Logical modelling of regulatory networks with GINsim 2.3

Complementing ODE-Based System Analysis Using Boolean Networks Derived from an Euler-Like Transformation

In this paper, we present a systematic transition scheme for a large class of ordinary differential equations (ODEs) into Boolean networks. Our transition scheme can be applied to any system of ODEs whose right hand sides can be written as sums and products of monotone functions. It performs an Euler-like step which uses the signs of the right hand sides to obtain the Boolean update functions for every variable of the corresponding discrete model. The discrete model can, on one hand, be considered as another representation of the biological system or, alternatively, it can be used to further the analysis of the original ODE model. Since the generic transformation method does not guarantee any property conservation, a subsequent validation step is required. Depending on the purpose of the model this step can be based on experimental data or ODE simulations and characteristics. Analysis of the resulting Boolean model, both on its own and in comparison with the ODE model, then allows to investigate system properties not accessible in a purely continuous setting. The method is exemplarily applied to a previously published model of the bovine estrous cycle, which leads to new insights regarding the regulation among the components, and also indicates strongly that the system is tailored to generate stable oscillations.

Approximating Attractors of Boolean Networks by Iterative CTL Model Checking

This paper introduces the notion of approximating asynchronous attractors of Boolean networks by minimal trap spaces. We define three criteria for determining the quality of an approximation: "faithfulness" which requires that the oscillating variables of all attractors in a trap space correspond to their dimensions, "univocality" which requires that there is a unique attractor in each trap space, and "completeness" which requires that there are no attractors outside of a given set of trap spaces. Each is a reachability property for which we give equivalent model checking queries. Whereas faithfulness and univocality can be decided by model checking the corresponding subnetworks, the naive query for completeness must be evaluated on the full state space. Our main result is an alternative approach which is based on the iterative refinement of an initially poor approximation. The algorithm detects so-called autonomous sets in the interaction graph, variables that contain all their regulators, and considers their intersection and extension in order to perform model checking on the smallest possible state spaces. A benchmark, in which we apply the algorithm to 18 published Boolean networks, is given. In each case, the minimal trap spaces are faithful, univocal, and complete, which suggests that they are in general good approximations for the asymptotics of Boolean networks.

Discovery of Drug Synergies in Gastric Cancer Cells Predicted by Logical Modeling

Discovery of efficient anti-cancer drug combinations is a major challenge, since experimental testing of all possible combinations is clearly impossible. Recent efforts to computationally predict drug combination responses retain this experimental search space, as model definitions typically rely on extensive drug perturbation data. We developed a dynamical model representing a cell fate decision network in the AGS gastric cancer cell line, relying on background knowledge extracted from literature and databases. We defined a set of logical equations recapitulating AGS data observed in cells in their baseline proliferative state. Using the modeling software GINsim, model reduction and simulation compression techniques were applied to cope with the vast state space of large logical models and enable simulations of pairwise applications of specific signaling inhibitory chemical substances. Our simulations predicted synergistic growth inhibitory action of five combinations from a total of 21 possible pairs. Four of the predicted synergies were confirmed in AGS cell growth real-time assays, including known effects of combined MEK-AKT or MEK-PI3K inhibitions, along with novel synergistic effects of combined TAK1-AKT or TAK1-PI3K inhibitions. Our strategy reduces the dependence on a priori drug perturbation experimentation for well-characterized signaling networks, by demonstrating that a model predictive of combinatorial drug effects can be inferred from background knowledge on unperturbed and proliferating cancer cells. Our modeling approach can thus contribute to preclinical discovery of efficient anticancer drug combinations, and thereby to development of strategies to tailor treatment to individual cancer patients.

Symmetry structure in discrete models of biochemical systems: natural subsystems and the weak control hierarchy in a new model of computation driven by interactions

Interaction computing is inspired by the observation that cell metabolic/regulatory systems construct order dynamically, through constrained interactions between their components and based on a wide range of possible inputs and environmental conditions. The goals of this work are to (i) identify and understand mathematically the natural subsystems and hierarchical relations in natural systems enabling this and (ii) use the resulting insights to define a new model of computation based on interactions that is useful for both biology and computation. The dynamical characteristics of the cellular pathways studied in systems biology relate, mathematically, to the computational characteristics of automata derived from them, and their internal symmetry structures to computational power. Finite discrete automata models of biological systems such as the lac operon, the Krebs cycle and p53-mdm2 genetic regulation constructed from systems biology models have canonically associated algebraic structures (their transformation semigroups). These contain permutation groups (local substructures exhibiting symmetry) that correspond to 'pools of reversibility'. These natural subsystems are related to one another in a hierarchical manner by the notion of 'weak control'. We present natural subsystems arising from several biological examples and their weak control hierarchies in detail. Finite simple non-Abelian groups are found in biological examples and can be harnessed to realize finitary universal computation. This allows ensembles of cells to achieve any desired finitary computational transformation, depending on external inputs, via suitably constrained interactions. Based on this, interaction machines that grow and change their structure recursively are introduced and applied, providing a natural model of computation driven by interactions.

A Minimal Regulatory Network of Extrinsic and Intrinsic Factors Recovers Observed Patterns of CD4+ T Cell Differentiation and Plasticity

CD4+ T cells orchestrate the adaptive immune response in vertebrates. While both experimental and modeling work has been conducted to understand the molecular genetic mechanisms involved in CD4+ T cell responses and fate attainment, the dynamic role of intrinsic (produced by CD4+ T lymphocytes) versus extrinsic (produced by other cells) components remains unclear, and the mechanistic and dynamic understanding of the plastic responses of these cells remains incomplete. In this work, we studied a regulatory network for the core transcription factors involved in CD4+ T cell-fate attainment. We first show that this core is not sufficient to recover common CD4+ T phenotypes. We thus postulate a minimal Boolean regulatory network model derived from a larger and more comprehensive network that is based on experimental data. The minimal network integrates transcriptional regulation, signaling pathways and the micro-environment. This network model recovers reported configurations of most of the characterized cell types (Th0, Th1, Th2, Th17, Tfh, Th9, iTreg, and Foxp3-independent T regulatory cells). This transcriptional-signaling regulatory network is robust and recovers mutant configurations that have been reported experimentally. Additionally, this model recovers many of the plasticity patterns documented for different T CD4+ cell types, as summarized in a cell-fate map. We tested the effects of various micro-environments and transient perturbations on such transitions among CD4+ T cell types. Interestingly, most cell-fate transitions were induced by transient activations, with the opposite behavior associated with transient inhibitions. Finally, we used a novel methodology was used to establish that T-bet, TGF-β and suppressors of cytokine signaling proteins are keys to recovering observed CD4+ T cell plastic responses. In conclusion, the observed CD4+ T cell-types and transition patterns emerge from the feedback between the intrinsic or intracellular regulatory core and the micro-environment. We discuss the broader use of this approach for other plastic systems and possible therapeutic interventions.

A Semiquantitative Framework for Gene Regulatory Networks: Increasing the Time and Quantitative Resolution of Boolean Networks

Boolean models have been instrumental in predicting general features of gene networks and more recently also as explorative tools in specific biological applications. In this study we introduce a basic quantitative and a limited time resolution to a discrete (Boolean) framework. Quantitative resolution is improved through the employ of normalized variables in unison with an additive approach. Increased time resolution stems from the introduction of two distinct priority classes. Through the implementation of a previously published chondrocyte network and T helper cell network, we show that this addition of quantitative and time resolution broadens the scope of biological behaviour that can be captured by the models. Specifically, the quantitative resolution readily allows models to discern qualitative differences in dosage response to growth factors. The limited time resolution, in turn, can influence the reachability of attractors, delineating the likely long term system behaviour. Importantly, the information required for implementation of these features, such as the nature of an interaction, is typically obtainable from the literature. Nonetheless, a trade-off is always present between additional computational cost of this approach and the likelihood of extending the model’s scope. Indeed, in some cases the inclusion of these features does not yield additional insight. This framework, incorporating increased and readily available time and semi-quantitative resolution, can help in substantiating the litmus test of dynamics for gene networks, firstly by excluding unlikely dynamics and secondly by refining falsifiable predictions on qualitative behaviour.

Predicting genetic interactions from Boolean models of biological networks

Genetic interaction can be defined as a deviation of the phenotypic quantitative effect of a double gene mutation from the effect predicted from single mutations using a simple (e.g., multiplicative or linear additive) statistical model. Experimentally characterized genetic interaction networks in model organisms provide important insights into relationships between different biological functions. We describe a computational methodology allowing us to systematically and quantitatively characterize a Boolean mathematical model of a biological network in terms of genetic interactions between all loss of function and gain of function mutations with respect to all model phenotypes or outputs. We use the probabilistic framework defined in MaBoSS software, based on continuous time Markov chains and stochastic simulations. In addition, we suggest several computational tools for studying the distribution of double mutants in the space of model phenotype probabilities. We demonstrate this methodology on three published models for each of which we derive the genetic interaction networks and analyze their properties. We classify the obtained interactions according to their class of epistasis, dependence on the chosen initial conditions and the phenotype. The use of this methodology for validating mathematical models from experimental data and designing new experiments is discussed.

A Model for p38MAPK-Induced Astrocyte Senescence

Experimental evidence indicates that aging leads to accumulation of senescent cells in tissues and they develop a secretory phenotype (also known as SASP, for senescence-associated secretory phenotype) that can contribute to chronic inflammation and diseases. Recent results have showed that markers of senescence in astrocytes from aged brains are increased in brains with Alzheimer’s disease. These studies strongly involved the stress kinase p38MAPK in the regulation of the secretory phenotype of astrocytes, yet the molecular mechanisms underlying the onset of senescence and SASP activation remain unclear. In this work, we propose a discrete logical model for astrocyte senescence determined by the level of DNA damage (reparable or irreparable DNA strand breaks) where the kinase p38MAPK plays a central role in the regulation of senescence and SASP. The model produces four alternative stable states: proliferation, transient cycle arrest, apoptosis and senescence (and SASP) computed from its inputs representing DNA damages. Perturbations of the model were performed through gene gain or loss of functions and compared with results concerning cultures of normal and mutant astrocytes showing agreement in most cases. Moreover, the model allows some predictions that remain to be tested experimentally.

Boolean modeling: a logic-based dynamic approach for understanding signaling and regulatory networks and for making useful predictions

The biomolecules inside or near cells form a complex interacting system. Cellular phenotypes and behaviors arise from the totality of interactions among the components of this system. A fruitful way of modeling interacting biomolecular systems is by network-based dynamic models that characterize each component by a state variable, and describe the change in the state variables due to the interactions in the system. Dynamic models can capture the stable state patterns of this interacting system and can connect them to different cell fates or behaviors. A Boolean or logic model characterizes each biomolecule by a binary state variable that relates the abundance of that molecule to a threshold abundance necessary for downstream processes. The regulation of this state variable is described in a parameter free manner, making Boolean modeling a practical choice for systems whose kinetic parameters have not been determined. Boolean models integrate the body of knowledge regarding the components and interactions of biomolecular systems, and capture the system's dynamic repertoire, for example the existence of multiple cell fates. These models were used for a variety of systems and led to important insights and predictions. Boolean models serve as an efficient exploratory model, a guide for follow-up experiments, and as a foundation for more quantitative models.

Quantitative and logic modelling of molecular and gene networks

Behaviours of complex biomolecular systems are often irreducible to the elementary properties of their individual components. Explanatory and predictive mathematical models are therefore useful for fully understanding and precisely engineering cellular functions. The development and analyses of these models require their adaptation to the problems that need to be solved and the type and amount of available genetic or molecular data. Quantitative and logic modelling are among the main methods currently used to model molecular and gene networks. Each approach comes with inherent advantages and weaknesses. Recent developments show that hybrid approaches will become essential for further progress in synthetic biology and in the development of virtual organisms.

Integrating interactive computational modeling in biology curricula

While the use of computer tools to simulate complex processes such as computer circuits is normal practice in fields like engineering, the majority of life sciences/biological sciences courses continue to rely on the traditional textbook and memorization approach. To address this issue, we explored the use of the Cell Collective platform as a novel, interactive, and evolving pedagogical tool to foster student engagement, creativity, and higher-level thinking. Cell Collective is a Web-based platform used to create and simulate dynamical models of various biological processes. Students can create models of cells, diseases, or pathways themselves or explore existing models. This technology was implemented in both undergraduate and graduate courses as a pilot study to determine the feasibility of such software at the university level. First, a new (In Silico Biology) class was developed to enable students to learn biology by "building and breaking it" via computer models and their simulations. This class and technology also provide a non-intimidating way to incorporate mathematical and computational concepts into a class with students who have a limited mathematical background. Second, we used the technology to mediate the use of simulations and modeling modules as a learning tool for traditional biological concepts, such as T cell differentiation or cell cycle regulation, in existing biology courses. Results of this pilot application suggest that there is promise in the use of computational modeling and software tools such as Cell Collective to provide new teaching methods in biology and contribute to the implementation of the "Vision and Change" call to action in undergraduate biology education by providing a hands-on approach to biology.

Cooperative development of logical modelling standards and tools with CoLoMoTo

The identification of large regulatory and signalling networks involved in the control of crucial cellular processes calls for proper modelling approaches. Indeed, models can help elucidate properties of these networks, understand their behaviour and provide (testable) predictions by performing in silico experiments. In this context, qualitative, logical frameworks have emerged as relevant approaches, as demonstrated by a growing number of published models, along with new methodologies and software tools. This productive activity now requires a concerted effort to ensure model reusability and interoperability between tools. Following an outline of the logical modelling framework, we present the most important achievements of the Consortium for Logical Models and Tools, along with future objectives. Our aim is to advertise this open community, which welcomes contributions from all researchers interested in logical modelling or in related mathematical and computational developments.

Computational cell fate modelling for discovery of rewiring in apoptotic network for enhanced cancer drug sensitivity

The ongoing cancer research has shown that malignant tumour cells have highly disrupted signalling transduction pathways. In cancer cells, signalling pathways are altered to satisfy the demands of continuous proliferation and survival. The changes in signalling pathways supporting uncontrolled cell growth, termed as rewiring, can lead to dysregulation of cell fates e.g. apoptosis. Hence comparative analysis of normal and oncogenic signal transduction pathways may provide insights into mechanisms of cancer drug-resistance and facilitate the discovery of novel and effective anti-cancer therapies. Here we propose a hybrid modelling approach based on ordinary differential equation (ODE) and machine learning to map network rewiring in the apoptotic pathways that may be responsible for the increase of drug sensitivity of tumour cells in triple-negative breast cancer. Our method employs Genetic Algorithm to search for the most likely network topologies by iteratively generating simulated protein phosphorylation data using ODEs and the rewired network and then fitting the simulated data with real data of cancer signalling and cell fate. Most of our predictions are consistent with experimental evidence from literature. Combining the strengths of knowledge-driven and data-driven approaches, our hybrid model can help uncover molecular mechanisms of cancer cell fate at systems level.

Descriptive vs. mechanistic network models in plant development in the post-genomic era

Network modeling is now a widespread practice in systems biology, as well as in integrative genomics, and it constitutes a rich and diverse scientific research field. A conceptually clear understanding of the reasoning behind the main existing modeling approaches, and their associated technical terminologies, is required to avoid confusions and accelerate the transition towards an undeniable necessary more quantitative, multidisciplinary approach to biology. Herein, we focus on two main network-based modeling approaches that are commonly used depending on the information available and the intended goals: inference-based methods and system dynamics approaches. As far as data-based network inference methods are concerned, they enable the discovery of potential functional influences among molecular components. On the other hand, experimentally grounded network dynamical models have been shown to be perfectly suited for the mechanistic study of developmental processes. How do these two perspectives relate to each other? In this chapter, we describe and compare both approaches and then apply them to a given specific developmental module. Along with the step-by-step practical implementation of each approach, we also focus on discussing their respective goals, utility, assumptions, and associated limitations. We use the gene regulatory network (GRN) involved in Arabidopsis thaliana Root Stem Cell Niche patterning as our illustrative example. We show that descriptive models based on functional genomics data can provide important background information consistent with experimentally supported functional relationships integrated in mechanistic GRN models. The rationale of analysis and modeling can be applied to any other well-characterized functional developmental module in multicellular organisms, like plants and animals.

Dynamical modeling of the cell cycle and cell fate emergence in Caulobacter crescentus

The division of Caulobacter crescentus, a model organism for studying cell cycle and differentiation in bacteria, generates two cell types: swarmer and stalked. To complete its cycle, C. crescentus must first differentiate from the swarmer to the stalked phenotype. An important regulator involved in this process is CtrA, which operates in a gene regulatory network and coordinates many of the interactions associated to the generation of cellular asymmetry. Gaining insight into how such a differentiation phenomenon arises and how network components interact to bring about cellular behavior and function demands mathematical models and simulations. In this work, we present a dynamical model based on a generalization of the Boolean abstraction of gene expression for a minimal network controlling the cell cycle and asymmetric cell division in C. crescentus. This network was constructed from data obtained from an exhaustive search in the literature. The results of the simulations based on our model show a cyclic attractor whose configurations can be made to correspond with the current knowledge of the activity of the regulators participating in the gene network during the cell cycle. Additionally, we found two point attractors that can be interpreted in terms of the network configurations directing the two cell types. The entire network is shown to be operating close to the critical regime, which means that it is robust enough to perturbations on dynamics of the network, but adaptable to environmental changes.

Multi-level modeling of light-induced stomatal opening offers new insights into its regulation by drought

Plant guard cells gate CO2 uptake and transpirational water loss through stomatal pores. As a result of decades of experimental investigation, there is an abundance of information on the involvement of specific proteins and secondary messengers in the regulation of stomatal movements and on the pairwise relationships between guard cell components. We constructed a multi-level dynamic model of guard cell signal transduction during light-induced stomatal opening and of the effect of the plant hormone abscisic acid (ABA) on this process. The model integrates into a coherent network the direct and indirect biological evidence regarding the regulation of seventy components implicated in stomatal opening. Analysis of this signal transduction network identified robust cross-talk between blue light and ABA, in which [Ca2+]c plays a key role, and indicated an absence of cross-talk between red light and ABA. The dynamic model captured more than 10(31) distinct states for the system and yielded outcomes that were in qualitative agreement with a wide variety of previous experimental results. We obtained novel model predictions by simulating single component knockout phenotypes. We found that under white light or blue light, over 60%, and under red light, over 90% of all simulated knockouts had similar opening responses as wild type, showing that the system is robust against single node loss. The model revealed an open question concerning the effect of ABA on red light-induced stomatal opening. We experimentally showed that ABA is able to inhibit red light-induced stomatal opening, and our model offers possible hypotheses for the underlying mechanism, which point to potential future experiments. Our modelling methodology combines simplicity and flexibility with dynamic richness, making it well suited for a wide class of biological regulatory systems.

Modelling the onset of senescence at the G1/S cell cycle checkpoint

BACKGROUND

DNA damage (single or double-strand breaks) triggers adapted cellular responses. These responses are elicited through signalling pathways, which activate cell cycle checkpoints and basically lead to three cellular fates: cycle arrest promoting DNA repair, senescence (permanent arrest) or cell death. Cellular senescence is known for having a tumour-suppressive function and its regulation arouses a growing scientific interest. Here, we advance a qualitative model covering DNA damage response pathways, focusing on G1/S checkpoint enforcement, supposedly more sensitive to arrest than G2/M checkpoint.

RESULTS

We define a discrete, logical model encompassing ATM (ataxia telangiectasia mutated) and ATR (ATM and Rad3-related) pathways activation upon DNA damage, as well as G1/S checkpoint main components. It also includes the stress responsive protein p38MAPK (mitogen-activated protein kinase 14) known to be involved in the regulation of senescence. The model has four outcomes that convey alternative cell fates: proliferation, (transient) cell cycle arrest, apoptosis and senescence. Different levels of DNA damage are considered, defined by distinct combinations of single and double-strand breaks. Each leads to a single stable state denoting the cell fate adopted upon this specific damage. A range of model perturbations corresponding to gene loss-of-function or gain-of-function is compared to experimental mutations.

CONCLUSIONS

As a step towards an integrative model of DNA-damage response pathways to better cover the onset of senescence, our model focuses on G1/S checkpoint enforcement. This model qualitatively agrees with most experimental observations, including experiments involving mutations. Furthermore, it provides some predictions.

Anti-inflammatory effects of reactive oxygen species - a multi-valued logical model validated by formal concept analysis

Background

Recent findings suggest that in pancreatic acinar cells stimulated with bile acid, a pro-apoptotic effect of reactive oxygen species (ROS) dominates their effect on necrosis and spreading of inflammation. The first effect presumably occurs via cytochrome C release from the inner mitochondrial membrane. A pro-necrotic effect – similar to the one of Ca²⁺ – can be strong opening of mitochondrial pores leading to breakdown of the membrane potential, ATP depletion, sustained Ca²⁺ increase and premature activation of digestive enzymes. To explain published data and to understand ROS effects during the onset of acute pancreatitis, a model using multi-valued logic is constructed. Formal concept analysis (FCA) is used to validate the model against data as well as to analyze and visualize rules that capture the dynamics.

Results

Simulations for two different levels of bile stimulation and for inhibition or addition of antioxidants reproduce the qualitative behaviour shown in the experiments. Based on reported differences of ROS production and of ROS induced pore opening, the model predicts a more uniform apoptosis/necrosis ratio for higher and lower bile stimulation in liver cells than in pancreatic acinar cells. FCA confirms that essential dynamical features of the data are captured by the model. For instance, high necrosis always occurs together with at least a medium level of apoptosis. At the same time, FCA helps to reveal subtle differences between data and simulations. The FCA visualization underlines the protective role of ROS against necrosis.

Conclusions

The analysis of the model demonstrates how ROS and decreased antioxidant levels contribute to apoptosis. Studying the induction of necrosis via a sustained Ca²⁺ increase, we implemented the commonly accepted hypothesis of ATP depletion after strong bile stimulation. Using an alternative model, we demonstrate that this process is not necessary to generate the dynamics of the measured variables. Opening of plasma membrane channels could also lead to a prolonged increase of Ca²⁺ and to necrosis. Finally, the analysis of the model suggests a direct experimental testing for the model-based hypothesis of a self-enhancing cycle of cytochrome C release and ROS production by interruption of the mitochondrial electron transport chain.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-014-0101-7) contains supplementary material, which is available to authorized users.

An integrative modeling framework reveals plasticity of TGF-β signaling

Background

The TGF-β transforming growth factor is the most pleiotropic cytokine controlling a broad range of cellular responses that include proliferation, differentiation and apoptosis. The context-dependent multifunctional nature of TGF-β is associated with complex signaling pathways. Differential models describe the dynamics of the TGF-β canonical pathway, but modeling the non-canonical networks constitutes a major challenge. Here, we propose a qualitative approach to explore all TGF-β-dependent signaling pathways.

Results

Using a new formalism, CADBIOM, which is based on guarded transitions and includes temporal parameters, we have built the first discrete model of TGF-β signaling networks by automatically integrating the 137 human signaling maps from the Pathway Interaction Database into a single unified dynamic model. Temporal property-checking analyses of 15934 trajectories that regulate 145 TGF-β target genes reveal the association of specific pathways with distinct biological processes. We identify 31 different combinations of TGF-β with other extracellular stimuli involved in non-canonical TGF-β pathways that regulate specific gene networks. Extensive analysis of gene expression data further demonstrates that genes sharing CADBIOM trajectories tend to be co-regulated.

Conclusions

As applied here to TGF-β signaling, CADBIOM allows, for the first time, a full integration of highly complex signaling pathways into dynamic models that permit to explore cell responses to complex microenvironment stimuli.

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

Gene regulatory network models for floral organ determination

Understanding how genotypes map unto phenotypes implies an integrative understanding of the processes regulating cell differentiation and morphogenesis, which comprise development. Such a task requires the use of theoretical and computational approaches to integrate and follow the concerted action of multiple genetic and nongenetic components that hold highly nonlinear interactions. Gene regulatory network (GRN) models have been proposed to approach such task. GRN models have become very useful to understand how such types of interactions restrict the multi-gene expression patterns that characterize different cell-fates. More recently, such temporal single-cell models have been extended to recover the temporal and spatial components of morphogenesis. Since the complete genomic GRN is still unknown and intractable for any organism, and some clear developmental modules have been identified, we focus here on the analysis of well-curated and experimentally grounded small GRN modules. One of the first experimentally grounded GRN that was proposed and validated corresponds to the regulatory module involved in floral organ determination. In this chapter we use this GRN as an example of the methodologies involved in: (1) formalizing and integrating molecular genetic data into the logical functions (Boolean functions) that rule gene interactions and dynamics in a Boolean GRN; (2) the algorithms and computational approaches used to recover the steady-states that correspond to each cell type, as well as the set of initial GRN configurations that lead to each one of such states (i.e., basins of attraction); (3) the approaches used to validate a GRN model using wild type and mutant or overexpression data, or to test the robustness of the GRN being proposed; (4) some of the methods that have been used to incorporate random fluctuations in the GRN Boolean functions and enable stochastic GRN models to address the temporal sequence with which gene configurations and cell fates are attained; (5) the methodologies used to approximate discrete Boolean GRN to continuous systems and their use in further dynamic analyses. The methodologies explained for the GRN of floral organ determination developed here in detail can be applied to any other functional developmental module.

Multiscale modeling and synaptic plasticity

Synaptic plasticity is a major convergence point for theory and computation, and the process of plasticity engages physiology, cell, and molecular biology. In its many manifestations, plasticity is at the hub of basic neuroscience questions about memory and development, as well as more medically themed questions of neural damage and recovery. As an important cellular locus of memory, synaptic plasticity has received a huge amount of experimental and theoretical attention. If computational models have tended to pick specific aspects of plasticity, such as STDP, and reduce them to an equation, some experimental studies are equally guilty of oversimplification each time they identify a new molecule and declare it to be the last word in plasticity and learning. Multiscale modeling begins with the acknowledgment that synaptic function spans many levels of signaling, and these are so tightly coupled that we risk losing essential features of plasticity if we focus exclusively on any one level. Despite the technical challenges and gaps in data for model specification, an increasing number of multiscale modeling studies have taken on key questions in plasticity. These have provided new insights, but importantly, they have opened new avenues for questioning. This review discusses a wide range of multiscale models in plasticity, including their technical landscape and their implications.

Computational modeling of the main signaling pathways involved in mast cell activation

A global and rigorous understanding of the signaling pathways and cross-regulatory processes involved in mast cell activation requires the integration of published information with novel functional datasets into a comprehensive computational model. Based on an exhaustive curation of the existing literature and using the software CellDesigner, we have built and annotated a comprehensive molecular map for the FcεRI signaling network. This map can be used to visualize and interpret high-throughput expression data. Furthermore, leaning on this map and using the logical modeling software GINsim, we have derived a qualitative dynamical model, which recapitulates the most salient features of mast cell activation. The resulting logical model can be used to explore the dynamical properties of the system and its responses to different stimuli, in normal or mutant conditions.

SBML qualitative models: a model representation format and infrastructure to foster interactions between qualitative modelling formalisms and tools

BACKGROUND

Qualitative frameworks, especially those based on the logical discrete formalism, are increasingly used to model regulatory and signalling networks. A major advantage of these frameworks is that they do not require precise quantitative data, and that they are well-suited for studies of large networks. While numerous groups have developed specific computational tools that provide original methods to analyse qualitative models, a standard format to exchange qualitative models has been missing.

RESULTS

We present the Systems Biology Markup Language (SBML) Qualitative Models Package ("qual"), an extension of the SBML Level 3 standard designed for computer representation of qualitative models of biological networks. We demonstrate the interoperability of models via SBML qual through the analysis of a specific signalling network by three independent software tools. Furthermore, the collective effort to define the SBML qual format paved the way for the development of LogicalModel, an open-source model library, which will facilitate the adoption of the format as well as the collaborative development of algorithms to analyse qualitative models.

CONCLUSIONS

SBML qual allows the exchange of qualitative models among a number of complementary software tools. SBML qual has the potential to promote collaborative work on the development of novel computational approaches, as well as on the specification and the analysis of comprehensive qualitative models of regulatory and signalling networks.

Integrative modelling of the influence of MAPK network on cancer cell fate decision

The Mitogen-Activated Protein Kinase (MAPK) network consists of tightly interconnected signalling pathways involved in diverse cellular processes, such as cell cycle, survival, apoptosis and differentiation. Although several studies reported the involvement of these signalling cascades in cancer deregulations, the precise mechanisms underlying their influence on the balance between cell proliferation and cell death (cell fate decision) in pathological circumstances remain elusive. Based on an extensive analysis of published data, we have built a comprehensive and generic reaction map for the MAPK signalling network, using CellDesigner software. In order to explore the MAPK responses to different stimuli and better understand their contributions to cell fate decision, we have considered the most crucial components and interactions and encoded them into a logical model, using the software GINsim. Our logical model analysis particularly focuses on urinary bladder cancer, where MAPK network deregulations have often been associated with specific phenotypes. To cope with the combinatorial explosion of the number of states, we have applied novel algorithms for model reduction and for the compression of state transition graphs, both implemented into the software GINsim. The results of systematic simulations for different signal combinations and network perturbations were found globally coherent with published data. In silico experiments further enabled us to delineate the roles of specific components, cross-talks and regulatory feedbacks in cell fate decision. Finally, tentative proliferative or anti-proliferative mechanisms can be connected with established bladder cancer deregulations, namely Epidermal Growth Factor Receptor (EGFR) over-expression and Fibroblast Growth Factor Receptor 3 (FGFR3) activating mutations.

Depending on environmental conditions, strongly intertwined cellular signalling pathways are activated, involving activation/inactivation of proteins and genes in response to external and/or internal stimuli. Alterations of some components of these pathways can lead to wrong cell behaviours. For instance, cancer-related deregulations lead to high proliferation of malignant cells enabling sustained tumour growth. Understanding the precise mechanisms underlying these pathways is necessary to delineate efficient therapeutical approaches for each specific tumour type. We particularly focused on the Mitogen-Activated Protein Kinase (MAPK) signalling network, whose involvement in cancer is well established, although the precise conditions leading to its positive or negative influence on cell proliferation are still poorly understood. We tackled this problem by first collecting sparse published biological information into a comprehensive map describing the MAPK network in terms of stylised chemical reactions. This information source was then used to build a dynamical Boolean model recapitulating network responses to characteristic stimuli observed in selected bladder cancers. Systematic model simulations further allowed us to link specific network components and interactions with proliferative/anti-proliferative cell responses.

Biological networks 101: computational modeling for molecular biologists

Computational modeling of biological networks permits the comprehensive analysis of cells and tissues to define molecular phenotypes and novel hypotheses. Although a large number of software tools have been developed, the versatility of these tools is limited by mathematical complexities that prevent their broad adoption and effective use by molecular biologists. This study clarifies the basic aspects of molecular modeling, how to convert data into useful input, as well as the number of time points and molecular parameters that should be considered for molecular regulatory models with both explanatory and predictive potential. We illustrate the necessary experimental preconditions for converting data into a computational model of network dynamics. This model requires neither a thorough background in mathematics nor precise data on intracellular concentrations, binding affinities or reaction kinetics. Finally, we show how an interactive model of crosstalk between signal transduction pathways in primary human articular chondrocytes allows insight into processes that regulate gene expression.

Dynamical modeling and analysis of large cellular regulatory networks

The dynamical analysis of large biological regulatory networks requires the development of scalable methods for mathematical modeling. Following the approach initially introduced by Thomas, we formalize the interactions between the components of a network in terms of discrete variables, functions, and parameters. Model simulations result in directed graphs, called state transition graphs. We are particularly interested in reachability properties and asymptotic behaviors, which correspond to terminal strongly connected components (or "attractors") in the state transition graph. A well-known problem is the exponential increase of the size of state transition graphs with the number of network components, in particular when using the biologically realistic asynchronous updating assumption. To address this problem, we have developed several complementary methods enabling the analysis of the behavior of large and complex logical models: (i) the definition of transition priority classes to simplify the dynamics; (ii) a model reduction method preserving essential dynamical properties, (iii) a novel algorithm to compact state transition graphs and directly generate compressed representations, emphasizing relevant transient and asymptotic dynamical properties. The power of an approach combining these different methods is demonstrated by applying them to a recent multilevel logical model for the network controlling CD4+ T helper cell response to antigen presentation and to a dozen cytokines. This model accounts for the differentiation of canonical Th1 and Th2 lymphocytes, as well as of inflammatory Th17 and regulatory T cells, along with many hybrid subtypes. All these methods have been implemented into the software GINsim, which enables the definition, the analysis, and the simulation of logical regulatory graphs.

Model composition through model reduction: a combined model of CD95 and NF-κB signaling pathways

Background

Many mathematical models characterizing mechanisms of cell fate decisions have been constructed recently. Their further study may be impossible without development of methods of model composition, which is complicated by the fact that several models describing the same processes could use different reaction chains or incomparable sets of parameters. Detailed models not supported by sufficient volume of experimental data suffer from non-unique choice of parameter values, non-reproducible results, and difficulty of analysis. Thus, it is necessary to reduce existing models to identify key elements determining their dynamics, and it is also required to design the methods allowing us to combine them.

Results

Here we propose a new approach to model composition, based on reducing several models to the same level of complexity and subsequent combining them together. Firstly, we suggest a set of model reduction tools that can be systematically applied to a given model. Secondly, we suggest a notion of a minimal complexity model. This model is the simplest one that can be obtained from the original model using these tools and still able to approximate experimental data. Thirdly, we propose a strategy for composing the reduced models together. Connection with the detailed model is preserved, which can be advantageous in some applications. A toolbox for model reduction and composition has been implemented as part of the BioUML software and tested on the example of integrating two previously published models of the CD95 (APO-1/Fas) signaling pathways. We show that the reduced models lead to the same dynamical behavior of observable species and the same predictions as in the precursor models. The composite model is able to recapitulate several experimental datasets which were used by the authors of the original models to calibrate them separately, but also has new dynamical properties.

Conclusion

Model complexity should be comparable to the complexity of the data used to train the model. Systematic application of model reduction methods allows implementing this modeling principle and finding models of minimal complexity compatible with the data. Combining such models is much easier than of precursor models and leads to new model properties and predictions.

Approaches to modeling gene regulatory networks: a gentle introduction

This chapter is split into two main sections; first, I will present an introduction to gene networks. Second, I will discuss various approaches to gene network modeling which will include some examples for using different data sources. Computational modeling has been used for many different biological systems and many approaches have been developed addressing the different needs posed by the different application fields. The modeling approaches presented here are not limited to gene regulatory networks and occasionally I will present other examples. The material covered here is an update based on several previous publications by Thomas Schlitt and Alvis Brazma (FEBS Lett 579(8),1859-1866, 2005; Philos Trans R Soc Lond B Biol Sci 361(1467), 483-494, 2006; BMC Bioinformatics 8(suppl 6), S9, 2007) that formed the foundation for a lecture on gene regulatory networks at the In Silico Systems Biology workshop series at the European Bioinformatics Institute in Hinxton.

Using answer set programming to integrate RNA expression with signalling pathway information to infer how mutations affect ageing

A challenge of systems biology is to integrate incomplete knowledge on pathways with existing experimental data sets and relate these to measured phenotypes. Research on ageing often generates such incomplete data, creating difficulties in integrating RNA expression with information about biological processes and the phenotypes of ageing, including longevity. Here, we develop a logic-based method that employs Answer Set Programming, and use it to infer signalling effects of genetic perturbations, based on a model of the insulin signalling pathway. We apply our method to RNA expression data from Drosophila mutants in the insulin pathway that alter lifespan, in a foxo dependent fashion. We use this information to deduce how the pathway influences lifespan in the mutant animals. We also develop a method for inferring the largest common sub-paths within each of our signalling predictions. Our comparisons reveal consistent homeostatic mechanisms across both long- and short-lived mutants. The transcriptional changes observed in each mutation usually provide negative feedback to signalling predicted for that mutation. We also identify an S6K-mediated feedback in two long-lived mutants that suggests a crosstalk between these pathways in mutants of the insulin pathway, in vivo. By formulating the problem as a logic-based theory in a qualitative fashion, we are able to use the efficient search facilities of Answer Set Programming, allowing us to explore larger pathways, combine molecular changes with pathways and phenotype and infer effects on signalling in in vivo, whole-organism, mutants, where direct signalling stimulation assays are difficult to perform. Our methods are available in the web-service NetEffects: http://www.ebi.ac.uk/thornton-srv/software/NetEffects.

Bio-logic builder: a non-technical tool for building dynamical, qualitative models

Computational modeling of biological processes is a promising tool in biomedical research. While a large part of its potential lies in the ability to integrate it with laboratory research, modeling currently generally requires a high degree of training in mathematics and/or computer science. To help address this issue, we have developed a web-based tool, Bio-Logic Builder, that enables laboratory scientists to define mathematical representations (based on a discrete formalism) of biological regulatory mechanisms in a modular and non-technical fashion. As part of the user interface, generalized “bio-logic” modules have been defined to provide users with the building blocks for many biological processes. To build/modify computational models, experimentalists provide purely qualitative information about a particular regulatory mechanisms as is generally found in the laboratory. The Bio-Logic Builder subsequently converts the provided information into a mathematical representation described with Boolean expressions/rules. We used this tool to build a number of dynamical models, including a 130-protein large-scale model of signal transduction with over 800 interactions, influenza A replication cycle with 127 species and 200+ interactions, and mammalian and budding yeast cell cycles. We also show that any and all qualitative regulatory mechanisms can be built using this tool.

Qualitative reasoning for biological network inference from systematic perturbation experiments

The systematic perturbation of the components of a biological system has been proven among the most informative experimental setups for the identification of causal relations between the components. In this paper, we present Systematic Perturbation-Qualitative Reasoning (SPQR), a novel Qualitative Reasoning approach to automate the interpretation of the results of systematic perturbation experiments. Our method is based on a qualitative abstraction of the experimental data: for each perturbation experiment, measured values of the observed variables are modeled as lower, equal or higher than the measurements in the wild type condition, when no perturbation is applied. The algorithm exploits a set of IF-THEN rules to infer causal relations between the variables, analyzing the patterns of propagation of the perturbation signals through the biological network, and is specifically designed to minimize the rate of false positives among the inferred relations. Tested on both simulated and real perturbation data, SPQR indeed exhibits a significantly higher precision than the state of the art.

The Cell Collective: toward an open and collaborative approach to systems biology

BACKGROUND

Despite decades of new discoveries in biomedical research, the overwhelming complexity of cells has been a significant barrier to a fundamental understanding of how cells work as a whole. As such, the holistic study of biochemical pathways requires computer modeling. Due to the complexity of cells, it is not feasible for one person or group to model the cell in its entirety.

RESULTS

The Cell Collective is a platform that allows the world-wide scientific community to create these models collectively. Its interface enables users to build and use models without specifying any mathematical equations or computer code - addressing one of the major hurdles with computational research. In addition, this platform allows scientists to simulate and analyze the models in real-time on the web, including the ability to simulate loss/gain of function and test what-if scenarios in real time.

CONCLUSIONS

The Cell Collective is a web-based platform that enables laboratory scientists from across the globe to collaboratively build large-scale models of various biological processes, and simulate/analyze them in real time. In this manuscript, we show examples of its application to a large-scale model of signal transduction.

miR-9 controls the timing of neurogenesis through the direct inhibition of antagonistic factors

The timing of commitment and cell-cycle exit within progenitor populations during neurogenesis is a fundamental decision that impacts both the number and identity of neurons produced during development. We show here that microRNA-9 plays a key role in this process through the direct inhibition of targets with antagonistic functions. Across the ventricular zone of the developing zebrafish hindbrain, miR-9 expression occurs at a range of commitment stages. Abrogating miR-9 function transiently delays cell-cycle exit, leading to the increased generation of late-born neuronal populations. Target protection analyses in vivo identify the progenitor-promoting genes her6 and zic5 and the cell-cycle exit-promoting gene elavl3/HuC as sequential targets of miR-9 as neurogenesis proceeds. We propose that miR-9 activity generates an ambivalent progenitor state poised to respond to both progenitor maintenance and commitment cues, which may be necessary to adjust neuronal production to local extrinsic signals during late embryogenesis.

An overview of existing modeling tools making use of model checking in the analysis of biochemical networks

Model checking is a well-established technique for automatically verifying complex systems. Recently, model checkers have appeared in computer tools for the analysis of biochemical (and gene regulatory) networks. We survey several such tools to assess the potential of model checking in computational biology. Next, our overview focuses on direct applications of existing model checkers, as well as on algorithms for biochemical network analysis influenced by model checking, such as those using binary decision diagrams (BDDs) or Boolean-satisfiability solvers. We conclude with advantages and drawbacks of model checking for the analysis of biochemical networks.

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.

On parameter synthesis by parallel model checking

An important problem in current computational systems biology is to analyze models of biological systems dynamics under parameter uncertainty. This paper presents a novel algorithm for parameter synthesis based on parallel model checking. The algorithm is conceptually universal with respect to the modeling approach employed. We introduce the algorithm, show its scalability, and examine its applicability on several biological models.

Relating the chondrocyte gene network to growth plate morphology: from genes to phenotype

During endochondral ossification, chondrocyte growth and differentiation is controlled by many local signalling pathways. Due to crosstalks and feedback mechanisms, these interwoven pathways display a network like structure. In this study, a large-scale literature based logical model of the growth plate network was developed. The network is able to capture the different states (resting, proliferating and hypertrophic) that chondrocytes go through as they progress within the growth plate. In a first corroboration step, the effect of mutations in various signalling pathways of the growth plate network was investigated.

An integrative model links multiple inputs and signaling pathways to the onset of DNA synthesis in hepatocytes

During liver regeneration, quiescent hepatocytes re-enter the cell cycle to proliferate and compensate for lost tissue. Multiple signals including hepatocyte growth factor, epidermal growth factor, tumor necrosis factor α, interleukin-6, insulin and transforming growth factor β orchestrate these responses and are integrated during the G₁ phase of the cell cycle. To investigate how these inputs influence DNA synthesis as a measure for proliferation, we established a large-scale integrated logical model connecting multiple signaling pathways and the cell cycle. We constructed our model based upon established literature knowledge, and successively improved and validated its structure using hepatocyte-specific literature as well as experimental DNA synthesis data. Model analyses showed that activation of the mitogen-activated protein kinase and phosphatidylinositol 3-kinase pathways was sufficient and necessary for triggering DNA synthesis. In addition, we identified key species in these pathways that mediate DNA replication. Our model predicted oncogenic mutations that were compared with the COSMIC database, and proposed intervention targets to block hepatocyte growth factor-induced DNA synthesis, which we validated experimentally. Our integrative approach demonstrates that, despite the complexity and size of the underlying interlaced network, logical modeling enables an integrative understanding of signaling-controlled proliferation at the cellular level, and thus can provide intervention strategies for distinct perturbation scenarios at various regulatory levels.

TranscriptomeBrowser 3.0: introducing a new compendium of molecular interactions and a new visualization tool for the study of gene regulatory networks

Background

Deciphering gene regulatory networks by in silico approaches is a crucial step in the study of the molecular perturbations that occur in diseases. The development of regulatory maps is a tedious process requiring the comprehensive integration of various evidences scattered over biological databases. Thus, the research community would greatly benefit from having a unified database storing known and predicted molecular interactions. Furthermore, given the intrinsic complexity of the data, the development of new tools offering integrated and meaningful visualizations of molecular interactions is necessary to help users drawing new hypotheses without being overwhelmed by the density of the subsequent graph.

Results

We extend the previously developed TranscriptomeBrowser database with a set of tables containing 1,594,978 human and mouse molecular interactions. The database includes: (i) predicted regulatory interactions (computed by scanning vertebrate alignments with a set of 1,213 position weight matrices), (ii) potential regulatory interactions inferred from systematic analysis of ChIP-seq experiments, (iii) regulatory interactions curated from the literature, (iv) predicted post-transcriptional regulation by micro-RNA, (v) protein kinase-substrate interactions and (vi) physical protein-protein interactions. In order to easily retrieve and efficiently analyze these interactions, we developed In-teractomeBrowser, a graph-based knowledge browser that comes as a plug-in for Transcriptome-Browser. The first objective of InteractomeBrowser is to provide a user-friendly tool to get new insight into any gene list by providing a context-specific display of putative regulatory and physical interactions. To achieve this, InteractomeBrowser relies on a "cell compartments-based layout" that makes use of a subset of the Gene Ontology to map gene products onto relevant cell compartments. This layout is particularly powerful for visual integration of heterogeneous biological information and is a productive avenue in generating new hypotheses. The second objective of InteractomeBrowser is to fill the gap between interaction databases and dynamic modeling. It is thus compatible with the network analysis software Cytoscape and with the Gene Interaction Network simulation software (GINsim). We provide examples underlying the benefits of this visualization tool for large gene set analysis related to thymocyte differentiation.

Conclusions

The InteractomeBrowser plugin is a powerful tool to get quick access to a knowledge database that includes both predicted and validated molecular interactions. InteractomeBrowser is available through the TranscriptomeBrowser framework and can be found at: http://tagc.univ-mrs.fr/tbrowser/. Our database is updated on a regular basis.

Logical modelling of gene regulatory networks with GINsim

Discrete mathematical formalisms are well adapted to model large biological networks, for which detailed kinetic data are scarce. This chapter introduces the reader to a well-established qualitative (logical) framework for the modelling of regulatory networks. Relying on GINsim, a software implementing this logical formalism, we guide the reader step by step towards the definition and the analysis of a simple model of the lysis-lysogeny decision in the bacteriophage λ.

Cell death and life in cancer: mathematical modeling of cell fate decisions

Tumor development is characterized by a compromised balance between cell life and death decision mechanisms, which are tightly regulated in normal cells. Understanding this process provides insights for developing new treatments for fighting with cancer. We present a study of a mathematical model describing cellular choice between survival and two alternative cell death modalities: apoptosis and necrosis. The model is implemented in discrete modeling formalism and allows to predict probabilities of having a particular cellular phenotype in response to engagement of cell death receptors. Using an original parameter sensitivity analysis developed for discrete dynamic systems, we determine variables that appear to be critical in the cellular fate decision and discuss how they are exploited by existing cancer therapies.

"Antelope": a hybrid-logic model checker for branching-time Boolean GRN analysis

Background

In Thomas' formalism for modeling gene regulatory networks (GRNs), branching time, where a state can have more than one possible future, plays a prominent role. By representing a certain degree of unpredictability, branching time can model several important phenomena, such as (a) asynchrony, (b) incompletely specified behavior, and (c) interaction with the environment. Introducing more than one possible future for a state, however, creates a difficulty for ordinary simulators, because infinitely many paths may appear, limiting ordinary simulators to statistical conclusions. Model checkers for branching time, by contrast, are able to prove properties in the presence of infinitely many paths.

Results

We have developed Antelope ("Analysis of Networks through TEmporal-LOgic sPEcifications", http://turing.iimas.unam.mx:8080/AntelopeWEB/), a model checker for analyzing and constructing Boolean GRNs. Currently, software systems for Boolean GRNs use branching time almost exclusively for asynchrony. Antelope, by contrast, also uses branching time for incompletely specified behavior and environment interaction. We show the usefulness of modeling these two phenomena in the development of a Boolean GRN of the Arabidopsis thaliana root stem cell niche.

There are two obstacles to a direct approach when applying model checking to Boolean GRN analysis. First, ordinary model checkers normally only verify whether or not a given set of model states has a given property. In comparison, a model checker for Boolean GRNs is preferable if it reports the set of states having a desired property. Second, for efficiency, the expressiveness of many model checkers is limited, resulting in the inability to express some interesting properties of Boolean GRNs.

Antelope tries to overcome these two drawbacks: Apart from reporting the set of all states having a given property, our model checker can express, at the expense of efficiency, some properties that ordinary model checkers (e.g., NuSMV) cannot. This additional expressiveness is achieved by employing a logic extending the standard Computation-Tree Logic (CTL) with hybrid-logic operators.

Conclusions

We illustrate the advantages of Antelope when (a) modeling incomplete networks and environment interaction, (b) exhibiting the set of all states having a given property, and (c) representing Boolean GRN properties with hybrid CTL.

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.

ADAM: analysis of discrete models of biological systems using computer algebra

BACKGROUND

Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed.

RESULTS

We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second.

CONCLUSIONS

Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics.

ADAM: analysis of discrete models of biological systems using computer algebra

Background

Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed.

Results

We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second.

Conclusions

Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics.

An application programming interface for CellNetAnalyzer

CellNetAnalyzer (CNA) is a MATLAB toolbox providing computational methods for studying structure and function of metabolic and cellular signaling networks. In order to allow non-experts to use these methods easily, CNA provides GUI-based interactive network maps as a means of parameter input and result visualization. However, with the availability of high-throughput data, there is a need to make CNA's functionality also accessible in batch mode for automatic data processing. Furthermore, as some algorithms of CNA are of general relevance for network analysis it would be desirable if they could be called as sub-routines by other applications. For this purpose, we developed an API (application programming interface) for CNA allowing users (i) to access the content of network models in CNA, (ii) to use CNA's network analysis capabilities independent of the GUI, and (iii) to interact with the GUI to facilitate the development of graphical plugins. Here we describe the organization of network projects in CNA and the application of the new API functions to these projects. This includes the creation of network projects from scratch, loading and saving of projects and scenarios, and the application of the actual analysis methods. Furthermore, API functions for the import/export of metabolic models in SBML format and for accessing the GUI are described. Lastly, two example applications demonstrate the use and versatile applicability of CNA's API. CNA is freely available for academic use and can be downloaded from http://www.mpi-magdeburg.mpg.de/projects/cna/cna.html.