The complexity of cell signaling and the need for a new mechanics

A multiscale model of the regulation of aquaporin 2 recycling

The response of cells to their environment is driven by a variety of proteins and messenger molecules. In eukaryotes, their distribution and location in the cell are regulated by the vesicular transport system. The transport of aquaporin 2 between membrane and storage region is a crucial part of the water reabsorption in renal principal cells, and its malfunction can lead to Diabetes insipidus. To understand the regulation of this system, we aggregated pathways and mechanisms from literature and derived three models in a hypothesis-driven approach. Furthermore, we combined the models to a single system to gain insight into key regulatory mechanisms of Aquaporin 2 recycling. To achieve this, we developed a multiscale computational framework for the modeling and simulation of cellular systems. The analysis of the system rationalizes that the compartmentalization of cAMP in renal principal cells is a result of the protein kinase A signalosome and can only occur if specific cellular components are observed in conjunction. Endocytotic and exocytotic processes are inherently connected and can be regulated by the same protein kinase A signal.

A biochemical network modeling of a whole-cell

All cellular processes can be ultimately understood in terms of respective fundamental biochemical interactions between molecules, which can be modeled as networks. Very often, these molecules are shared by more than one process, therefore interconnecting them. Despite this effect, cellular processes are usually described by separate networks with heterogeneous levels of detail, such as metabolic, protein-protein interaction, and transcription regulation networks. Aiming at obtaining a unified representation of cellular processes, we describe in this work an integrative framework that draws concepts from rule-based modeling. In order to probe the capabilities of the framework, we used an organism-specific database and genomic information to model the whole-cell biochemical network of the Mycoplasma genitalium organism. This modeling accounted for 15 cellular processes and resulted in a single component network, indicating that all processes are somehow interconnected. The topological analysis of the network showed structural consistency with biological networks in the literature. In order to validate the network, we estimated gene essentiality by simulating gene deletions and compared the results with experimental data available in the literature. We could classify 212 genes as essential, being 95% of them consistent with experimental results. Although we adopted a relatively simple organism as a case study, we suggest that the presented framework has the potential for paving the way to more integrated studies of whole organisms leading to a systemic analysis of cells on a broader scale. The modeling of other organisms using this framework could provide useful large-scale models for different fields of research such as bioengineering, network biology, and synthetic biology, and also provide novel tools for medical and industrial applications.

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.

A comprehensive, mechanistically detailed, and executable model of the cell division cycle in Saccharomyces cerevisiae

Understanding how cellular functions emerge from the underlying molecular mechanisms is a key challenge in biology. This will require computational models, whose predictive power is expected to increase with coverage and precision of formulation. Genome-scale models revolutionised the metabolic field and made the first whole-cell model possible. However, the lack of genome-scale models of signalling networks blocks the development of eukaryotic whole-cell models. Here, we present a comprehensive mechanistic model of the molecular network that controls the cell division cycle in Saccharomyces cerevisiae. We use rxncon, the reaction-contingency language, to neutralise the scalability issues preventing formulation, visualisation and simulation of signalling networks at the genome-scale. We use parameter-free modelling to validate the network and to predict genotype-to-phenotype relationships down to residue resolution. This mechanistic genome-scale model offers a new perspective on eukaryotic cell cycle control, and opens up for similar models-and eventually whole-cell models-of human cells.

Using rxncon to Develop Rule-Based Models

We present a protocol for building, validating, and simulating models of signal transduction networks. These networks are challenging modeling targets due to the combinatorial complexity and sparse data, which have made it a major challenge even to formalize the current knowledge. To address this, the community has developed methods to model biomolecular reaction networks based on site dynamics. The strength of this approach is that reactions and states can be defined at variable resolution, which makes it possible to adapt the model resolution to the empirical data. This improves both scalability and accuracy, making it possible to formalize large models of signal transduction networks. Here, we present a method to build and validate large models of signal transduction networks. The workflow is based on rxncon, the reaction-contingency language. In a five-step process, we create a mechanistic network model, convert it into an executable Boolean model, use the Boolean model to evaluate and improve the network, and finally export the rxncon model into a rule-based format. We provide an introduction to the rxncon language and an annotated, step-by-step protocol for the workflow. Finally, we create a small model of the insulin signaling pathway to illustrate the protocol, together with some of the challenges-and some of their solutions-in modeling signal transduction.

A hierarchy of affinities between cytokine receptors and the common gamma chain leads to pathway cross-talk

Cytokines belonging to the common gamma chain (γ_c) family depend on the shared γ_c receptor subunit for signaling. We report the existence of a fast, cytokine-induced pathway cross-talk acting at the receptor level, resulting from a limiting amount of γ_c on the surface of T cells. We found that this limited abundance of γ_c reduced interleukin-4 (IL-4) and IL-21 responses after IL-7 preexposure but not vice versa. Computational modeling combined with quantitative experimental assays indicated that the asymmetric cross-talk resulted from the ability of the "private" IL-7 receptor subunits (IL-7Rα) to bind to many of the γ_c molecules even before stimulation with cytokine. Upon exposure of T cells to IL-7, the high affinity of the IL-7Rα:IL-7 complex for γ_c further reduced the amount of free γ_c in a manner dependent on the concentration of IL-7. Measurements of bioluminescence resonance energy transfer (BRET) between IL-4Rα and γ_c were reduced when IL-7Rα was overexpressed. Furthermore, in a system expressing IL-7Rα, IL-4Rα, and γ_c, BRET between IL-4Rα and γ_c increased after IL-4 binding and decreased when cells were preexposed to IL-7, supporting the assumption that IL-7Rα and the IL-7Rα:IL-7 complex limit the accessibility of γ_c for other cytokine receptor complexes. We propose that in complex inflammatory environments, such asymmetric cross-talk establishes a hierarchy of cytokine responsiveness.

Inhibition of VEGFR2 Activation and Its Downstream Signaling to ERK1/2 and Calcium by Thrombospondin-1 (TSP1): In silico Investigation

VEGF signaling through VEGFR2 is a central regulator of the angiogenic response. Inhibition of VEGF signaling by the stress-induced matricellular protein TSP1 plays a role in modulating the angiogenic response to VEGF in both health and disease. TSP1 binding to CD47 inhibits VEGFR2 activation. The full implications of this inhibitory interaction are unknown. We developed a detailed rule-based computational model to inquire if TSP1-CD47 signaling through VEGF had downstream effects upon ERK1/2 and calcium. Our Simulations suggest that enhanced degradation of VEGFR2 initiated by the binding of TSP1 to CD47 is sufficient to explain the inhibition of VEGFR2 phosphorylation, calcium elevation, and ERK1/2 activation downstream of VEGF. A complementary mechanism involving the recruitment of phosphatases to the VEGFR2 complex with consequent increase in the rate of receptor dephosphorylation may augment the inhibition of the VEGF signal. The model was then utilized to simulate the effect of inhibiting external TSP1 or the depletion of CD47 as potential therapeutic strategies in restoring VEGF signaling. Results suggest that depleting CD47 is a more efficient strategy in inhibiting the effects of TSP1/CD47 on VEGF signaling. Our results highlight the utility of in silico investigations in elucidating and clarifying molecular mechanisms at the intersection of TSP1 and VEGF biology and in differentiating between competing pro-angiogenic therapeutic strategies relevant to peripheral arterial disease (PAD) and wound healing.

Cuckoo search epistasis: a new method for exploring significant genetic interactions

The advent of high-throughput sequencing technology has resulted in the ability to measure millions of single-nucleotide polymorphisms (SNPs) from thousands of individuals. Although these high-dimensional data have paved the way for better understanding of the genetic architecture of common diseases, they have also given rise to challenges in developing computational methods for learning epistatic relationships among genetic markers. We propose a new method, named cuckoo search epistasis (CSE) for identifying significant epistatic interactions in population-based association studies with a case-control design. This method combines a computationally efficient Bayesian scoring function with an evolutionary-based heuristic search algorithm, and can be efficiently applied to high-dimensional genome-wide SNP data. The experimental results from synthetic data sets show that CSE outperforms existing methods including multifactorial dimensionality reduction and Bayesian epistasis association mapping. In addition, on a real genome-wide data set related to Alzheimer's disease, CSE identified SNPs that are consistent with previously reported results, and show the utility of CSE for application to genome-wide data.

SRC Homology 2 Domain Binding Sites in Insulin, IGF-1 and FGF receptor mediated signaling networks reveal an extensive potential interactome

Specific peptide ligand recognition by modular interaction domains is essential for the fidelity of information flow through the signal transduction networks that control cell behavior in response to extrinsic and intrinsic stimuli. Src homology 2 (SH2) domains recognize distinct phosphotyrosine peptide motifs, but the specific sites that are phosphorylated and the complement of available SH2 domains varies considerably in individual cell types. Such differences are the basis for a wide range of available protein interaction microstates from which signaling can evolve in highly divergent ways. This underlying complexity suggests the need to broadly map the signaling potential of systems as a prerequisite for understanding signaling in specific cell types as well as various pathologies that involve signal transduction such as cancer, developmental defects and metabolic disorders. This report describes interactions between SH2 domains and potential binding partners that comprise initial signaling downstream of activated fibroblast growth factor (FGF), insulin (Ins), and insulin-like growth factor-1 (IGF-1) receptors. A panel of 50 SH2 domains screened against a set of 192 phosphotyrosine peptides defines an extensive potential interactome while demonstrating the selectivity of individual SH2 domains. The interactions described confirm virtually all previously reported associations while describing a large set of potential novel interactions that imply additional complexity in the signaling networks initiated from activated receptors. This study of pTyr ligand binding by SH2 domains provides valuable insight into the selectivity that underpins complex signaling networks that are assembled using modular protein interaction domains.

A statistical procedure to map high-order epistasis for complex traits

Genetic interactions or epistasis have been thought to play a pivotal role in shaping the formation, development and evolution of life. Previous work focused on lower-order interactions between a pair of genes, but it is obviously inadequate to explain a complex network of genetic interactions and pathways. We review and assess a statistical model for characterizing high-order epistasis among more than two genes or quantitative trait loci (QTLs) that control a complex trait. The model includes a series of start-of-the-art standard procedures for estimating and testing the nature and magnitude of QTL interactions. Results from simulation studies and real data analysis warrant the statistical properties of the model and its usefulness in practice. High-order epistatic mapping will provide a routine procedure for charting a detailed picture of the genetic regulation mechanisms underlying the phenotypic variation of complex traits.

Multiscale models of cell signaling

Computational models of signal transduction face challenges of scale below the resolution of a single cell. Here, we organize these challenges around three key interfaces for multiscale models of cell signaling: molecules to pathways, pathways to networks, and networks to outcomes. Each interface requires its own set of computational approaches and systems-level data, and no single approach or dataset can effectively bridge all three interfaces. This suggests that realistic "whole-cell" models of signaling will need to agglomerate different model types that span critical intracellular scales. Future multiscale models will be valuable for understanding the impact of signaling mutations or population variants that lead to cellular diseases such as cancer.

Rule-based modeling of signal transduction: a primer

Biological cells accomplish their physiological functions using interconnected networks of genes, proteins, and other biomolecules. Most interactions in biological signaling networks, such as bimolecular association or covalent modification, can be modeled in a physically realistic manner using elementary reaction kinetics. However, the size and combinatorial complexity of such reaction networks have hindered such a mechanistic approach, leading many to conclude that it is premature and to adopt alternative statistical or phenomenological approaches. The recent development of rule-based modeling languages, such as BioNetGen (BNG) and Kappa, enables the precise and succinct encoding of large reaction networks. Coupled with complementary advances in simulation methods, these languages circumvent the combinatorial barrier and allow mechanistic modeling on a much larger scale than previously possible. These languages are also intuitive to the biologist and accessible to the novice modeler. In this chapter, we provide a self-contained tutorial on modeling signal transduction networks using the BNG Language and related software tools. We review the basic syntax of the language and show how biochemical knowledge can be articulated using reaction rules, which can be used to capture a broad range of biochemical and biophysical phenomena in a concise and modular way. A model of ligand-activated receptor dimerization is examined, with a detailed treatment of each step of the modeling process. Sections discussing modeling theory, implicit and explicit model assumptions, and model parameterization are included, with special focus on retaining biophysical realism and avoiding common pitfalls. We also discuss the more advanced case of compartmental modeling using the compartmental extension to BioNetGen. In addition, we provide a comprehensive set of example reaction rules that cover the various aspects of signal transduction, from signaling at the membrane to gene regulation. The reader can modify these reaction rules to model their own systems of interest.

Systems biology in immunology: a computational modeling perspective

Systems biology is an emerging discipline that combines high-content, multiplexed measurements with informatic and computational modeling methods to better understand biological function at various scales. Here we present a detailed review of the methods used to create computational models and to conduct simulations of immune function. We provide descriptions of the key data-gathering techniques employed to generate the quantitative and qualitative data required for such modeling and simulation and summarize the progress to date in applying these tools and techniques to questions of immunological interest, including infectious disease. We include comments on what insights modeling can provide that complement information obtained from the more familiar experimental discovery methods used by most investigators and the reasons why quantitative methods are needed to eventually produce a better understanding of immune system operation in health and disease.

Rule-based modelling and simulation of biochemical systems with molecular finite automata

The authors propose a theoretical formalism, molecular finite automata (MFA), to describe individual proteins as rule-based computing machines. The MFA formalism provides a framework for modelling individual protein behaviours and systems-level dynamics via construction of programmable and executable machines. Models specified within this formalism explicitly represent the context-sensitive dynamics of individual proteins driven by external inputs and represent protein-protein interactions as synchronised machine reconfigurations. Both deterministic and stochastic simulations can be applied to quantitatively compute the dynamics of MFA models. They apply the MFA formalism to model and simulate a simple example of a signal-transduction system that involves an MAP kinase cascade and a scaffold protein.

A general model for multilocus epistatic interactions in case-control studies

Background

Epistasis, i.e., the interaction of alleles at different loci, is thought to play a central role in the formation and progression of complex diseases. The complexity of disease expression should arise from a complex network of epistatic interactions involving multiple genes.

Methodology

We develop a general model for testing high-order epistatic interactions for a complex disease in a case-control study. We incorporate the quantitative genetic theory of high-order epistasis into the setting of cases and controls sampled from a natural population. The new model allows the identification and testing of epistasis and its various genetic components.

Conclusions

Simulation studies were used to examine the power and false positive rates of the model under different sampling strategies. The model was used to detect epistasis in a case-control study of inflammatory bowel disease, in which five SNPs at a candidate gene were typed, leading to the identification of a significant three-locus epistasis.

RuleMonkey: software for stochastic simulation of rule-based models

Background

The system-level dynamics of many molecular interactions, particularly protein-protein interactions, can be conveniently represented using reaction rules, which can be specified using model-specification languages, such as the BioNetGen language (BNGL). A set of rules implicitly defines a (bio)chemical reaction network. The reaction network implied by a set of rules is often very large, and as a result, generation of the network implied by rules tends to be computationally expensive. Moreover, the cost of many commonly used methods for simulating network dynamics is a function of network size. Together these factors have limited application of the rule-based modeling approach. Recently, several methods for simulating rule-based models have been developed that avoid the expensive step of network generation. The cost of these "network-free" simulation methods is independent of the number of reactions implied by rules. Software implementing such methods is now needed for the simulation and analysis of rule-based models of biochemical systems.

Results

Here, we present a software tool called RuleMonkey, which implements a network-free method for simulation of rule-based models that is similar to Gillespie's method. The method is suitable for rule-based models that can be encoded in BNGL, including models with rules that have global application conditions, such as rules for intramolecular association reactions. In addition, the method is rejection free, unlike other network-free methods that introduce null events, i.e., steps in the simulation procedure that do not change the state of the reaction system being simulated. We verify that RuleMonkey produces correct simulation results, and we compare its performance against DYNSTOC, another BNGL-compliant tool for network-free simulation of rule-based models. We also compare RuleMonkey against problem-specific codes implementing network-free simulation methods.

Conclusions

RuleMonkey enables the simulation of rule-based models for which the underlying reaction networks are large. It is typically faster than DYNSTOC for benchmark problems that we have examined. RuleMonkey is freely available as a stand-alone application http://public.tgen.org/rulemonkey. It is also available as a simulation engine within GetBonNie, a web-based environment for building, analyzing and sharing rule-based models.

Communications: Hamiltonian regulated cell signaling network

Cell signaling is fundamental to cell survival and disease progression. Traditional approaches to study these networks have focused largely on probabilistic approaches, with a large number of ad hoc assumptions. In this paper, we develop a linear Hamiltonian model to study the integrin signaling network. The integrin signaling network is central to cell adhesion, migration, and differentiation, but has not been studied in the same detail as other cell cycle networks. In this study, the integrin signaling network with 16 nodes in thermal fluctuations is analyzed through ensemble averages on the linear Hamiltonian model. This new and analytically rigorous approach offers a quick method to find out the dominant nodes in the complex network, which operate in the thermal noise regime. The robust on/off transitions due to the different initial inputs also reflect the inherent structure in the network, providing new insights into structure and function of the network.

Propagation of kinetic uncertainties through a canonical topology of the TLR4 signaling network in different regions of biochemical reaction space

Background

Signal transduction networks represent the information processing systems that dictate which dynamical regimes of biochemical activity can be accessible to a cell under certain circumstances. One of the major concerns in molecular systems biology is centered on the elucidation of the robustness properties and information processing capabilities of signal transduction networks. Achieving this goal requires the establishment of causal relations between the design principle of biochemical reaction systems and their emergent dynamical behaviors.

Methods

In this study, efforts were focused in the construction of a relatively well informed, deterministic, non-linear dynamic model, accounting for reaction mechanisms grounded on standard mass action and Hill saturation kinetics, of the canonical reaction topology underlying Toll-like receptor 4 (TLR4)-mediated signaling events. This signaling mechanism has been shown to be deployed in macrophages during a relatively short time window in response to lypopolysaccharyde (LPS) stimulation, which leads to a rapidly mounted innate immune response. An extensive computational exploration of the biochemical reaction space inhabited by this signal transduction network was performed via local and global perturbation strategies. Importantly, a broad spectrum of biologically plausible dynamical regimes accessible to the network in widely scattered regions of parameter space was reconstructed computationally. Additionally, experimentally reported transcriptional readouts of target pro-inflammatory genes, which are actively modulated by the network in response to LPS stimulation, were also simulated. This was done with the main goal of carrying out an unbiased statistical assessment of the intrinsic robustness properties of this canonical reaction topology.

Results

Our simulation results provide convincing numerical evidence supporting the idea that a canonical reaction mechanism of the TLR4 signaling network is capable of performing information processing in a robust manner, a functional property that is independent of the signaling task required to be executed. Nevertheless, it was found that the robust performance of the network is not solely determined by its design principle (topology), but this may be heavily dependent on the network's current position in biochemical reaction space. Ultimately, our results enabled us the identification of key rate limiting steps which most effectively control the performance of the system under diverse dynamical regimes.

Conclusions

Overall, our in silico study suggests that biologically relevant and non-intuitive aspects on the general behavior of a complex biomolecular network can be elucidated only when taking into account a wide spectrum of dynamical regimes attainable by the system. Most importantly, this strategy provides the means for a suitable assessment of the inherent variational constraints imposed by the structure of the system when systematically probing its parameter space.

Science Signaling Podcast: 28 July 2009

Science Signaling 's Chief Scientific Editor discusses complexity in signaling networks.