Quantitative Model Refinement as a Solution to the Combinatorial Size Explosion of Biomodels

AbstractBuilding a large system through a systematic, step-by-step refinement of an initial abstract specification is a well established technique in software engineering, not yet much explored in systems biology. In the case of systems biology, one starts from an abstract, high-level model of a biological system and aims to add more and more details about its reactants and/or reactions, through a number of consecutive refinement steps. The refinement should be done in a quantitatively correct way, so that (some of) the numerical properties of the model (such as the experimental fit and validation) are preserved. In this study, we focus on the data-refinement mechanism where the aim is to increase the level of details of some of the reactants of a given model. That is, we analyse the case when a model is refined by substituting a given species by several types of subspecies. We show in this paper how the refined model can be systematically obtained from the original one. As a case study for this methodology we choose a recently introduced model for the eukaryotic heat shock response, [I. Petre, A. Mizera, C. L. Hyder, A. Meinander, A. Mikhailov, R.I. Morimoto, L. Sistonen, J. E. Eriksson, R.-J. Back, A simple mass-action model for the eukaryotic heat shock response and its mathematical validation, Natural Computing, 10(1), 595–612, 2011.]. We refine this model by including details about the acetylation of the heat shock factors and its influence on the heat shock response. The refined model has a significantly higher number of kinetic parameters and variables. However, we show that our methodology allows us to preserve the experimental fit/validation of the model with minimal computational effort

A study on systems modeling frameworks and their interoperability

'What is in a model?' is a question that any systems modeler has asked at least once when working with a biological system. To answer this question we must understand how every species and reaction in a model are biologically related to each other, which in the case of cellular systems requires an understanding of local protein and gene interactions at the domain level. Typical modeling approaches like reaction-networks do not explicitly encode this information, which can obfuscate the assumptions made by a model and limit their further analysis, comparison and re-use. Additionally, the multi-state nature of the elements in a model can lead to a combinatorial explosion of the interactions in the model, pushing reaction-networks to their limits. Rule-based modeling is a modeling paradigm that addresses these issues through the use of a graph-based representation of each species's interaction domains and their local interactions. In this paradigm, reaction \emph{rules} describe a class of reactions and are represented as graph rewriting operations that encode biological processes like bond formation and post-translational modification. This allows for a concise, explicit encoding of how species interact, modify and are related to each other while at the same time managing the enormous number of potential molecular interactions in a multi-state system. In this work I present two different approaches that aim to bring the benefits of rule-based modeling's graph representation to other modeling paradigms: \emph{Atomizer} and \emph{MCell-R}. Atomizer is an algorithm for the extraction of structural and process information from reaction-network models, which I use to encode the model in a rule-based format. Once we have an explicit understanding of what is in a model and how entities in a model interact, we can then perform meta-modeling operations like model analysis, alignment, comparison and visualization, which I demonstrate through the application of Atomizer to a large dataset of reaction network models. MCell-R is a framework for the efficient modeling and simulation of multi-state, multi-component spatial systems. The framework consists of an integration of the NFsim rule-based simulation engine together with the MCell spatial modeling system, which highlights the utility of bringing rule-based paradigms into reaction based platforms

Scalable reaction network modeling with automatic validation of consistency in Event-B

Constructing a large biological model is a difficult, error-prone process. Small errors in writing a part of the model cascade to the system level and their sources are difficult to trace back. In this paper we extend a recent approach based on Event-B, a state-based formal method with refinement as its central ingredient, allowing us to validate for model consistency step-by-step in an automated way. We demonstrate this approach on a model of the heat shock response in eukaryotes and its scalability on a model of the ErbB signaling pathway. All consistency properties of the model were proved automatically with computer support.</p

Graph matching, theory and SAT implementation

International audienceIn systems biology, large biochemical reaction networks can either be represented by bipartitegraphs or by systems of ordinary differential equations. Modelers want to determine the existenceof reductions between those reaction networks. Because, it is not possible to decide this existencewith equation systems, a previous thesis [1] focussed on graph structures. A subgraph epimorphism(SEPI) framework was developed and gave results close to biologists’ expectations.Three main difficulties of the SEPI framework have been identified. First, establishing whethertwo models are linked through a SEPI is complex and computationally expensive. Second, thenumber of SEPIs found can be huge, making the analysis of SEPI sets between two given graphsvery difficult for biologists. Finally, some existing SEPIs do not have a biological interpretation.This diploma thesis led to three combined ways to improve the framework. One way consisted toredefine the decision problem into an optimisation problem to restrict the set of solutions. Asecond way was to determine, together with biologists, restrictions on one of the framework’soperations in order to filter irrelevant reductions. Lastly, a preprocessing step has been introduced,consisting of rewriting graphs according to subgraph isomorphism relations. The impact ofthese three combined implementations has been evaluated on models of the BioModels database.Results demonstrated that it contributed to make the SEPI framework more relevant, efficientand functional

Toward Accessible Multilevel Modeling in Systems Biology: A Rule-based Language Concept

Promoted by advanced experimental techniques for obtaining high-quality data and the steadily accumulating knowledge about the complexity of life, modeling biological systems at multiple interrelated levels of organization attracts more and more attention recently. Current approaches for modeling multilevel systems typically lack an accessible formal modeling language or have major limitations with respect to expressiveness. The aim of this thesis is to provide a comprehensive discussion on associated problems and needs and to propose a concrete solution addressing them

Toward Multiscale Models of Cyanobacterial Growth

Oxygenic photosynthesis dominates global primary productivity ever since its evolution more than three billion years ago. While many aspects of phototrophic growth are well understood, it remains a considerable challenge to elucidate the manifold dependencies and interconnections between the diverse cellular processes that together facilitate the synthesis of new cells. Phototrophic growth involves the coordinated action of several layers of cellular functioning, ranging from the photosynthetic light reactions and the electron transport chain, to carbon-concentrating mechanisms and the assimilation of inorganic carbon. It requires the synthesis of new building blocks by cellular metabolism, protection against excessive light, as well as diurnal regulation by a circadian clock and the orchestration of gene expression and cell division. Computational modeling allows us to quantitatively describe these cellular functions and processes relevant for phototrophic growth. As yet, however, computational models are mostly confined to the inner workings of individual cellular processes, rather than describing the manifold interactions between them in the context of a living cell. Using cyanobacteria as model organisms, this contribution seeks to summarize existing computational models that are relevant to describe phototrophic growth and seeks to outline their interactions and dependencies. Our ultimate aim is to understand cellular functioning and growth as the outcome of a coordinated operation of diverse yet interconnected cellular processes.Peer Reviewe

Infobiotics : computer-aided synthetic systems biology

Until very recently Systems Biology has, despite its stated goals, been too reductive in terms of the models being constructed and the methods used have been, on the one hand, unsuited for large scale adoption or integration of knowledge across scales, and on the other hand, too fragmented. The thesis of this dissertation is that better computational languages and seamlessly integrated tools are required by systems and synthetic biologists to enable them to meet the significant challenges involved in understanding life as it is, and by designing, modelling and manufacturing novel organisms, to understand life as it could be. We call this goal, where everything necessary to conduct model-driven investigations of cellular circuitry and emergent effects in populations of cells is available without significant context-switching, “one-pot” in silico synthetic systems biology in analogy to “one-pot” chemistry and “one-pot” biology. Our strategy is to increase the understandability and reusability of models and experiments, thereby avoiding unnecessary duplication of effort, with practical gains in the efficiency of delivering usable prototype models and systems. Key to this endeavour are graphical interfaces that assists novice users by hiding complexity of the underlying tools and limiting choices to only what is appropriate and useful, thus ensuring that the results of in silico experiments are consistent, comparable and reproducible. This dissertation describes the conception, software engineering and use of two novel software platforms for systems and synthetic biology: the Infobiotics Workbench for modelling, in silico experimentation and analysis of multi-cellular biological systems; and DNA Library Designer with the DNALD language for the compact programmatic specification of combinatorial DNA libraries, as the first stage of a DNA synthesis pipeline, enabling methodical exploration biological problem spaces. Infobiotics models are formalised as Lattice Population P systems, a novel framework for the specification of spatially-discrete and multi-compartmental rule-based models, imbued with a stochastic execution semantics. This framework was developed to meet the needs of real systems biology problems: hormone transport and signalling in the root of Arabidopsis thaliana, and quorum sensing in the pathogenic bacterium Pseudomonas aeruginosa. Our tools have also been used to prototype a novel synthetic biological system for pattern formation, that has been successfully implemented in vitro. Taken together these novel software platforms provide a complete toolchain, from design to wet-lab implementation, of synthetic biological circuits, enabling a step change in the scale of biological investigations that is orders of magnitude greater than could previously be performed in one in silico “pot”

Infobiotics : computer-aided synthetic systems biology

Until very recently Systems Biology has, despite its stated goals, been too reductive in terms of the models being constructed and the methods used have been, on the one hand, unsuited for large scale adoption or integration of knowledge across scales, and on the other hand, too fragmented. The thesis of this dissertation is that better computational languages and seamlessly integrated tools are required by systems and synthetic biologists to enable them to meet the significant challenges involved in understanding life as it is, and by designing, modelling and manufacturing novel organisms, to understand life as it could be. We call this goal, where everything necessary to conduct model-driven investigations of cellular circuitry and emergent effects in populations of cells is available without significant context-switching, “one-pot” in silico synthetic systems biology in analogy to “one-pot” chemistry and “one-pot” biology. Our strategy is to increase the understandability and reusability of models and experiments, thereby avoiding unnecessary duplication of effort, with practical gains in the efficiency of delivering usable prototype models and systems. Key to this endeavour are graphical interfaces that assists novice users by hiding complexity of the underlying tools and limiting choices to only what is appropriate and useful, thus ensuring that the results of in silico experiments are consistent, comparable and reproducible. This dissertation describes the conception, software engineering and use of two novel software platforms for systems and synthetic biology: the Infobiotics Workbench for modelling, in silico experimentation and analysis of multi-cellular biological systems; and DNA Library Designer with the DNALD language for the compact programmatic specification of combinatorial DNA libraries, as the first stage of a DNA synthesis pipeline, enabling methodical exploration biological problem spaces. Infobiotics models are formalised as Lattice Population P systems, a novel framework for the specification of spatially-discrete and multi-compartmental rule-based models, imbued with a stochastic execution semantics. This framework was developed to meet the needs of real systems biology problems: hormone transport and signalling in the root of Arabidopsis thaliana, and quorum sensing in the pathogenic bacterium Pseudomonas aeruginosa. Our tools have also been used to prototype a novel synthetic biological system for pattern formation, that has been successfully implemented in vitro. Taken together these novel software platforms provide a complete toolchain, from design to wet-lab implementation, of synthetic biological circuits, enabling a step change in the scale of biological investigations that is orders of magnitude greater than could previously be performed in one in silico “pot”

Novel modeling formalisms and simulation tools in computational biosystems

Tese de doutoramento em BioengenhariaThe goal of Systems Biology is to understand the complex behavior that emerges from the interaction among the cellular components. Industrial biotechnology is one of the areas of application, where new approaches for metabolic engineering are developed, through the creation of new models and tools for simulation and optimization of the microbial metabolism. Although whole-cell modeling is one of the goals of Systems Biology, so far most models address only one kind of biological network independently. This work explores the integration of di erent kinds of biological networks with a focus on the improvement of simulation of cellular metabolism. The bacterium Escherichia coli is the most well characterized model organism and is used as our case-study. An extensive review of modeling formalisms that have been used in Systems Biology is presented in this work. It includes several formalisms, including Boolean networks, Bayesian networks, Petri nets, process algebras, constraint-based models, di erential equations, rule-based models, interacting state machines, cellular automata and agent-based models. We compare the features provided by these formalisms and classify the most suitable ones for the creation of a common framework for modeling, analysis and simulation of integrated biological networks. Currently, there is a separation between dynamic and constraint-based modeling of metabolism. Dynamic models are based on detailed kinetic reconstructions of central metabolic pathways, whereas constraint-based models are based on genome-scale stoichiometric reconstructions. Here, we explore the gap between both formulations and evaluate how dynamic models can be used to reduce the solution space of constraint-based models in order to eliminate kinetically infeasible solutions. The limitations of both kinds of models are leading to new approaches to build kinetic models at the genome-scale. The generation of kinetic models from stoichiometric reconstructions can be performed within the same framework as a transformation from discrete to continuous Petri nets. However, the size of these networks results in models with a large number of parameters. In this scope, we develop and implement structural reduction methods that adjust the level of detail of metabolic networks without loss of information, which can be applied prior to the kinetic inference to build dynamic models with a smaller number of parameters. In order to account for enzymatic regulation, which is not present in constraint-based models, we propose the utilization of Extended Petri nets. This results in a better sca old for the kinetic inference process. We evaluate the impact of accounting for enzymatic regulation in the simulation of the steady-state phenotype of mutant strains by performing knockouts and adjustment of enzyme expression levels. It can be observed that in some cases the impact is signi cant and may reveal new targets for rational strain design. In summary, we have created a solid framework with a common formalism and methods for metabolic modeling. This will facilitate the integration with gene regulatory networks, as we have already addressed many issues also associated with these networks, such as the trade-o between size and detail, and the representation of regulatory interactions.O objectivo da Biologia de Sistemas é compreender os comportamentos que resultam das complexas interacções entre todos os componentes celulares. A biotecnologia industrial é uma das áreas de aplicação, onde novas abordagens para a engenharia metabólica são desenvolvidas através da criação de novos modelos e ferramentas de simulação e optimização do metabolismo microbiano. Apesar de um dos principais objectivos da Biologia de Sistemas ser a criação de um modelo completo de uma célula, até ao momento a maioria dos modelos desenvolvidos incorpora de forma separada cada tipo de rede biológica. Este trabalho explora a integração de diferentes tipos de redes biológicas, focando melhorar a simulação do metabolismo celular. A bactéria Escherichia coli é o organismo modelo que estáa melhor caracterizado e é usado como caso de estudo. Neste trabalho é elaborada uma extensa revisão dos formalismos de modela ção que têm sido utilizados em Biologia de Sistemas. São considerados vários formalismos tais como, redes Booleanas, redes Bayesianas, redes de Petri, álgebras de processos, modelos baseados em restrições, equações diferenciais, modelos baseados em regras, máquinas de interacção de estados, autómatos celulares e modelos baseados em agentes. As funcionalidades inerentes a estes formalismos são analisadas de forma a classificar os mesmos pelo seu potencial em servir de base à criação de uma plataforma para modela ção, análise e simulação de redes biológicas integradas. Actualmente, existe uma separação entre modelação dinâmica e modelação baseada em restrições para o metabolismo celular. Os modelos dinâmicos consistem em reconstruções cinéticas detalhadas de vias centrais do metabolismo, enquanto que os modelos baseados em restrições são construídos à escala genómica com base apenas na estequiometria das reacçõoes. Neste trabalho explora-se a separação entre os dois tipos de formulação e é avaliada a forma como os modelos dinâmicos podem ser utilizados para reduzir o espaço de soluções de modelos baseados em restrições de forma a eliminar soluções inalcançáveis. As limitações impostas por ambos os tipos de modelos estão a conduzir à criação de novas abordagens para a construção de modelos cinéticos à escala genómica. A geração de modelos cinéticos a partir de reconstruções estequiométricas pode ser feita dentro de um mesmo formalismo através da transformação de redes de Petri discretas em redes de Petri contínuas. No entanto, devido ao tamanho destas redes, os modelos resultantes incluem um número extremamente grande de parâmetros. Neste trabalho são implementados métodos para a redução estrutural de redes metabólicas sem perda de informação, que permitem ajustar o nível de detalhe das redes. Estes métodos podem ser aplicados à inferência de cinéticas, de forma a gerar modelos dinâmicos com um menor número de parâmetros. De forma a considerar efeitos de regulação enzimática, os quais não são representados em modelos baseados em restrições, propõe-se a utilização de redes de Petri complementadas com arcos regulatórios. Este formalismo é utilizado como base para o processo de inferência cinética. A influência da regulação enzimática na determinação do estado estacionário de estirpes mutantes é avaliada através da análise da remoção de reacções e da variação dos níveis de expressão enzimática. Observa-se que em alguns casos esta influência é significativa e pode ser utilizada para obter novas estratégias de manipulação de estirpes. Em suma, neste trabalho foi criada uma plataforma sólida para modelação do metabolismo baseada num formalismo comum. Esta plataforma facilitará a integração com redes de regulação genética, pois foram abordados vários problemas que também se colocam nestas redes, tais como o ajuste entre o tamanho da rede e o seu nível de detalhe, bem como a representação de interacções regulatórias entre componentes da rede