Quantification of short term signaling by the epidermal growth factor receptor

Kinetic modeling as a tool to integrate multilevel dynamic experimental data

The metabolic networks are the most well-studied biochemical systems, with an abundance of in vitro and in vivo data available for quantitative estimation of its kinetic parameters. In this chapter, we present our approach to developing mathematical description of metabolic pathways. The model-based integration of reaction kinetics and the utilization of different types of experimental data including temporal dependencies have been described in detail. Software package DBSolve7 which allows us to develop kinetic model of the biochemical system and integrate experimental data has been presented.

Association rate constants of ras-effector interactions are evolutionarily conserved

Evolutionary conservation of protein interaction properties has been shown to be a valuable indication for functional importance. Here we use homology interface modeling of 10 Ras-effector complexes by selecting ortholog proteins from 12 organisms representing the major eukaryotic branches, except plants. We find that with increasing divergence time the sequence similarity decreases with respect to the human protein, but the affinities and association rate constants are conserved as predicted by the protein design algorithm, FoldX. In parallel we have done computer simulations on a minimal network based on Ras-effector interactions, and our results indicate that in the absence of negative feedback, changes in kinetics that result in similar binding constants have strong consequences on network behavior. This, together with the previous results, suggests an important biological role, not only for equilibrium binding constants but also for kinetics in signaling processes involving Ras-effector interactions. Our findings are important to take into consideration in system biology approaches and simulations of biological networks.

Cellular signal transductions processes are based on protein interactions. Proteins can either associate transiently with each other or form stable complexes, and the strength of the interaction is described by the affinity (the affinity is the ratio between the rate of dissociation and association). Protein complexes with similar affinities can bind and dissociate with different rates, and these rates describe the kinetic properties of protein binding. These kinetic rates are important for signaling; however, to what extent individual changes in such rate constants are biologically important or whether the affinity is more crucial might be different in different signaling processes. In this study we analyze whether association rates are conserved during evolution, because evolutionary conservation of protein biochemical properties is usually a valuable indication of its importance. We analyzed the binding of Ras proteins to effector domains, which are central proteins in many signal transduction pathways, in different organisms. On the basis of homology modeling and energy calculations we find that association rates are conserved, although the sequence similarity decreases compared to the human protein. Our finding should encourage further analysis of the importance of kinetics for cellular signal transduction.

Modelling the dynamics of signalling pathways

In the present chapter we discuss methodologies for the modelling, calibration and validation of cellular signalling pathway dynamics. The discussion begins with the typical range of techniques for modelling that might be employed to go from the chemical kinetics to a mathematical model of biochemical pathways. In particular, we consider the decision-making processes involved in selecting the right mechanism and level of detail of representation of the biochemical interactions. These include the choice between (i) deterministic and stochastic chemical kinetics representations, (ii) discrete and continuous time models and (iii) representing continuous and discrete state processes. We then discuss the task of calibrating the models using information available in web-based databases. For situations in which the data are not available from existing sources we discuss model calibration based upon measured data and system identification methods. Such methods, together with mathematical modelling databases and computational tools, are often available in standard packages. We therefore make explicit mention of a range of popular and useful sites. As an example of the whole modelling and calibration process, we discuss a study of the cross-talk between the IL-1 (interleukin-1)-stimulated NF-kappaB (nuclear factor kappaB) pathway and the TGF-beta (transforming growth factor beta)-stimulated Smad2 pathway.

Simulation of crosstalk between small GTPase RhoA and EGFR-ERK signaling pathway via MEKK1

MOTIVATION

Small GTPase RhoA regulates cell-cycle progression via several mechanisms. Apart from its actions via ROCK, RhoA has recently been found to activate a scaffold protein MEKK1 known to promote ERK activation. We examined whether RhoA can substantially affect ERK activity via this MEKK1-mediated crosstalk between RhoA and EGFR-ERK pathway. By extending the published EGFR-ERK simulation models represented by ordinary differential equations, we developed a simulation model that includes this crosstalk, which was validated with a number of experimental findings and published simulation results.

RESULTS

Our simulation suggested that, via this crosstalk, RhoA elevation substantially prolonged duration of ERK activation at both normal and reduced Ras levels. Our model suggests ERK may be activated in the absence of Ras. When Ras is overexpressed, RhoA elevation significantly prolongs duration of ERK activation but reduces the amount of active ERK partly due to competitive binding between ERK and RhoA to MEKK1. Our results indicated possible roles of RhoA in affecting ERK activities via MEKK1-mediated crosstalk, which seems to be supported by indications from several experimental studies that may also implicate the collective regulation of cell fate and progression of cancer and other diseases.

Molecular systems biology of ErbB1 signaling: bridging the gap through multiscale modeling and high-performance computing

The complexity in intracellular signaling mechanisms relevant for the conquest of many diseases resides at different levels of organization with scales ranging from the subatomic realm relevant to catalytic functions of enzymes to the mesoscopic realm relevant to the cooperative association of molecular assemblies and membrane processes. Consequently, the challenge of representing and quantifying functional or dysfunctional modules within the networks remains due to the current limitations in our understanding of mesoscopic biology, i.e., how the components assemble into functional molecular ensembles. A multiscale approach is necessary to treat a hierarchy of interactions ranging from molecular (nm, ns) to signaling (microm, ms) length and time scales, which necessitates the development and application of specialized modeling tools. Complementary to multiscale experimentation (encompassing structural biology, mechanistic enzymology, cell biology, and single molecule studies) multiscale modeling offers a powerful and quantitative alternative for the study of functional intracellular signaling modules. Here, we describe the application of a multiscale approach to signaling mediated by the ErbB1 receptor which constitutes a network hub for the cell's proliferative, migratory, and survival programs. Through our multiscale model, we mechanistically describe how point-mutations in the ErbB1 receptor can profoundly alter signaling characteristics leading to the onset of oncogenic transformations. Specifically, we describe how the point mutations induce cascading fragility mechanisms at the molecular scale as well as at the scale of the signaling network to preferentially activate the survival factor Akt. We provide a quantitative explanation for how the hallmark of preferential Akt activation in cell-lines harboring the constitutively active mutant ErbB1 receptors causes these cell-lines to be addicted to ErbB1-mediated generation of survival signals. Consequently, inhibition of ErbB1 activity leads to a remarkable therapeutic response in the addicted cell lines.

From pathway to population--a multiscale model of juxtacrine EGFR-MAPK signalling

BACKGROUND

Most mathematical models of biochemical pathways consider either signalling events that take place within a single cell in isolation, or an 'average' cell which is considered to be representative of a cell population. Likewise, experimental measurements are often averaged over populations consisting of hundreds of thousands of cells. This approach ignores the fact that even within a genetically-homogeneous population, local conditions may influence cell signalling and result in phenotypic heterogeneity. We have developed a multi-scale computational model that accounts for emergent heterogeneity arising from the influences of intercellular signalling on individual cells within a population. Our approach was to develop an ODE model of juxtacrine EGFR-ligand activation of the MAPK intracellular pathway and to couple this to an agent-based representation of individual cells in an expanding epithelial cell culture population. This multi-scale, multi-paradigm approach has enabled us to simulate Extracellular signal-regulated kinase (Erk) activation in a population of cells and to examine the consequences of interpretation at a single cell or population-based level using virtual assays.

RESULTS

A model consisting of a single pair of interacting agents predicted very different Erk activation (phosphorylation) profiles, depending on the formation rate and stability of intercellular contacts, with the slow formation of stable contacts resulting in low but sustained activation of Erk, and transient contacts resulting in a transient Erk signal. Extension of this model to a population consisting of hundreds to thousands of interacting virtual cells revealed that the activated Erk profile measured across the entire cell population was very different and may appear to contradict individual cell findings, reflecting heterogeneity in population density across the culture. This prediction was supported by immunolabelling of an epithelial cell population grown in vitro, which confirmed heterogeneity of Erk activation.

CONCLUSION

These results illustrate that mean experimental data obtained from analysing entire cell populations is an oversimplification, and should not be extrapolated to deduce the signal:response paradigm of individual cells. This multi-scale, multi-paradigm approach to biological simulation provides an important conceptual tool in addressing how information may be integrated over multiple scales to predict the behaviour of a biological system.

Quantitative modeling perspectives on the ErbB system of cell regulatory processes

The complexities of the processes involved in ErbB-mediated regulation of cellular phenotype are broadly appreciated, so much so that it might be reasonably argued that this highly studied system provided significant impetus for the systems perspective on cell signaling processes in general. Recent years have seen major advances in the level of characterization of the ErbB system as well as our ability to make measurements of the system. This new data provides significant new insight, while at the same time creating new challenges for making quantitative statements and predictions with certainty. Here, we discuss recent advances in each of these directions and the interplay between them, with a particular focus on quantitative modeling approaches to interpret data and provide predictive power. Our discussion follows the sequential order of ErbB pathway activation, beginning with considerations of receptor/ligand interactions and dynamics, proceeding to the generation of intracellular signals, and ending with determination of cellular phenotype. As discussed herein, these processes become increasingly difficult to describe or interpret in terms of traditional models, and we review emerging methodologies to address this complexity.

ALC: automated reduction of rule-based models

Background

Combinatorial complexity is a challenging problem for the modeling of cellular signal transduction since the association of a few proteins can give rise to an enormous amount of feasible protein complexes. The layer-based approach is an approximative, but accurate method for the mathematical modeling of signaling systems with inherent combinatorial complexity. The number of variables in the simulation equations is highly reduced and the resulting dynamic models show a pronounced modularity. Layer-based modeling allows for the modeling of systems not accessible previously.

Results

ALC (Automated Layer Construction) is a computer program that highly simplifies the building of reduced modular models, according to the layer-based approach. The model is defined using a simple but powerful rule-based syntax that supports the concepts of modularity and macrostates. ALC performs consistency checks on the model definition and provides the model output in different formats (C MEX, MATLAB, Mathematica and SBML) as ready-to-run simulation files. ALC also provides additional documentation files that simplify the publication or presentation of the models. The tool can be used offline or via a form on the ALC website.

Conclusion

ALC allows for a simple rule-based generation of layer-based reduced models. The model files are given in different formats as ready-to-run simulation files.

Dose-to-duration encoding and signaling beyond saturation in intracellular signaling networks

The cellular response elicited by an environmental cue typically varies with the strength of the stimulus. For example, in the yeast Saccharomyces cerevisiae, the concentration of mating pheromone determines whether cells undergo vegetative growth, chemotropic growth, or mating. This implies that the signaling pathways responsible for detecting the stimulus and initiating a response must transmit quantitative information about the intensity of the signal. Our previous experimental results suggest that yeast encode pheromone concentration as the duration of the transmitted signal. Here we use mathematical modeling to analyze possible biochemical mechanisms for performing this “dose-to-duration” conversion. We demonstrate that modulation of signal duration increases the range of stimulus concentrations for which dose-dependent responses are possible; this increased dynamic range produces the counterintuitive result of “signaling beyond saturation” in which dose-dependent responses are still possible after apparent saturation of the receptors. We propose a mechanism for dose-to-duration encoding in the yeast pheromone pathway that is consistent with current experimental observations. Most previous investigations of information processing by signaling pathways have focused on amplitude encoding without considering temporal aspects of signal transduction. Here we demonstrate that dose-to-duration encoding provides cells with an alternative mechanism for processing and transmitting quantitative information about their surrounding environment. The ability of signaling pathways to convert stimulus strength into signal duration results directly from the nonlinear nature of these systems and emphasizes the importance of considering the dynamic properties of signaling pathways when characterizing their behavior. Understanding how signaling pathways encode and transmit quantitative information about the external environment will not only deepen our understanding of these systems but also provide insight into how to reestablish proper function of pathways that have become dysregulated by disease.

Cells must be able to detect and respond to changes in their surroundings. Often environmental cues, such as hormones or growth factors, are received by membrane receptors that in turn activate intracellular signaling pathways. These pathways then transmit information about the stimulus to the cellular components required to elicit an appropriate response. In many cases, the nature of the response depends on the dose of the stimulus. Thus, in addition to relaying qualitative information (e.g., the presence or absence of a stimulus), signaling pathways must also transmit quantitative information about the intensity of the stimulus. Here we introduce “dose-to-duration” encoding as an effective strategy for relaying such information. We demonstrate that by providing a mechanism for overcoming saturation effects, modulation of signal duration increases the range of stimulus concentrations for which dose-dependent responses are possible. This increased dynamic range produces the counterintuitive result of “signaling beyond saturation” in which dose-dependent responses are still possible after apparent saturation of the receptors. Finally, we demonstrate that dose-to-duration encoding is used in the yeast mating response pathway and presents a simple mechanism that can account for current experimental observations.

Perspectives on Mathematical Modeling for Receptor-Mediated Processes

Mathematical modeling is a potent in silico tool that can help investigate, interpret, and predict the behavior of biological systems. The first step is to develop a working hypothesis of the biology. Then by "translating" the biological phenomena into equations, models can harness the power of mathematical analysis techniques to explore the dynamics and interactions of the biological components. Models can be used together with traditional experimental models to help design new experiments, test hypotheses, identify mechanisms, and predict outcomes. This article reviews the process of building, calibrating, and using mathematical models in the context of the kinetics of receptor and signal transduction biology. An example model related to the androgen receptor-mediated regulation of the prostate is presented to illustrate the steps in the modeling process and to highlight the potential for mathematical modeling in this area.

Exact model reduction of combinatorial reaction networks

BACKGROUND

Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models.

RESULTS

We introduce methods that extend and complete the already introduced approach. For instance, we provide techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization. Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures. The developed methods are used to reduce a model of EGF and insulin receptor crosstalk comprising 5,182 ordinary differential equations (ODEs) to a model with 87 ODEs.

CONCLUSION

The methods, presented in this contribution, significantly enhance the available methods to exactly reduce models of combinatorial reaction networks.

Drug targets for tumorigenesis: insights from structural analysis of EGFR signaling network

Deciphering the complex network structure is crucial in drug target identification. This study presents a framework incorporating graph theoretic and network decomposition methods to analyze system-level properties of the comprehensive map of the epidermal growth factor receptor (EGFR) signaling, which is a good candidate model system to study the general mechanisms of signal transduction. The graph theoretic analysis of the EGFR network indicates that it has small-world characteristics with scale-free topology. The employment of network decomposition analysis enlightened the system-level properties, such as network cross-talk, specific molecules in each pathway and participation of molecules in the network. Participating in a significant fraction of the fundamental paths connecting the ligands to the phenotypes, cofactor GTP and complex Gbeta/Ggamma were identified as "housekeeping" molecules, through which all pathways of EGFR network are cross-talking. c-Src-Shc complex is identified as important due to its role in all fundamental paths through tumorigenesis and being specific to this phenotype. Inhibitors of this complex may be good anti-cancer agents having very little or no effect on other phenotypes.

Protein cooperation: from neurons to networks

A constant pattern through the development of cellular life is that not only cells but also subcellular components such as proteins, either being enzymes, receptors, signaling or structural proteins, strictly cooperate. Discerning how protein cooperation originated and propagates over evolutionary time, how proteins work together to a shared outcome far beyond mere interaction, thus represents a theoretical and experimental challenge for evolutionary, molecular, and computational biology, and a timely fruition also for biotechnology. In this review, we describe some basic principles sustaining not only cellular but especially protein cooperative behavior, with particular emphasis on neurobiological systems. We illustrate experimental results and numerical models substantiating that bench research, as well as computer analysis, indeed concurs in recognizing the natural propensity of proteins to cooperate. At the cellular level, we exemplify network connectivity in the thalamus, hippocampus and basal ganglia. At the protein level, we depict numerical models about the receptosome, the protein machinery connecting neurotransmitters or growth factors to specific, unique downstream effector proteins. We primarily focus on the purinergic P2/P1 receptor systems for extracellular purine and pyrimidine nucleotides/nucleosides. By spanning concepts such as single-molecule biology to membrane computing, we seek to stimulate a scientific debate on the implications of protein cooperation in neurobiological systems.

A molecular signaling model of platelet phosphoinositide and calcium regulation during homeostasis and P2Y1 activation

To quantify how various molecular mechanisms are integrated to maintain platelet homeostasis and allow responsiveness to adenosine diphosphate (ADP), we developed a computational model of the human platelet. Existing kinetic information for 77 reactions, 132 fixed kinetic rate constants, and 70 species was combined with electrochemical calculations, measurements of platelet ultrastructure, novel experimental results, and published single-cell data. The model accurately predicted: (1) steady-state resting concentrations for intracellular calcium, inositol 1,4,5-trisphosphate, diacylglycerol, phosphatidic acid, phosphatidylinositol, phosphatidylinositol phosphate, and phosphatidylinositol 4,5-bisphosphate; (2) transient increases in intracellular calcium, inositol 1,4,5-trisphosphate, and G(q)-GTP in response to ADP; and (3) the volume of the platelet dense tubular system. A more stringent test of the model involved stochastic simulation of individual platelets, which display an asynchronous calcium spiking behavior in response to ADP. Simulations accurately reproduced the broad frequency distribution of measured spiking events and demonstrated that asynchronous spiking was a consequence of stochastic fluctuations resulting from the small volume of the platelet. The model also provided insights into possible mechanisms of negative-feedback signaling, the relative potency of platelet agonists, and cell-to-cell variation across platelet populations. This integrative approach to platelet biology offers a novel and complementary strategy to traditional reductionist methods.

Unbiased tau-leap methods for stochastic simulation of chemically reacting systems

The tau-leap method first developed by Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)] can significantly speed up stochastic simulation of certain chemically reacting systems with acceptable losses in accuracy. Recently, several improved tau-leap methods, including the binomial, multinomial, and modified tau-leap methods, have been developed. However, in all these tau-leap methods, the mean of the number of times, K(m), that the mth reaction channel fires during a leap is not equal to the true mean. Therefore, all existing tau-leap methods produce biased simulation results, which limit the simulation accuracy and speed. In this paper, we analyze the mean of K(m) based on the chemical master equation. Using this analytical result, we develop unbiased Poisson and binomial tau-leap methods. Moreover, we analyze the variance of K(m), and then develop an unbiased Poisson/Gaussian/binomial tau-leap method to correct the errors in both the mean and variance of K(m). Simulation results demonstrate that our unbiased tau-leap method can significantly improve simulation accuracy without sacrificing speed.

A structured approach for the engineering of biochemical network models, illustrated for signalling pathways

Quantitative models of biochemical networks (signal transduction cascades, metabolic pathways, gene regulatory circuits) are a central component of modern systems biology. Building and managing these complex models is a major challenge that can benefit from the application of formal methods adopted from theoretical computing science. Here we provide a general introduction to the field of formal modelling, which emphasizes the intuitive biochemical basis of the modelling process, but is also accessible for an audience with a background in computing science and/or model engineering. We show how signal transduction cascades can be modelled in a modular fashion, using both a qualitative approach--qualitative Petri nets, and quantitative approaches--continuous Petri nets and ordinary differential equations (ODEs). We review the major elementary building blocks of a cellular signalling model, discuss which critical design decisions have to be made during model building, and present a number of novel computational tools that can help to explore alternative modular models in an easy and intuitive manner. These tools, which are based on Petri net theory, offer convenient ways of composing hierarchical ODE models, and permit a qualitative analysis of their behaviour. We illustrate the central concepts using signal transduction as our main example. The ultimate aim is to introduce a general approach that provides the foundations for a structured formal engineering of large-scale models of biochemical networks.

Stimulus design for model selection and validation in cell signaling

Mechanism-based chemical kinetic models are increasingly being used to describe biological signaling. Such models serve to encapsulate current understanding of pathways and to enable insight into complex biological processes. One challenge in model development is that, with limited experimental data, multiple models can be consistent with known mechanisms and existing data. Here, we address the problem of model ambiguity by providing a method for designing dynamic stimuli that, in stimulus–response experiments, distinguish among parameterized models with different topologies, i.e., reaction mechanisms, in which only some of the species can be measured. We develop the approach by presenting two formulations of a model-based controller that is used to design the dynamic stimulus. In both formulations, an input signal is designed for each candidate model and parameterization so as to drive the model outputs through a target trajectory. The quality of a model is then assessed by the ability of the corresponding controller, informed by that model, to drive the experimental system. We evaluated our method on models of antibody–ligand binding, mitogen-activated protein kinase (MAPK) phosphorylation and de-phosphorylation, and larger models of the epidermal growth factor receptor (EGFR) pathway. For each of these systems, the controller informed by the correct model is the most successful at designing a stimulus to produce the desired behavior. Using these stimuli we were able to distinguish between models with subtle mechanistic differences or where input and outputs were multiple reactions removed from the model differences. An advantage of this method of model discrimination is that it does not require novel reagents, or altered measurement techniques; the only change to the experiment is the time course of stimulation. Taken together, these results provide a strong basis for using designed input stimuli as a tool for the development of cell signaling models.

A major focus of systems biology is the development of mechanism-based models of cell signaling pathways. These models hold the promise of encapsulating our understanding of complex biological processes while also predicting new behavior. However, as these models become more complex, it can be difficult to distinguish between model alternatives. One means of improved model discrimination involves making measurements of additional components in the biological system to provide more detailed data. Here we present an alternative, which is to apply a time-varying input while monitoring the same network components. This new method was able to discriminate among models with subtle mechanistic differences. A particular advantage is that for many cases, time-varying input stimulation is fairly easy to apply experimentally, whereas measuring additional network components can involve the creation of new reagents or measurement assays. Thus, we believe that the application of time-varying input stimulation will become a powerful tool in the field of systems biology as the community places increased emphasis on the development of quantitative, mechanistic, and predictive models of biological network behavior.

Simulation of the regulation of EGFR endocytosis and EGFR-ERK signaling by endophilin-mediated RhoA-EGFR crosstalk

Deregulations of EGFR endocytosis in EGFR-ERK signaling are known to cause cancers and developmental disorders. Mutations that impaired c-Cbl-EGFR association delay EGFR endocytosis and produce higher mitogenic signals in lung cancer. ROCK, an effector of small GTPase RhoA was shown to negatively regulate EGFR endocytosis via endophilin A1. A mathematical model was developed to study how RhoA and ROCK regulate EGFR endocytosis. Our study suggested that over-expressing RhoA as well as ROCK prolonged ERK activation partly by reducing EGFR endocytosis. Overall, our study hypothesized an alternative role of RhoA in tumorigenesis in addition to its regulation of cytoskeleton and cell motility.

How quantitative measures unravel design principles in multi-stage phosphorylation cascades

We investigate design principles of linear multi-stage phosphorylation cascades by using quantitative measures for signaling time, signal duration and signal amplitude. We compare alternative pathway structures by varying the number of phosphorylations and the length of the cascade. We show that a model for a weakly activated pathway does not reflect the biological context well, unless it is restricted to certain parameter combinations. Focusing therefore on a more general model, we compare alternative structures with respect to a multivariate optimization criterion. We test the hypothesis that the structure of a linear multi-stage phosphorylation cascade is the result of an optimization process aiming for a fast response, defined by the minimum of the product of signaling time and signal duration. It is then shown that certain pathway structures minimize this criterion. Several popular models of MAPK cascades form the basis of our study. These models represent different levels of approximation, which we compare and discuss with respect to the quantitative measures.

The Beta Workbench: a computational tool to study the dynamics of biological systems

We introduce the Beta Workbench (BWB), a scalable tool built on top of the newly defined BlenX language to model, simulate and analyse biological systems. We show the features and the incremental modelling process supported by the BWB on a running example based on the mitogen-activated kinase pathway. Finally, we provide a comparison with related approaches and some hints for future extensions.

Role of network branching in eliciting differential short-term signaling responses in the hypersensitive epidermal growth factor receptor mutants implicated in lung cancer

We study the effects of EGFR inhibition in wild-type and mutant cell lines upon tyrosine kinase inhibitor TKI treatment through a systems level deterministic and spatially homogeneous model to help characterize the hypersensitive response of the cancer cell lines harboring constitutively active mutant kinases to inhibitor treatment. By introducing a molecularly resolved branched network systems model (the molecular resolution is introduced for EGFR reactions and interactions in order to distinguish differences in activation between wild-type and mutants), we are able to quantify differences in (1) short-term signaling in downstream ERK and Akt activation, (2) the changes in the cellular inhibition EC50 associated with receptor phosphorylation (i.e., 50% inhibition of receptor phosphorylation in the cellular context), and (3) EC50 for the inhibition of activated downstream markers ERK-(p) and Akt-(p), where (p) denotes phosphorylated, upon treatment with the inhibitors in cell lines carrying both wild-type and mutant forms of the receptor. Using the branched signaling model, we illustrate a possible mechanism for preferential Akt activation in the cell lines harboring the oncogenic mutants of EGFR implicated in non-small-cell lung cancer and the enhanced efficacy of the inhibitor erlotinib especially in ablating the cellular Akt-(p) response. Using a simple phenomenological model to describe the effect of Akt activation on cellular decisions, we discuss how this preferential Akt activation is conducive to cellular oncogene addiction and how its disruption can lead to dramatic apoptotic response and hence remarkable inhibitor efficacies. We also identify key network nodes of our branched signaling model through sensitivity analysis as those rendering the network hypersensitive to enhanced ERK-(p) and Akt-(p); intriguingly, the identified nodes have a strong correlation with species implicated in oncogenic transformations in human cancers as well as in drug resistance mechanisms identified for the inhibitors in non-small-cell lung cancer therapy.

Quantifying the effects of co-expressing EGFR and HER2 on HER activation and trafficking

The human epidermal growth factor receptor (HER) system is an intricately regulated system that plays critical roles in development and tumorigenesis. Here, we apply integrated experimentation and modeling to analyze HER receptor activation in a panel of cell lines expressing endogenous levels of EGFR/HER1 and different levels of HER2. A mathematical model that includes the fundamental processes involved in receptor activation and trafficking was used to fit the experimental data, and values of the independent parameters for active receptor dimer formation affinities, trafficking rates and relative phosphorylation levels were estimated. Obtained parameter values quantitatively support the existing ideas on the effect of HER2 on EGFR dynamics, and enable us to predict the abundances of various phosphorylated receptor dimers in the cell lines.

An ultrasensitive sorting mechanism for EGF receptor endocytosis

Background

The Epidermal Growth Factor (EGF) receptor has been shown to internalize via clathrin-independent endocytosis (CIE) in a ligand concentration dependent manner. From a modeling point of view, this resembles an ultrasensitive response, which is the ability of signaling networks to suppress a response for low input values and to increase to a pre-defined level for inputs exceeding a certain threshold. Several mechanisms to generate this behaviour have been described theoretically, the underlying assumptions of which, however, have not been experimentally demonstrated for the EGF receptor internalization network.

Results

Here, we present a mathematical model of receptor sorting into alternative pathways that explains the EGF-concentration dependent response of CIE. The described mechanism involves a saturation effect of the dominant clathrin-dependent endocytosis pathway and implies distinct steady-states into which the system is forced for low vs high EGF stimulations. The model is minimal since no experimentally unjustified reactions or parameter assumptions are imposed. We demonstrate the robustness of the sorting effect for large parameter variations and give an analytic derivation for alternative steady-states that are reached. Further, we describe extensibility of the model to more than two pathways which might play a role in contexts other than receptor internalization.

Conclusion

Our main result is that a scenario where different endocytosis routes consume the same form of receptor corroborates the observation of a clear-cut, stimulus dependent sorting. This is especially important since a receptor modification discriminating between the pathways has not been found experimentally. The model is not restricted to EGF receptor internalization and might account for ultrasensitivity in other cellular contexts.

Cross-scale sensitivity analysis of a non-small cell lung cancer model: linking molecular signaling properties to cellular behavior

Sensitivity analysis is an effective tool for systematically identifying specific perturbations in parameters that have significant effects on the behavior of a given biosystem, at the scale investigated. In this work, using a two-dimensional, multiscale non-small cell lung cancer (NSCLC) model, we examine the effects of perturbations in system parameters which span both molecular and cellular levels, i.e. across scales of interest. This is achieved by first linking molecular and cellular activities and then assessing the influence of parameters at the molecular level on the tumor's spatio-temporal expansion rate, which serves as the output behavior at the cellular level. Overall, the algorithm operated reliably over relatively large variations of most parameters, hence confirming the robustness of the model. However, three pathway components (proteins PKC, MEK, and ERK) and eleven reaction steps were determined to be of critical importance by employing a sensitivity coefficient as an evaluation index. Each of these sensitive parameters exhibited a similar changing pattern in that a relatively larger increase or decrease in its value resulted in a lesser influence on the system's cellular performance. This study provides a novel cross-scaled approach to analyzing sensitivities of computational model parameters and proposes its application to interdisciplinary biomarker studies.

Topological analysis of MAPK cascade for kinetic ErbB signaling

Ligand-induced homo- and hetero-dimer formation of ErbB receptors results in different biological outcomes irrespective of recruitment and activation of similar effector proteins. Earlier experimental research indicated that cells expressing both EGFR (epidermal growth factor receptor) and the ErbB4 receptor (E1/4 cells) induced E1/4 cell-specific B-Raf activation and higher extracellular signal-regulated kinase (ERK) activation, followed by cellular transformation, than cells solely expressing EGFR (E1 cells) in Chinese hamster ovary (CHO) cells. Since our experimental data revealed the presence of positive feedback by ERK on upstream pathways, it was estimated that the cross-talk/feedback pathway structure of the Raf-MEK-ERK cascade might affect ERK activation dynamics in our cell system. To uncover the regulatory mechanism concerning the ERK dynamics, we used topological models and performed parameter estimation for all candidate structures that possessed ERK-mediated positive feedback regulation of Raf. The structure that reliably reproduced a series of experimental data regarding signal amplitude and duration of the signaling molecules was selected as a solution. We found that the pathway structure is characterized by ERK-mediated positive feedback regulation of B-Raf and B-Raf-mediated negative regulation of Raf-1. Steady-state analysis of the estimated structure indicated that the amplitude of Ras activity might critically affect ERK activity through ERK-B-Raf positive feedback coordination with sustained B-Raf activation in E1/4 cells. However, Rap1 that positively regulates B-Raf activity might be less effective concerning ERK and B-Raf activity. Furthermore, we investigated how such Ras activity in E1/4 cells can be regulated by EGFR/ErbB4 heterodimer-mediated signaling. From a sensitivity analysis of the detailed upstream model for Ras activation, we concluded that Ras activation dynamics is dominated by heterodimer-mediated signaling coordination with a large initial speed of dimerization when the concentration of the ErbB4 receptor is considerably high. Such characteristics of the signaling cause the preferential binding of the Grb2-SOS complex to heterodimer-mediated signaling molecules.

Biochemical basis for the functional switch that regulates hepatocyte growth factor receptor tyrosine kinase activation

Ligand-induced dimerization of receptor tyrosine kinases (RTKs) modulates a system of linked biochemical reactions, sharply switching the RTK from a quiescent state to an active state that becomes phosphorylated and triggers intracellular signaling pathways. To improve our understanding of this molecular switch, we developed a quantitative model for hepatocyte growth factor receptor (c-MET) activation using parameters derived in large part from c-MET kinetic and thermodynamic experiments. Our model accurately produces the qualitative and quantitative dynamic features of c-MET phosphorylation observed in cells following ligand binding, including a rapid transient buildup of phosphorylated c-MET at high ligand concentrations. In addition, our model predicts a slow buildup of phosphorylated c-MET under conditions of reduced phosphatase activity and no extracellular agonist. Significantly, this predicted response is observed in cells treated with phosphatase inhibitors, further validating our model. Parameter sensitivity studies clearly show that synergistic oligomerization-dependent changes in c-MET kinetic, thermodynamic, and dephosphorylation properties result in the selective activation of the dimeric receptor, confirming that this model can be used to accurately evaluate the relative importance of linked biochemical reactions important for c-MET activation. Our model suggests that the functional differences observed between c-MET monomers and dimers may have incrementally evolved to optimize cell surface signaling responses.

Three-dimensional multihelical microfluidic mixers for rapid mixing of liquids

Rapid mixing of liquids is important for most microfluidic applications. However, mixing is slow in conventional micromixers, because, in the absence of turbulence, mixing here occurs by molecular diffusion. Recent experiments show that mixing can be enhanced by generating transient flow resulting in chaotic advection. While these are planar microchannels, here we show that three-dimensional orientations of fluidic vessels and channels can enhance significantly mixing of liquids. In particular, we present a novel, multihelical microchannel system built in soft gels, for which the helix angle, helix radius, axial length, and even the asymmetry of the channel cross section are easily tailored to achieve the desired mixing. Mixing efficiency increases with helix angle and asymmetry of channel cross section, which leads to orders of magnitude reduction in mixing length over conventional mixers. This new scheme of generating 3D microchannels will help in miniaturization of devices, process intensification, and generation of multifunctional process units for microfluidic applications.

Activation of the epidermal growth factor receptor by hydrogels in artificial tears

Most formulations of artificial tears include high-molecular weight hydrophilic polymers (hydrogels) that are usually thought to serve to enhance viscosity and to act as demulcents. A few reports have indicated that application of some of the polymers accelerates healing of wounds in epithelia. Since activation of the epidermal growth factor (EGF) receptor is critical for spontaneous corneal epithelial wound healing, we tested commonly used hydrogels for their ability to activate the EGF receptor and enhance closure of wounds. Five structurally unrelated hydrogels used in artificial tears were found to activate the EGF receptor. Importantly, two of the hydrogels enhanced wound healing in an organ culture model. We propose that the efficacy of hydrogels in treating dry eye may be related to their ability to activate the EGF receptor, and that hydrogels are inexpensive, safe agents to promote healing of wounds in the cornea and possibly in other tissues.

Simulating non-small cell lung cancer with a multiscale agent-based model

BACKGROUND

The epidermal growth factor receptor (EGFR) is frequently overexpressed in many cancers, including non-small cell lung cancer (NSCLC). In silico modeling is considered to be an increasingly promising tool to add useful insights into the dynamics of the EGFR signal transduction pathway. However, most of the previous modeling work focused on the molecular or the cellular level only, neglecting the crucial feedback between these scales as well as the interaction with the heterogeneous biochemical microenvironment.

RESULTS

We developed a multiscale model for investigating expansion dynamics of NSCLC within a two-dimensional in silico microenvironment. At the molecular level, a specific EGFR-ERK intracellular signal transduction pathway was implemented. Dynamical alterations of these molecules were used to trigger phenotypic changes at the cellular level. Examining the relationship between extrinsic ligand concentrations, intrinsic molecular profiles and microscopic patterns, the results confirmed that increasing the amount of available growth factor leads to a spatially more aggressive cancer system. Moreover, for the cell closest to nutrient abundance, a phase-transition emerges where a minimal increase in extrinsic ligand abolishes the proliferative phenotype altogether.

CONCLUSION

Our in silico results indicate that in NSCLC, in the presence of a strong extrinsic chemotactic stimulus (and depending on the cell's location) downstream EGFR-ERK signaling may be processed more efficiently, thereby yielding a migration-dominant cell phenotype and overall, an accelerated spatio-temporal expansion rate.

Signalling control strength

Metabolic control analysis (MCA) has become what it is, largely because the special organization of living cells led to rather specific questions. These questions focused on the role of enzymes, genes, and, in subsequent generalizations, on well-defined process activities. With an emphasis on the work by Heinrich and co-workers, the theory behind MCA is summarized in a way that leads naturally to its extensions to hierarchical systems, such as gene expression and signal transduction, and to control beyond the steady state. The analysis of the control properties of signal transduction cascades is reviewed with an emphasis on the relative importance of the protein kinases and the protein phosphatases. The two types of enzyme are both important for the amplitude of signal transduction, whereas phosphatases may be more important for the later phases of signal transduction and for its duration. Novel MCA of concentrations and fluxes that vary with time is explicated. It is concluded that the clarity and operationality of concepts such as control strength (now control coefficient) plus the clear theoretical frameworks provided by Heinrich and colleagues, should enable us greatly to reduce the Babylonian confusion that could otherwise occur in the data deluges of Systems Biology.

SRC family kinases and receptors: analysis of three activation mechanisms by dynamic systems modeling

Src family kinases (SFKs) interact with a number of cellular receptors. They participate in diverse signaling pathways and cellular functions. Most of the receptors involved in SFK signaling are characterized by similar modes of regulation. This computational study discusses a general kinetic model of SFK-receptor interaction. The analysis of the model reveals three major ways of SFK activation: release of inhibition by C-terminal Src kinase, weakening of the inhibitory intramolecular phosphotyrosine-SH2 interaction, and amplification of a stimulating kinase activity. The SFK model was then extended to simulate interaction with growth factor and T-cell receptors. The modular SFK signaling system was shown to adapt to the requirements of specific signaling contexts and yield qualitatively different responses in the different simulated environments. The model also provides a systematic overview of the major interactions between SFKs and various cellular signaling systems and identifies their common properties.

Ligand-dependent responses of the ErbB signaling network: experimental and modeling analyses

Deregulation of ErbB signaling plays a key role in the progression of multiple human cancers. To help understand ErbB signaling quantitatively, in this work we combine traditional experiments with computational modeling, building a model that describes how stimulation of all four ErbB receptors with epidermal growth factor (EGF) and heregulin (HRG) leads to activation of two critical downstream proteins, extracellular-signal-regulated kinase (ERK) and Akt. Model analysis and experimental validation show that (i) ErbB2 overexpression, which occurs in approximately 25% of all breast cancers, transforms transient EGF-induced signaling into sustained signaling, (ii) HRG-induced ERK activity is much more robust to the ERK cascade inhibitor U0126 than EGF-induced ERK activity, and (iii) phosphoinositol-3 kinase is a major regulator of post-peak but not pre-peak EGF-induced ERK activity. Sensitivity analysis leads to the hypothesis that ERK activation is robust to parameter perturbation at high ligand doses, while Akt activation is not.

Robustness analysis of EGFR signaling network with a multi-objective evolutionary algorithm

Robustness, the ability to maintain performance in the face of perturbations and uncertainty, is believed to be a necessary property of biological systems. In this paper, we address the issue of robustness in an important signal transduction network--epidermal growth factor receptor (EGFR) network. First, we analyze the robustness in the EGFR signaling network using all rate constants against the Gauss variation which was described as "the reference parameter set" in the previous study [Kholodenko, B.N., Demin, O.V., Moehren, G., Hoek, J.B., 1999. Quantification of short term signaling by the epidermal growth factor receptor. J. Biol. Chem. 274, 30169-30181]. The simulation results show that signal time, signal duration and signal amplitude of the EGRR signaling network are relatively not robust against the simultaneous variation of the reference parameter set. Second, robustness is quantified using some statistical quantities. Finally, a multi-objective evolutionary algorithm (MOEA) is presented to search reaction rate constants which optimize the robustness of network and compared with the NSGA-II, which is a representation of a class of modern multi-objective evolutionary algorithms. Our simulation results demonstrate that signal time, signal duration and signal amplitude of the four key components--the most downstream variable in each of the pathways: R-Sh-G-S, R-PLP, R-G-S and the phosphorylated receptor RP in EGRR signaling network for the optimized parameter sets have better robustness than those for the reference parameter set and the NSGA-II. These results can provide valuable insight into experimental designs and the dynamics of the signal-response relationship between the dimerized and activated EGFR and the activation of downstream proteins.

The impact of the regulatory design on the response of epidermal growth factor receptor-mediated signal transduction towards oncogenic mutations

Epidermal growth factor receptor (EGFR)-mediated signal transduction is often hyperactivated in tumour cells and therefore considered a promising target for cancer therapy. A number of computational models have been developed which describe the pathway in great detail. These models are similar in their description of the activation events. The deactivation of the EGFR signalling seems to be cell type-specific and is less understood. Deactivation via receptor internalization, feedback inhibition of son of sevenless (SOS) by double phosphorylated, extracellular signal-regulated kinase (ERKPP) or transiently activated Ras-GTPase activating protein (Ras-GAP) proteins is discussed to play a role. In this study we address the question of to what extent the effect of oncogenic perturbations on EGFR signalling depend on the specific regulation structure. This is investigated using a detailed pathway model under two regulatory modes: the negative feedback via ERKPP to SOS and feed-forward deactivation via transiently activated Ras-GAP proteins. We show that the effect of receptor overexpression differs qualitatively under both regulations. In the system with transiently activated Ras-GAP it may result in an attenuation of the ERK activation. Such a nonintuitive effect was also observed experimentally. In general we find the model with transiently activated Ras-GAP to have a higher robustness towards receptor overexpression and Ras mutations. In particular, we demonstrate that this model can compensate for these oncogenic perturbations if the regulation is strong. The negative feedback can not protect the system against Ras mutations. A general sensitivity analysis, however, shows a higher robustness of the model under negative feedback, indicating the limited significance of such analyses for the prediction of specific oncogenic perturbations.

EGF-receptor-mediated mammary epithelial cell migration is driven by sustained ERK signaling from autocrine stimulation

EGF family ligands are synthesized as membrane-anchored precursors whose proteolytic release yields mature diffusible factors that can activate cell surface receptors in autocrine or paracrine mode. Expression of these ligands is altered in pathological states and in physiological processes, such as development and tissue regeneration. Despite the widely documented biological importance of autocrine EGF signaling, quantitative relationships between protease-mediated ligand release and consequent cell behavior have not been rigorously investigated. We thus explored the relationship between autocrine EGF release rates and cell behavioral responses along with activation of ERK, a key downstream signal, by expressing chimeric ligand precursors and modulating their proteolytic shedding using a metalloprotease inhibitor in human mammary epithelial cells. We found that ERK activation increased monotonically with increasing ligand release rate despite concomitant downregulation of EGF receptor levels. Cell migration speed was directly related to ligand release rate and proportional to steady-state phospho-ERK levels. Moreover, migration speed was significantly greater for autocrine stimulation compared with exogenous stimulation, even at comparable phospho-ERK levels. By contrast, cell proliferation rates were approximately equivalent at all ligand release rates and were similar regardless of whether the ligand was presented endogenously or exogenously. Thus, in our mammary epithelial cell system, migration and proliferation are differentially sensitive to the mode of EGF ligand presentation.

Reduced modeling of signal transduction - a modular approach

Background

Combinatorial complexity is a challenging problem in detailed and mechanistic mathematical modeling of signal transduction. This subject has been discussed intensively and a lot of progress has been made within the last few years. A software tool (BioNetGen) was developed which allows an automatic rule-based set-up of mechanistic model equations. In many cases these models can be reduced by an exact domain-oriented lumping technique. However, the resulting models can still consist of a very large number of differential equations.

Results

We introduce a new reduction technique, which allows building modularized and highly reduced models. Compared to existing approaches further reduction of signal transduction networks is possible. The method also provides a new modularization criterion, which allows to dissect the model into smaller modules that are called layers and can be modeled independently. Hallmarks of the approach are conservation relations within each layer and connection of layers by signal flows instead of mass flows. The reduced model can be formulated directly without previous generation of detailed model equations. It can be understood and interpreted intuitively, as model variables are macroscopic quantities that are converted by rates following simple kinetics. The proposed technique is applicable without using complex mathematical tools and even without detailed knowledge of the mathematical background. However, we provide a detailed mathematical analysis to show performance and limitations of the method. For physiologically relevant parameter domains the transient as well as the stationary errors caused by the reduction are negligible.

Conclusion

The new layer based reduced modeling method allows building modularized and strongly reduced models of signal transduction networks. Reduced model equations can be directly formulated and are intuitively interpretable. Additionally, the method provides very good approximations especially for macroscopic variables. It can be combined with existing reduction methods without any difficulties.

Cellular signaling is potentially regulated by cell density in receptor trafficking networks

Previous work has shown that receptor trafficking is a potential site for the control of signaling pathways. In most biological experiments, the ligand concentration and cell density vary within a wide range among different systems. However, there is less attention to systematically analyze how much cellular signal response is affected by cell densities. Here, we use a quantitative mathematical model to investigate signal responses in different receptor trafficking networks by simultaneous variations of ligand concentration and cell density. Computational analysis of the model revealed that receptor trafficking networks have potential sigmoid responses to ratio between ligand and surface receptor number per cell, which is a key factor to control the signaling responses in receptor trafficking networks. Furthermore, cell density also affects the robustness of dose-response curve upon the variation of binding affinity.

Modeling signal transduction networks: a comparison of two stochastic kinetic simulation algorithms

Computational efficiency of stochastic kinetic algorithms depend on factors such as the overall species population, the total number of reactions, and the average number of nodal interactions or connectivity in a network. These size measures of the network model can have a significant impact on computational efficiency. In this study, two scalable biological networks are used to compare the size scaling efficiencies of two popular and conceptually distinct stochastic kinetic simulation algorithms--the random substrate method of Firth and Bray (FB), and the Gillespie algorithm as implemented using the Gibson-Bruck method (GGB). The arithmetic computational efficiencies of these two algorithms, respectively, scale with the square of the total species population and the logarithm of the total number of active reactions. The two scalable models considered are the size scalable model (SSM), a four compartment reaction model for a signal transduction network involving receptors with single phosphorylation binding sites, and the variable connectivity model (VCM), a single compartment model where receptors possess multiple phosphorylation binding sites. The SSM has fixed species connectivity while the connectivity between species in VCM increases with the number of phosphorylation sites. For SSM, we find that, as the total species population is increased over four orders of magnitude, the GGB algorithm performs significantly better than FB for all three SSM compartment models considered. In contrast, for VCM, we find that as the overall species population decreases while the number of phosphorylation sites increases (implying an increase in network linkage) there exists a crossover point where the computational demands of the GGB method exceed that of the FB.

Time-dependent sensitivity analysis of biological networks: coupled MAPK and PI3K signal transduction pathways

Sensitivity analysis has been widely used in the studies of complicated chemical reaction and biological networks, for example, in combustion studies and metabolic control analysis of pathways. In the latter cases, the responses of system properties at steady states with respect to changes of parameters, such as initial concentrations and rate constants, are often expressed as sensitivities. Besides steady-state sensitivities, time-dependent sensitivities should be useful; however, the explicit use of them in analyzing complicated biological systems has so far been limited. Using the coupled mitogen activated protein kinase (MAPK)-phophatidylinoisitol 3'-kinase (PI3K) system of the Ras pathways, known to be involved in about 30% of human cancers, as an example, we show that time-dependent sensitivities are useful for the studies of complex biological systems. They provide, for example, the following information: (a) multiple time scales existing in a complex system involving cross-talks and feedback loops; (b) the signs and strengths of responses to perturbations (as system complication increases, the signs of global responses are not always easily determined; for example, response may change sign more than once as time evolves); (c) beyond concentration dynamics, sensitivities revealing further details about the intricate dynamics and the effects of the cross-talks; (d) ranking of vulnerability of nodes of a biological network using integrated sensitivity-a first step toward the identification of drug targets; (e) reduced sensitivity serving as a measure of the stability or robustness of pathways. Our results indicate that the role of the PI3K branch in the coupled pathways is to enhance the robustness of the MAPK pathway. More importantly, they demonstrate that time-dependent sensitivity analysis can be a valuable tool in system biology.

A systems biology approach to the pathogenesis of obesity-related nonalcoholic fatty liver disease using reverse phase protein microarrays for multiplexed cell signaling analysis

Nonalcoholic fatty liver disease (NAFLD) is a common cause of chronic liver disease. Omental adipose tissue, a biologically active organ secreting adipokines and cytokines, may play a role in the development of NAFLD. We tested this hypothesis with reverse-phase protein microarrays (RPA) for multiplexed cell signaling analysis of adipose tissue from patients with NAFLD. Omental adipose tissue was obtained from 99 obese patients. Liver biopsies obtained at the time of surgery were all read by the same hepatopathologist. Adipose tissue was exposed to rapid pressure cycles to extract protein lysates. RPA was used to investigate intracellular signaling. Analysis of 54 different kinase substrates and cell signaling endpoints showed that an insulin signaling pathway is deranged in different locations in NAFLD patients. Furthermore, components of insulin receptor-mediated signaling differentiate most of the conditions on the NAFLD spectrum. For example, PKA (protein kinase A) and AKT/mTOR (protein kinase B/mammalian target of rapamycin) pathway derangement accurately discriminates patients with NASH from those with the non-progressive forms of NAFLD. PKC (protein kinase C) delta, AKT, and SHC phosphorylation changes occur in patients with simple steatosis. Amounts of the FKHR (forkhead factor Foxo1)phosphorylated at S256 residue were significantly correlated with AST/ALT ratio in all morbidly obese patients. Furthermore, amounts of cleaved caspase 9 and pp90RSK S380 were positively correlated in patients with NASH. Specific insulin pathway signaling events are altered in the adipose tissue of patients with NASH compared with patients with nonprogressive forms of NAFLD.

CONCLUSION

These findings provide evidence for the role of omental fat in the pathogenesis, and potentially, the progression of NAFLD.

Introduction to systems biology

The developments in the molecular biosciences have made possible a shift to combined molecular and system-level approaches to biological research under the name of Systems Biology. It integrates many types of molecular knowledge, which can best be achieved by the synergistic use of models and experimental data. Many different types of modeling approaches are useful depending on the amount and quality of the molecular data available and the purpose of the model. Analysis of such models and the structure of molecular networks have led to the discovery of principles of cell functioning overarching single species. Two main approaches of systems biology can be distinguished. Top-down systems biology is a method to characterize cells using system-wide data originating from the Omics in combination with modeling. Those models are often phenomenological but serve to discover new insights into the molecular network under study. Bottom-up systems biology does not start with data but with a detailed model of a molecular network on the basis of its molecular properties. In this approach, molecular networks can be quantitatively studied leading to predictive models that can be applied in drug design and optimization of product formation in bioengineering. In this chapter we introduce analysis of molecular network by use of models, the two approaches to systems biology, and we shall discuss a number of examples of recent successes in systems biology.

A multiscale computational approach to dissect early events in the Erb family receptor mediated activation, differential signaling, and relevance to oncogenic transformations

We describe a hierarchical multiscale computational approach based on molecular dynamics simulations, free energy-based molecular docking simulations, deterministic network-based kinetic modeling, and hybrid discrete/continuum stochastic dynamics protocols to study the dimer-mediated receptor activation characteristics of the Erb family receptors, specifically the epidermal growth factor receptor (EGFR). Through these modeling approaches, we are able to extend the prior modeling of EGF-mediated signal transduction by considering specific EGFR tyrosine kinase (EGFRTK) docking interactions mediated by differential binding and phosphorylation of different C-terminal peptide tyrosines on the RTK tail. By modeling signal flows through branching pathways of the EGFRTK resolved on a molecular basis, we are able to transcribe the effects of molecular alterations in the receptor (e.g., mutant forms of the receptor) to differing kinetic behavior and downstream signaling response. Our molecular dynamics simulations show that the drug sensitizing mutation (L834R) of EGFR stabilizes the active conformation to make the system constitutively active. Docking simulations show preferential characteristics (for wildtype vs. mutant receptors) in inhibitor binding as well as preferential enhancement of phosphorylation of particular substrate tyrosines over others. We find that in comparison to the wildtype system, the L834R mutant RTK preferentially binds the inhibitor erlotinib, as well as preferentially phosphorylates the substrate tyrosine Y1068 but not Y1173. We predict that these molecular level changes result in preferential activation of the Akt signaling pathway in comparison to the Erk signaling pathway for cells with normal EGFR expression. For cells with EGFR over expression, the mutant over activates both Erk and Akt pathways, in comparison to wildtype. These results are consistent with qualitative experimental measurements reported in the literature. We discuss these consequences in light of how the network topology and signaling characteristics of altered (mutant) cell lines are shaped differently in relationship to native cell lines.