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

Capturing Biomarkers and Molecular Targets in Cellular Landscapes From Dynamic Reaction Network Models and Machine Learning

Computational dynamic ODE models of cell function describing biochemical reactions have been created for decades, but on a small scale. Still, they have been highly effective in describing and predicting behaviors. For example, oscillatory phospho-ERK levels were predicted and confirmed in MAPK signaling encompassing both positive and negative feedback loops. These models typically were limited and not adapted to large datasets so commonly found today. But importantly, ODE models describe reaction networks in well-mixed systems representing the cell and can be simulated with ordinary differential equations that are solved deterministically. Stochastic solutions, which can account for noisy reaction networks, in some cases, also improve predictions. Today, dynamic ODE models rarely encompass an entire cell even though it might be expected that an upload of the large genomic, transcriptomic, and proteomic datasets may allow whole cell models. It is proposed here to combine output from simulated dynamic ODE models, completed with omics data, to discover both biomarkers in cancer a priori and molecular targets in the Machine Learning setting.

Inhibition of RPS6K reveals context-dependent Akt activity in luminal breast cancer cells

Aberrant signaling through insulin (Ins) and insulin-like growth factor I (IGF1) receptors contribute to the risk and advancement of many cancer types by activating cell survival cascades. Similarities between these pathways have thus far prevented the development of pharmacological interventions that specifically target either Ins or IGF1 signaling. To identify differences in early Ins and IGF1 signaling mechanisms, we developed a dual receptor (IGF1R & InsR) computational response model. The model suggested that ribosomal protein S6 kinase (RPS6K) plays a critical role in regulating MAPK and Akt activation levels in response to Ins and IGF1 stimulation. As predicted, perturbing RPS6K kinase activity led to an increased Akt activation with Ins stimulation compared to IGF1 stimulation. Being able to discern differential downstream signaling, we can explore improved anti-IGF1R cancer therapies by eliminating the emergence of compensation mechanisms without disrupting InsR signaling.

Does frequency-dependent cell proliferation exhibit a Fano-type resonance?

We examined PC12 cell proliferation in environments with temporally varying epidermal growth factor concentrations by means of a microfluidic system. Our measurements revealed frequency-dependent cell behaviour over an observation period of three days. The cell population either increased, decreased or remained constant depending on the frequency of epidermal growth factor applied. A plot of the apparent proliferation rate as a function of growth-factor frequency was mathematically described by the Fano line-shape formula. In the context of linear response theory, these results imply that the PC12 cells compute zero, first and second-order time derivatives of the ligand concentration and utilise this information to decide to proliferate or die. We discuss a physical model based on periodic forcing of coupled oscillators that accounts for these observations. Our results and analysis suggest the possibility to influence cell fate by controlling the dynamics of the extracellular environment.

A scalable method for parameter-free simulation and validation of mechanistic cellular signal transduction network models

The metabolic modelling community has established the gold standard for bottom-up systems biology with reconstruction, validation and simulation of mechanistic genome-scale models. Similar methods have not been established for signal transduction networks, where the representation of complexes and internal states leads to scalability issues in both model formulation and execution. While rule- and agent-based methods allow efficient model definition and execution, respectively, model parametrisation introduces an additional layer of uncertainty due to the sparsity of reliably measured parameters. Here, we present a scalable method for parameter-free simulation of mechanistic signal transduction networks. It is based on rxncon and uses a bipartite Boolean logic with separate update rules for reactions and states. Using two generic update rules, we enable translation of any rxncon model into a unique Boolean model, which can be used for network validation and simulation-allowing the prediction of system-level function directly from molecular mechanistic data. Through scalable model definition and simulation, and the independence of quantitative parameters, it opens up for simulation and validation of mechanistic genome-scale models of signal transduction networks.

Scaling methods for accelerating kinetic Monte Carlo simulations of chemical reaction networks

Various kinetic Monte Carlo algorithms become inefficient when some of the population sizes in a system are large, which gives rise to a large number of reaction events per unit time. Here, we present a new acceleration algorithm based on adaptive and heterogeneous scaling of reaction rates and stoichiometric coefficients. The algorithm is conceptually related to the commonly used idea of accelerating a stochastic simulation by considering a subvolume λΩ (0 < λ < 1) within a system of interest, which reduces the number of reaction events per unit time occurring in a simulation by a factor 1/λ at the cost of greater error in unbiased estimates of first moments and biased overestimates of second moments. Our new approach offers two unique benefits. First, scaling is adaptive and heterogeneous, which eliminates the pitfall of overaggressive scaling. Second, there is no need for an a priori classification of populations as discrete or continuous (as in a hybrid method), which is problematic when discreteness of a chemical species changes during a simulation. The method requires specification of only a single algorithmic parameter, N_c, a global critical population size above which populations are effectively scaled down to increase simulation efficiency. The method, which we term partial scaling, is implemented in the open-source BioNetGen software package. We demonstrate that partial scaling can significantly accelerate simulations without significant loss of accuracy for several published models of biological systems. These models characterize activation of the mitogen-activated protein kinase ERK, prion protein aggregation, and T-cell receptor signaling.

Multicellular Models Bridging Intracellular Signaling and Gene Transcription to Population Dynamics

Cell signaling and gene transcription occur at faster time scales compared to cellular death, division, and evolution. Bridging these multiscale events in a model is computationally challenging. We introduce a framework for the systematic development of multiscale cell population models. Using message passing interface (MPI) parallelism, the framework creates a population model from a single-cell biochemical network model. It launches parallel simulations on a single-cell model and treats each stand-alone parallel process as a cell object. MPI mediates cell-to-cell and cell-to-environment communications in a server-client fashion. In the framework, model-specific higher level rules link the intracellular molecular events to cellular functions, such as death, division, or phenotype change. Cell death is implemented by terminating a parallel process, while cell division is carried out by creating a new process (daughter cell) from an existing one (mother cell). We first demonstrate these capabilities by creating two simple example models. In one model, we consider a relatively simple scenario where cells can evolve independently. In the other model, we consider interdependency among the cells, where cellular communication determines their collective behavior and evolution under a temporally evolving growth condition. We then demonstrate the framework’s capability by simulating a full-scale model of bacterial quorum sensing, where the dynamics of a population of bacterial cells is dictated by the intercellular communications in a time-evolving growth environment.

Generalizing Gillespie's Direct Method to Enable Network-Free Simulations

Gillespie's direct method for stochastic simulation of chemical kinetics is a staple of computational systems biology research. However, the algorithm requires explicit enumeration of all reactions and all chemical species that may arise in the system. In many cases, this is not feasible due to the combinatorial explosion of reactions and species in biological networks. Rule-based modeling frameworks provide a way to exactly represent networks containing such combinatorial complexity, and generalizations of Gillespie's direct method have been developed as simulation engines for rule-based modeling languages. Here, we provide both a high-level description of the algorithms underlying the simulation engines, termed network-free simulation algorithms, and how they have been applied in systems biology research. We also define a generic rule-based modeling framework and describe a number of technical details required for adapting Gillespie's direct method for network-free simulation. Finally, we briefly discuss potential avenues for advancing network-free simulation and the role they continue to play in modeling dynamical systems in biology.

An Overview of Network-Based and -Free Approaches for Stochastic Simulation of Biochemical Systems

Stochastic simulation has been widely used to model the dynamics of biochemical reaction networks. Several algorithms have been proposed that are exact solutions of the chemical master equation, following the work of Gillespie. These stochastic simulation approaches can be broadly classified into two categories: network-based and -free simulation. The network-based approach requires that the full network of reactions be established at the start, while the network-free approach is based on reaction rules that encode classes of reactions, and by applying rule transformations, it generates reaction events as they are needed without ever having to derive the entire network. In this study, we compare the efficiency and limitations of several available implementations of these two approaches. The results allow for an informed selection of the implementation and methodology for specific biochemical modeling applications.

Src homology 2 domains enhance tyrosine phosphorylation in vivo by protecting binding sites in their target proteins from dephosphorylation

Phosphotyrosine (pTyr)-dependent signaling is critical for many cellular processes. It is highly dynamic, as signal output depends not only on phosphorylation and dephosphorylation rates but also on the rates of binding and dissociation of effectors containing phosphotyrosine-dependent binding modules such as Src homology 2 (SH2) and phosphotyrosine-binding (PTB) domains. Previous in vitro studies suggested that binding of SH2 and PTB domains can enhance protein phosphorylation by protecting the sites bound by these domains from phosphatase-mediated dephosphorylation. To test whether this occurs in vivo, we used the binding of growth factor receptor bound 2 (GRB2) to phosphorylated epidermal growth factor receptor (EGFR) as a model system. We analyzed the effects of SH2 domain overexpression on protein tyrosine phosphorylation by quantitative Western and far-Western blotting, mass spectrometry, and computational modeling. We found that SH2 overexpression results in a significant, dose-dependent increase in EGFR tyrosine phosphorylation, particularly of sites corresponding to the binding specificity of the overexpressed SH2 domain. Computational models using experimentally determined EGFR phosphorylation and dephosphorylation rates, and pTyr-EGFR and GRB2 concentrations, recapitulated the experimental findings. Surprisingly, both modeling and biochemical analyses suggested that SH2 domain overexpression does not result in a major decrease in the number of unbound phosphorylated SH2 domain-binding sites. Our results suggest that signaling via SH2 domain binding is buffered over a relatively wide range of effector concentrations and that SH2 domain proteins with overlapping binding specificities are unlikely to compete with one another for phosphosites in vivo.

Automated visualization of rule-based models

Frameworks such as BioNetGen, Kappa and Simmune use "reaction rules" to specify biochemical interactions compactly, where each rule specifies a mechanism such as binding or phosphorylation and its structural requirements. Current rule-based models of signaling pathways have tens to hundreds of rules, and these numbers are expected to increase as more molecule types and pathways are added. Visual representations are critical for conveying rule-based models, but current approaches to show rules and interactions between rules scale poorly with model size. Also, inferring design motifs that emerge from biochemical interactions is an open problem, so current approaches to visualize model architecture rely on manual interpretation of the model. Here, we present three new visualization tools that constitute an automated visualization framework for rule-based models: (i) a compact rule visualization that efficiently displays each rule, (ii) the atom-rule graph that conveys regulatory interactions in the model as a bipartite network, and (iii) a tunable compression pipeline that incorporates expert knowledge and produces compact diagrams of model architecture when applied to the atom-rule graph. The compressed graphs convey network motifs and architectural features useful for understanding both small and large rule-based models, as we show by application to specific examples. Our tools also produce more readable diagrams than current approaches, as we show by comparing visualizations of 27 published models using standard graph metrics. We provide an implementation in the open source and freely available BioNetGen framework, but the underlying methods are general and can be applied to rule-based models from the Kappa and Simmune frameworks also. We expect that these tools will promote communication and analysis of rule-based models and their eventual integration into comprehensive whole-cell models.

Agent-based re-engineering of ErbB signaling: a modeling pipeline for integrative systems biology

Motivation

Experiments in systems biology are generally supported by a computational model which quantitatively estimates the parameters of the system by finding the best fit to the experiment. Mathematical models have proved to be successful in reverse engineering the system. The data generated is interpreted to understand the dynamics of the underlying phenomena. The question we have sought to answer is that - is it possible to use an agent-based approach to re-engineer a biological process, making use of the available knowledge from experimental and modelling efforts? Can the bottom-up approach benefit from the top-down exercise so as to create an integrated modelling formalism for systems biology? We propose a modelling pipeline that learns from the data given by reverse engineering, and uses it for re-engineering the system, to carry out in-silico experiments.

Results

A mathematical model that quantitatively predicts co-expression of EGFR-HER2 receptors in activation and trafficking has been taken for this study. The pipeline architecture takes cues from the population model that gives the rates of biochemical reactions, to formulate knowledge-based rules for the particle model. Agent-based simulations using these rules, support the existing facts on EGFR-HER2 dynamics. We conclude that, re-engineering models, built using the results of reverse engineering, opens up the possibility of harnessing the power pack of data which now lies scattered in literature. Virtual experiments could then become more realistic when empowered with the findings of empirical cell biology and modelling studies.

Availability and Implementation

Implemented on the Agent Modelling Framework developed in-house. C ++ code templates available in Supplementary material .

Contact

liz.csir@gmail.com.

Supplementary information

Supplementary data are available at Bioinformatics online.

A rule-based model of insulin signalling pathway

BACKGROUND

The insulin signalling pathway (ISP) is an important biochemical pathway, which regulates some fundamental biological functions such as glucose and lipid metabolism, protein synthesis, cell proliferation, cell differentiation and apoptosis. In the last years, different mathematical models based on ordinary differential equations have been proposed in the literature to describe specific features of the ISP, thus providing a description of the behaviour of the system and its emerging properties. However, protein-protein interactions potentially generate a multiplicity of distinct chemical species, an issue referred to as "combinatorial complexity", which results in defining a high number of state variables equal to the number of possible protein modifications. This often leads to complex, error prone and difficult to handle model definitions.

RESULTS

In this work, we present a comprehensive model of the ISP, which integrates three models previously available in the literature by using the rule-based modelling (RBM) approach. RBM allows for a simple description of a number of signalling pathway characteristics, such as the phosphorylation of signalling proteins at multiple sites with different effects, the simultaneous interaction of many molecules of the signalling pathways with several binding partners, and the information about subcellular localization where reactions take place. Thanks to its modularity, it also allows an easy integration of different pathways. After RBM specification, we simulated the dynamic behaviour of the ISP model and validated it using experimental data. We the examined the predicted profiles of all the active species and clustered them in four clusters according to their dynamic behaviour. Finally, we used parametric sensitivity analysis to show the role of negative feedback loops in controlling the robustness of the system.

CONCLUSIONS

The presented ISP model is a powerful tool for data simulation and can be used in combination with experimental approaches to guide the experimental design. The model is available at http://sysbiobig.dei.unipd.it/ was submitted to Biomodels Database ( https://www.ebi.ac.uk/biomodels-main/ # MODEL 1604100005).

Annotation of rule-based models with formal semantics to enable creation, analysis, reuse and visualization

MOTIVATION

Biological systems are complex and challenging to model and therefore model reuse is highly desirable. To promote model reuse, models should include both information about the specifics of simulations and the underlying biology in the form of metadata. The availability of computationally tractable metadata is especially important for the effective automated interpretation and processing of models. Metadata are typically represented as machine-readable annotations which enhance programmatic access to information about models. Rule-based languages have emerged as a modelling framework to represent the complexity of biological systems. Annotation approaches have been widely used for reaction-based formalisms such as SBML. However, rule-based languages still lack a rich annotation framework to add semantic information, such as machine-readable descriptions, to the components of a model.

RESULTS

We present an annotation framework and guidelines for annotating rule-based models, encoded in the commonly used Kappa and BioNetGen languages. We adapt widely adopted annotation approaches to rule-based models. We initially propose a syntax to store machine-readable annotations and describe a mapping between rule-based modelling entities, such as agents and rules, and their annotations. We then describe an ontology to both annotate these models and capture the information contained therein, and demonstrate annotating these models using examples. Finally, we present a proof of concept tool for extracting annotations from a model that can be queried and analyzed in a uniform way. The uniform representation of the annotations can be used to facilitate the creation, analysis, reuse and visualization of rule-based models. Although examples are given, using specific implementations the proposed techniques can be applied to rule-based models in general.

AVAILABILITY AND IMPLEMENTATION

The annotation ontology for rule-based models can be found at http://purl.org/rbm/rbmo The krdf tool and associated executable examples are available at http://purl.org/rbm/rbmo/krdf

CONTACT

anil.wipat@newcastle.ac.uk or vdanos@inf.ed.ac.uk.

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.

Analytical reduction of combinatorial complexity arising from multiple protein modification sites

Combinatorial complexity is a major obstacle to ordinary differential equation (ODE) modelling of biochemical networks. For example, a protein with 10 sites that can each be unphosphorylated, phosphorylated or bound to adaptor protein requires 3(10) ODEs. This problem is often dealt with by making ad hoc assumptions which have unclear validity and disallow modelling of site-specific dynamics. Such site-specific dynamics, however, are important in many biological systems. We show here that for a common biological situation where adaptors bind modified sites, binding is slow relative to modification/demodification, and binding to one modified site hinders binding to other sites, for a protein with n modification sites and m adaptor proteins the number of ODEs needed to simulate the site-specific dynamics of biologically relevant, lumped bound adaptor states is independent of the number of modification sites and equal to m + 1, giving a significant reduction in system size. These considerations can be relaxed considerably while retaining reasonably accurate descriptions of the true system dynamics. We apply the theory to model, using only 11 ODEs, the dynamics of ligand-induced phosphorylation of nine tyrosines on epidermal growth factor receptor (EGFR) and primary recruitment of six signalling proteins (Grb2, PI3K, PLCγ1, SHP2, RasA1 and Shc1). The model quantitatively accounts for experimentally determined site-specific phosphorylation and dephosphorylation rates, differential affinities of binding proteins for the phosphorylated sites and binding protein expression levels. Analysis suggests that local concentration of site-specific phosphatases such as SHP2 in membrane subdomains by a factor of approximately 10(7) is critical for effective site-specific regulation. We further show how our framework can be extended with minimal effort to consider binding cooperativity between Grb2 and c-Cbl, which is important for receptor trafficking. Our theory has potentially broad application to reduce combinatorial complexity and allow practical simulation of a variety ODE models relevant to systems biology and pharmacology applications to allow exploration of key aspects of complexity that control signal flux.

Modeling for (physical) biologists: an introduction to the rule-based approach

Models that capture the chemical kinetics of cellular regulatory networks can be specified in terms of rules for biomolecular interactions. A rule defines a generalized reaction, meaning a reaction that permits multiple reactants, each capable of participating in a characteristic transformation and each possessing certain, specified properties, which may be local, such as the state of a particular site or domain of a protein. In other words, a rule defines a transformation and the properties that reactants must possess to participate in the transformation. A rule also provides a rate law. A rule-based approach to modeling enables consideration of mechanistic details at the level of functional sites of biomolecules and provides a facile and visual means for constructing computational models, which can be analyzed to study how system-level behaviors emerge from component interactions.

Modeling biomolecular site dynamics in immunoreceptor signaling systems

The immune system plays a central role in human health. The activities of immune cells, whether defending an organism from disease or triggering a pathological condition such as autoimmunity, are driven by the molecular machinery of cellular signaling systems. Decades of experimentation have elucidated many of the biomolecules and interactions involved in immune signaling and regulation, and recently developed technologies have led to new types of quantitative, systems-level data. To integrate such information and develop nontrivial insights into the immune system, computational modeling is needed, and it is essential for modeling methods to keep pace with experimental advances. In this chapter, we focus on the dynamic, site-specific, and context-dependent nature of interactions in immunoreceptor signaling (i.e., the biomolecular site dynamics of immunoreceptor signaling), the challenges associated with capturing these details in computational models, and how these challenges have been met through use of rule-based modeling approaches.

Multi-state modeling of biomolecules

Multi-state modeling of biomolecules refers to a series of techniques used to represent and compute the behavior of biological molecules or complexes that can adopt a large number of possible functional states. Biological signaling systems often rely on complexes of biological macromolecules that can undergo several functionally significant modifications that are mutually compatible. Thus, they can exist in a very large number of functionally different states. Modeling such multi-state systems poses two problems: the problem of how to describe and specify a multi-state system (the “specification problem”) and the problem of how to use a computer to simulate the progress of the system over time (the “computation problem”). To address the specification problem, modelers have in recent years moved away from explicit specification of all possible states and towards rule-based formalisms that allow for implicit model specification, including the κ-calculus [1], BioNetGen [2]–[5], the Allosteric Network Compiler [6], and others [7], [8]. To tackle the computation problem, they have turned to particle-based methods that have in many cases proved more computationally efficient than population-based methods based on ordinary differential equations, partial differential equations, or the Gillespie stochastic simulation algorithm[9], [10]. Given current computing technology, particle-based methods are sometimes the only possible option. Particle-based simulators fall into two further categories: nonspatial simulators, such as StochSim [11], DYNSTOC [12], RuleMonkey [9], [13], and the Network-Free Stochastic Simulator (NFSim) [14], and spatial simulators, including Meredys [15], SRSim [16], [17], and MCell [18]–[20]. Modelers can thus choose from a variety of tools, the best choice depending on the particular problem. Development of faster and more powerful methods is ongoing, promising the ability to simulate ever more complex signaling processes in the future.

From proteomes to complexomes in the era of systems biology

Protein complexes carry out almost the entire signaling and functional processes in the cell. The protein complex complement of a cell, and its network of complex-complex interactions, is referred to here as the complexome. Computational methods to predict protein complexes from proteomics data, resulting in network representations of complexomes, have recently being developed. In addition, key advances have been made toward understanding the network and structural organization of complexomes. We review these bioinformatics advances, and their discovery-potential, as well as the merits of integrating proteomics data with emerging methods in systems biology to study protein complex signaling. It is envisioned that improved integration of proteomics and systems biology, incorporating the dynamics of protein complexes in space and time, may lead to more predictive models of cell signaling networks for effective modulation.

Exact hybrid particle/population simulation of rule-based models of biochemical systems

Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational modifications. Rule-based modeling overcomes this problem by representing molecules as structured objects and encoding their interactions as pattern-based rules. This greatly simplifies the process of model specification, avoiding the tedious and error prone task of manually enumerating all species and reactions that can potentially exist in a system. From a simulation perspective, rule-based models can be expanded algorithmically into fully-enumerated reaction networks and simulated using a variety of network-based simulation methods, such as ordinary differential equations or Gillespie's algorithm, provided that the network is not exceedingly large. Alternatively, rule-based models can be simulated directly using particle-based kinetic Monte Carlo methods. This “network-free” approach produces exact stochastic trajectories with a computational cost that is independent of network size. However, memory and run time costs increase with the number of particles, limiting the size of system that can be feasibly simulated. Here, we present a hybrid particle/population simulation method that combines the best attributes of both the network-based and network-free approaches. The method takes as input a rule-based model and a user-specified subset of species to treat as population variables rather than as particles. The model is then transformed by a process of “partial network expansion” into a dynamically equivalent form that can be simulated using a population-adapted network-free simulator. The transformation method has been implemented within the open-source rule-based modeling platform BioNetGen, and resulting hybrid models can be simulated using the particle-based simulator NFsim. Performance tests show that significant memory savings can be achieved using the new approach and a monetary cost analysis provides a practical measure of its utility.

Rule-based modeling is a modeling paradigm that addresses the problem of combinatorial complexity in biochemical systems. The key idea is to specify only those components of a biological macromolecule that are directly involved in a biochemical transformation. Until recently, this “pattern-based” approach greatly simplified the process of model building but did nothing to improve the performance of model simulation. This changed with the introduction of “network-free” simulation methods, which operate directly on the compressed rule set of a rule-based model rather than on a fully-enumerated set of reactions and species. However, these methods represent every molecule in a system as a particle, limiting their use to systems containing less than a few million molecules. Here, we describe an extension to the network-free approach that treats rare, complex species as particles and plentiful, simple species as population variables, while retaining the exact dynamics of the model system. By making more efficient use of computational resources for species that do not require the level of detail of a particle representation, this hybrid particle/population approach can simulate systems much larger than is possible using network-free methods and is an important step towards realizing the practical simulation of detailed, mechanistic models of whole cells.

Navigating the multilayered organization of eukaryotic signaling: a new trend in data integration

The ever-increasing capacity of biological molecular data acquisition outpaces our ability to understand the meaningful relationships between molecules in a cell. Multiple databases were developed to store and organize these molecular data. However, emerging fundamental questions about concerted functions of these molecules in hierarchical cellular networks are poorly addressed. Here we review recent advances in the development of publically available databases that help us analyze the signal integration and processing by multilayered networks that specify biological responses in model organisms and human cells

Rule-based modeling: a computational approach for studying biomolecular site dynamics in cell signaling systems

Rule-based modeling was developed to address the limitations of traditional approaches for modeling chemical kinetics in cell signaling systems. These systems consist of multiple interacting biomolecules (e.g., proteins), which themselves consist of multiple parts (e.g., domains, linear motifs, and sites of phosphorylation). Consequently, biomolecules that mediate information processing generally have the potential to interact in multiple ways, with the number of possible complexes and posttranslational modification states tending to grow exponentially with the number of binary interactions considered. As a result, only large reaction networks capture all possible consequences of the molecular interactions that occur in a cell signaling system, which is problematic because traditional modeling approaches for chemical kinetics (e.g., ordinary differential equations) require explicit network specification. This problem is circumvented through representation of interactions in terms of local rules. With this approach, network specification is implicit and model specification is concise. Concise representation results in a coarse graining of chemical kinetics, which is introduced because all reactions implied by a rule inherit the rate law associated with that rule. Coarse graining can be appropriate if interactions are modular, and the coarseness of a model can be adjusted as needed. Rules can be specified using specialized model-specification languages, and recently developed tools designed for specification of rule-based models allow one to leverage powerful software engineering capabilities. A rule-based model comprises a set of rules, which can be processed by general-purpose simulation and analysis tools to achieve different objectives (e.g., to perform either a deterministic or stochastic simulation).

Machines vs. ensembles: effective MAPK signaling through heterogeneous sets of protein complexes

Despite the importance of intracellular signaling networks, there is currently no consensus regarding the fundamental nature of the protein complexes such networks employ. One prominent view involves stable signaling machines with well-defined quaternary structures. The combinatorial complexity of signaling networks has led to an opposing perspective, namely that signaling proceeds via heterogeneous pleiomorphic ensembles of transient complexes. Since many hypotheses regarding network function rely on how we conceptualize signaling complexes, resolving this issue is a central problem in systems biology. Unfortunately, direct experimental characterization of these complexes has proven technologically difficult, while combinatorial complexity has prevented traditional modeling methods from approaching this question. Here we employ rule-based modeling, a technique that overcomes these limitations, to construct a model of the yeast pheromone signaling network. We found that this model exhibits significant ensemble character while generating reliable responses that match experimental observations. To contrast the ensemble behavior, we constructed a model that employs hierarchical assembly pathways to produce scaffold-based signaling machines. We found that this machine model could not replicate the experimentally observed combinatorial inhibition that arises when the scaffold is overexpressed. This finding provides evidence against the hierarchical assembly of machines in the pheromone signaling network and suggests that machines and ensembles may serve distinct purposes in vivo. In some cases, e.g. core enzymatic activities like protein synthesis and degradation, machines assembled via hierarchical energy landscapes may provide functional stability for the cell. In other cases, such as signaling, ensembles may represent a form of weak linkage, facilitating variation and plasticity in network evolution. The capacity of ensembles to signal effectively will ultimately shape how we conceptualize the function, evolution and engineering of signaling networks.

Intracellular signaling networks are central to a cell's ability to adapt to its environment. Developing the capacity to effectively manipulate such networks would have a wide range of applications, from cancer therapy to synthetic biology. This requires a thorough understanding of the mechanisms of signal transduction, particularly the kinds of protein complexes that are formed during transmission of extracellular information to the nucleus. Traditionally, signaling complexes have been largely perceived (albeit often implicitly) as machine-like structures. However, the number of molecular complexes that could theoretically be formed by complex signaling networks is astronomically large. This has led to the pleiomorphic ensemble hypothesis, which posits that diverse and rapidly changing sets of transient protein complexes can transmit and process information. Our goal was to use computational approaches, specifically rule-based modeling, to test these hypotheses. We constructed a model of the prototypical yeast mating pathway and found significant ensemble-like behavior. Our results thus demonstrated that ensembles can in fact transmit extracellular signals with minimal noise. Additionally, a comparison of this model with one tailored to generate machine-like complexes displayed notable phenotypic differences, revealing potential advantages for ensemble-like signaling. Our demonstration that ensembles can function effectively will have a significant impact on how we conceptualize signaling and other processes inside cells.

Information content and scalability in signal transduction network reconstruction formats

One of the first steps towards holistic understanding of cellular networks is the integration of the available information in a human and machine readable format. This network reconstruction process is well established for metabolic networks, and numerous genome wide metabolic reconstructions are already available. Extending these strategies to signalling networks has proven difficult, primarily due to the combinatorial nature of regulatory modifications. The combinatorial nature of possible protein-protein interactions and post translational modifications affects both network size and the correspondence between the reconstructed network and the underlying empirical data. Here, we discuss different approaches to reconstruction of signal transduction networks. We divide the current approaches into topological, specific state based and reaction-contingency based, and discuss their different information content and scalability. The discussion focusses on graphical formats but the points are in general applicable also to mathematical models and databases. While the formats have complementary strengths especially for small networks, reaction-contingency based formats have a number of advantages in the light of global network reconstruction. In particular, they minimise the need for assumptions, maximise the congruence with empirical data, and scale efficiently with network size.