Edward C. Stites

Specification, annotation, visualization and simulation of a large rule-based model for ERBB receptor signaling

BackgroundMathematical/computational models are needed to understand cell signaling networks, which are complex. Signaling proteins contain multiple functional components and multiple sites of post-translational modification. The multiplicity of components and sites of modification ensures that interactions among signaling proteins have the potential to generate myriad protein complexes and post-translational modification states. As a result, the number of chemical species that can be populated in a cell signaling network, and hence the number of equations in an ordinary differential equation model required to capture the dynamics of these species, is prohibitively large. To overcome this problem, the rule-based modeling approach has been developed for representing interactions within signaling networks efficiently and compactly through coarse-graining of the chemical kinetics of molecular interactions.ResultsHere, we provide a demonstration that the rule-based modeling approach can be used to specify and simulate a large model for ERBB receptor signaling that accounts for site-specific details of protein-protein interactions. The model is considered large because it corresponds to a reaction network containing more reactions than can be practically enumerated. The model encompasses activation of ERK and Akt, and it can be simulated using a network-free simulator, such as NFsim, to generate time courses of phosphorylation for 55 individual serine, threonine, and tyrosine residues. The model is annotated and visualized in the form of an extended contact map.ConclusionsWith the development of software that implements novel computational methods for calculating the dynamics of large-scale rule-based representations of cellular signaling networks, it is now possible to build and analyze models that include a significant fraction of the protein interactions that comprise a signaling network, with incorporation of the site-specific details of the interactions. Modeling at this level of detail is important for understanding cellular signaling.

A systems perspective of ras signaling in cancer.

The development of cancer reflects the complex interactions and properties of many proteins functioning as part of large biochemical networks within the cancer cell. Although traditional experimental models have provided us with wonderful insights on the behavior of individual proteins within a cancer cell, they have been deficient in simultaneously keeping track of many proteins and their interactions in large networks. Computational models have emerged as a powerful tool for investigating biochemical networks due to their ability to meaningfully assimilate numerous network properties. Using the well-studied Ras oncogene as an example, we discuss the use of models to investigate pathologic Ras signaling and describe how these models could play a role in the development of new cancer drugs and the design of individualized treatment regimens.

Sensitivity and versatility of an adaptive system for controlling cyclic movements using functional neuromuscular stimulation

This study evaluated an adaptive control system (the PG/PS control system (see J. J. Abbas and H.J. Chizeck, vol. 42, p. 1117-27, 1995)) that had been designed for generating cyclic movements using functional neuromuscular stimulation (FNS). Extensive simulations using computer-based models indicated that a broad range of control system parameter values performed well across a diverse population of model systems. The bet that manual tuning is not required for each individual makes this control system particularly attractive for implementation in FNS systems outside of research laboratories.

The response of cancers to BRAF inhibition underscores the importance of cancer systems biology.

Targeting the receptor and a mutant component may be an effective colon cancer treatment. The BRAF inhibitor vemurafenib has become an important treatment option for melanoma patients, the majority of whom have a BRAF(V600E) mutation driving their malignancy. However, this same agent does not generally benefit colon cancer patients who have the BRAF(V600E) mutation. Recent work suggests that BRAF(V600E) inhibition by vemurafenib results in decreased negative feedback to the epidermal growth factor receptor (EGFR) pathway and that the different clinical responses are due to differences in the amount of EGFR present in these two cancers. The experimental work that identified the feedback signaling was an elegant mix of functional genomic approaches and focused, hypothesis-driven cellular and molecular biology. The results of these studies suggest that combined treatment of BRAF(V600E)-driven colon cancers with both vemurafenib and EGFR inhibitors is worth clinical evaluation.

Innovations of the Rule-Based Modeling Approach

New modeling approaches are needed to tackle the complexity of cell signaling systems. An emerging approach is rule-based modeling, in which protein-protein interactions are represented at the level of functional components. By using rules to represent interactions, a modeler can avoid enumerating the reachable chemical species in a system, which is a necessity in traditional modeling approaches. A set of rules can be used to generate a reaction network, or to perform simulations with or without network generation. Although the rule-based approach is a relatively recent development in biology, it is based on concepts that have proven useful in other fields. In this chapter, we discuss innovations of the rule-based modeling approach, relative to traditional approaches for modeling chemical kinetics. These innovations include the use of rules to concisely capture the dynamics of molecular interactions, the view of models as programs, and agent-based computational approaches that can be applied to simulate the chemical kinetics of a system characterized by a large traditional model. These innovations should enable the development of models that can relate the molecular state of a cell to its phenotype, even though vast and complex networks bridge perturbations at the molecular level to fates and activities at the cellular level. In the future, we expect that validated rule-based models will be useful for model-guided studies of cell signaling mechanisms, interpretation of temporal phosphoproteomic data, and cell engineering applications.

Use of mechanistic models to integrate and analyze multiple proteomic datasets.

Proteins in cell signaling networks tend to interact promiscuously through low-affinity interactions. Consequently, evaluating the physiological importance of mapped interactions can be difficult. Attempts to do so have tended to focus on single, measurable physicochemical factors, such as affinity or abundance. For example, interaction importance has been assessed on the basis of the relative affinities of binding partners for a protein of interest, such as a receptor. However, multiple factors can be expected to simultaneously influence the recruitment of proteins to a receptor (and the potential of these proteins to contribute to receptor signaling), including affinity, abundance, and competition, which is a network property. Here, we demonstrate that measurements of protein copy numbers and binding affinities can be integrated within the framework of a mechanistic, computational model that accounts for mass action and competition. We use cell line-specific models to rank the relative importance of protein-protein interactions in the epidermal growth factor receptor (EGFR) signaling network for 11 different cell lines. Each model accounts for experimentally characterized interactions of six autophosphorylation sites in EGFR with proteins containing a Src homology 2 and/or phosphotyrosine-binding domain. We measure importance as the predicted maximal extent of recruitment of a protein to EGFR following ligand-stimulated activation of EGFR signaling. We find that interactions ranked highly by this metric include experimentally detected interactions. Proteins with high importance rank in multiple cell lines include proteins with recognized, well-characterized roles in EGFR signaling, such as GRB2 and SHC1, as well as a protein with a less well-defined role, YES1. Our results reveal potential cell line-specific differences in recruitment.

Mechanistic modeling to investigate signaling by oncogenic Ras mutants

Mathematical models based on biochemical reaction mechanisms can be a powerful complement to experimental investigations of cell signaling networks. In principle, such models have the potential to find the behaviors that result from well‐understood component interactions and their measurable properties, such as concentrations and rate constants. As cancer results from the acquisition of mutations that alter the expression level and/or the biochemistry of proteins encoded by mutated genes, mathematical models of cell signaling networks would also seem to have the potential to predict how these changes alter cell signaling to produce a cancer phenotype. Ras is commonly found in cancer and has been extensively characterized at the level of detail needed to develop such models. Here, we consider how biochemical mechanism‐based models have been used to study mutant Ras signaling. These models demonstrate that it is clearly possible to use observable properties of individual reactions to predict how the entire system behaves to produce the high levels of signal that drive the cancer phenotype. These models also demonstrate differences in how models are developed and studied. Their evaluation suggests which approaches are most promising for future work. WIREs Syst Biol Med 2012, 4:117–127. doi: 10.1002/wsbm.156

Mathematical investigation of how oncogenic ras mutants promote ras signaling.

We have used a mathematical model of the Ras signaling network to link observable biochemical properties with cellular levels of RasGTP. Although there is abundant data characterizing Ras biochemistry, attributing specific changes in biochemical properties to observed phenotypes has been hindered by the scope and complexity of Ras regulation. A mathematical model of the Ras signaling module, therefore, appeared to be of value for this problem. The model described the core architecture shared by pathways that signal through Ras. Mass-action kinetics and ordinary differential equations were used to describe network reactions. Needed parameters were largely available in the published literature and resulted in a model with good agreement to experimental data. Computational analysis of the model resulted in several unanticipated predictions and suggested experiments that subsequently validated some of these predictions.

Differences in sensitivity to EGFR inhibitors could be explained by described biochemical differences between oncogenic Ras mutants

Emerging data suggest different activating Ras mutants may have different biological behaviors. The most striking example may be in colon cancer, where activating KRAS mutations generally indicate a lack of benefit to treatment with EGFR inhibitors, although the activating KRAS G13D mutation appears to be an exception. As KRAS G13D generally shares the same biochemical defects as the other oncogenic KRAS mutants, a mechanism for differential sensitivity is not apparent. Here, a previously developed mathematical model of Ras mutant signaling is used to investigate this problem. The purpose of the analysis is to determine whether differential response is consistent with known mechanisms of Ras signaling, and to determine if any known features of Ras mutants provide an explanation for differential sensitivity. Computational analysis of the mathematical model finds that differential response to upstream inhibition between cancers with different Ras mutants is indeed consistent with known mechanisms of Ras biology. Moreover, model analysis demonstrates that the subtle biochemical differences between G13D and G12D (and G12V) mutants are sufficient to enable differential response to upstream inhibition. Simulations suggest that wild-type Ras within the G13D mutant context is more effectively inhibited by upstream inhibitors than when it is in the G12D or G12V contexts. This difference is a consequence of an elevated Km for the G13D mutant. The identification of a single parameter that influences sensitivity is significant in that it suggests an approach to evaluate other, less common, Ras mutations for their anticipated response to upstream inhibition.

Chemical kinetic mechanistic models to investigate cancer biology and impact cancer medicine.

Traditional experimental biology has provided a mechanistic understanding of cancer in which the malignancy develops through the acquisition of mutations that disrupt cellular processes. Several drugs developed to target such mutations have now demonstrated clinical value. These advances are unequivocal testaments to the value of traditional cellular and molecular biology. However, several features of cancer may limit the pace of progress that can be made with established experimental approaches alone. The mutated genes (and resultant mutant proteins) function within large biochemical networks. Biochemical networks typically have a large number of component molecules and are characterized by a large number of quantitative properties. Responses to a stimulus or perturbation are typically nonlinear and can display qualitative changes that depend upon the specific values of variable system properties. Features such as these can complicate the interpretation of experimental data and the formulation of logical hypotheses that drive further research. Mathematical models based upon the molecular reactions that define these networks combined with computational studies have the potential to deal with these obstacles and to enable currently available information to be more completely utilized. Many of the pressing problems in cancer biology and cancer medicine may benefit from a mathematical treatment. As work in this area advances, one can envision a future where such models may meaningfully contribute to the clinical management of cancer patients.