Integration of Boolean models exemplified on hepatocyte signal transduction

The number of mathematical models for biological pathways is rapidly growing. In particular, Boolean modelling proved to be suited to describe large cellular signalling networks. Systems biology is at the threshold to holistic understanding of comprehensive networks. In order to reach this goal, connection and integration of existing models of parts of cellular networks into more comprehensive network models is necessary. We discuss model combination approaches for Boolean models. Boolean modelling is qualitative rather than quantitative and does not require detailed kinetic information. We show that these models are useful precursors for large-scale quantitative models and that they are comparatively easy to combine. We propose modelling standards for Boolean models as a prerequisite for smooth model integration. Using these standards, we demonstrate the coupling of two logical models on two different examples concerning cellular interactions in the liver. In the first example, we show the integration of two Boolean models of two cell types in order to describe their interaction. In the second example, we demonstrate the combination of two models describing different parts of the network of a single cell type. Combination of partial models into comprehensive network models will take systems biology to the next level of understanding. The combination of logical models facilitated by modelling standards is a valuable example for the next step towards this goal.     

How mathematical modelling elucidates signalling in Bacillus subtilis

Appropriate stimulus perception, signal processing and transduction ensure optimal adaptation of bacteria to environmental challenges. In the Gram‐positive model bacterium Bacillus subtilis signalling networks and molecular interactions therein are well‐studied, making this species a suitable candidate for the application of mathematical modelling. Here, we review systems biology approaches, focusing on chemotaxis, sporulation, σ^B‐dependent general stress response and competence. Processes like chemotaxis and Z‐ring assembly depend critically on the subcellular localization of proteins. Environmental response strategies, including sporulation and competence, are characterized by phenotypic heterogeneity in isogenic cultures. The examples of mathematical modelling also include investigations that have demonstrated how operon structure and signalling dynamics are intricately interwoven to establish optimal responses. Our review illustrates that these interdisciplinary approaches offer new insights into the response of B. subtilis to environmental challenges. These case studies reveal modelling as a tool to increase the understanding of complex systems, to help formulating hypotheses and to guide the design of more directed experiments that test predictions.     

From computational modelling of the intrinsic apoptosis pathway to a systems-based analysis of chemotherapy resistance: achievements,perspectives and challenges in systems medicine

Our understanding of the mitochondrial or intrinsic apoptosis pathway and its role in chemotherapy resistance has increased significantly in recent years by a combination of experimental studies and mathematical modelling. This combined approach enhanced the quantitative and kinetic understanding of apoptosis signal transduction, but also provided new insights that systems-emanating functions (i.e., functions that cannot be attributed to individual network components but that are instead established by multi-component interplay) are crucial determinants of cell fate decisions. Among these features are molecular thresholds, cooperative protein functions, feedback loops and functional redundancies that provide systems robustness, and signalling topologies that allow ultrasensitivity or switch-like responses. The successful development of kinetic systems models that recapitulate biological signal transduction observed in living cells have now led to the first translational studies, which have exploited and validated such models in a clinical context. Bottom-up strategies that use pathway models in combination with higher-level modelling at the tissue, organ and whole body-level therefore carry great potential to eventually deliver a new generation of systems-based diagnostic tools that may contribute to the development of personalised and predictive medicine approaches. Here we review major achievements in the systems biology of intrinsic apoptosis signalling, discuss challenges for further model development, perspectives for higher-level integration of apoptosis models and finally discuss requirements for the development of systems medical solutions in the coming years.     

Modelling protein functional domains in signal transduction using Maude

Modelling of protein-protein interactions in signal transduction is receiving increased attention in computational biology. This paper describes recent research in the application of Maude, a symbolic language founded on rewriting logic, to the modelling of functional domains within signalling proteins. Protein functional domains (PFDs) are a critical focus of modern signal transduction research. In general, Maude models can simulate biological signalling networks and produce specific testable hypotheses at various levels of abstraction. Developing symbolic models of signalling proteins containing functional domains is important because of the potential to generate analyses of complex signalling networks based on structure-function relationships.     

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.     

A framework for mapping,visualisation and automatic model creation of signal‐transduction networks

Intracellular signalling systems are highly complex. This complexity makes handling, analysis and visualisation of available knowledge a major challenge in current signalling research. Here, we present a novel framework for mapping signal‐transduction networks that avoids the combinatorial explosion by breaking down the network in reaction and contingency information. It provides two new visualisation methods and automatic export to mathematical models. We use this framework to compile the presently most comprehensive map of the yeast MAP kinase network. Our method improves previous strategies by combining (I) more concise mapping adapted to empirical data, (II) individual referencing for each piece of information, (III) visualisation without simplifications or added uncertainty, (IV) automatic visualisation in multiple formats, (V) automatic export to mathematical models and (VI) compatibility with established formats. The framework is supported by an open source software tool that facilitates integration of the three levels of network analysis: definition, visualisation and mathematical modelling. The framework is species independent and we expect that it will have wider impact in signalling research on any system.     

Kinetic analysis of the MAPK and PI3K/Akt signaling pathways

Computational modeling of signal transduction is currently attracting much attention as it can promote the understanding of complex signal transduction mechanisms. Although several mathematical models have been used to examine signaling pathways, little attention has been given to crosstalk mechanisms. In this study, an attempt was made to develop a computational model for the pathways involving growth-factor-mediated mitogen-activated protein kinase (MAPK) and phosphatidylinositol 3'-kinase/protein kinase B (PI3K/Akt). In addition, the dynamics of the protein activities were analyzed based on a set of kinetic data. The simulation approach integrates the information on several levels and predicts systems behavior. The in-silico analysis conducted revealed that the Raf and Akt pathways act independently.     

How do cilia organize signalling cascades?

Cilia and flagella are closely related centriole-nucleated protrusions of the cell with roles in motility and signal transduction. Two of the best-studied signalling pathways organized by cilia are the transduction cascade for the morphogen Hedgehog in vertebrates and the mating pathway that initiates gamete fusion in the unicellular green alga Chlamydomonas reinhardtii. What is the role of cilia in these signalling transduction cascades? In both Hedgehog and mating pathways, all signalling intermediates have been found to localize to cilia, and, for some signalling factors, ciliary localization is regulated by pathway activation. Given a concentration factor of three orders of magnitude provided by translocating a protein into the cilium, the compartment model proposes that cilia act as miniaturized reaction tubes bringing signalling factors and processing enzymes in close proximity. On the other hand, the scaffolding model views the intraflagellar transport machinery, whose primary function is to build cilia and flagella, as a molecular scaffold for the mating transduction cascade at the flagellar membrane. While these models may coexist, it is hoped that a precise understanding of the mechanisms that govern signalling inside cilia will provide a satisfying answer to the question ‘how do cilia organize signalling?’. This review covers the evidence supporting each model of signalling and outlines future directions that may address which model applies in given biological settings.     

Meeting report: Signal transduction meets systems biology

ABSTRACT: In the 21st century, systems-wide analyses of biological processes are getting more and more realistic. Especially for the in depth analysis of signal transduction pathways and networks, various approaches of systems biology are now successfully used. The EU FP7 large integrated project SYBILLA (Systems Biology of T-cell Activation in Health and Disease) coordinates such an endeavor. By using a combination of experimental data sets and computational modelling, the consortium strives for gaining a detailed and mechanistic understanding of signal transduction processes that govern T-cell activation. In order to foster the interaction between systems biologists and experimentally working groups, SYBILLA co-organized the 15th meeting "Signal Transduction: Receptors, Mediators and Genes" together with the Signal Transduction Society (STS). Thus, the annual STS conference, held from November 7 to 9, 2011 in Weimar, Germany, provided an interdisciplinary forum for research on signal transduction with a major focus on systems biology addressing signalling events in T-cells. Here we report on a selection of ongoing projects of SYBILLA and how they were discussed at this interdisciplinary conference.     

In silico tools for signal transduction research

Signal transduction is a fundamental process that takes place in all living organisms and understanding how this event occurs at the cellular level is of vital importance to virtually all fields of biomedicine. There are several major steps involved in deciphering the signalling pathways: (a) Which molecules are involved in signalling? (b) Who talks to whom?, ie making sense of the molecular interactions in a context-dependent way. (c) Where are the signalling events taking place?, eg when a resting cell becomes activated. The challenge lies in reconstructing signalling modules and networks evoked in a particular response to a single input as well as correlating the signalling response to different cellular inputs. There is also the need for interpretation of cross-talk between signalling modules in response to single and multiple inputs. To follow up these questions there are many good databases that provide an information system on regulatory networks. This review aims to find some of the bioinformatics tools and websites available to conduct signal transduction research and to discuss the representation of databases available for the processes of signalling. The databases considered here can provide a well-structured overview on the subject and a basis for advanced bioinformatics analysis to interpret the function of genomic sequences or to analyse signalling networks within a cell. However, the knowledge of most signalling pathways is incomplete and for this reason the existing databases will provide insight, but very rarely a more complete picture.     

Approximations and their consequences for dynamic modelling of signal transduction pathways

Signal transduction is the process by which the cell converts one kind of signal or stimulus into another. This involves a sequence of biochemical reactions, carried out by proteins. The dynamic response of complex cell signalling networks can be modelled and simulated in the framework of chemical kinetics. The mathematical formulation of chemical kinetics results in a system of coupled differential equations. Simplifications can arise through assumptions and approximations. The paper provides a critical discussion of frequently employed approximations in dynamic modelling of signal transduction pathways. We discuss the requirements for conservation laws, steady state approximations, and the neglect of components. We show how these approximations simplify the mathematical treatment of biochemical networks but we also demonstrate differences between the complete system and its approximations with respect to the transient and steady state behavior.     

Structural and functional diversity of adaptor proteins involved in tyrosine kinase signalling

Adaptors are proteins of multi-modular structure without enzymatic activity. Their capacity to organise large, temporary protein complexes by linking proteins together in a regulated and selective fashion makes them of outstanding importance in the establishment and maintenance of specificity and efficiency in all known signal transduction pathways. This review focuses on the structural and functional characterisation of adaptors involved in tyrosine kinase (TK) signalling. TK-linked adaptors can be distinguished by their domain composition and binding specificities. However, such structural classifications have proven inadequate as indicators of functional roles. A better way to understand the logic of signalling networks might be to look at functional aspects of adaptor proteins such as signalling specificity, negative versus positive contribution to signal propagation, or their position in the signalling hierarchy. All of these functions are dynamic, suggesting that adaptors have important regulatory roles rather than acting only as stable linkers in signal transduction.     

Pathway databases and tools for their exploitation: benefits,current limitations and challenges

In past years, comprehensive representations of cell signalling pathways have been developed by manual curation from literature, which requires huge effort and would benefit from information stored in databases and from automatic retrieval and integration methods. Once a reconstruction of the network of interactions is achieved, analysis of its structural features and its dynamic behaviour can take place. Mathematical modelling techniques are used to simulate the complex behaviour of cell signalling networks, which ultimately sheds light on the mechanisms leading to complex diseases or helps in the identification of drug targets. A variety of databases containing information on cell signalling pathways have been developed in conjunction with methodologies to access and analyse the data. In principle, the scenario is prepared to make the most of this information for the analysis of the dynamics of signalling pathways. However, are the knowledge repositories of signalling pathways ready to realize the systems biology promise? In this article we aim to initiate this discussion and to provide some insights on this issue.     

In vivo functions of mitogen-activated protein kinases: conclusions from knock-in and knock-out mice

Multicellular organisms achieve intercellular communication by means of signalling molecules whose effect on the target cell is mediated by signal transduction pathways. Such pathways relay, amplify and integrate signals to elicit appropriate biological responses. Protein kinases form crucial intermediate components of numerous signalling pathways. One group of protein kinases, the mitogen-activated protein kinases (MAP kinases) are kinases involved in signalling pathways that respond primarily to mitogens and stress stimuli. In vitro studies revealed that the MAP kinases are implicated in several cellular processes, including cell division, differentiation, cell survival/apoptosis, gene expression, motility and metabolism. As such, dysfunction of specific MAP kinases is associated with diseases such as cancer and immunological disorders. However, the genuine in vivo functions of many MAP kinases remain elusive. Genetically modified mouse models deficient in a specific MAP kinase or expressing a constitutive active or a dominant negative variant of a particular MAP kinase offer valuable tools for elucidating the biological role of these protein kinases. In this review, we focus on the current status of MAP kinase knock-in and knock-out mouse models and their phenotypes. Moreover, examples of the application of MAP kinase transgenic mice for validating therapeutic properties of specific MAP kinase inhibitors, and for investigating the role of MAP kinase in pathogen-host interactions will be discussed.     

Protein complexes mediate signalling in plant responses to hormones,light, sucrose and pathogens

Living organisms use complex pathways of signal perception and transduction to respond to stimuli in their environments. In plants, putative signal transduction components have been identified through mutant screens and comparative analysis of genome sequences of model eukaryotes. Several pieces in a large series of puzzles have now been identified and a current challenge is to determine how these pieces interconnect. Functional analysis of the encoded proteins has necessitated a change from genetic to biochemical approaches. In recent years, the application of techniques such as two-hybrid screening and epitope tagging has facilitated the study of protein-protein interactions and has increased our understanding of cellular signalling mechanisms. One focus of present research is the ubiquitin/proteasome-mediated degradation of proteins. Increasing evidence suggests this is a control common to many plant signalling pathways including development and responsiveness to hormones, light and sucrose. A central challenge in the study of plant disease resistance has been to identify protein complexes that contain host defence proteins and pathogenicity factors. In this review we summarize the latest developments in these areas where the existence of protein complexes has been demonstrated to be of fundamental importance in plant signalling.     

Current topics in signal transduction in bacteria

Among the signal transfer systems in bacteria two types predominate: two-component regulatory systems and quorum sensing systems. Both types of system can mediate signal transfer across the bacterial cell envelope; however, the signalling molecule typically is not taken up into the cells in the former type of system, whereas it usually is in the latter. The Two-component systems include the recently described (eukaryotic) phosphorelay systems; quorum sensing systems can be based upon autoinducers of the N-acylated homoserine lactones, and on autoinducers of a peptidic nature. A single bacterial cell contains many signalling modules that primarily operate in parallel. This may give rise to neural-network behaviour. Recently, however, for both types of basic signal transfer modules, it has been demonstrated that they also can be organised in series (i.e. in a hierarchical order). Besides their hierarchical position in the signal transduction network of the cell, the spatial distribution of individual signalling modules may also be an important factor in their efficiency in signal transfer. Many challenges lie hidden in future work to understand these signal transfer processes in more detail. These are discussed here, with emphasis on the mutual interactions between different signal transfer processes. Successful contributions to this work will require rigorous mathematical modelling of the performance of signal transduction components, and -networks, as well as studies on light-sensing signal transduction systems, because of the unsurpassed time resolution obtainable in those latter systems, the opportunity to apply repeated reproducible stimuli, etc. The increased understanding of bacterial behaviour that already has resulted – and may further result – from these studies, can be used to fine-tune the beneficial activities of bacteria and/or more efficiently inhibit their deleterious ones.     

PATHLOGIC-S: A Scalable Boolean Framework for Modelling Cellular Signalling

Curated databases of signal transduction have grown to describe several thousand reactions, and efficient use of these data requires the development of modelling tools to elucidate and explore system properties. We present PATHLOGIC-S, a Boolean specification for a signalling model, with its associated GPL-licensed implementation using integer programming techniques. The PATHLOGIC-S specification has been designed to function on current desktop workstations, and is capable of providing analyses on some of the largest currently available datasets through use of Boolean modelling techniques to generate predictions of stable and semi-stable network states from data in community file formats. PATHLOGIC-S also addresses major problems associated with the presence and modelling of inhibition in Boolean systems, and reduces logical incoherence due to common inhibitory mechanisms in signalling systems. We apply this approach to signal transduction networks including Reactome and two pathways from the Panther Pathways database, and present the results of computations on each along with a discussion of execution time. A software implementation of the framework and model is freely available under a GPL license.     

Signalling Network Construction for Modelling Plant Defence Response

Plant defence signalling response against various pathogens, including viruses, is a complex phenomenon. In resistant interaction a plant cell perceives the pathogen signal, transduces it within the cell and performs a reprogramming of the cell metabolism leading to the pathogen replication arrest. This work focuses on signalling pathways crucial for the plant defence response, i.e., the salicylic acid, jasmonic acid and ethylene signal transduction pathways, in the Arabidopsis thaliana model plant. The initial signalling network topology was constructed manually by defining the representation formalism, encoding the information from public databases and literature, and composing a pathway diagram. The manually constructed network structure consists of 175 components and 387 reactions. In order to complement the network topology with possibly missing relations, a new approach to automated information extraction from biological literature was developed. This approach, named Bio3graph, allows for automated extraction of biological relations from the literature, resulting in a set of (component1, reaction, component2) triplets and composing a graph structure which can be visualised, compared to the manually constructed topology and examined by the experts. Using a plant defence response vocabulary of components and reaction types, Bio3graph was applied to a set of 9,586 relevant full text articles, resulting in 137 newly detected reactions between the components. Finally, the manually constructed topology and the new reactions were merged to form a network structure consisting of 175 components and 524 reactions. The resulting pathway diagram of plant defence signalling represents a valuable source for further computational modelling and interpretation of omics data. The developed Bio3graph approach, implemented as an executable language processing and graph visualisation workflow, is publically available at http://ropot.ijs.si/bio3graph/and can be utilised for modelling other biological systems, given that an adequate vocabulary is provided.