Power-law models of signal transduction pathways

The mathematical modelling of signal transduction pathways has become a valuable aid to understanding the complex interactions involved in intracellular signalling mechanisms. An important aspect of the mathematical modelling process is the selection of the model type and structure. Until recently, the convention has been to use a standard kinetic model, often with the Michaelis-Menten steady state assumption. However this model form, although valuable, is only one of a number of choices, and the aim of this article is to consider the mathematical structure and essential features of an alternative model form--the power-law model. Specifically, we analyse how power-law models can be applied to increase our understanding of signal transduction pathways when there may be limited prior information. We distinguish between two kinds of power law models: a) Detailed power-law models, as a tool for investigating pathways when the structure of protein-protein interactions is completely known, and; b) Simplified power-law models, for the analysis of systems with incomplete structural information or insufficient quantitative data for generating detailed models. If sufficient data of high quality are available, the advantage of detailed power-law models is that they are more realistic representations of non-homogenous or crowded cellular environments. The advantages of the simplified power-law model formulation are illustrated using some case studies in cell signalling. In particular, the investigation on the effects of signal inhibition and feedback loops and the validation of structural hypotheses are discussed.     

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.     

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.     

Bioactive peptides,networks and systems biology

Bioactive peptides are a group of diverse intercellular signalling molecules. Almost half a century of research on this topic has resulted in an enormous amount of data. In this essay, a general perspective to interpret all these data will be given. In classical endocrinology, neuropeptides were thought of as simple signalling molecules that each elicit one response. However, the fact that the total bioactive peptide signal is far from simple puts this view under pressure. Cells and tissues express many different bioactive peptides and they are also able to respond to many different bioactive peptides, indicating that multiple receptors and signal transduction pathways are present in a single cell. Therefore, the authors suggest that the bioactive peptide signalling system should be regarded in the context of network and systems biology. Bioactive peptides can best be viewed as an extension of the protein interaction network that allows regulating and fine‐tuning the metabolism of the different cells and tissues in the body. The cell thus responds to the ‘peptidome’ instead of to a single peptide. The intracellular part of this signalling network consists of the various signalling transduction cascades. Recently, new systems biology approaches have emerged for the modelling of cell signalling. The network and systems biology approach is also able to shed new light on the evolution of intercellular signalling.     

Cellulat: an agent-based intracellular signalling model

The theory of behaviour-based systems (or autonomous agents) constitutes a useful approach for the modelling of intracellular signalling networks. In this sense, a cell can be seen as an adaptive autonomous agent or as a society of such agents, where each can exhibit a particular behaviour depending on its cognitive capabilities. We present an intracellular signalling model obtained by integrating several computational techniques into an agent-based paradigm. Cellulat, the model, takes into account two essential aspects of the intracellular signalling networks: (1) cognitive capacities, which are modelled as the agent abilities to interact with the surrounding medium and (2) a spatial organisation, this last obtained using a shared data structure through which the agents communicate between them. We propose a methodology for the modelling of intracellular signalling pathway using Cellulat and we discuss the goal of a virtual laboratory based on our model and presently under development.     

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.     

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.     

Simulations of stressosome activation emphasize allosteric interactions between RsbR and RsbT

Background

The stressosome is a bacterial signalling complex that responds to environmental changes by initiating a protein partner switching cascade, which leads to the release of the alternative sigma factor, σ^B. Stress perception increases the phosphorylation of the stressosome sensor protein, RsbR, and the scaffold protein, RsbS, by the protein kinase, RsbT. Subsequent dissociation of RsbT from the stressosome activates the σ^B cascade. However, the sequence of physical events that occur in the stressosome during signal transduction is insufficiently understood.

Results

Here, we use computational modelling to correlate the structure of the stressosome with the efficiency of the phosphorylation reactions that occur upon activation by stress. In our model, the phosphorylation of any stressosome protein is dependent upon its nearest neighbours and their phosphorylation status. We compare different hypotheses about stressosome activation and find that only the model representing the allosteric activation of the kinase RsbT, by phosphorylated RsbR, qualitatively reproduces the experimental data.

Conclusions

Our simulations and the associated analysis of published data support the following hypotheses: (i) a simple Boolean model is capable of reproducing stressosome dynamics, (ii) different stressors induce identical stressosome activation patterns, and we also confirm that (i) phosphorylated RsbR activates RsbT, and (ii) the main purpose of RsbX is to dephosphorylate RsbS-P.     

Control of high osmolarity signalling in the yeast Saccharomyces cerevisiae

Signal transduction pathways control cellular responses to extrinsic and intrinsic signals. The yeast HOG (High Osmolarity Glycerol) response pathway mediates cellular adaptation to hyperosmotic stress. Pathway architecture as well as the flow of signal have been studied to a very high degree of detail. Recently, the yeast HOG pathway has become a popular model to analyse systems level properties of signal transduction. Those studies addressed, using experimentation and modelling, the role of basal signalling, robustness against perturbation, as well as adaptation and feedback control. These recent findings provide exciting insight into the higher control levels of signalling through this MAPK system of potential general importance.     

A rule-based model of barley morphogenesis, with special respect to shading and gibberellic acid signal transduction

BACKGROUND AND AIMS: Functional-structural plant models (FSPM) constitute a paradigm in plant modelling that combines 3D structural and graphical modelling with the simulation of plant processes. While structural aspects of plant development could so far be represented using rule-based formalisms such as Lindenmayer systems, process models were traditionally written using a procedural code. The faithful representation of structures interacting with functions across scales, however, requires a new modelling formalism. Therefore relational growth grammars (RGG) were developed on the basis of Lindenmayer systems. METHODS: In order to implement and test RGG, a new modelling language, the eXtended L-system language (XL) was created. Models using XL are interpreted by the interactive, Java-based modelling platform GroIMP. Three models, a semi-quantitative gibberellic acid (GA) signal transduction model, and a phytochrome-based shade detection and object avoidance model, both coupled to an existing morphogenetic structural model of barley (Hordeum vulgare L.), serve as examples to demonstrate the versatility and suitability of RGG and XL to represent the interaction of diverse biological processes across hierarchical scales. KEY RESULTS: The dynamics of the concentrations in the signal transduction network could be modelled qualitatively and the phenotypes of GA-response mutants faithfully reproduced. The light model used here was simple to use yet effective enough to carry out local measurement of red:far-red ratios. Suppression of tillering at low red:far-red ratios could be simulated. CONCLUSIONS: The RGG formalism is suitable for implementation of multi-scaled FSPM of plants interacting with their environment via hormonal control. However, their ensuing complexity requires careful design. On the positive side, such an FSPM displays knowledge gaps better thereby guiding future experimental design.     

Quantitative analysis of protein phosphorylations and interactions by multi-colour IP-FCM as an input for kinetic modelling of signalling networks

Background

To understand complex biological signalling mechanisms, mathematical modelling of signal transduction pathways has been applied successfully in last few years. However, precise quantitative measurements of signal transduction events such as activation-dependent phosphorylation of proteins, remains one bottleneck to this success.

Methodology/Principal Findings

We use multi-colour immunoprecipitation measured by flow cytometry (IP-FCM) for studying signal transduction events to unrivalled precision. In this method, antibody-coupled latex beads capture the protein of interest from cellular lysates and are then stained with differently fluorescent-labelled antibodies to quantify the amount of the immunoprecipitated protein, of an interaction partner and of phosphorylation sites. The fluorescence signals are measured by FCM. Combining this procedure with beads containing defined amounts of a fluorophore allows retrieving absolute numbers of stained proteins, and not only relative values. Using IP-FCM we derived multidimensional data on the membrane-proximal T-cell antigen receptor (TCR-CD3) signalling network, including the recruitment of the kinase ZAP70 to the TCR-CD3 and subsequent ZAP70 activation by phosphorylation in the murine T-cell hybridoma and primary murine T cells. Counter-intuitively, these data showed that cell stimulation by pervanadate led to a transient decrease of the phospho-ZAP70/ZAP70 ratio at the TCR. A mechanistic mathematical model of the underlying processes demonstrated that an initial massive recruitment of non-phosphorylated ZAP70 was responsible for this behaviour. Further, the model predicted a temporal order of multisite phosphorylation of ZAP70 (with Y319 phosphorylation preceding phosphorylation at Y493) that we subsequently verified experimentally.

Conclusions/Significance

The quantitative data sets generated by IP-FCM are one order of magnitude more precise than Western blot data. This accuracy allowed us to gain unequalled insight into the dynamics of the TCR-CD3-ZAP70 signalling network.     

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.     

Discrete Logic Modelling Optimization to Contextualize Prior Knowledge Networks Using PRUNET

High-throughput technologies have led to the generation of an increasing amount of data in different areas of biology. Datasets capturing the cell’s response to its intra- and extra-cellular microenvironment allows such data to be incorporated as signed and directed graphs or influence networks. These prior knowledge networks (PKNs) represent our current knowledge of the causality of cellular signal transduction. New signalling data is often examined and interpreted in conjunction with PKNs. However, different biological contexts, such as cell type or disease states, may have distinct variants of signalling pathways, resulting in the misinterpretation of new data. The identification of inconsistencies between measured data and signalling topologies, as well as the training of PKNs using context specific datasets (PKN contextualization), are necessary conditions to construct reliable, predictive models, which are current challenges in the systems biology of cell signalling. Here we present PRUNET, a user-friendly software tool designed to address the contextualization of a PKNs to specific experimental conditions. As the input, the algorithm takes a PKN and the expression profile of two given stable steady states or cellular phenotypes. The PKN is iteratively pruned using an evolutionary algorithm to perform an optimization process. This optimization rests in a match between predicted attractors in a discrete logic model (Boolean) and a Booleanized representation of the phenotypes, within a population of alternative subnetworks that evolves iteratively. We validated the algorithm applying PRUNET to four biological examples and using the resulting contextualized networks to predict missing expression values and to simulate well-characterized perturbations. PRUNET constitutes a tool for the automatic curation of a PKN to make it suitable for describing biological processes under particular experimental conditions. The general applicability of the implemented algorithm makes PRUNET suitable for a variety of biological processes, for instance cellular reprogramming or transitions between healthy and disease states.     

Signal transduction pathways in Synechocystis sp. PCC 6803 and biotechnological implications under abiotic stress

Cyanobacteria have developed various response mechanisms in long evolution to sense and adapt to external or internal changes under abiotic stresses. The signal transduction system of a model cyanobacterium Synechocystis sp. PCC 6803 includes mainly two-component signal transduction systems of eukaryotic-type serine/threonine kinases (STKs), on which most have been investigated at present. These two-component systems play a major role in regulating cell activities in cyanobacteria. More and more co-regulation and crosstalk regulations among signal transduction systems had been discovered due to increasing experimental data, and they are of great importance in corresponding to abiotic stresses. However, mechanisms of their functions remain unknown. Nevertheless, the two signal transduction systems function as an integral network for adaption in different abiotic stresses. This review summarizes available knowledge on the signal transduction network in Synechocystis sp. PCC 6803 and biotechnological implications under various stresses, with focuses on the co-regulation and crosstalk regulations among various stress-responding signal transduction systems.     

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.     

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.     

Towards mechanistic models of plant organ growth

Modelling and simulation are increasingly used as tools in the study of plant growth and developmental processes. By formulating experimentally obtained knowledge as a system of interacting mathematical equations, it becomes feasible for biologists to gain a mechanistic understanding of the complex behaviour of biological systems. In this review, the modelling tools that are currently available and the progress that has been made to model plant development, based on experimental knowledge, are described. In terms of implementation, it is argued that, for the modelling of plant organ growth, the cellular level should form the cornerstone. It integrates the output of molecular regulatory networks to two processes, cell division and cell expansion, that drive growth and development of the organ. In turn, these cellular processes are controlled at the molecular level by hormone signalling. Therefore, combining a cellular modelling framework with regulatory modules for the regulation of cell division, expansion, and hormone signalling could form the basis of a functional organ growth simulation model. The current state of progress towards this aim is that the regulation of the cell cycle and hormone transport have been modelled extensively and these modules could be integrated. However, much less progress has been made on the modelling of cell expansion, which urgently needs to be addressed. A limitation of the current generation models is that they are largely qualitative. The possibilities to characterize existing and future models more quantitatively will be discussed. Together with experimental methods to measure crucial model parameters, these modelling techniques provide a basis to develop a Systems Biology approach to gain a fundamental insight into the relationship between gene function and whole organ behaviour.