Modeling formalisms in Systems Biology

Systematic Analysis of Quantitative Logic Model Ensembles Predicts Drug Combination Effects on Cell Signaling Networks

A major challenge in developing anticancer therapies is determining the efficacies of drugs and their combinations in physiologically relevant microenvironments. We describe here our application of "constrained fuzzy logic" (CFL) ensemble modeling of the intracellular signaling network for predicting inhibitor treatments that reduce the phospho-levels of key transcription factors downstream of growth factors and inflammatory cytokines representative of hepatocellular carcinoma (HCC) microenvironments. We observed that the CFL models successfully predicted the effects of several kinase inhibitor combinations. Furthermore, the ensemble predictions revealed ambiguous predictions that could be traced to a specific structural feature of these models, which we resolved with dedicated experiments, finding that IL-1α activates downstream signals through TAK1 and not MEKK1 in HepG2 cells. We conclude that CFL-Q2LM (Querying Quantitative Logic Models) is a promising approach for predicting effective anticancer drug combinations in cancer-relevant microenvironments.

Process-based design of dynamical biological systems

The computational design of dynamical systems is an important emerging task in synthetic biology. Given desired properties of the behaviour of a dynamical system, the task of design is to build an in-silico model of a system whose simulated be- haviour meets these properties. We introduce a new, process-based, design methodology for addressing this task. The new methodology combines a flexible process-based formalism for specifying the space of candidate designs with multi-objective optimization approaches for selecting the most appropriate among these candidates. We demonstrate that the methodology is general enough to both formulate and solve tasks of designing deterministic and stochastic systems, successfully reproducing plausible designs reported in previous studies and proposing new designs that meet the design criteria, but have not been previously considered.

A Network-Based Data Integration Approach to Support Drug Repurposing and Multi-Target Therapies in Triple Negative Breast Cancer

The integration of data and knowledge from heterogeneous sources can be a key success factor in drug design, drug repurposing and multi-target therapies. In this context, biological networks provide a useful instrument to highlight the relationships and to model the phenomena underlying therapeutic action in cancer. In our work, we applied network-based modeling within a novel bioinformatics pipeline to identify promising multi-target drugs. Given a certain tumor type/subtype, we derive a disease-specific Protein-Protein Interaction (PPI) network by combining different data-bases and knowledge repositories. Next, the application of suitable graph-based algorithms allows selecting a set of potentially interesting combinations of drug targets. A list of drug candidates is then extracted by applying a recent data fusion approach based on matrix tri-factorization. Available knowledge about selected drugs mechanisms of action is finally exploited to identify the most promising candidates for planning in vitro studies. We applied this approach to the case of Triple Negative Breast Cancer (TNBC), a subtype of breast cancer whose biology is poorly understood and that lacks of specific molecular targets. Our “in-silico” findings have been confirmed by a number of in vitro experiments, whose results demonstrated the ability of the method to select candidates for drug repurposing.

Modelling with ANIMO: between fuzzy logic and differential equations

BACKGROUND

Computational support is essential in order to reason on the dynamics of biological systems. We have developed the software tool ANIMO (Analysis of Networks with Interactive MOdeling) to provide such computational support and allow insight into the complex networks of signaling events occurring in living cells. ANIMO makes use of timed automata as an underlying model, thereby enabling analysis techniques from computer science like model checking. Biology experts are able to use ANIMO via a user interface specifically tailored for biological applications. In this paper we compare the use of ANIMO with some established formalisms on two case studies.

RESULTS

ANIMO is a powerful and user-friendly tool that can compete with existing continuous and discrete paradigms. We show this by presenting ANIMO models for two case studies: Drosophila melanogaster circadian clock, and signal transduction events downstream of TNF α and EGF in HT-29 human colon carcinoma cells. The models were originally developed with ODEs and fuzzy logic, respectively.

CONCLUSIONS

Two biological case studies that have been modeled with respectively ODE and fuzzy logic models can be conveniently modeled using ANIMO. The ANIMO models require less parameters than ODEs and are more precise than fuzzy logic. For this reason we position the modelling paradigm of ANIMO between ODEs and fuzzy logic.

Convergence Properties of Posttranslationally Modified Protein-Protein Switching Networks with Fast Decay Rates

A significant conceptual difficulty in the use of switching systems to model regulatory networks is the presence of so-called "black walls," co-dimension 1 regions of phase space with a vector field pointing inward on both sides of the hyperplane. Black walls result from the existence of direct negative self-regulation in the system. One biologically inspired way of removing black walls is the introduction of intermediate variables that mediate the negative self-regulation. In this paper, we study such a perturbation. We replace a switching system with a higher-dimensional switching system with rapidly decaying intermediate proteins, and compare the dynamics between the two systems. We find that the while the individual solutions of the original system can be approximated for a finite time by solutions of a sufficiently close perturbed system, there are always solutions that are not well approximated for any fixed perturbation. We also study a particular example, where global basins of attraction of the perturbed system have a strikingly different form than those of the original system. We perform this analysis using techniques that are adapted to dealing with non-smooth systems.

Constructing kinetic models of metabolism at genome-scales: A review

Constraint-based modeling of biological networks (metabolism, transcription and signal transduction), although used successfully in many applications, suffer from specific limitations such as the lack of representation of metabolite concentrations and enzymatic regulation, which are necessary for a complete physiologically relevant model. Kinetic models conversely overcome these shortcomings and enable dynamic analysis of biological systems for enhanced in silico hypothesis generation. Nonetheless, kinetic models also have limitations for modeling at genome-scales chiefly due to: (i) model non-linearity; (ii) computational tractability; (iii) parameter identifiability; (iv) estimability; and (v) uncertainty. In order to support further development of kinetic models as viable alternatives to constraint-based models, this review presents a brief description of the existing obstacles towards building genome-scale kinetic models. Specific kinetic modeling frameworks capable of overcoming these obstacles are covered in this review. The tractability and physiological feasibility of these models are discussed with the objective of using available in vivo experimental observations to define the model parameter space. Among the different methods discussed, Monte Carlo kinetic models of metabolism stand out as potentially tractable methods to model genome scale networks while also addressing in vivo parameter uncertainty.

eSTGt: a programming and simulation environment for population dynamics

Background

We have previously presented a formal language for describing population dynamics based on environment-dependent Stochastic Tree Grammars (eSTG). The language captures in broad terms the effect of the changing environment while abstracting away details on interaction among individuals. An eSTG program consists of a set of stochastic tree grammar transition rules that are context-free. Transition rule probabilities and rates, however, can depend on global parameters such as population size, generation count and elapsed time. In addition, each individual may have an internal state, which can change during transitions.

Results

This paper presents eSTGt (eSTG tool), an eSTG programming and simulation environment. When executing a program, the tool generates the corresponding lineage trees as well as the internal states values, which can then be analyzed either through the tool’s GUI or using MATLAB’s command-line environment.

Conclusions

The presented tool allows researchers to use existing biological knowledge in order to model the dynamics of a developmental process and analyze its behavior throughout the historical events. Simulated lineage trees can be used to validate various hypotheses in silico and to predict the behavior of dynamical systems under various conditions. Written under MATLAB environment, the tool also enables to easily integrate the output data within the user’s downstream analysis.

Boolean modeling techniques for protein co-expression networks in systems medicine

INTRODUCTION

Application of systems biology/systems medicine approaches is promising for proteomics/biomedical research, but requires selection of an adequate modeling type.

AREAS COVERED

This article reviews the existing Boolean network modeling approaches, which provide in comparison with alternative modeling techniques several advantages for the processing of proteomics data. Application of methods for inference, reduction and validation of protein co-expression networks that are derived from quantitative high-throughput proteomics measurements is presented. It's also shown how Boolean models can be used to derive system-theoretic characteristics that describe both the dynamical behavior of such networks as a whole and the properties of different cell states (e.g. healthy or diseased cell states). Furthermore, application of methods derived from control theory is proposed in order to simulate the effects of therapeutic interventions on such networks, which is a promising approach for the computer-assisted discovery of biomarkers and drug targets. Finally, the clinical application of Boolean modeling analyses is discussed. Expert commentary: Boolean modeling of proteomics data is still in its infancy. Progress in this field strongly depends on provision of a repository with public access to relevant reference models. Also required are community supported standards that facilitate input of both proteomics and patient related data (e.g. age, gender, laboratory results, etc.).

A Six-Stage Workflow for Robust Application of Systems Pharmacology

Quantitative and systems pharmacology (QSP) is increasingly being applied in pharmaceutical research and development. One factor critical to the ultimate success of QSP is the establishment of commonly accepted language, technical criteria, and workflows. We propose an integrated workflow that bridges conceptual objectives with underlying technical detail to support the execution, communication, and evaluation of QSP projects.

Translation of Genotype to Phenotype by a Hierarchy of Cell Subsystems

Accurately translating genotype to phenotype requires accounting for the functional impact of genetic variation at many biological scales. Here we present a strategy for genotype-phenotype reasoning based on existing knowledge of cellular subsystems. These subsystems and their hierarchical organization are defined by the Gene Ontology or a complementary ontology inferred directly from previously published datasets. Guided by the ontology's hierarchical structure, we organize genotype data into an "ontotype," that is, a hierarchy of perturbations representing the effects of genetic variation at multiple cellular scales. The ontotype is then interpreted using logical rules generated by machine learning to predict phenotype. This approach substantially outperforms previous, non-hierarchical methods for translating yeast genotype to cell growth phenotype, and it accurately predicts the growth outcomes of two new screens of 2,503 double gene knockouts impacting DNA repair or nuclear lumen. Ontotypes also generalize to larger knockout combinations, setting the stage for interpreting the complex genetics of disease.

Aging and computational systems biology

Aging research is undergoing a paradigm shift, which has led to new and innovative methods of exploring this complex phenomenon. The systems biology approach endeavors to understand biological systems in a holistic manner, by taking account of intrinsic interactions, while also attempting to account for the impact of external inputs, such as diet. A key technique employed in systems biology is computational modeling, which involves mathematically describing and simulating the dynamics of biological systems. Although a large number of computational models have been developed in recent years, these models have focused on various discrete components of the aging process, and to date no model has succeeded in completely representing the full scope of aging. Combining existing models or developing new models may help to address this need and in so doing could help achieve an improved understanding of the intrinsic mechanisms which underpin aging.

Coordinating Role of RXRα in Downregulating Hepatic Detoxification during Inflammation Revealed by Fuzzy-Logic Modeling

During various inflammatory processes circulating cytokines including IL-6, IL-1β, and TNFα elicit a broad and clinically relevant impairment of hepatic detoxification that is based on the simultaneous downregulation of many drug metabolizing enzymes and transporter genes. To address the question whether a common mechanism is involved we treated human primary hepatocytes with IL-6, the major mediator of the acute phase response in liver, and characterized acute phase and detoxification responses in quantitative gene expression and (phospho-)proteomics data sets. Selective inhibitors were used to disentangle the roles of JAK/STAT, MAPK, and PI3K signaling pathways. A prior knowledge-based fuzzy logic model comprising signal transduction and gene regulation was established and trained with perturbation-derived gene expression data from five hepatocyte donors. Our model suggests a greater role of MAPK/PI3K compared to JAK/STAT with the orphan nuclear receptor RXRα playing a central role in mediating transcriptional downregulation. Validation experiments revealed a striking similarity of RXRα gene silencing versus IL-6 induced negative gene regulation (r_s = 0.79; P<0.0001). These results concur with RXRα functioning as obligatory heterodimerization partner for several nuclear receptors that regulate drug and lipid metabolism.

During inflammation, circulating proinflammatory cytokines such as TNFα, IL-1ß, and IL-6, which are produced by, e.g., Kupffer cells, macrophages, or tumor cells, play important roles in hepatocellular signaling pathways and in the regulation of cellular homeostasis. In particular, these cytokines are responsible for the acute phase response (APR) but also for a dramatic reduction of drug detoxification capacity due to impaired expression of numerous genes coding for drug metabolic enzymes and transporters. Here we used high-throughput (phospho-)proteomic and gene expression data to investigate the impact of canonical signaling pathways in mediating IL-6-induced downregulation of drug metabolism related genes. We performed chemical inhibition perturbations to show that most of the IL-6 effects on gene expression are mediated through the MAPK and PI3K/AKT pathways. We constructed a prior knowledge network as basis for a fuzzy logic model that was trained with extensive gene expression data to identify critical regulatory nodes. Our results suggest that the nuclear receptor RXRα plays a central role, which was convincingly validated by RXRα gene silencing experiments. This work shows how computational modeling can support identifying decisive regulatory events from large-scale experimental data.

Anatomy and Physiology of Multiscale Modeling and Simulation in Systems Medicine

Systems medicine is the application of systems biology concepts, methods, and tools to medical research and practice. It aims to integrate data and knowledge from different disciplines into biomedical models and simulations for the understanding, prevention, cure, and management of complex diseases. Complex diseases arise from the interactions among disease-influencing factors across multiple levels of biological organization from the environment to molecules. To tackle the enormous challenges posed by complex diseases, we need a modeling and simulation framework capable of capturing and integrating information originating from multiple spatiotemporal and organizational scales. Multiscale modeling and simulation in systems medicine is an emerging methodology and discipline that has already demonstrated its potential in becoming this framework. The aim of this chapter is to present some of the main concepts, requirements, and challenges of multiscale modeling and simulation in systems medicine.

Computational Modeling of Human Metabolism and Its Application to Systems Biomedicine

Modern high-throughput techniques offer immense opportunities to investigate whole-systems behavior, such as those underlying human diseases. However, the complexity of the data presents challenges in interpretation, and new avenues are needed to address the complexity of both diseases and data. Constraint-based modeling is one formalism applied in systems biology. It relies on a genome-scale reconstruction that captures extensive biochemical knowledge regarding an organism. The human genome-scale metabolic reconstruction is increasingly used to understand normal cellular and disease states because metabolism is an important factor in many human diseases. The application of human genome-scale reconstruction ranges from mere querying of the model as a knowledge base to studies that take advantage of the model's topology and, most notably, to functional predictions based on cell- and condition-specific metabolic models built based on omics data.An increasing number and diversity of biomedical questions are being addressed using constraint-based modeling and metabolic models. One of the most successful biomedical applications to date is cancer metabolism, but constraint-based modeling also holds great potential for inborn errors of metabolism or obesity. In addition, it offers great prospects for individualized approaches to diagnostics and the design of disease prevention and intervention strategies. Metabolic models support this endeavor by providing easy access to complex high-throughput datasets. Personalized metabolic models have been introduced. Finally, constraint-based modeling can be used to model whole-body metabolism, which will enable the elucidation of metabolic interactions between organs and disturbances of these interactions as either causes or consequence of metabolic diseases. This chapter introduces constraint-based modeling and describes some of its contributions to systems biomedicine.

Discrete Element Framework for Modelling Extracellular Matrix, Deformable Cells and Subcellular Components

This paper presents a framework for modelling biological tissues based on discrete particles. Cell components (e.g. cell membranes, cell cytoskeleton, cell nucleus) and extracellular matrix (e.g. collagen) are represented using collections of particles. Simple particle to particle interaction laws are used to simulate and control complex physical interaction types (e.g. cell-cell adhesion via cadherins, integrin basement membrane attachment, cytoskeletal mechanical properties). Particles may be given the capacity to change their properties and behaviours in response to changes in the cellular microenvironment (e.g., in response to cell-cell signalling or mechanical loadings). Each particle is in effect an ‘agent’, meaning that the agent can sense local environmental information and respond according to pre-determined or stochastic events. The behaviour of the proposed framework is exemplified through several biological problems of ongoing interest. These examples illustrate how the modelling framework allows enormous flexibility for representing the mechanical behaviour of different tissues, and we argue this is a more intuitive approach than perhaps offered by traditional continuum methods. Because of this flexibility, we believe the discrete modelling framework provides an avenue for biologists and bioengineers to explore the behaviour of tissue systems in a computational laboratory.

Modelling is an important tool in understanding the behaviour of biological tissues. In this paper we advocate a new modelling framework in which cells and tissues are represented by a collection of particles with associated properties. The particles interact with each other and can change their behaviour in response to changes in their environment. We demonstrate how the propose framework can be used to represent the mechanical behaviour of different tissues with much greater flexibility as compared to traditional continuum based methods.

Supervised learning methods in modeling of CD4+ T cell heterogeneity

Background

Modeling of the immune system – a highly non-linear and complex system – requires practical and efficient data analytic approaches. The immune system is composed of heterogeneous cell populations and hundreds of cell types, such as neutrophils, eosinophils, macrophages, dendritic cells, T cells, and B cells. Each cell type is highly diverse and can be further differentiated into subsets with unique and overlapping functions. For example, CD4+ T cells can be differentiated into Th1, Th2, Th17, Th9, Th22, Treg, Tfh, as well as Tr1. Each subset plays different roles in the immune system. To study molecular mechanisms of cell differentiation, computational systems biology approaches can be used to represent these processes; however, the latter often requires building complex intracellular signaling models with a large number of equations to accurately represent intracellular pathways and biochemical reactions. Furthermore, studying the immune system entails integration of complex processes which occur at different time and space scales.

Methods

This study presents and compares four supervised learning methods for modeling CD4+ T cell differentiation: Artificial Neural Networks (ANN), Random Forest (RF), Support Vector Machines (SVM), and Linear Regression (LR). Application of supervised learning methods could reduce the complexity of Ordinary Differential Equations (ODEs)-based intracellular models by only focusing on the input and output cytokine concentrations. In addition, this modeling framework can be efficiently integrated into multiscale models.

Results

Our results demonstrate that ANN and RF outperform the other two methods. Furthermore, ANN and RF have comparable performance when applied to in silico data with and without added noise. The trained models were also able to reproduce dynamic behavior when applied to experimental data; in four out of five cases, model predictions based on ANN and RF correctly predicted the outcome of the system. Finally, the running time of different methods was compared, which confirms that ANN is considerably faster than RF.

Conclusions

Using machine learning as opposed to ODE-based method reduces the computational complexity of the system and allows one to gain a deeper understanding of the complex interplay between the different related entities.

Towards integrative systems pharmacology models in oncology drug development

Quantitative systems pharmacology (QSP) modeling represents an emerging area of value to further streamline knowledge integration and to better inform decision making processes in drug development. QSP models reside at the interface between systems biology models and pharmacological models, yet their concrete implementation still needs to be established further. This review outlines key modeling techniques in both of these areas and to subsequently discuss challenges and opportunities for further integration, in oncology drug development.

Domain-specific model selection for structural identification of the Rab5-Rab7 dynamics in endocytosis

Background

Given its recent rapid development and the central role that modeling plays in the discipline, systems biology clearly needs methods for automated modeling of dynamical systems. Process-based modeling focuses on explanatory models of dynamical systems; it constructs such models from measured time-course data and formalized modeling knowledge. In this paper, we apply process-based modeling to the practically relevant task of modeling the Rab5-Rab7 conversion switch in endocytosis. The task is difficult due to the limited observability of the system variables and the noisy measurements, which pose serious challenges to the process of model selection. To address these issues, we propose a domain-specific model selection criteria that take into account knowledge about the necessary properties of the simulated model behavior.

Results

In a series of modeling experiments, we compare the results of process-based modeling obtained with different model selection criteria. The first is the standard maximum likelihood criterion based solely on least-squares model error. The second one is a parsimony-based criterion that also takes into account model complexity. We also introduce three domain-specific criteria based on domain expert expectations about the simulated behavior of an endocytosis model. According to the first criterion, 90 of the candidate models are indistinguishable. Furthermore, taking into account the complexity of the model does not lead to better model selection. However, the use of domain-specific criteria results in a remarkable improvement over the other two model selection criteria.

Conclusions

We demonstrate the applicability of process-based modeling to the task of modeling the Rab5-Rab7 dynamics in endocytosis. Our experiments show that the domain-specific criteria outperform the standard domain-independent criteria for model selection. We also find that some of the model structures discarded as implausible in previous studies lead to the expected Rab5-Rab7 switch behavior.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0175-x) contains supplementary material, which is available to authorized users.

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.

Convergence behaviour and Control in Non-Linear Biological Networks

Control of genetic regulatory networks is challenging to define and quantify. Previous control centrality metrics, which aim to capture the ability of individual nodes to control the system, have been found to suffer from plausibility and applicability problems. Here we present a new approach to control centrality based on network convergence behaviour, implemented as an extension of our genetic regulatory network simulation framework Jimena ( http://stefan-karl.de/jimena). We distinguish three types of network control, and show how these mathematical concepts correspond to experimentally verified node functions and signalling pathways in immunity and cell differentiation: Total control centrality quantifies the impact of node mutations and identifies potential pharmacological targets such as genes involved in oncogenesis (e.g. zinc finger protein GLI2 or bone morphogenetic proteins in chondrocytes). Dynamic control centrality describes relaying functions as observed in signalling cascades (e.g. src kinase or Jak/Stat pathways). Value control centrality measures the direct influence of the value of the node on the network (e.g. Indian hedgehog as an essential regulator of proliferation in chondrocytes). Surveying random scale-free networks and biological networks, we find that control of the network resides in few high degree driver nodes and networks can be controlled best if they are sparsely connected.

Co-evolution of strain design methods based on flux balance and elementary mode analysis

More than a decade ago, the first genome-scale metabolic models for two of the most relevant microbes for biotechnology applications, Escherichia coli and Saccaromyces cerevisiae, were published. Shortly after followed the publication of OptKnock, the first strain design method using bilevel optimization to couple cellular growth with the production of a target product. This initiated the development of a family of strain design methods based on the concept of flux balance analysis. Another family of strain design methods, based on the concept of elementary mode analysis, has also been growing. Although the computation of elementary modes is hindered by computational complexity, recent breakthroughs have allowed applying elementary mode analysis at the genome scale. Here we review and compare strain design methods and look back at the last 10 years of in silico strain design with constraint-based models. We highlight some features of the different approaches and discuss the utilization of these methods in successful in vivo metabolic engineering applications.

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Computational strain design methods are divided into two main families.

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We trace the evolutionary history of these two families.

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Surveyed successful cases of model-guided strain design for industrial applications.

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Most proposed methods have not yet been tested in real applications.

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Agreement between in silico and in vivo results shows potential of tested methods.

Data-driven integration of genome-scale regulatory and metabolic network models

Microbes are diverse and extremely versatile organisms that play vital roles in all ecological niches. Understanding and harnessing microbial systems will be key to the sustainability of our planet. One approach to improving our knowledge of microbial processes is through data-driven and mechanism-informed computational modeling. Individual models of biological networks (such as metabolism, transcription, and signaling) have played pivotal roles in driving microbial research through the years. These networks, however, are highly interconnected and function in concert-a fact that has led to the development of a variety of approaches aimed at simulating the integrated functions of two or more network types. Though the task of integrating these different models is fraught with new challenges, the large amounts of high-throughput data sets being generated, and algorithms being developed, means that the time is at hand for concerted efforts to build integrated regulatory-metabolic networks in a data-driven fashion. In this perspective, we review current approaches for constructing integrated regulatory-metabolic models and outline new strategies for future development of these network models for any microbial system.

Integrative analysis of metabolic models - from structure to dynamics

The characterization of biological systems with respect to their behavior and functionality based on versatile biochemical interactions is a major challenge. To understand these complex mechanisms at systems level modeling approaches are investigated. Different modeling formalisms allow metabolic models to be analyzed depending on the question to be solved, the biochemical knowledge and the availability of experimental data. Here, we describe a method for an integrative analysis of the structure and dynamics represented by qualitative and quantitative metabolic models. Using various formalisms, the metabolic model is analyzed from different perspectives. Determined structural and dynamic properties are visualized in the context of the metabolic model. Interaction techniques allow the exploration and visual analysis thereby leading to a broader understanding of the behavior and functionality of the underlying biological system. The System Biology Metabolic Model Framework (SBM (2) - Framework) implements the developed method and, as an example, is applied for the integrative analysis of the crop plant potato.

Integration of metabolomics data into metabolic networks

Metabolite levels together with their corresponding metabolic fluxes are integrative outcomes of biochemical transformations and regulatory processes and they can be used to characterize the response of biological systems to genetic and/or environmental changes. However, while changes in transcript or to some extent protein levels can usually be traced back to one or several responsible genes, changes in fluxes and particularly changes in metabolite levels do not follow such rationale and are often the outcome of complex interactions of several components. The increasing quality and coverage of metabolomics technologies have fostered the development of computational approaches for integrating metabolic read-outs with large-scale models to predict the physiological state of a system. Constraint-based approaches, relying on the stoichiometry of the considered reactions, provide a modeling framework amenable to analyses of large-scale systems and to the integration of high-throughput data. Here we review the existing approaches that integrate metabolomics data in variants of constrained-based approaches to refine model reconstructions, to constrain flux predictions in metabolic models, and to relate network structural properties to metabolite levels. Finally, we discuss the challenges and perspectives in the developments of constraint-based modeling approaches driven by metabolomics data.

Lineage grammars: describing, simulating and analyzing population dynamics

Background

Precise description of the dynamics of biological processes would enable the mathematical analysis and computational simulation of complex biological phenomena. Languages such as Chemical Reaction Networks and Process Algebras cater for the detailed description of interactions among individuals and for the simulation and analysis of ensuing behaviors of populations. However, often knowledge of such interactions is lacking or not available. Yet complete oblivion to the environment would make the description of any biological process vacuous. Here we present a language for describing population dynamics that abstracts away detailed interaction among individuals, yet captures in broad terms the effect of the changing environment, based on environment-dependent Stochastic Tree Grammars (eSTG). It is comprised of a set of stochastic tree grammar transition rules, which are context-free and as such abstract away specific interactions among individuals. Transition rule probabilities and rates, however, can depend on global parameters such as population size, generation count, and elapsed time.

Results

We show that eSTGs conveniently describe population dynamics at multiple levels including cellular dynamics, tissue development and niches of organisms. Notably, we show the utilization of eSTG for cases in which the dynamics is regulated by environmental factors, which affect the fate and rate of decisions of the different species. eSTGs are lineage grammars, in the sense that execution of an eSTG program generates the corresponding lineage trees, which can be used to analyze the evolutionary and developmental history of the biological system under investigation. These lineage trees contain a representation of the entire events history of the system, including the dynamics that led to the existing as well as to the extinct individuals.

Conclusions

We conclude that our suggested formalism can be used to easily specify, simulate and analyze complex biological systems, and supports modular description of local biological dynamics that can be later used as “black boxes” in a larger scope, thus enabling a gradual and hierarchical definition and simulation of complex biological systems. The simple, yet robust formalism enables to target a broad class of stochastic dynamic behaviors, especially those that can be modeled using global environmental feedback regulation rather than direct interaction between individuals.

Systematic evaluation of methods for integration of transcriptomic data into constraint-based models of metabolism

Constraint-based models of metabolism are a widely used framework for predicting flux distributions in genome-scale biochemical networks. The number of published methods for integration of transcriptomic data into constraint-based models has been rapidly increasing. So far the predictive capability of these methods has not been critically evaluated and compared. This work presents a survey of recently published methods that use transcript levels to try to improve metabolic flux predictions either by generating flux distributions or by creating context-specific models. A subset of these methods is then systematically evaluated using published data from three different case studies in E. coli and S. cerevisiae. The flux predictions made by different methods using transcriptomic data are compared against experimentally determined extracellular and intracellular fluxes (from 13C-labeling data). The sensitivity of the results to method-specific parameters is also evaluated, as well as their robustness to noise in the data. The results show that none of the methods outperforms the others for all cases. Also, it is observed that for many conditions, the predictions obtained by simple flux balance analysis using growth maximization and parsimony criteria are as good or better than those obtained using methods that incorporate transcriptomic data. We further discuss the differences in the mathematical formulation of the methods, and their relation to the results we have obtained, as well as the connection to the underlying biological principles of metabolic regulation.

Mathematical model of a telomerase transcriptional regulatory network developed by cell-based screening: analysis of inhibitor effects and telomerase expression mechanisms

Cancer cells depend on transcription of telomerase reverse transcriptase (TERT). Many transcription factors affect TERT, though regulation occurs in context of a broader network. Network effects on telomerase regulation have not been investigated, though deeper understanding of TERT transcription requires a systems view. However, control over individual interactions in complex networks is not easily achievable. Mathematical modelling provides an attractive approach for analysis of complex systems and some models may prove useful in systems pharmacology approaches to drug discovery. In this report, we used transfection screening to test interactions among 14 TERT regulatory transcription factors and their respective promoters in ovarian cancer cells. The results were used to generate a network model of TERT transcription and to implement a dynamic Boolean model whose steady states were analysed. Modelled effects of signal transduction inhibitors successfully predicted TERT repression by Src-family inhibitor SU6656 and lack of repression by ERK inhibitor FR180204, results confirmed by RT-QPCR analysis of endogenous TERT expression in treated cells. Modelled effects of GSK3 inhibitor 6-bromoindirubin-3′-oxime (BIO) predicted unstable TERT repression dependent on noise and expression of JUN, corresponding with observations from a previous study. MYC expression is critical in TERT activation in the model, consistent with its well known function in endogenous TERT regulation. Loss of MYC caused complete TERT suppression in our model, substantially rescued only by co-suppression of AR. Interestingly expression was easily rescued under modelled Ets-factor gain of function, as occurs in TERT promoter mutation. RNAi targeting AR, JUN, MXD1, SP3, or TP53, showed that AR suppression does rescue endogenous TERT expression following MYC knockdown in these cells and SP3 or TP53 siRNA also cause partial recovery. The model therefore successfully predicted several aspects of TERT regulation including previously unknown mechanisms. An extrapolation suggests that a dominant stimulatory system may programme TERT for transcriptional stability.

Tumour cells acquire the ability to divide and multiply indefinitely whereas normal cells can undergo only a limited number of divisions. The switch to immortalisation of the tumour cell is dependent on maintaining the integrity of telomere DNA which forms chromosome ends and is achieved through activation of the telomerase enzyme by turning on synthesis of the TERT gene, which is usually silenced in normal cells. Suppressing telomerase is toxic to cancer cells and it is widely believed that understanding TERT regulation could lead to potential cancer therapies. Previous studies have identified many of the factors which individually contribute to activate or repress TERT levels in cancer cells. However, transcription factors do not behave in isolation in cells, but rather as a complex co-operative network displaying inter-regulation. Therefore, full understanding of TERT regulation will require a broader view of the transcriptional network. In this paper we take a computational modelling approach to study TERT regulation at the network level. We tested interactions between 14 TERT-regulatory factors in an ovarian cancer cell line using a screening approach and developed a model to analyse which network interventions were able to silence TERT.

Reverse engineering and identification in systems biology: strategies, perspectives and challenges

The interplay of mathematical modelling with experiments is one of the central elements in systems biology. The aim of reverse engineering is to infer, analyse and understand, through this interplay, the functional and regulatory mechanisms of biological systems. Reverse engineering is not exclusive of systems biology and has been studied in different areas, such as inverse problem theory, machine learning, nonlinear physics, (bio)chemical kinetics, control theory and optimization, among others. However, it seems that many of these areas have been relatively closed to outsiders. In this contribution, we aim to compare and highlight the different perspectives and contributions from these fields, with emphasis on two key questions: (i) why are reverse engineering problems so hard to solve, and (ii) what methods are available for the particular problems arising from systems biology?

Morpheus: a user-friendly modeling environment for multiscale and multicellular systems biology

Summary: Morpheus is a modeling environment for the simulation and integration of cell-based models with ordinary differential equations and reaction-diffusion systems. It allows rapid development of multiscale models in biological terms and mathematical expressions rather than programming code. Its graphical user interface supports the entire workflow from model construction and simulation to visualization, archiving and batch processing.

Availability and implementation: Binary packages are available at http://imc.zih.tu-dresden.de/wiki/morpheus for Linux, Mac OSX and MS Windows.

Contact:walter.deback@tu-dresden.de

Supplementary information:Supplementary data are available at Bioinformatics online.

Multi-agent model of hepatitis C virus infection

OBJECTIVES

The objective of this study is to design a method for modeling hepatitis C virus (HCV) infection using multi-agent simulation and to verify it in practice.

METHODS AND MATERIALS

In this paper, first, the modeling of HCV infection using a multi-agent system is compared with the most commonly used model type, which is based on differential equations. Then, the implementation and results of the model using a multi-agent simulation is presented. To find the values of the parameters used in the model, a method using inverted simulation flow and genetic algorithm is proposed. All of the data regarding HCV infection are taken from the paper describing the model based on the differential equation to which the proposed method is compared.

RESULTS

Important advantages of the proposed method are noted and demonstrated: these include flexibility, clarity, re-usability and the possibility to model more complex dependencies. Then, the simulation framework that uses the proposed approach is successfully implemented in C++ and is verified by comparing it to the approach based on differential equations. The verification proves that an objective function that performs the best is the function that minimizes the maximal differences in the data. Finally, an analysis of one of the already known models is performed, and it is proved that it incorrectly models a decay in the hepatocytes number by 40%.

CONCLUSIONS

The proposed method has many advantages in comparison to the currently used model types and can be used successfully for analyzing HCV infection. With almost no modifications, it can also be used for other types of viral infections.

Genome-scale models of metabolism and gene expression extend and refine growth phenotype prediction

Growth is a fundamental process of life. Growth requirements are well-characterized experimentally for many microbes; however, we lack a unified model for cellular growth. Such a model must be predictive of events at the molecular scale and capable of explaining the high-level behavior of the cell as a whole. Here, we construct an ME-Model for Escherichia coli--a genome-scale model that seamlessly integrates metabolic and gene product expression pathways. The model computes ~80% of the functional proteome (by mass), which is used by the cell to support growth under a given condition. Metabolism and gene expression are interdependent processes that affect and constrain each other. We formalize these constraints and apply the principle of growth optimization to enable the accurate prediction of multi-scale phenotypes, ranging from coarse-grained (growth rate, nutrient uptake, by-product secretion) to fine-grained (metabolic fluxes, gene expression levels). Our results unify many existing principles developed to describe bacterial growth.

Spatial rule-based modeling: a method and its application to the human mitotic kinetochore

A common problem in the analysis of biological systems is the combinatorial explosion that emerges from the complexity of multi-protein assemblies. Conventional formalisms, like differential equations, Boolean networks and Bayesian networks, are unsuitable for dealing with the combinatorial explosion, because they are designed for a restricted state space with fixed dimensionality. To overcome this problem, the rule-based modeling language, BioNetGen, and the spatial extension, SRSim, have been developed. Here, we describe how to apply rule-based modeling to integrate experimental data from different sources into a single spatial simulation model and how to analyze the output of that model. The starting point for this approach can be a combination of molecular interaction data, reaction network data, proximities, binding and diffusion kinetics and molecular geometries at different levels of detail. We describe the technique and then use it to construct a model of the human mitotic inner and outer kinetochore, including the spindle assembly checkpoint signaling pathway. This allows us to demonstrate the utility of the procedure, show how a novel perspective for understanding such complex systems becomes accessible and elaborate on challenges that arise in the formulation, simulation and analysis of spatial rule-based models.

Information content and scalability in signal transduction network reconstruction formats

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

Biologic complexity in sickle cell disease: implications for developing targeted therapeutics

Current therapy for sickle cell disease (SCD) is limited to supportive treatment of complications, red blood cell transfusions, hydroxyurea, and stem cell transplantation. Difficulty in the translation of mechanistically based therapies may be the result of a reductionist approach focused on individual pathways, without having demonstrated their relative contribution to SCD complications. Many pathophysiologic processes in SCD are likely to interact simultaneously to contribute to acute vaso-occlusion or chronic vasculopathy. Applying concepts of systems biology and network medicine, models were developed to show relationships between the primary defect of sickle hemoglobin (Hb S) polymerization and the outcomes of acute pain and chronic vasculopathy. Pathophysiologic processes such as inflammation and oxidative stress are downstream by-products of Hb S polymerization, transduced through secondary pathways of hemolysis and vaso-occlusion. Pain, a common clinical trials endpoint, is also complex and may be influenced by factors outside of sickle cell polymerization and vascular occlusion. Future sickle cell research needs to better address the biologic complexity of both sickle cell disease and pain. The relevance of individual pathways to important sickle cell outcomes needs to be demonstrated in vivo before investing in expensive and labor-intensive clinical trials.

Bridging the genotype-phenotype gap: what does it take?

The genotype-phenotype map (GP map) concept applies to any time point in the ontogeny of a living system. It is the outcome of very complex dynamics that include environmental effects, and bridging the genotype-phenotype gap is synonymous with understanding these dynamics. The context for this understanding is physiology, and the disciplinary goals of physiology do indeed demand the physiological community to seek this understanding. We claim that this task is beyond reach without use of mathematical models that bind together genetic and phenotypic data in a causally cohesive way. We provide illustrations of such causally cohesive genotype-phenotype models where the phenotypes span from gene expression profiles to development of whole organs. Bridging the genotype-phenotype gap also demands that large-scale biological ('omics') data and associated bioinformatics resources be more effectively integrated with computational physiology than is currently the case. A third major element is the need for developing a phenomics technology way beyond current state of the art, and we advocate the establishment of a Human Phenome Programme solidly grounded on biophysically based mathematical descriptions of human physiology.

Defining systems biology: a brief overview of the term and field

Here we provide a broad overview of the definition of the term "systems biology" as well as pinpoint specific events in biological research and beyond that are consistently cited to have contributed and led to the current science of in silico systems biology. Since there have been many reviews and historical accounts describing the term, it would be impossible to include all single references. However, we do attempt to provide a consensus vision of how the field has evolved and consequently the terminology that followed it. We also highlight the development and general acceptance, and use, of standards for model representations as being crucial to the continued success of the in silico systems biology field.

Conceptual Model-based Systems Biology: mapping knowledge and discovering gaps in the mRNA transcription cycle

We propose a Conceptual Model-based Systems Biology framework for qualitative modeling, executing, and eliciting knowledge gaps in molecular biology systems. The framework is an adaptation of Object-Process Methodology (OPM), a graphical and textual executable modeling language. OPM enables concurrent representation of the system's structure-the objects that comprise the system, and behavior-how processes transform objects over time. Applying a top-down approach of recursively zooming into processes, we model a case in point-the mRNA transcription cycle. Starting with this high level cell function, we model increasingly detailed processes along with participating objects. Our modeling approach is capable of modeling molecular processes such as complex formation, localization and trafficking, molecular binding, enzymatic stimulation, and environmental intervention. At the lowest level, similar to the Gene Ontology, all biological processes boil down to three basic molecular functions: catalysis, binding/dissociation, and transporting. During modeling and execution of the mRNA transcription model, we discovered knowledge gaps, which we present and classify into various types. We also show how model execution enhances a coherent model construction. Identification and pinpointing knowledge gaps is an important feature of the framework, as it suggests where research should focus and whether conjectures about uncertain mechanisms fit into the already verified model.

Mosaic: making biological sense of complex networks

Summary: We present a Cytoscape plugin called Mosaic to support interactive network annotation, partitioning, layout and coloring based on gene ontology or other relevant annotations.

Availability: Mosaic is distributed for free under the Apache v2.0 open source license and can be downloaded via the Cytoscape plugin manager. A detailed user manual is available on the Mosaic web site (http://nrnb.org/tools/mosaic).

Contact:apico@gladstone.ucsf.edu