Quantification of short term signaling by the epidermal growth factor receptor

Multinomial tau-leaping method for stochastic kinetic simulations

We introduce the multinomial tau-leaping (MtauL) method for general reaction networks with multichannel reactant dependencies. The MtauL method is an extension of the binomial tau-leaping method where efficiency is improved in several ways. First, tau-leaping steps are determined simply and efficiently using a priori information and Poisson distribution-based estimates of expectation values for reaction numbers over a tentative tau-leaping step. Second, networks are partitioned into closed groups of reactions and corresponding reactants in which no group reactant set is found in any other group. Third, product formation is factored into upper-bound estimation of the number of times a particular reaction occurs. Together, these features allow larger time steps where the numbers of reactions occurring simultaneously in a multichannel manner are estimated accurately using a multinomial distribution. Furthermore, we develop a simple procedure that places a specific upper bound on the total reaction number to ensure non-negativity of species populations over a single multiple-reaction step. Using two disparate test case problems involving cellular processes--epidermal growth factor receptor signaling and a lactose operon model--we show that the tau-leaping based methods such as the MtauL algorithm can significantly reduce the number of simulation steps thus increasing the numerical efficiency over the exact stochastic simulation algorithm by orders of magnitude.

Quantitative proteomic assessment of very early cellular signaling events

Technical limitations have prevented proteomic analyses of events occurring less than 30 s after signal initiation. We developed an automated, continuous quench-flow system allowing quantitative proteomic assessment of very early cellular signaling events (qPACE) with a time resolution of 1 s. Using this technique, we determined that autophosphorylation of the epidermal growth factor receptor occurs within 1 s after ligand stimulation and is followed rapidly by phosphorylation of the downstream signaling intermediates Src homologous and collagen-like protein and phospholipase C gamma 1.

Dynamics of biological systems: role of systems biology in medical research

Cellular systems are networks of interacting components that change with time in response to external and internal events. Studying the dynamic behavior of these networks is the basis for an understanding of cellular functions and disease mechanisms. Quantitative time-series data leading to meaningful models can improve our knowledge of human physiology in health and disease, and aid the search for earlier diagnoses, better therapies and a healthier life. The advent of systems biology is about to take the leap into clinical research and medical applications. This review emphasizes the importance of a dynamic view and understanding of cell function. We discuss the potential for computer-aided mathematical modeling of biological systems in medical research with examples from some of the major therapeutic areas: cancer, cardiovascular, diabetic and neurodegenerative medicine.

Increasing the power to detect causal associations by combining genotypic and expression data in segregating populations

To dissect common human diseases such as obesity and diabetes, a systematic approach is needed to study how genes interact with one another, and with genetic and environmental factors, to determine clinical end points or disease phenotypes. Bayesian networks provide a convenient framework for extracting relationships from noisy data and are frequently applied to large-scale data to derive causal relationships among variables of interest. Given the complexity of molecular networks underlying common human disease traits, and the fact that biological networks can change depending on environmental conditions and genetic factors, large datasets, generally involving multiple perturbations (experiments), are required to reconstruct and reliably extract information from these networks. With limited resources, the balance of coverage of multiple perturbations and multiple subjects in a single perturbation needs to be considered in the experimental design. Increasing the number of experiments, or the number of subjects in an experiment, is an expensive and time-consuming way to improve network reconstruction. Integrating multiple types of data from existing subjects might be more efficient. For example, it has recently been demonstrated that combining genotypic and gene expression data in a segregating population leads to improved network reconstruction, which in turn may lead to better predictions of the effects of experimental perturbations on any given gene. Here we simulate data based on networks reconstructed from biological data collected in a segregating mouse population and quantify the improvement in network reconstruction achieved using genotypic and gene expression data, compared with reconstruction using gene expression data alone. We demonstrate that networks reconstructed using the combined genotypic and gene expression data achieve a level of reconstruction accuracy that exceeds networks reconstructed from expression data alone, and that fewer subjects may be required to achieve this superior reconstruction accuracy. We conclude that this integrative genomics approach to reconstructing networks not only leads to more predictive network models, but also may save time and money by decreasing the amount of data that must be generated under any given condition of interest to construct predictive network models.

Complex phenotypes such as common human diseases are caused by variations in DNA in many genes that interact in complex ways with a number of environmental factors. These multifactorial gene and environmental perturbations induce changes in molecular networks that in turn lead to phenotypic changes in the organism under study. The comprehensive monitoring of transcript abundances using gene expression microarrays in different tissues over a large number of individuals in a population can be used to reconstruct molecular networks that underlie higher-order phenotypes such as disease. The cost to generate these large-scale gene activity measurements over large numbers of individuals can be extreme. However, by integrating DNA variation and gene activity data monitored in each individual in a given population of interest, we demonstrate that the power to elucidate molecular networks that drive complex phenotypes can be significantly enhanced, without increasing the sample size. Using a biologically realistic simulation framework, we demonstrate that molecular networks reconstructed using the combined DNA variation and gene activity data are more accurate than molecular networks reconstructed from gene activity data alone, implying that adding DNA variation data might allow us to use fewer subjects to produce molecular networks that better explain complex phenotypes such as disease.

Membrane-permeable calmodulin inhibitors (e.g. W-7/W-13) bind to membranes, changing the electrostatic surface potential: dual effect of W-13 on epidermal growth factor receptor activation

Membrane-permeable calmodulin inhibitors, such as the napthalenesulfonamide derivatives W-7/W-13, trifluoperazine, and calmidazolium, are used widely to investigate the role of calcium/calmodulin (Ca2+/CaM) in living cells. If two chemically different inhibitors (e.g. W-7 and trifluoperazine) produce similar effects, investigators often assume the effects are due to CaM inhibition. Zeta potential measurements, however, show that these amphipathic weak bases bind to phospholipid vesicles at the same concentrations as they inhibit Ca2+/CaM; this suggests that they also bind to the inner leaflet of the plasma membrane, reducing its negative electrostatic surface potential. This change will cause electrostatically bound clusters of basic residues on peripheral (e.g. Src and K-Ras4B) and integral (e.g. epidermal growth factor receptor (EGFR)) proteins to translocate from the membrane to the cytoplasm. We measured inhibitor-mediated translocation of a simple basic peptide corresponding to the calmodulin-binding juxtamembrane region of the EGFR on model membranes; W-7/W-13 causes translocation of this peptide from membrane to solution, suggesting that caution must be exercised when interpreting the results obtained with these inhibitors in living cells. We present evidence that they exert dual effects on autophosphorylation of EGFR; W-13 inhibits epidermal growth factor-dependent EGFR autophosphorylation under different experimental conditions, but in the absence of epidermal growth factor, W-13 stimulates autophosphorylation of the receptor in four different cell types. Our interpretation is that the former effect is due to W-13 inhibition of Ca2+/CaM, but the latter results could be due to binding of W-13 to the plasma membrane.

Thermodynamically feasible kinetic models of reaction networks

The dynamics of biological reaction networks are strongly constrained by thermodynamics. An holistic understanding of their behavior and regulation requires mathematical models that observe these constraints. However, kinetic models may easily violate the constraints imposed by the principle of detailed balance, if no special care is taken. Detailed balance demands that in thermodynamic equilibrium all fluxes vanish. We introduce a thermodynamic-kinetic modeling (TKM) formalism that adapts the concepts of potentials and forces from irreversible thermodynamics to kinetic modeling. In the proposed formalism, the thermokinetic potential of a compound is proportional to its concentration. The proportionality factor is a compound-specific parameter called capacity. The thermokinetic force of a reaction is a function of the potentials. Every reaction has a resistance that is the ratio of thermokinetic force and reaction rate. For mass-action type kinetics, the resistances are constant. Since it relies on the thermodynamic concept of potentials and forces, the TKM formalism structurally observes detailed balance for all values of capacities and resistances. Thus, it provides an easy way to formulate physically feasible, kinetic models of biological reaction networks. The TKM formalism is useful for modeling large biological networks that are subject to many detailed balance relations.

System properties of ErbB receptor signaling for the understanding of cancer progression

An intracellular signal transduction network constitutes an assembled machinery to control the dynamics of kinase-phosphatase cascade and gene expression. Spatio-temporal analyses of the cellular process can explain the biochemical role of the receptor tyrosine kinases in cancer development from a system point of view.

The nature of systems biology

The advent of functional genomics has enabled the molecular biosciences to come a long way towards characterizing the molecular constituents of life. Yet, the challenge for biology overall is to understand how organisms function. By discovering how function arises in dynamic interactions, systems biology addresses the missing links between molecules and physiology. Top-down systems biology identifies molecular interaction networks on the basis of correlated molecular behavior observed in genome-wide "omics" studies. Bottom-up systems biology examines the mechanisms through which functional properties arise in the interactions of known components. Here, we outline the challenges faced by systems biology and discuss limitations of the top-down and bottom-up approaches, which, despite these limitations, have already led to the discovery of mechanisms and principles that underlie cell function.

Mathematical modeling of intracellular signaling pathways

Dynamic modeling and simulation of signal transduction pathways is an important topic in systems biology and is obtaining growing attention from researchers with experimental or theoretical background. Here we review attempts to analyze and model specific signaling systems. We review the structure of recurrent building blocks of signaling pathways and their integration into more comprehensive models, which enables the understanding of complex cellular processes. The variety of mechanisms found and modeling techniques used are illustrated with models of different signaling pathways. Focusing on the close interplay between experimental investigation of pathways and the mathematical representations of cellular dynamics, we discuss challenges and perspectives that emerge in studies of signaling systems.

Systems interface biology

The field of systems biology has attracted the attention of biologists, engineers, mathematicians, physicists, chemists and others in an endeavour to create systems-level understanding of complex biological networks. In particular, systems engineering methods are finding unique opportunities in characterizing the rich behaviour exhibited by biological systems. In the same manner, these new classes of biological problems are motivating novel developments in theoretical systems approaches. Hence, the interface between systems and biology is of mutual benefit to both disciplines.

Quantifying gene network connectivity in silico: scalability and accuracy of a modular approach

Large, complex data sets that are generated from microarray experiments, create a need for systematic analysis techniques to unravel the underlying connectivity of gene regulatory networks. A modular approach, previously proposed by Kholodenko and co-workers, helps to scale down the network complexity into more computationally manageable entities called modules. A functional module includes a gene's mRNA, promoter and resulting products, thus encompassing a large set of interacting states. The essential elements of this approach are described in detail for a three-gene model network and later extended to a ten-gene model network, demonstrating scalability. The network architecture is identified by analysing in silico steady-state changes in the activities of only the module outputs, communicating intermediates, that result from specific perturbations applied to the network modules one at a time. These steady-state changes form the system response matrix, which is used to compute the network connectivity or network interaction map. By employing a known biochemical network, the accuracy of the modular approach and its sensitivity to key assumptions are evaluated.

Systems analysis of circadian time-dependent neuronal epidermal growth factor receptor signaling

BACKGROUND

Identifying the gene regulatory networks governing physiological signal integration remains an important challenge in circadian biology. Epidermal growth factor receptor (EGFR) has been implicated in circadian function and is expressed in the suprachiasmatic nuclei (SCN), the core circadian pacemaker. The transcription networks downstream of EGFR in the SCN are unknown but, by analogy to other SCN inputs, we expect the response to EGFR activation to depend on circadian timing.

RESULTS

We have undertaken a systems-level analysis of EGFR circadian time-dependent signaling in the SCN. We collected gene-expression profiles to study how the SCN response to EGFR activation depends on circadian timing. Mixed-model analysis of variance (ANOVA) was employed to identify genes with circadian time-dependent EGFR regulation. The expression data were integrated with transcription-factor binding predictions through gene group enrichment analyses to generate robust hypotheses about transcription-factors responsible for the circadian phase-dependent EGFR responses.

CONCLUSION

The analysis results suggest that the transcriptional response to EGFR signaling in the SCN may be partly mediated by established transcription-factors regulated via EGFR transcription-factors (AP1, Ets1, C/EBP), transcription-factors involved in circadian clock entrainment (CREB), and by core clock transcription-factors (Ror alpha). Quantitative real-time PCR measurements of several transcription-factor expression levels support a model in which circadian time-dependent EGFR responses are partly achieved by circadian regulation of upstream signaling components. Our study suggests an important role for EGFR signaling in SCN function and provides an example for gaining physiological insights through systems-level analysis.

Depicting combinatorial complexity with the molecular interaction map notation

To help us understand how bioregulatory networks operate, we need a standard notation for diagrams analogous to electronic circuit diagrams. Such diagrams must surmount the difficulties posed by complex patterns of protein modifications and multiprotein complexes. To meet that challenge, we have designed the molecular interaction map (MIM) notation (http://discover.nci.nih.gov/mim/). Here we show the advantages of the MIM notation for three important types of diagrams: (1) explicit diagrams that define specific pathway models for computer simulation; (2) heuristic maps that organize the available information about molecular interactions and encompass the possible processes or pathways; and (3) diagrams of combinatorially complex models. We focus on signaling from the epidermal growth factor receptor family (EGFR, ErbB), a network that reflects the major challenges of representing in a compact manner the combinatorial complexity of multimolecular complexes. By comparing MIMs with other diagrams of this network that have recently been published, we show the utility of the MIM notation. These comparisons may help cell and systems biologists adopt a graphical language that is unambiguous and generally understood.

An integrated agent-mathematical model of the effect of intercellular signalling via the epidermal growth factor receptor on cell proliferation

We have previously developed Epitheliome, a software agent representation of the growth and repair characteristics of epithelial cell populations, where cell behaviour is governed by a number of simple rules. In this paper, we describe how this model has been extended to incorporate an example of a molecular 'mechanism' behind a rule-in this case, how signalling by both endogenous and exogenous ligands of the epidermal growth factor receptor (EGFR) can impact on the proliferation of cell agents. We have developed a mathematical model representing release of endogenous ligand by cells, three-dimensional diffusion of the secreted molecules through a volume of cell culture medium, ligand-receptor binding, and bound receptor internalization and trafficking. Information relating to quantities of molecular species associated with each cell agent is frequently exchanged between the agent and signalling models, and the ratio of bound to free receptors determines cell cycle progression and hence the proliferative behaviour of the cell agents. We have applied this integrated model to examine the effect of plating density on tissue growth via autocrine/paracrine signalling. This predicts that cell growth is dependent on the concentration of exogenous ligand, but where this is limited, then growth becomes dependent on cell density and the availability of endogenous ligand. We have further modified the calcium concentration of the medium to modulate the formation of intercellular bonds between cells and shown that the increased propensity for cells to form colonies in physiological calcium does not result in significantly different patterns of receptor occupancy. In conclusion, our approach demonstrates that by combining agent-based and mathematical modelling paradigms, it is possible to probe the complex feedback relationship between the behaviour of individual cells and their interaction with one another and their environment.

Approaches to biosimulation of cellular processes

Modelling and simulation are at the heart of the rapidly developing field of systems biology. This paper reviews various types of models, simulation methods, and theoretical approaches that are presently being used in the quantitative description of cellular processes. We first describe how molecular interaction networks can be represented by means of stoichiometric, topological and kinetic models. We briefly discuss the formulation of kinetic models using mesoscopic (stochastic) or macroscopic (continuous) approaches, and we go on to describe how detailed models of molecular interaction networks (silicon cells) can be constructed on the basis of experimentally determined kinetic parameters for cellular processes. We show how theory can help in analyzing models by applying control analysis to a recently published silicon cell model. Finally, we review some of the theoretical approaches available to analyse kinetic models and experimental data, respectively.

EGF-ERBB signalling: towards the systems level

Signalling through the ERBB/HER receptors is intricately involved in human cancer and already serves as a target for several cancer drugs. Because of its inherent complexity, it is useful to envision ERBB signalling as a bow-tie-configured, evolvable network, which shares modularity, redundancy and control circuits with robust biological and engineered systems. Because network fragility is an inevitable trade-off of robustness, systems-level understanding is expected to generate therapeutic opportunities to intercept aberrant network activation.

Integrated mechanistic and data-driven modelling for multivariate analysis of signalling pathways

Mathematical models of highly interconnected and multivariate signalling networks provide useful tools to understand these complex systems. However, effective approaches to extracting multivariate regulation information from these models are still lacking. In this study, we propose a data-driven modelling framework to analyse large-scale multivariate datasets generated from mathematical models. We used an ordinary differential equation based model for the Fas apoptotic pathway as an example. The first step in our approach was to cluster simulation outputs generated from models with varied protein initial concentrations. Subsequently, decision tree analysis was applied, in which we used protein concentrations to predict the simulation outcomes. Our results suggest that no single subset of proteins can determine the pathway behaviour. Instead, different subsets of proteins with different concentrations ranges can be important. We also used the resulting decision tree to identify the minimal number of perturbations needed to change pathway behaviours. In conclusion, our framework provides a novel approach to understand the multivariate dependencies among molecules in complex networks, and can potentially be used to identify combinatorial targets for therapeutic interventions.

Systems biology and combination therapy in the quest for clinical efficacy

Combinatorial control of biological processes, in which redundancy and multifunctionality are the norm, fundamentally limits the therapeutic index that can be achieved by even the most potent and highly selective drugs. Thus, it will almost certainly be necessary to use new 'targeted' pharmaceuticals in combinations. Multicomponent drugs are standard in cytotoxic chemotherapy, but their development has required arduous empirical testing. However, experimentally validated numerical models should greatly aid in the formulation of new combination therapies, particularly those tailored to the needs of specific patients. This perspective focuses on opportunities and challenges inherent in the application of mathematical modeling and systems approaches to pharmacology, specifically with respect to the idea of achieving combinatorial selectivity through use of multicomponent drugs.

Rules for modeling signal-transduction systems

Formalized rules for protein-protein interactions have recently been introduced to represent the binding and enzymatic activities of proteins in cellular signaling. Rules encode an understanding of how a system works in terms of the biomolecules in the system and their possible states and interactions. A set of rules can be as easy to read as a diagrammatic interaction map, but unlike most such maps, rules have precise interpretations. Rules can be processed to automatically generate a mathematical or computational model for a system, which enables explanatory and predictive insights into the system's behavior. Rules are independent units of a model specification that facilitate model revision. Instead of changing a large number of equations or lines of code, as may be required in the case of a conventional mathematical model, a protein interaction can be introduced or modified simply by adding or changing a single rule that represents the interaction of interest. Rules can be defined and visualized by using graphs, so no specialized training in mathematics or computer science is necessary to create models or to take advantage of the representational precision of rules. Rules can be encoded in a machine-readable format to enable electronic storage and exchange of models, as well as basic knowledge about protein-protein interactions. Here, we review the motivation for rule-based modeling; applications of the approach; and issues that arise in model specification, simulation, and testing. We also discuss rule visualization and exchange and the software available for rule-based modeling.

Mathematical model of phosphatidylinositol-4,5-bisphosphate hydrolysis mediated by epidermal growth factor receptor generating diacylglycerol

Phosphatidylinositol-4,5-bisphosphate (PIP2) is hydrolyzed in response to the tyrosine phosphorylation of the epidermal growth factor receptor (EGFR) and plays an important role in regulating cell proliferation and differentiation through the generation of second messengers diacylglycerol (DAG) and trisphosphate inositol (IP3) which lead to the activation of protein kinase C (PKC) and increased levels of intracellular calcium, respectively. In the paper, a mathematical model was established to simulate the accumulation of DAG due to PIP2 hydrolysis mediated by EGFR. Molecular mechanisms between DAG, PIP2, EGFR and phosphatidylinositol transfer protein (PITP) were explained successfully, and positive cooperativity which existed between phospholipase C-gamma1 (PLC-gamma1) and PIP2 was also explained. In the model the effects of parameters on simulation of PIP2 hydrolysis were analyzed and the efficacies of some molecular intervention strategies were predicted. To test the coherence between the model and the biological response to epidermal growth factor (EGF) in cells, the levels of DAG and the tyrosine phosphorylation-EGFRs in NIH3T3 mouse embryonic fibroblast (MEF) were determined by biochemical experiments which showed that the accumulation of DAG was a sigmoidal function of phosphorylation-EGFR concentration, and the consistency between the mathematical model and experimental results was confirmed. In brief, this mathematical model provided a new idea for the further study of the dynamic change of biological characteristics in inositol phospholipid hydrolysis, predicting the efficacy of molecular intervention and the relationship between the metabolisms of inositol phospholipid and other signal transduction pathways.

Membrane computing: Brief introduction, recent results and applications

The internal organization and functioning of living cells, as well as their cooperation in tissues and higher order structures, can be a rich source of inspiration for computer science, not fully exploited at the present date. Membrane computing is an answer to this challenge, well developed at the theoretical (mathematical and computability theory) level, already having several applications (via usual computers), but without having yet a bio-lab implementation. After briefly discussing some general issues related to natural computing, this paper provides an informal introduction to membrane computing, focused on the main ideas, the main classes of results and of applications. Then, three recent achievements, of three different types, are briefly presented, with emphasis on the usefulness of membrane computing as a framework for devising models of interest for biological and medical research.

Scaffolding protein Grb2-associated binder 1 sustains epidermal growth factor-induced mitogenic and survival signaling by multiple positive feedback loops

Grb2-associated binder 1 (GAB1) is a scaffold protein involved in numerous interactions that propagate signaling by growth factor and cytokine receptors. Here we explore in silico and validate in vivo the role of GAB1 in the control of mitogenic (Ras/MAPK) and survival (phosphatidylinositol 3-kinase (PI3K)/Akt) signaling stimulated by epidermal growth factor (EGF). We built a comprehensive mechanistic model that allows for reliable predictions of temporal patterns of cellular responses to EGF under diverse perturbations, including different EGF doses, GAB1 suppression, expression of mutant proteins, and pharmacological inhibitors. We show that the temporal dynamics of GAB1 tyrosine phosphorylation is significantly controlled by positive GAB1-PI3K feedback and negative MAPK-GAB1 feedback. Our experimental and computational results demonstrate that the essential function of GAB1 is to enhance PI3K/Akt activation and extend the duration of Ras/MAPK signaling. By amplifying positive interactions between survival and mitogenic pathways, GAB1 plays the critical role in cell proliferation and tumorigenesis.

Cell-signalling dynamics in time and space

The specificity of cellular responses to receptor stimulation is encoded by the spatial and temporal dynamics of downstream signalling networks. Temporal dynamics are coupled to spatial gradients of signalling activities, which guide pivotal intracellular processes and tightly regulate signal propagation across a cell. Computational models provide insights into the complex relationships between the stimuli and the cellular responses, and reveal the mechanisms that are responsible for signal amplification, noise reduction and generation of discontinuous bistable dynamics or oscillations.

Computational modeling of extracellular mechanotransduction

Mechanotransduction may occur through numerous mechanisms, including potentially through autocrine signaling in a dynamically changing extracellular space. We developed a computational model to analyze how alterations in the geometry of an epithelial lateral intercellular space (LIS) affect the concentrations of constitutively shed ligands inside and below the LIS. The model employs the finite element method to solve for the concentration of ligands based on the governing ligand diffusion-convection equations inside and outside of the LIS, and assumes idealized parallel plate geometry and an impermeable tight junction at the apical surface. Using the model, we examined the temporal relationship between geometric changes and ligand concentration, and the dependence of this relationship on system characteristics such as ligand diffusivity, shedding rate, and rate of deformation. Our results reveal how the kinetics of mechanical deformation can be translated into varying rates of ligand accumulation, a potentially important mechanism for cellular discrimination of varying rate-mechanical processes. Furthermore, our results demonstrate that rapid changes in LIS geometry can transiently increase ligand concentrations in underlying media or tissues, suggesting a mechanism for communication of mechanical state between epithelial and subepithelial cells. These results underscore both the plausibility and complexity of the proposed extracellular mechanotransduction mechanism.

Modeling the effects of HER/ErbB1-3 coexpression on receptor dimerization and biological response

The human epidermal growth factor receptor (HER/ErbB) system comprises the epidermal growth factor receptor (EGFR/HER1) and three other homologs, namely HERs 2-4. This receptor system plays a critical role in cell proliferation and differentiation and receptor overexpression has been associated with poor prognosis in cancers of the epithelium. Here, we examine the effect of coexpressing varying levels of HERs 1-3 on the receptor dimerization patterns using a detailed kinetic model for HER/ErbB dimerization and trafficking. Our results indicate that coexpression of EGFR with HER2 or HER3 biases signaling to the cell surface and retards signal downregulation. In addition, simultaneous coexpression of HERs 1-3 leads to an abundance of HER2-HER3 heterodimers, which are known to be potent inducers of cell growth and transformation. Our new approach to use parameter dependence analysis in experimental design reveals that measurements of HER3 phosphorylation and HER2 internalization ratio may prove to be especially useful for the estimation of critical model parameters. Further, we examine the effect of receptor dimerization patterns on biological response using a simple phenomenological model. Results indicate that coexpression of EGFR with HER2 and HER3 at low to moderate levels may enable cells to match the response of a high HER2 expresser.

Computational modelling of the receptor-tyrosine-kinase-activated MAPK pathway

The MAPK (mitogen-activated protein kinase) pathway is one of the most important and intensively studied signalling pathways. It is at the heart of a molecular-signalling network that governs the growth, proliferation, differentiation and survival of many, if not all, cell types. It is de-regulated in various diseases, ranging from cancer to immunological, inflammatory and degenerative syndromes, and thus represents an important drug target. Over recent years, the computational or mathematical modelling of biological systems has become increasingly valuable, and there is now a wide variety of mathematical models of the MAPK pathway which have led to some novel insights and predictions as to how this system functions. In the present review we give an overview of the processes involved in modelling a biological system using the popular approach of ordinary differential equations. Focusing on the MAPK pathway, we introduce the features and functions of the pathway itself before comparing the available models and describing what new biological insights they have led to.

Trading the micro-world of combinatorial complexity for the macro-world of protein interaction domains

Membrane receptors and proteins involved in signal transduction display numerous binding domains and operate as molecular scaffolds generating a variety of parallel reactions and protein complexes. The resulting combinatorial explosion of the number of feasible chemical species and, hence, different states of a network greatly impedes mechanistic modeling of signaling systems. Here we present novel general principles and identify kinetic requirements that allow us to replace a mechanistic picture of all possible micro-states and transitions by a macro-description of states of separate binding sites of network proteins. This domain-oriented approach dramatically reduces computational models of cellular signaling networks by dissecting mechanistic trajectories into the dynamics of macro- and meso-variables. We specify the conditions when the temporal dynamics of micro-states can be exactly or approximately expressed in terms of the product of the relative concentrations of separate domains. We prove that our macro-modeling approach equally applies to signaling systems with low population levels, analyzed by stochastic rather than deterministic equations. Thus, our results greatly facilitate quantitative analysis and computational modeling of multi-protein signaling networks.

A domain-oriented approach to the reduction of combinatorial complexity in signal transduction networks

BACKGROUND

Receptors and scaffold proteins possess a number of distinct domains and bind multiple partners. A common problem in modeling signaling systems arises from a combinatorial explosion of different states generated by feasible molecular species. The number of possible species grows exponentially with the number of different docking sites and can easily reach several millions. Models accounting for this combinatorial variety become impractical for many applications.

RESULTS

Our results show that under realistic assumptions on domain interactions, the dynamics of signaling pathways can be exactly described by reduced, hierarchically structured models. The method presented here provides a rigorous way to model a large class of signaling networks using macro-states (macroscopic quantities such as the levels of occupancy of the binding domains) instead of micro-states (concentrations of individual species). The method is described using generic multidomain proteins and is applied to the molecule LAT.

CONCLUSION

The presented method is a systematic and powerful tool to derive reduced model structures describing the dynamics of multiprotein complex formation accurately.

Cancer: a Systems Biology disease

Cancer research has focused on the identification of molecular differences between cancerous and healthy cells. The emerging picture is overwhelmingly complex. Molecules out of many parallel signal transduction pathways are involved. Their activities appear to be controlled by multiple factors. The action of regulatory circuits, cross-talk between pathways and the non-linear reaction kinetics of biochemical processes complicate the understanding and prediction of the outcome of intracellular signaling. In addition, interactions between tumor and other cell types give rise to a complex supra-cellular communication network. If cancer is such a complex system, how can one ever predict the effect of a mutation in a particular gene on a functionality of the entire system? And, how should one go about identifying drug targets? Here, we argue that one aspect is to recognize, where the essence resides, i.e. recognize cancer as a Systems Biology disease. Then, more cancer biologists could become systems biologists aiming to provide answers to some of the above systemic questions. To this aim, they should integrate the available knowledge stemming from quantitative experimental results through mathematical models. Models that have contributed to the understanding of complex biological systems are discussed. We show that the architecture of a signaling network is important for determining the site at which an oncologist should intervene. Finally, we discuss the possibility of applying network-based drug design to cancer treatment and how rationalized therapies, such as the application of kinase inhibitors, may benefit from Systems Biology.

Computational processing and error reduction strategies for standardized quantitative data in biological networks

High-quality quantitative data generated under standardized conditions is critical for understanding dynamic cellular processes. We report strategies for error reduction, and algorithms for automated data processing and for establishing the widely used techniques of immunoprecipitation and immunoblotting as highly precise methods for the quantification of protein levels and modifications. To determine the stoichiometry of cellular components and to ensure comparability of experiments, relative signals are converted to absolute values. A major source for errors in blotting techniques are inhomogeneities of the gel and the transfer procedure leading to correlated errors. These correlations are prevented by randomized gel loading, which significantly reduces standard deviations. Further error reduction is achieved by using housekeeping proteins as normalizers or by adding purified proteins in immunoprecipitations as calibrators in combination with criteria-based normalization. Additionally, we developed a computational tool for automated normalization, validation and integration of data derived from multiple immunoblots. In this way, large sets of quantitative data for dynamic pathway modeling can be generated, enabling the identification of systems properties and the prediction of targets for efficient intervention.

Towards building the silicon cell: a modular approach

Systems Biology aims to understand quantitatively how properties of biological systems can be understood as functions of the characteristics of, and interactions between their macromolecular components. Whereas, traditional biochemistry focused on isolation and characterization of cellular components, the challenge for Systems Biology lies in integration of this knowledge and the knowledge about molecular interactions. Computer models play an important role in this integration. We here discuss an approach with which we aim to link kinetic models on small parts of metabolism together, so as to form detailed kinetic models of larger chunks of metabolism, and ultimately of the entire living cell. Specifically, we will discuss techniques that can be used to model a sub-network in isolation of a larger network of which it is a part, while still maintaining the dynamics of the larger complete network. We will start by outlining the JWS online system, the silicon cell project, and the type of models we propose. JWS online is a model repository, which can be used for the storage, simulation and analysis of kinetic models. We advocate to integrate a top-down approach, where measurements on the complete system are used to derive fluxes in a detailed structural model, with a bottom-up approach, consisting of the integration of molecular mechanism-based detailed kinetic models into the structural model.

A network model of early events in epidermal growth factor receptor signaling that accounts for combinatorial complexity

We consider a model of early events in signaling by the epidermal growth factor (EGF) receptor (EGFR). The model includes EGF, EGFR, the adapter proteins Grb2 and Shc, and the guanine nucleotide exchange factor Sos, which is activated through EGF-induced formation of EGFR-Grb2-Sos and EGFR-Shc-Grb2-Sos assemblies at the plasma membrane. The protein interactions involved in signaling can potentially generate a diversity of protein complexes and phosphoforms; however, this diversity has been largely ignored in models of EGFR signaling. Here, we develop a model that accounts more fully for potential molecular diversity by specifying rules for protein interactions and then using these rules to generate a reaction network that includes all chemical species and reactions implied by the protein interactions. We obtain a model that predicts the dynamics of 356 molecular species, which are connected through 3749 unidirectional reactions. This network model is compared with a previously developed model that includes only 18 chemical species but incorporates the same scope of protein interactions. The predictions of this model are reproduced by the network model, which also yields new predictions. For example, the network model predicts distinct temporal patterns of autophosphorylation for different tyrosine residues of EGFR. A comparison of the two models suggests experiments that could lead to mechanistic insights about competition among adapter proteins for EGFR binding sites and the role of EGFR monomers in signal transduction.

Dynamic characteristics of transient responses

Transient responses of signaling molecules are seen in a wide variety of cellular processes that are mediated by distinct molecular mechanisms. Although transient responses might intuitively be thought to depend on the absolute concentration of growth factors or the intensity of stimulation, we here introduce that some transient responses are prompted by temporal rate of increase of stimulation, rather than intensity of stimulation, by three independent mechanisms. These include the Ras system with fast activation and slow inactivation, the ERK-dependent negative feedback loop system, and the receptor degradation system, all of which can be commonly seen in various signaling networks. In addition, we show the distinct transient and steady state characteristics of these systems.

Control of MAPK signalling: from complexity to what really matters

Oncogenesis results from changes in kinetics or in abundance of proteins in signal transduction networks. Recently, it was shown that control of signalling cannot reside in a single gene product, and might well be dispersed over many components. Which of the reactions in these complex networks are most important, and how can the existing molecular information be used to understand why particular genes are oncogenes whereas others are not? We implement a new method to help address such questions. We apply control analysis to a detailed kinetic model of the epidermal growth factor-induced mitogen-activated protein kinase network. We determine the control of each reaction with respect to three biologically relevant characteristics of the output of this network: the amplitude, duration and integrated output of the transient phosphorylation of extracellular signal-regulated kinase (ERK). We confirm that control is distributed, but far from randomly: a small proportion of reactions substantially control signalling. In particular, the activity of Raf is in control of all characteristics of the transient profile of ERK phosphorylation, which may clarify why Raf is an oncogene. Most reactions that really matter for one signalling characteristic are also important for the other characteristics. Our analysis also predicts the effects of mutations and changes in gene expression.

A mathematical model of combination therapy using the EGFR signaling network

An increasing awareness of the significance of abnormal signal transduction in tumors and the concomitant development of target-based drugs to selectively modulate aberrantly-activated signaling pathways has given rise to a variety of promising new strategies in cancer treatment. This paper uses mathematical modeling to investigate a novel type of combination therapy in which multiple nodes in a signaling cascade are targeted simultaneously with selective inhibitors, pursuing the hypothesis that such an approach may induce the desired signal attenuation with lower doses of the necessary agents than when one node is targeted in isolation. A mathematical model is presented which builds upon previous theoretical work on EGFR signaling, simulating the effect of administering multiple kinase inhibitors in various combinations. The model demonstrates that attenuation of biochemical signals is significantly enhanced when multiple upstream processes are inhibited, in comparison with the inhibition of a single upstream process. Moreover, this enhanced attenuation is most pronounced in signals downstream of serially-connected target points. In addition, the inhibition of serially-connected processes appears to have a supra-additive (synergistic) effect on the attenuation of downstream signals, owing to the highly non-linear relationships between network parameters and signals.

An electrostatic engine model for autoinhibition and activation of the epidermal growth factor receptor (EGFR/ErbB) family

We propose a new mechanism to explain autoinhibition of the epidermal growth factor receptor (EGFR/ErbB) family of receptor tyrosine kinases based on a structural model that postulates both their juxtamembrane and protein tyrosine kinase domains bind electrostatically to acidic lipids in the plasma membrane, restricting access of the kinase domain to substrate tyrosines. Ligand-induced dimerization promotes partial trans autophosphorylation of ErbB1, leading to a rapid rise in intracellular [Ca²⁺] that can activate calmodulin. We postulate the Ca²⁺/calmodulin complex binds rapidly to residues 645–660 of the juxtamembrane domain, reversing its net charge from +8 to −8 and repelling it from the negatively charged inner leaflet of the membrane. The repulsion has two consequences: it releases electrostatically sequestered phosphatidylinositol 4,5-bisphosphate (PIP₂), and it disengages the kinase domain from the membrane, allowing it to become fully active and phosphorylate an adjacent ErbB molecule or other substrate. We tested various aspects of the model by measuring ErbB juxtamembrane peptide binding to phospholipid vesicles using both a centrifugation assay and fluorescence correlation spectroscopy; analyzing the kinetics of interactions between ErbB peptides, membranes, and Ca²⁺/calmodulin using fluorescence stop flow; assessing ErbB1 activation in Cos1 cells; measuring fluorescence resonance energy transfer between ErbB peptides and PIP₂; and making theoretical electrostatic calculations on atomic models of membranes and ErbB juxtamembrane and kinase domains.

The multifarious short-term regulation of ammonium assimilation of Escherichia coli: dissection using an in silico replica

Ammonium assimilation in Escherichia coli is regulated through multiple mechanisms (metabolic, signal transduction leading to covalent modification, transcription, and translation), which (in-)directly affect the activities of its two ammonium-assimilating enzymes, i.e. glutamine synthetase (GS) and glutamate dehydrogenase (GDH). Much is known about the kinetic properties of the components of the regulatory network that these enzymes are part of, but the ways in which, and the extents to which the network leads to subtle and quasi-intelligent regulation are unappreciated. To determine whether our present knowledge of the interactions between and the kinetic properties of the components of this network is complete - to the extent that when integrated in a kinetic model it suffices to calculate observed physiological behaviour - we now construct a kinetic model of this network, based on all of the kinetic data on the components that is available in the literature. We use this model to analyse regulation of ammonium assimilation at various carbon statuses for cells that have adapted to low and high ammonium concentrations. We show how a sudden increase in ammonium availability brings about a rapid redirection of the ammonium assimilation flux from GS/glutamate synthase (GOGAT) to GDH. The extent of redistribution depends on the nitrogen and carbon status of the cell. We develop a method to quantify the relative importance of the various regulators in the network. We find the importance is shared among regulators. We confirm that the adenylylation state of GS is the major regulator but that a total of 40% of the regulation is mediated by ADP (22%), glutamate (10%), glutamine (7%) and ATP (1%). The total steady-state ammonium assimilation flux is remarkably robust against changes in the ammonium concentration, but the fluxes through GS and GDH are completely nonrobust. Gene expression of GOGAT above a threshold value makes expression of GS under ammonium-limited conditions, and of GDH under glucose-limited conditions, sufficient for ammonium assimilation.

The Silicon Cell initiative: working towards a detailed kinetic description at the cellular level

The Silicon Cell initiative aims to understand cellular systems on the basis of the characteristics of their components. As a tool to achieve this, detailed kinetic models at the network reaction level are being constructed. Such detailed kinetic models are extremely useful for medical and biotechnological applications and form strong tools for fundamental studies. Several recently constructed detailed kinetic models on metabolism (glycolysis), signal transduction (EGF receptor), and the eukaryotic cell cycle (Saccharomyces cerevisiae) have been used to exemplify the Silicon Cell project. These models are stored and made accessible via the JWS Online Cellular Systems Modeling project, a web-based repository of kinetic models. Using a web-browser the models can be interrogated via a user-friendly graphical interface. The goal of the two projects is to combine models on parts of cellular systems and ultimately to construct detailed kinetic models at the cellular level.

Signaling through receptors and scaffolds: independent interactions reduce combinatorial complexity

After activation, many receptors and their adaptor proteins act as scaffolds displaying numerous docking sites and engaging multiple targets. The consequent assemblage of a variety of protein complexes results in a combinatorial increase in the number of feasible molecular species presenting different states of a receptor-scaffold signaling module. Tens of thousands of such microstates emerge even for the initial signal propagation events, greatly impeding a quantitative analysis of networks. Here, we demonstrate that the assumption of independence of molecular events occurring at distinct sites enables us to approximate a mechanistic picture of all possible microstates by a macrodescription of states of separate domains, i.e., macrostates that correspond to experimentally verifiable variables. This analysis dissects a highly branched network into interacting pathways originated by protein complexes assembled on different sites of receptors and scaffolds. We specify when the temporal dynamics of any given microstate can be expressed using the product of the relative concentrations of individual sites. The methods presented here are equally applicable to deterministic and stochastic calculations of the temporal dynamics. Our domain-oriented approach drastically reduces the number of states, processes, and kinetic parameters to be considered for quantification of complex signaling networks that propagate distinct physiological responses.

A comprehensive pathway map of epidermal growth factor receptor signaling

The epidermal growth factor receptor (EGFR) signaling pathway is one of the most important pathways that regulate growth, survival, proliferation, and differentiation in mammalian cells. Reflecting this importance, it is one of the best-investigated signaling systems, both experimentally and computationally, and several computational models have been developed for dynamic analysis. A map of molecular interactions of the EGFR signaling system is a valuable resource for research in this area. In this paper, we present a comprehensive pathway map of EGFR signaling and other related pathways. The map reveals that the overall architecture of the pathway is a bow-tie (or hourglass) structure with several feedback loops. The map is created using CellDesigner software that enables us to graphically represent interactions using a well-defined and consistent graphical notation, and to store it in Systems Biology Markup Language (SBML).

CADLIVE dynamic simulator: direct link of biochemical networks to dynamic models

We have developed the CADLIVE (Computer-Aided Design of LIVing systEms) Simulator that provided a rule-based automatic way to convert biochemical network maps into dynamic models, which enables simulating their dynamics without going through all of the reactions down to the details of exact kinetic parameters. The simulator supports the biochemical reaction maps that are generated by the previously developed GUI editor. Notice that the part of the GUI editor had been previously published, but, as yet, not the simulator. To directly link biochemical network maps to dynamic simulation, we have created the strategy of three layers and two stages with the efficient conversion rules in an XML representation. This strategy divides a molecular network into three layers, i.e., gene, protein, and metabolic layers, and partitions the conversion process into two stages. Once a biochemical map is provided, CADLIVE automatically builds a mathematical model, thereby facilitating one to simulate and analyze it. In order to demonstrate the feasibility of CADLIVE, we analyzed the Escherichia coli nitrogen-assimilation system (64 equations with 64 variables) that consists of multiple and complicated negative and positive feedback loops. CADLIVE predicted that the glnK gene is responsible for hysteresis or reversibility of nitrogen-related (Ntr) gene expression with respect to the ammonia concentration, supporting the experimental observation of the runaway expression of the Ntr genes.

Cell Stimulus and Lysis in a Microfluidic Device with Segmented Gas−Liquid Flow

We describe a microfluidic device with rapid stimulus and lysis of mammalian cells for resolving fast transient responses in cell signaling networks. The device uses segmented gas-liquid flow to enhance mixing and has integrated thermoelectric heaters and coolers to control the temperature during cell stimulus and lysis. Potential negative effects of segmented flow on cell responses are investigated in three different cell types, with no morphological changes and no activation of the cell stress-sensitive mitogen activated protein kinases observed. Jurkat E6-1 cells are stimulated in the device using alpha-CD3, and the resulting activations of ERK and JNK are presented for different time points. Stimulation of cells performed on chip results in pathway activation identical to that of conventionally treated cells under the same conditions.

Sustained MAPK activation is dependent on continual NGF receptor regeneration

It still remains intriguing how signal specificity is achieved when different signals are relayed by the common intracellular signal transduction pathways. A well documented example for signal specificity determination is found in rat phaeochromocytoma PC12 cells where epidermal growth factor (EGF) stimulation produces a transient mitogen-activated protein kinase (MAPK) activation and leads to cell proliferation while nerve growth factor (NGF) initiates a sustained MAPK activation and induces cell differentiation. In this simulation, we demonstrated that NGF-induced sustained MAPK activation may mainly depend on continual regeneration of NGF receptors and that the presence of a small pool of surface receptors is enough to maintain a sustained MAPK activation. On the other hand, MAPK activation is not significantly sensitive to the half-life of internalized receptors and the levels of NGF-specific MAPK phosphatase MAP kinase phosphatase-3 (MKP-3), though cytoplasmic persistence of internalized NGF-bound receptors and the MKP-3 dependent feedback control also contribute to the sustaining of MAPK activation. These results are consistent with the recent experimental evidence that persistent tyrosine receptor kinase A (TrkA) activity is necessary to maintain transcription in the differentiating PC12 cells (Chang et al. 2003) and a sustained Src kinase activity is detected in response to NGF stimulation (Gatti 2003). It is suggested that sustained or transient MAPK activation induced by different growth factor and neurotrophins, which is crucial to their signaling specificity, could be satisfactorily accounted for by their specific receptor turnover kinetics rather than by the activation of specific downstream signaling cascades.

In silico identification of the key components and steps in IFN-gamma induced JAK-STAT signaling pathway

Systems biology efforts are increasingly adopting quantitative, mechanistic modeling to study cellular signal transduction pathways and other networks. However, it is uncertain whether the particular set of kinetic parameter values of the model closely approximates the corresponding biological system. We propose that the parameters be assigned statistical distributions that reflect the degree of uncertainty for a comprehensive simulation analysis. From this analysis, we globally identify the key components and steps in signal transduction networks at a systems level. We investigated a recent mathematical model of interferon gamma induced Janus kinase-signal transducers and activators of transcription (JAK-STAT) signaling pathway by applying multi-parametric sensitivity analysis that is based on simultaneous variation of the parameter values. We find that suppressor of cytokine signaling-1, nuclear phosphatases, cytoplasmic STAT1, and the corresponding reaction steps are sensitive perturbation points of this pathway.

Sensitivity, principal component and flux analysis applied to signal transduction: the case of epidermal growth factor mediated signaling

MOTIVATION

Novel high-throughput genomic and proteomic tools are allowing the integration of information from a range of biological assays into a single conceptual framework. This framework is often described as a network of biochemical reactions. We present strategies for the analysis of such networks.

RESULTS

The direct differential method is described for the systematic evaluation of scaled sensitivity coefficients in reaction networks. Principal component analysis, based on an eigenvalue-eigenvector analysis of the scaled sensitivity coefficient matrix, is applied to rank individual reactions in the network based on their effect on system output. When combined with flux analysis, sensitivity analysis allows model reduction or simplification. Using epidermal growth factor (EGF) mediated signaling and trafficking as an example of signal transduction, we demonstrate that sensitivity analysis quantitatively reveals the dependence of dual-phosphorylated extracellular signal-regulated kinase (ERK) concentration on individual reaction rate constants. It predicts that EGF mediated reactions proceed primarily via an Shc-dependent pathway. Further, it suggests that receptor internalization and endosomal signaling are important features regulating signal output only at low EGF dosages and at later times.

Prediction and validation of the distinct dynamics of transient and sustained ERK activation

To elucidate the hidden dynamics of extracellular-signal-regulated kinase (ERK) signalling networks, we developed a simulation model of ERK signalling networks by constraining in silico dynamics based on in vivo dynamics in PC12 cells. We predicted and validated that transient ERK activation depends on rapid increases of epidermal growth factor and nerve growth factor (NGF) but not on their final concentrations, whereas sustained ERK activation depends on the final concentration of NGF but not on the temporal rate of increase. These ERK dynamics depend on Ras and Rap1 dynamics, the inactivation processes of which are growth-factor-dependent and -independent, respectively. Therefore, the Ras and Rap1 systems capture the temporal rate and concentration of growth factors, and encode these distinct physical properties into transient and sustained ERK activation, respectively.