosphorylated Shc with its numerous partners, including activated membrane receptors.

Importance of input perturbations and stochastic gene expression in the reverse engineering of genetic regulatory networks: insights from an identifiability analysis of an in silico network

Gene expression profiles are an increasingly common data source that can yield insights into the functions of cells at a system-wide level. The present work considers the limitations in information content of gene expression data for reverse engineering regulatory networks. An in silico genetic regulatory network was constructed for this purpose. Using the in silico network, a formal identifiability analysis was performed that considered the accuracy with which the parameters in the network could be estimated using gene expression data and prior structural knowledge (which transcription factors regulate which genes) as a function of the input perturbation and stochastic gene expression. The analysis yielded experimentally relevant results. It was observed that, in addition to prior structural knowledge, prior knowledge of kinetic parameters, particularly mRNA degradation rate constants, was necessary for the network to be identifiable. Also, with the exception of cases where the noise due to stochastic gene expression was high, complex perturbations were more favorable for identifying the network than simple ones. Although the results may be specific to the network considered, the present study provides a framework for posing similar questions in other systems.

Downregulation of cytochromes P450 in growth-stimulated rat hepatocytes: role of c-Myc induction and impaired C/EBP binding to DNA

BACKGROUND/AIMS

Several cytochromes P450 (CYPs) are expressed in differentiated hepatocytes, but downregulated in growth-stimulated cells. We determined the signals involved in CYP downregulation by epidermal growth factor (EGF).

METHODS

Rat hepatocytes were cultured with or without diverse substances for 72 h and EGF for the last 48 h.

RESULTS

EGF increased c-myc mRNA and protein, and decreased CYP mRNAs and proteins; both effects were prevented by two agents blocking c-myc transcription (retinoic acid and DMSO) and two antisense c-myc oligomers. Despite unchanged CCAAT-enhancer binding protein alpha (C/EBPalpha) and increased C/EBPbeta levels, nuclear proteins of EGF-treated cells did not bind to a C/EBP DNA probe in a gel mobility shift assay. This binding was restored when cells were co-treated with both EGF and c-myc antisense oligomers (preventing c-Myc induction). The N-terminal c-Myc domain added to control nuclear extracts prevented C/EBP DNA binding. A monoclonal anti-c-Myc antibody co-immunoprecipitated c-Myc, C/EBPalpha and C/EBPbeta from nuclear extracts. In cells not treated with EGF, an antisense C/EBPalpha oligomer decreased CYP expression.

CONCLUSIONS

EGF overexpresses c-Myc, decreases C/EBP binding to DNA and downregulates CYPs. We suggest that c-Myc may form inactive complexes with C/EBPs, thus decreasing C/EBP-mediated CYP transactivation.

An integrated model of epidermal growth factor receptor trafficking and signal transduction

Endocytic trafficking of many types of receptors can have profound effects on subsequent signaling events. Quantitative models of these processes, however, have usually considered trafficking and signaling independently. Here, we present an integrated model of both the trafficking and signaling pathway of the epidermal growth factor receptor (EGFR) using a probability weighted-dynamic Monte Carlo simulation. Our model consists of hundreds of distinct endocytic compartments and approximately 13,000 reactions/events that occur over a broad spatio-temporal range. By using a realistic multicompartment model, we can investigate the distribution of the receptors among cellular compartments as well as their potential signal transduction characteristics. Our new model also allows the incorporation of physiochemical aspects of ligand-receptor interactions, such as pH-dependent binding in different endosomal compartments. To determine the utility of this approach, we simulated the differential activation of the EGFR by two of its ligands, epidermal growth factor (EGF) and transforming growth factor-alpha (TGF-alpha). Our simulations predict that when EGFR is activated with TGF-alpha, receptor activation is biased toward the cell surface whereas EGF produces a signaling bias toward the endosomal compartment. Experiments confirm these predictions from our model and simulations. Our model accurately predicts the kinetics and extent of receptor downregulation induced by either EGF or TGF-alpha. Our results suggest that receptor trafficking controls the compartmental bias of signal transduction, rather than simply modulating signal magnitude. Our model provides a new approach to evaluating the complex effect of receptor trafficking on signal transduction. Importantly, the stochastic and compartmental nature of the simulation allows these models to be directly tested by high-throughput approaches, such as quantitative image analysis.

A computational model on the modulation of mitogen-activated protein kinase (MAPK) and Akt pathways in heregulin-induced ErbB signalling

ErbB tyrosine kinase receptors mediate mitogenic signal cascade by binding a variety of ligands and recruiting the different cassettes of adaptor proteins. In the present study, we examined heregulin (HRG)-induced signal transduction of ErbB4 receptor and found that the phosphatidylinositol 3'-kinase (PI3K)-Akt pathway negatively regulated the extracellular signal-regulated kinase (ERK) cascade by phosphorylating Raf-1 on Ser(259). As the time-course kinetics of Akt and ERK activities seemed to be transient and complex, we constructed a mathematical simulation model for HRG-induced ErbB4 receptor signalling to explain the dynamics of the regulation mechanism in this signal transduction cascade. The model reflected well the experimental results observed in HRG-induced ErbB4 cells and in other modes of growth hormone-induced cell signalling that involve Raf-Akt cross-talk. The model suggested that HRG signalling is regulated by protein phosphatase 2A as well as Raf-Akt cross-talk, and protein phosphatase 2A modulates the kinase activity in both the PI3K-Akt and MAPK (mitogen-activated protein kinase) pathways.

Structure of the GnRH receptor-stimulated signaling network: insights from genomics

The GnRH receptor influences gene expression in the gonadotrope through activating signaling cascades that modulate transcription factor expression and activity. A longstanding question in neuroendocrinology is how instructions received at the membrane in the form of the pattern of receptor stimulation are processed into specific biosynthetic changes at each gonadotropin promoter. Signal transduction from the membrane to preformed transcription factors relies on recognition of altered conformations. Signal transduction through the layers of the gene network also requires the biosynthesis of new transcription factors. The signal processing of this system depends on its molecular connectivity map and its feedback and feed-forward loops. Review of signal transduction, gene control, and genomic studies provide evidence of key loops that cross between cellular and nuclear compartments. Genomic studies suggest that the signal transduction and gene network form a continuum. We propose that information transfer in the gonadotrope depends on robust signaling modules that serve to integrate events at different time scales across cytoplasmic and nuclear compartments.

Quantitative analysis of HER2-mediated effects on HER2 and epidermal growth factor receptor endocytosis: distribution of homo- and heterodimers depends on relative HER2 levels

Endocytic trafficking plays an important role in the regulation of the epidermal growth factor receptor (EGFR) family. Many cell types express multiple EGFR family members (including EGFR, HER2, HER3, and/or HER4) that interact to form an array of homo- and heterodimers. Differential trafficking of these receptors should strongly affect signaling through this system by changing substrate access and heterodimerization efficiency. Because of the complexity of these dynamic processes, we used a quantitative and computational model to understand their integrated operation. Parameters characterizing EGFR and HER2 interactions were determined using experimental data obtained from mammary epithelial cells constructed to express different levels of HER2, enabling us to estimate receptor-specific internalization rate constants and dimer uncoupling rate constants. Significant novel results obtained from this work are as follows: first, that EGFR homodimerization and EGFR/HER2 heterodimerization occur with comparable affinities; second, that EGFR/HER2 heterodimers traffic as single entities. Furthermore, model predictions of the relationship of HER2 expression levels to consequent distribution of EGFR homodimers and EGFR/HER2 heterodimers suggest that the levels of HER2 found on normal cells are barely at the threshold necessary to drive efficient heterodimerization. Thus, altering HER2 concentrations, either overall or local, could provide an effective mechanism for regulating EGFR/HER2 heterodimerization and may explain why HER2 overexpression found in some cancers has such a profound effect on cell physiology.

Four-dimensional organization of protein kinase signaling cascades: the roles of diffusion, endocytosis and molecular motors

Extracellular signals received by membrane receptors are processed, encoded and transferred to the nucleus via phosphorylation and spatial relocation of protein members of multiple component pathways, such as mitogen activated protein kinase (MAPK) cascades. The receptor-induced membrane recruitment of the cytoplasmic protein SOS results in the activation of the Ras/MAPK cascade. It has been suggested that the membrane recruitment of signaling proteins causes an increase in the diffusion-limited rates. We have recently shown that this increase is too small to be responsible for enhanced signal transduction. Instead we demonstrate that the function of membrane localization is to increase the number (or average lifetime) of complexes between signaling partners. A hallmark of signaling pathways is the spatial separation of activation and deactivation mechanisms; e.g. a protein can be phosphorylated at the cell surface by a membrane-bound kinase and dephosphorylated in the cytosol by a cytosolic phosphatase. Given the measured values of protein diffusion coefficients and of phosphatase and kinase activities, the spatial separation is shown to result in precipitous phospho-protein gradients. When information transfer is hampered by slow protein diffusion and rapid dephosphorylation, phospho-protein trafficking within endocytic vesicles may be an efficient way to deliver messages to physiologically relevant locations. The proposed mechanism explains recent observations that various inhibitors of endocytosis can inhibit MAPK activation. Additional mechanisms facilitating the relay of signals from cell-surface receptors to the nucleus can involve the assembly of protein kinases on a scaffolding protein and active transport of signaling complexes by molecular motors. We also discuss long-range signaling within a cell, such as survival signaling in neurons. We hypothesize that ligand-independent waves of receptor activation or/and traveling waves of phosphorylated kinases emerge to spread the signals over long distances.

Binding to EGF receptor of a laminin-5 EGF-like fragment liberated during MMP-dependent mammary gland involution

Extracellular matrix (ECM) fragments or cryptic sites unmasked by proteinases have been postulated to affect tissue remodeling and cancer progression. Therefore, the elucidation of their identities and functions is of great interest. Here, we show that matrix metalloproteinases (MMPs) generate a domain (DIII) from the ECM macromolecule laminin-5. Binding of a recombinant DIII fragment to epidermal growth factor receptor stimulates downstream signaling (mitogen-activated protein kinase), MMP-2 gene expression, and cell migration. Appearance of this cryptic ECM ligand in remodeling mammary gland coincides with MMP-mediated involution in wild-type mice, but not in tissue inhibitor of metalloproteinase 3 (TIMP-3)-deficient mice, supporting physiological regulation of DIII liberation. These findings indicate that ECM cues may operate via direct stimulation of receptor tyrosine kinases in tissue remodeling, and possibly cancer invasion.

Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell

The physiological responses of cells to external and internal stimuli are governed by genes and proteins interacting in complex networks whose dynamical properties are impossible to understand by intuitive reasoning alone. Recent advances by theoretical biologists have demonstrated that molecular regulatory networks can be accurately modeled in mathematical terms. These models shed light on the design principles of biological control systems and make predictions that have been verified experimentally.

Long-range signal transmission in autocrine relays

Intracellular signaling induced by peptide growth factors can stimulate secretion of these molecules into the extracellular medium. In autocrine and paracrine networks, this can establish a positive feedback loop between ligand binding and ligand release. When coupled to intercellular communication by autocrine ligands, this positive feedback can generate constant-speed traveling waves. To demonstrate that, we propose a mechanistic model of autocrine relay systems. The model is relevant to the physiology of epithelial layers and to a number of in vitro experimental formats. Using asymptotic and numerical tools, we find that traveling waves in autocrine relays exist and have a number of unusual properties, such as an optimal ligand binding strength necessary for the maximal speed of propagation. We compare our results to recent observations of autocrine and paracrine systems and discuss the steps toward experimental tests of our predictions.

Modeling of signaling networks

Biochemical networks, including those containing signaling pathways, display a wide range of regulatory properties. These include the ability to propagate information across different time scales and to function as switches and oscillators. The mechanisms underlying these complex behaviors involve many interacting components and cannot be understood by experiments alone. The development of computational models and the integration of these models with experiments provide valuable insight into these complex systems-level behaviors. Here we review current approaches to the development of computational models of biochemical networks and describe the insights gained from models that integrate experimental data, using three examples that deal with ultrasensitivity, flexible bistability and oscillatory behavior. These types of complex behavior from relatively simple networks highlight the necessity of using theoretical approaches in understanding higher order biological functions.

Untangling the wires: a strategy to trace functional interactions in signaling and gene networks

Emerging technologies have enabled the acquisition of large genomics and proteomics data sets. However, current methodologies for analysis do not permit interpretation of the data in ways that unravel cellular networking. We propose a quantitative method for determining functional interactions in cellular signaling and gene networks. It can be used to explore cell systems at a mechanistic level or applied within a "modular" framework, which dramatically decreases the number of variables to be assayed. This method is based on a mathematical derivation that demonstrates how the topology and strength of network connections can be retrieved from experimentally measured network responses to successive perturbations of all modules. Importantly, our analysis can reveal functional interactions even when the components of the system are not all known. Under these circumstances, some connections retrieved by the analysis will not be direct but correspond to the interaction routes through unidentified elements. The method is tested and illustrated by using computer-generated responses of a modeled mitogen-activated protein kinase cascade and gene network.

Metabolic control in integrated biochemical systems

Traditional analyses of the control and regulation of steady-state concentrations and fluxes assume the activities of the enzymes to be constant. In living cells, a hierarchical control structure connects metabolic pathways to signal-transduction and gene-expression. Consequently, enzyme activities are not generally constant. This would seem to compromise analyses of control and regulation at the metabolic level. Here, we investigate the concept of metabolic quasi-steady state kinetics as a means of applying metabolic control analysis to hierarchical biochemical systems. We discuss four methods that enable the experimental determination of metabolic control coefficients, and demonstrate these by computer simulations. The best method requires extra measurement of enzyme activities, two others are simpler but are less accurate and one method is bound only to work under special conditions. Our results may assist in evaluating the relative importance of transcriptomics and metabolomics for functional genomics.

Interaction of the IP(3)-Ca(2+) and the FGF-MAPK signaling pathways in the Xenopus laevis embryo: a qualitative approach to the mesodermal induction problem

In this work we propose that the animal-vegetal gradient spatial distribution of the IP(3) receptors observed in the Xenopus embryo can effect a uniform FGF inducting input signal, allowing for different modes of transcription of the Xbra gene, producing the differentiation of the cells of the marginal zone. We analyze this hypothesis with a model for the interaction of the calcium signaling system with the MAPK cascade during the FGF mesodermal induction process, consisting of five non-linear coupled differential equations. A numerical treatment of a one- and two-cell system shows that the calcium flux between cells enhances the Raf activity levels, leading to oscillatory behavior. This qualitative result may be of consequence for the expression of the ventralizing characteristics of the FGF inducting signal.

Mathematical models of protein kinase signal transduction

We have developed a mathematical theory that describes the regulation of signaling pathways as a function of a limited number of key parameters. Our analysis includes linear kinase-phosphatase cascades, as well as systems containing feedback interactions, crosstalk with other signaling pathways, and/or scaffolding and G proteins. We find that phosphatases have a more pronounced effect than kinases on the rate and duration of signaling, whereas signal amplitude is controlled primarily by kinases. The simplest model pathways allow amplified signaling only at the expense of slow signal propagation. More complex and realistic pathways can combine high amplification and signaling rates with maintenance of a stable off-state. Our models also explain how different agonists can evoke transient or sustained signaling of the same pathway and provide a rationale for signaling pathway design.

Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors

We present a computational model that offers an integrated quantitative, dynamic, and topological representation of intracellular signal networks, based on known components of epidermal growth factor (EGF) receptor signal pathways. The model provides insight into signal-response relationships between the binding of EGF to its receptor at the cell surface and the activation of downstream proteins in the signaling cascade. It shows that EGF-induced responses are remarkably stable over a 100-fold range of ligand concentration and that the critical parameter in determining signal efficacy is the initial velocity of receptor activation. The predictions of the model agree well with experimental analysis of the effect of EGF on two downstream responses, phosphorylation of ERK-1/2 and expression of the target gene, c-fos.

Autocrine loops with positive feedback enable context-dependent cell signaling

We describe a mechanism for context-dependent cell signaling mediated by autocrine loops with positive feedback. We demonstrate that the composition of the extracellular medium can critically influence the intracellular signaling dynamics induced by extracellular stimuli. Specifically, in the epidermal growth factor receptor (EGFR) system, amplitude and duration of mitogen-activated protein kinase (MAPK) activation are modulated by the positive-feedback loop formed by the EGFR, the Ras-MAPK signaling pathway, and a ligand-releasing protease. The signaling response to a transient input is short-lived when most of the released ligand is lost to the cellular microenvironment by diffusion and/or interaction with an extracellular ligand-binding component. In contrast, the response is prolonged or persistent in a cell that is efficient in recapturing the endogenous ligand. To study functional capabilities of autocrine loops, we have developed a mathematical model that accounts for ligand release, transport, binding, and intracellular signaling. We find that context-dependent signaling arises as a result of dynamic interaction between the parts of an autocrine loop. Using the model, we can directly interpret experimental observations on context-dependent responses of autocrine cells to ionizing radiation. In human carcinoma cells, MAPK signaling patterns induced by a short pulse of ionizing radiation can be transient or sustained, depending on cell type and composition of the extracellular medium. On the basis of our model, we propose that autocrine loops in this, and potentially other, growth factor and cytokine systems may serve as modules for context-dependent cell signaling.

Temperature dependence of the epidermal growth factor receptor signaling network can be accounted for by a kinetic model

Stimulation of isolated hepatocytes with epidermal growth factor (EGF) causes rapid tyrosine phosphorylation of the EGF receptor (EGFR) and adapter/target proteins, which was monitored with 1 and 2 s resolution at 37, 20, and 4 degrees C. The temporal responses detected for multiple signaling proteins involve both transient and sustained phosphorylation patterns, which change dramatically at low temperatures. To account quantitatively for complex responses, we employed a mechanistic kinetic model of the EGFR pathway, formulated in molecular terms as cascades of protein interactions and phosphorylation and dephosphorylation reactions. Assuming differential temperature dependencies for different reaction groups, such as SH2 and PTB domain-mediated interactions, the EGFR kinase, and the phosphatases, good quantitative agreement was obtained between computer-simulated and measured responses. The kinetic model demonstrates that, for each protein-protein interaction, the dissociation rate constant, k(off), strongly decreases at low temperatures, whereas this decline may or may not be accompanied by a large decrease in the k(on) value. Temperature-induced changes in the maximal activities of the reactions catalyzed by the EGFR kinase were moderate, compared to such changes in the V(max) of the phosphatases. However, strong changes in both the V(max) and K(m) for phosphatases resulted in moderate changes in the V(max)/K(m) ratio, comparable to the corresponding changes in EGFR kinase activity, with a single exception for the receptor phosphatase at 4 degrees C. The model suggests a significant decrease in the rates of the EGF receptor dimerization and its dephosphorylation at 4 degrees C, which can be related to the phase transition in the membrane lipids. A combination of high-resolution experimental monitoring and molecular level kinetic modeling made it possible to quantitatively account for the temperature dependence of the integrative signaling responses.

Control analysis for autonomously oscillating biochemical networks

It has hitherto not been possible to analyze the control of oscillatory dynamic cellular processes in other than qualitative ways. The control coefficients, used in metabolic control analyses of steady states, cannot be applied directly to dynamic systems. We here illustrate a way out of this limitation that uses Fourier transforms to convert the time domain into the stationary frequency domain, and then analyses the control of limit cycle oscillations. In addition to the already known summation theorems for frequency and amplitude, we reveal summation theorems that apply to the control of average value, waveform, and phase differences of the oscillations. The approach is made fully operational in an analysis of yeast glycolytic oscillations. It follows an experimental approach, sampling from the model output and using discrete Fourier transforms of this data set. It quantifies the control of various aspects of the oscillations by the external glucose concentration and by various internal molecular processes. We show that the control of various oscillatory properties is distributed over the system enzymes in ways that differ among those properties. The models that are described in this paper can be accessed on http://jjj.biochem.sun.ac.za.

Kick-starting the cell cycle: From growth-factor stimulation to initiation of DNA replication

The essential genes, proteins and associated regulatory networks involved in the entry into the mammalian cell cycle are identified, from activation of growth-factor receptors to intracellular signal transduction pathways that impinge on the cell cycle machinery and ultimately on the initiation of DNA replication. Signaling pathways mediated by the oncoproteins Ras and Myc induce the activation of cyclin-dependent kinases CDK4 and CDK2, and the assembly and firing of pre-replication complexes require a collaboration among E2F, CDK2, and Cdc7 kinase. A proposed core mechanism of the restriction point, the major checkpoint prior to commitment to DNA synthesis, involves cyclin E/CDK2, the phosphatase Cdc25A, and the CDK inhibitor p27Kip1. (c) 2001 American Institute of Physics.

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

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

Suppression of epidermal growth factor-induced phospholipase C activation associated with actin rearrangement in rat hepatocytes in primary culture

Hepatocytes maintained in primary culture for periods of 1 to 24 hours exhibited a rapid decline in epidermal growth factor (EGF)-induced activation of phospholipase C (PLC), as was evident in a loss of EGF-induced inositol 1,4,5-trisphosphate (IP(3)) formation and mobilization of Ca(2+) from intracellular Ca(2+) stores. The loss of PLC activation was not the result of a decrease in EGF receptor or phospholipase C-gamma1 (PLCgamma1) protein levels, nor the result of a loss of tyrosine phosphorylation of these proteins, but was associated with a decrease in EGF-induced translocation of PLCgamma1 to the Triton-insoluble fraction, presumably reflecting binding to the actin cytoskeleton. Disruption of F-actin by treatment of cultured hepatocytes with cytochalasin D recovered the EGF-induced IP(3) formation and Ca(2+) mobilization to the same level and with the same dose-response relationship as was obtained in freshly isolated cells. Analysis of PLCgamma1 colocalization with F-actin by confocal microscopy showed that PLCgamma1 was mostly distributed diffusely in the cytosol, both in freshly plated cells and in cells in culture for 24 hours, despite marked differences in actin structures. EGF stimulation caused a modest redistribution of PLCgamma1 and a detectable increase in colocalization with cortical actin structures in freshly plated cells or in cytochalasin D-treated cells, but in cells that had been maintained and spread in culture only a limited PLCgamma1 relocation was detected to specific actin-structure associated with lamellipodia and membrane ruffles. We conclude that actin cytoskeletal structures can exert negative control over PLCgamma1 activity in hepatocytes and the interaction of the enzyme with specific actin structures dissociates PLCgamma1 tyrosine phosphorylation from activation of its enzymatic activity.

Macromolecular intelligence in microorganisms

Biochemistry and molecular biology have been focusing on the structural, catalytic, and regulatory properties of individual macromolecules from the perspective of clarifying the mechanisms of metabolism and gene expression. Complete genomes of 'primitive' living organisms seem to be substantially larger than necessary for metabolism and gene expression alone. This is in line with the findings of silent phenotypes for supposedly important genes, apparent redundancy of functions, and variegated networks of signal transduction and transcription factors. Here we propose that evolutionary optimization has been much more intensive than to lead to the bare minima necessary for autonomous life. Much more complex organisms prevail. Much of this complexity arises in the nonlinear interactions between cellular macromolecules and in subtle differences between paralogs (isoenzymes). The complexity can only be understood when analyzed quantitatively, for which quantitative experimentation is needed in living systems that are as simple and manipulatable as possible, yet complex in the above sense. We illustrate this for the glutamine synthetase cascade in Escherichia coli. By reviewing recent molecular findings, we show that this cascade is much more complex than necessary for simple regulation of ammonia assimilation. Simulations suggest that the function of this complexity may lie in quasi-intelligent behavior, including conditioning and learning.

Why cytoplasmic signalling proteins should be recruited to cell membranes

It has been suggested that localization of signal-transduction proteins close to the cell membrane causes an increase in their rate of encounter after activation. We maintain that such an increase in the first-encounter rate is too small to be responsible for truly enhanced signal transduction. Instead, the function of membrane localization is to increase the number (or average lifetime) of complexes between cognate signal transduction proteins and hence increase the extent of activation of downstream processes. This is achieved by concentrating the proteins in the small volume of the area just below the plasma membrane. The signal-transduction chain is viewed simply as operating at low default intensity because one of its components is present at a low concentration. The steady signalling level of the chain is enhanced 1000-fold by increasing the concentration of that component. This occurs upon 'piggyback' binding to a membrane protein, such as the activated receptor, initiating the signal-transduction chain. For the effect to occur, the protein translocated to the membrane cannot be free but has to remain organized by being piggyback bound to a receptor, membrane lipid(s) or scaffold. We discuss an important structural constraint imposed by this mechanism on signal transduction proteins that might also account for the presence of adaptor proteins.

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

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

Metabolic control analysis: biological applications and insights

Metabolic control analysis provides a robust mathematical and theoretical framework for describing metabolic and signaling pathways and networks, and for quantifying the controls over these processes. Its application has already shed light on some of the principles underlying the regulation of metabolic pathways, and it is well suited to the analysis of the types of data emerging from genomic studies.