The Silicon Cell initiative: working towards a detailed kinetic description at the cellular level

The Silicon Cell initiative aims to understand cellular systems on the basis of the characteristics of their components. As a tool to achieve this, detailed kinetic models at the network reaction level are being constructed. Such detailed kinetic models are extremely useful for medical and biotechnological applications and form strong tools for fundamental studies. Several recently constructed detailed kinetic models on metabolism (glycolysis), signal transduction (EGF receptor), and the eukaryotic cell cycle (Saccharomyces cerevisiae) have been used to exemplify the Silicon Cell project. These models are stored and made accessible via the JWS Online Cellular Systems Modeling project, a web-based repository of kinetic models. Using a web-browser the models can be interrogated via a user-friendly graphical interface. The goal of the two projects is to combine models on parts of cellular systems and ultimately to construct detailed kinetic models at the cellular level.     

A survey on methods for modeling and analyzing integrated biological networks

Understanding how cellular systems build up integrated responses to their dynamically changing environment is one of the open questions in Systems Biology. Despite their intertwinement, signaling networks, gene regulation and metabolism have been frequently modeled independently in the context of well-defined subsystems. For this purpose, several mathematical formalisms have been developed according to the features of each particular network under study. Nonetheless, a deeper understanding of cellular behavior requires the integration of these various systems into a model capable of capturing how they operate as an ensemble. With the recent advances in the "omics" technologies, more data is becoming available and, thus, recent efforts have been driven toward this integrated modeling approach. We herein review and discuss methodological frameworks currently available for modeling and analyzing integrated biological networks, in particular metabolic, gene regulatory and signaling networks. These include network-based methods and Chemical Organization Theory, Flux-Balance Analysis and its extensions, logical discrete modeling, Petri Nets, traditional kinetic modeling, Hybrid Systems and stochastic models. Comparisons are also established regarding data requirements, scalability with network size and computational burden. The methods are illustrated with successful case studies in large-scale genome models and in particular subsystems of various organisms.     

Integration of Boolean models exemplified on hepatocyte signal transduction

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

From steady-state to synchronized yeast glycolytic oscillations I: model construction

An existing detailed kinetic model for the steady-state behavior of yeast glycolysis was tested for its ability to simulate dynamic behavior. Using a small subset of experimental data, the original model was adapted by adjusting its parameter values in three optimization steps. Only small adaptations to the original model were required for realistic simulation of experimental data for limit-cycle oscillations. The greatest changes were required for parameter values for the phosphofructokinase reaction. The importance of ATP for the oscillatory mechanism and NAD(H) for inter-and intra-cellular communications and synchronization was evident in the optimization steps and simulation experiments. In an accompanying paper [du Preez F et al. (2012) FEBS J279, 2823-2836], we validate the model for a wide variety of experiments on oscillatory yeast cells. The results are important for re-use of detailed kinetic models in modular modeling approaches and for approaches such as that used in the Silicon Cell initiative. DATABASE: The mathematical models described here have been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/database/dupreez/index.html.     

Systems biology of lactic acid bacteria: a critical review

Understanding the properties of a system as emerging from the interaction of well described parts is the most important goal of Systems Biology. Although in the practice of Lactic Acid Bacteria (LAB) physiology we most often think of the parts as the proteins and metabolites, a wider interpretation of what a part is can be useful. For example, different strains or species can be the parts of a community, or we could study only the chemical reactions as the parts of metabolism (and forgetting about the enzymes that catalyze them), as is done in flux balance analysis. As long as we have some understanding of the properties of these parts, we can investigate whether their interaction leads to novel or unanticipated behaviour of the system that they constitute. There has been a tendency in the Systems Biology community to think that the collection and integration of data should continue ad infinitum, or that we will otherwise not be able to understand the systems that we study in their details. However, it may sometimes be useful to take a step back and consider whether the knowledge that we already have may not explain the system behaviour that we find so intriguing. Reasoning about systems can be difficult, and may require the application of mathematical techniques. The reward is sometimes the realization of unexpected conclusions, or in the worst case, that we still do not know enough details of the parts, or of the interactions between them. We will discuss a number of cases, with a focus on LAB-related work, where a typical systems approach has brought new knowledge or perspective, often counterintuitive, and clashing with conclusions from simpler approaches. Also novel types of testable hypotheses may be generated by the systems approach, which we will illustrate. Finally we will give an outlook on the fields of research where the systems approach may point the way for the near future.     

Sustained glycolytic oscillations in individual isolated yeast cells

Yeast glycolytic oscillations have been studied since the 1950s in cell-free extracts and intact cells. For intact cells, sustained oscillations have so far only been observed at the population level, i.e. for synchronized cultures at high biomass concentrations. Using optical tweezers to position yeast cells in a microfluidic chamber, we were able to observe sustained oscillations in individual isolated cells. Using a detailed kinetic model for the cellular reactions, we simulated the heterogeneity in the response of the individual cells, assuming small differences in a single internal parameter. This is the first time that sustained limit-cycle oscillations have been demonstrated in isolated yeast cells. DATABASE: The mathematical model described here has been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/database/gustavsson/index.html free of charge.     

Bayesian ranking of biochemical system models

MOTIVATION: There often are many alternative models of a biochemical system. Distinguishing models and finding the most suitable ones is an important challenge in Systems Biology, as such model ranking, by experimental evidence, will help to judge the support of the working hypotheses forming each model. Bayes factors are employed as a measure of evidential preference for one model over another. Marginal likelihood is a key component of Bayes factors, however computing the marginal likelihood is a difficult problem, as it involves integration of nonlinear functions in multidimensional space. There are a number of methods available to compute the marginal likelihood approximately. A detailed investigation of such methods is required to find ones that perform appropriately for biochemical modelling. RESULTS: We assess four methods for estimation of the marginal likelihoods required for computing Bayes factors. The Prior Arithmetic Mean estimator, the Posterior Harmonic Mean estimator, the Annealed Importance Sampling and the Annealing-Melting Integration methods are investigated and compared on a typical case study in Systems Biology. This allows us to understand the stability of the analysis results and make reliable judgements in uncertain context. We investigate the variance of Bayes factor estimates, and highlight the stability of the Annealed Importance Sampling and the Annealing-Melting Integration methods for the purposes of comparing nonlinear models. AVAILABILITY: Models used in this study are available in SBML format as the supplementary material to this article.     

From systems biology to systems biomedicine

Systems Biology is about combining theory, technology, and targeted experiments in a way that drives not only data accumulation but knowledge as well. The challenge in Systems Biomedicine is to furthermore translate mechanistic insights in biological systems to clinical application, with the central aim of improving patients' quality of life. The challenge is to find theoretically well-chosen models for the contextually correct and intelligible representation of multi-scale biological systems. In this review, we discuss the current state of Systems Biology, highlight the emergence of Systems Biomedicine, and highlight some of the topics and views that we think are important for the efficient application of Systems Theory in Biomedicine.     

Using views of Systems Biology Cloud: application for model building

A large and growing network (“cloud”) of interlinked terms and records of items of Systems Biology knowledge is available from the web. These items include pathways, reactions, substances, literature references, organisms, and anatomy, all described in different data sets. Here, we discuss how the knowledge from the cloud can be molded into representations (views) useful for data visualization and modeling. We discuss methods to create and use various views relevant for visualization, modeling, and model annotations, while hiding irrelevant details without unacceptable loss or distortion. We show that views are compatible with understanding substances and processes as sets of microscopic compounds and events respectively, which allows the representation of specializations and generalizations as subsets and supersets respectively. We explain how these methods can be implemented based on the bridging ontology Systems Biological Pathway Exchange (SBPAX) in the Systems Biology Linker (SyBiL) we have developed.     

E-photosynthesis: web-based platform for modeling of complex photosynthetic processes

E-photosynthesis framework is a web-based platform for modeling and analysis of photosynthetic processes. Compared to its earlier version, the present platform employs advanced software methods and technologies to support an effective implementation of vastly diverse kinetic models of photosynthesis. We report on the first phase implementation of the tool new version and demonstrate the functionalities of model visualization, presentation of model components, rate constants, initial conditions and of model annotation. The demonstration also includes export of a model to the Systems Biology Markup Language format and remote numerical simulation of the model.     

Web-based kinetic modelling using JWS Online

JWS Online is a repository of kinetic models, describing biological systems, which can be interactively run and interrogated over the Internet. It is implemented using a client-server strategy where the clients, in the form of web browser based Java applets, act as a graphical interface to the model servers, which perform the required numerical computations. AVAILABILITY: The JWS Online website is publicly accessible at http://jjj.biochem.sun.ac.za/ with mirrors at http://www.jjj.bio.vu.nl/ and http://jjj.vbi.vt.edu/     

The complexity of comparing reaction systems

MOTIVATION: As more genomic data becomes available there is increased attention on understanding the mechanisms encoded in the genome. New XML dialects like CellML and Systems Biology Markup Language (SBML) are being developed to describe biological networks of all types. In the absence of detailed kinetic information for these networks, stoichiometric data is an especially valuable source of information. Network databases are the next logical step beyond storing purely genomic information. Just as comparison of entries in genomic databases has been a vital algorithmic problem through the course of the sequencing project, comparison of networks in network databases will be a crucial problem as we seek to integrate higher-order network knowledge. RESULTS: We show that comparing the stoichiometric structure of two reactions systems is equivalent to the graph isomorphism problem. This is encouraging because graph isomorphism is, in practice, a tractable problem using heuristics. The analogous problem of searching for a subsystem of a reaction system is NP-complete. We also discuss heuristic issues in implementations for practical comparison of stoichiometric matrices.     

Exploring the gap between dynamic and constraint-based models of metabolism

Systems biology provides new approaches for metabolic engineering through the development of models and methods for simulation and optimization of microbial metabolism. Here we explore the relationship between two modeling frameworks in common use namely, dynamic models with kinetic rate laws and constraint-based flux models. We compare and analyze dynamic and constraint-based formulations of the same model of the central carbon metabolism of Escherichia coli. Our results show that, if unconstrained, the space of steady states described by both formulations is the same. However, the imposition of parameter-range constraints can be mapped into kinetically feasible regions of the solution space for the dynamic formulation that is not readily transferable to the constraint-based formulation. Therefore, with partial kinetic parameter knowledge, dynamic models can be used to generate constraints that reduce the solution space below that identified by constraint-based models, eliminating infeasible solutions and increasing the accuracy of simulation and optimization methods.     

Towards kinetic modeling of genome-scale metabolic networks without sacrificing stoichiometric,thermodynamic and physiological constraints

Mathematical modeling is an essential tool for the comprehensive understanding of cell metabolism and its interactions with the environmental and process conditions. Recent developments in the construction and analysis of stoichiometric models made it possible to define limits on steady-state metabolic behavior using flux balance analysis. However, detailed information on enzyme kinetics and enzyme regulation is needed to formulate kinetic models that can accurately capture the dynamic metabolic responses. The use of mechanistic enzyme kinetics is a difficult task due to uncertainty in the kinetic properties of enzymes. Therefore, the majority of recent works considered only mass action kinetics for reactions in metabolic networks. Herein, we applied the optimization and risk analysis of complex living entities (ORACLE) framework and constructed a large-scale mechanistic kinetic model of optimally grown Escherichia coli. We investigated the complex interplay between stoichiometry, thermodynamics, and kinetics in determining the flexibility and capabilities of metabolism. Our results indicate that enzyme saturation is a necessary consideration in modeling metabolic networks and it extends the feasible ranges of metabolic fluxes and metabolite concentrations. Our results further suggest that enzymes in metabolic networks have evolved to function at different saturation states to ensure greater flexibility and robustness of cellular metabolism.     

Metabolic modeling of Saccharomyces cerevisiae using the optimal control of homeostasis: a cybernetic model definition

A model is presented to describe the observed behavior of microorganisms that aim at metabolic homeostasis while growing and adapting to their environment in an optimal way. The cellular metabolism is seen as a network with a multiple controller system with both feedback and feedforward control, i.e., a model based on a dynamic optimal metabolic control. The dynamic network consists of aggregated pathways, each having a control setpoint for the metabolic states at a given growth rate. This set of strategies of the cell forms a true cybernetic model with a minimal number of assumptions. The cellular strategies and constraints were derived from metabolic flux analysis using an identified, biochemically relevant, stoichiometry matrix derived from experimental data on the cellular composition of continuous cultures of Saccharomyces cerevisiae. Based on these data a cybernetic model was developed to study its dynamic behavior. The growth rate of the cell is determined by the structural compounds and fluxes of compounds related to central metabolism. In contrast to many other cybernetic models, the minimal model does not consist of any assumed internal kinetic parameters or interactions. This necessitates the use of a stepwise integration with an optimization of the fluxes at every time interval. Some examples of the behavior of this model are given with respect to steady states and pulse responses. This model is very suitable for describing semiquantitatively dynamics of global cellular metabolism and may form a useful framework for including structured and more detailed kinetic models.     

BioModel engineering for multiscale Systems Biology

We discuss some motivational challenges arising from the need to model and analyse complex biological systems at multiple scales (spatial and temporal), and present a biomodel engineering framework to address some of these issues within the context of multiscale Systems Biology. Our methodology is based on a structured family of Petri net classes which enables the investigation of a given system using various modelling abstractions: qualitative, stochastic, continuous and hybrid, optionally in a spatial context. We illustrate our approach with case studies demonstrating hierarchical flattening, treatment of space, and hierarchical organisation of space.