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Computational models can help researchers to interpret data, understand biological functions, and make quantitative predictions. The Systems Biology Markup Language (SBML) is a file format for representing computational models in a declarative form that different software systems can exchange. SBML is oriented towards describing biological processes of the sort common in research on a number of topics, including metabolic pathways, cell signaling pathways, and many others. By supporting SBML as an input/output format, different tools can all operate on an identical representation of a model, removing opportunities for translation errors and assuring a common starting point for analyses and simulations. This document provides the specification for Release 2 of Version 2 of SBML Level 3 Core. The specification defines the data structures prescribed by SBML as well as their encoding in XML, the eXtensible Markup Language. Release 2 corrects some errors and clarifies some ambiguities discovered in Release 1. This specification also defines validation rules that determine the validity of an SBML document, and provides many examples of models in SBML form. Other materials and software are available from the SBML project website at http://sbml.org/.

One of use cases for metabolic network optimisation of biotechnologically applied microorganisms is the in silico design of new strains with an improved distribution of metabolic fluxes. Global stochastic optimisation methods (genetic algorithms, evolutionary programing, particle swarm and others) can optimise complicated nonlinear kinetic models and are friendly for unexperienced user: they can return optimisation results with default method settings (population size, number of generations and others) and without adaptation of the model. Drawbacks of these methods (stochastic behaviour, undefined duration of optimisation, possible stagnation and no guaranty of reaching optima) cause optimisation result misinterpretation risks considering the very diverse educational background of the systems biology and synthetic biology research community. Different methods implemented in the COPASI software package are tested in this study to determine their ability to find feasible solutions and assess the convergence speed to the best value of the objective function. Special attention is paid to the potential misinterpretation of results. Optimisation methods are tested with additional constraints that can be introduced to ensure the biological feasibility of the resulting optimised design: (1) total enzyme activity constraint (called also amino acid pool constraint) to limit the sum of enzyme concentrations and (2) homeostatic constraint limiting steady state metabolite concentration corridor around the steady state concentrations of metabolites in the original model. Impact of additional constraints on the performance of optimisation methods and misinterpretation risks is analysed.

Systems biology has experienced dramatic growth in the number, size, and complexity of computational models. To reproduce simulation results and reuse models, researchers must exchange unambiguous model descriptions. We review the latest edition of the Systems Biology Markup Language (SBML), a format designed for this purpose. A community of modelers and software authors developed SBML Level 3 over the past decade. Its modular form consists of a core suited to representing reaction‐based models and packages that extend the core with features suited to other model types including constraint‐based models, reaction‐diffusion models, logical network models, and rule‐based models. The format leverages two decades of SBML and a rich software ecosystem that transformed how systems biologists build and interact with models. More recently, the rise of multiscale models of whole cells and organs, and new data sources such as single‐cell measurements and live imaging, has precipitated new ways of integrating data with models. We provide our perspectives on the challenges presented by these developments and how SBML Level 3 provides the foundation needed to support this evolution., Over the past two decades, scientists from different fields have been developing SBML, a standard format for encoding computational models in biology and medicine. This article summarizes recent progress and gives perspectives on emerging challenges.

Gut-derived bacterial lipopolysaccharides (LPS) stimulate the secretion of tumour necrosis factor (TNF) from liver macrophages (MCs), liver sinusoidal endothelial cells (LSECs) and hepatic stellate cells (HSCs), which control the acute phase response in hepatocytes through activation of the NF-κB pathway. The individual and cooperative impact of nonparenchymal cells on this clinically relevant response has not been analysed in detail due to technical limitations. To gain an integrative view on this complex inter- and intracellular communication, we combined a multiscale mathematical model with quantitative, time-resolved experimental data of different primary murine liver cell types. We established a computational model for TNF-induced NF-κB signalling in hepatocytes, accurately describing dose-responsiveness for physiologically relevant cytokine concentrations. TNF secretion profiles were quantitatively measured for all nonparenchymal cell types upon LPS stimulation. This novel approach allowed the analysis of individual and collective paracrine TNF-mediated NF-κB induction in hepatocytes, revealing strongest effects of MCs and LSECs on hepatocellular NF-κB signalling. Simulations suggest that both cell types act together to maximize the NF-κB pathway response induced by low LPS concentrations (0.1 and 1 ng/mL). Higher LPS concentrations (≥ 5 ng/mL) induced sufficient TNF levels from MCs or LSECs to induce a strong and nonadjustable pathway response. Importantly, these simulations also revealed that the initial cytokine secretion (1-2 h after stimulation) rather than final TNF level (10 h after stimulation) defines the hepatocellular NF-κB response. This raises the question whether the current experimental standard of single high-dose cytokine administration is suitable to mimic in vivo cytokine exposure.The computational models described in this manuscript are available in the JWS database via the following link: https://jjj.bio.vu.nl/database/beuke.

Intracellular calcium oscillations have been widely studied. It is assumed that information is conveyed in the frequency, amplitude and shape of these oscillations. In particular, calcium signalling in mammalian liver cells has repeatedly been reported to display frequency coding so that an increasing amount of stimulus is translated into an increasing frequency of the oscillations. However, recently, we have shown that calcium oscillations in fish liver cells rather exhibit amplitude coding with increasing stimuli being translated into increasing amplitudes. Practical consequences of this difference are unknown so far. Here we investigated advantages and disadvantages of frequency vs. amplitude coding, in particular in environments with substantially changing temperatures (e.g. 10-20 degrees). For this purpose, we use computational modelling and a new approach to generate a calcium model exactly displaying a specific frequency and/or amplitude. We conclude that despite the advantages in flexibility that frequencies might offer for the transmission of information in the cell, amplitude coding is obviously more robust with respect to changes in environmental temperatures. This potentially explains the observed differences between two classes of organisms, one operating at constant temperatures whereas the other is not.

The therapeutic effect of a drug is governed by its pharmacokinetics which determine the downstream pharmacodynamic response within the cellular network. A complete understanding of the drug-effect relationship therefore requires multi-scale models which integrate the properties of the different physiological scales. Computational modelling of these individual scales has been successfully established in the past. However, coupling of the scales remains challenging, although it will provide a unique possibility of mechanistic and holistic analyses of therapeutic outcomes for varied treatment scenarios. We present a methodology to combine whole-body physiologically-based pharmacokinetic (PBPK) models with mechanistic intracellular models of signal transduction in the liver for therapeutic proteins. To this end, we developed a whole-body distribution model of IFN-α in human and a detailed intracellular model of the JAK/STAT signalling cascade in hepatocytes and coupled them at the liver of the whole-body human model. This integrated model infers the time-resolved concentration of IFN-α arriving at the liver after intravenous injection while simultaneously estimates the effect of this dose on the intracellular signalling behaviour in the liver. In our multi-scale physiologically-based pharmacokinetic/pharmacodynamic (PBPK/PD) model, receptor saturation is seen at low doses, thus giving mechanistic insights into the pharmacodynamic (PD) response. This model suggests a fourfold lower intracellular response after administration of a typical IFN-α dose to an individual as compared to the experimentally observed responses in in vitro setups. In conclusion, this work highlights clear differences between the observed in vitro and in vivo drug effects and provides important suggestions for future model-based study design.

The onset of aerobic fermentation (the so-called Crabtree effect) in yeast has long been of interest. However, the underlying mechanisms at the metabolic level are not yet fully understood. We developed a detailed kinetic model of the aerobic central metabolism of Saccharomyces cerevisiae comprising glycolysis, TCA cycle and major transport reactions across the mitochondrial membrane to investigate this phenomenon. It is the first one of this extent in the literature. The model is able to reproduce experimental steady state fluxes and time-course behavior after a glucose pulse. Due to the lack of parameter identifiability in the model, we analyze a model ensemble consisting of a set of differently parameterized models for robust findings. The model predicts that the cooperativity of pyruvate decarboxylase with respect to pyruvate and the capacity difference between alcohol dehydrogenase and the pyruvate dehydrogenase bypass play a major role for the onset of the Crabtree effect.

COPASI is software used for the creation, modification, simulation and computational analysis of kinetic models in various fields. It is open-source, available for all major platforms and provides a user-friendly graphical user interface, but is also controllable via the command line and scripting languages. These are likely reasons for its wide acceptance. We begin this review with a short introduction describing the general approaches and techniques used in computational modeling in the biosciences. Next we introduce the COPASI package, and its capabilities, before looking at typical applications of COPASI in biotechnology. BMBF [031L0104A]; Virtual Liver Project, National Institutes of Health (NIGMS) [GM080219]; BBSRC [BB/J019259/1]; BBSRC; EPSRC [BB/C008219/1]; Klaus Tschira Foundation; Virginia Bioinformatics Institute Over the years, COPASI has received funding from the following funding agencies and programmes: the BMBF funded de.NBI initiative (031L0104A) and Virtual Liver Project, National Institutes of Health (NIGMS Grant: GM080219), the BBSRC (grant BB/J019259/1), BBSRC and EPSRC (grant BB/C008219/1) as well as the Klaus Tschira Foundation and the Virginia Bioinformatics Institute. We would like to thank Norman Paton and Yang Cao for their collaboration. We would also like to thank all the programmers and student helpers that worked on COPASI over the years, particularly, Ralph Gauges, Joseph Dada, Ettore Murabito, Peyman Zarrineh, Natalia Simus and Irina Surovtsova. Marina Kaiser is acknowledged for literature digging. Finally, we would like to acknowledge the members of the COPASI user forum for their active support.

Glycolytic oscillations in yeast have been extensively studied. It is still unclear, if these oscillations are caused by the allosteric enzyme phosphofructokinase or the stoichiometry of glycolysis which contains an autocatalysis with respect to ATP. Bacterial glycolysis shows a different stoichiometry, however, also containing a stoichiometric autocatalysis. For Escherichia coli, the regulation of the enzyme phosphofructokinase is also assumed to be a major reason for oscillations to occur. We investigated glycolytic oscillations in a quantitative kinetic model for Streptococcus pyogenes set-up on the basis of experimental data. We found oscillations within physiologically feasible parameter ranges. We investigated the origin of these oscillations and conclude that, again, both the stoichiometry of the system, as well as its allosterically regulated enzymes can give rise to these oscillations. For the analysis we employed established and new optimization methods for finding oscillatory regimes and present these in the context of this study.

Transforming growth factor β (TGF- β ) ligands activate a signaling cascade with multiple cell context dependent outcomes. Disruption or disturbance leads to variant clinical disorders. To develop strategies for disease intervention, delineation of the pathway in further detail is required. Current theoretical models of this pathway describe production and degradation of signal mediating proteins and signal transduction from the cell surface into the nucleus, whereas feedback loops have not exhaustively been included. In this study we present a mathematical model to determine the relevance of feedback regulators (Arkadia, Smad7, Smurf1, Smurf2, SnoN and Ski) on TGF- β target gene expression and the potential to initiate stable oscillations within a realistic parameter space. We employed massive sampling of the parameters space to pinpoint crucial players for potential oscillations as well as transcriptional product levels. We identified Smad7 and Smurf2 with the highest impact on the dynamics. Based on these findings, we conducted preliminary time course experiments.

Systems biology has received an ever increasing interest during the last decade. A large amount of third-party funding is spent on this topic, which involves quantitative experimentation integrated with computational modeling. Industrial companies are also starting to use this approach more and more often, especially in pharmaceutical research and biotechnology. This leads to the question of whether such interest is wisely invested and whether there are success stories to be told for basic science and/or technology/biomedicine. In this review, we focus on the application of systems biology approaches that have been employed to shed light on both biochemical functions and previously unknown mechanisms. We point out which computational and experimental methods are employed most frequently and which trends in systems biology research can be observed. Finally, we discuss some problems that we have encountered in publications in the field.

Type I interferons (IFN) are important components of the innate antiviral response. A key signalling pathway activated by IFNα is the Janus kinase/signal transducer and activator of transcription (JAK/STAT) pathway. Major components of the pathway have been identified. However, critical kinetic properties that facilitate accelerated initiation of intracellular antiviral signalling and thereby promote virus elimination remain to be determined. By combining mathematical modelling with experimental analysis, we show that control of dynamic behaviour is not distributed among several pathway components but can be primarily attributed to interferon regulatory factor 9 (IRF9), constituting a positive feedback loop. Model simulations revealed that increasing the initial IRF9 concentration reduced the time to peak, increased the amplitude and enhanced termination of pathway activation. These model predictions were experimentally verified by IRF9 over-expression studies. Furthermore, acceleration of signal processing was linked to more rapid and enhanced expression of IFNα target genes. Thus, the amount of cellular IRF9 is a crucial determinant for amplification of early dynamics of IFNα-mediated signal transduction.

Parameterisation of kinetic models plays a central role in computational systems biology. Besides the lack of experimental data of high enough quality, some of the biggest challenges here are identification issues. Model parameters can be structurally non-identifiable because of functional relationships. Noise in measured data is usually considered to be a nuisance for parameter estimation. However, it turns out that intrinsic fluctuations in particle numbers can make parameters identifiable that were previously non-identifiable. The authors present a method to identify model parameters that are structurally non-identifiable in a deterministic framework. The method takes time course recordings of biochemical systems in steady state or transient state as input. Often a functional relationship between parameters presents itself by a one-dimensional manifold in parameter space containing parameter sets of optimal goodness. Although the system's behaviour cannot be distinguished on this manifold in a deterministic framework it might be distinguishable in a stochastic modelling framework. Their method exploits this by using an objective function that includes a measure for fluctuations in particle numbers. They show on three example models, immigration-death, gene expression and Epo-EpoReceptor interaction, that this resolves the non-identifiability even in the case of measurement noise with known amplitude. The method is applied to partially observed recordings of biochemical systems with measurement noise. It is simple to implement and it is usually very fast to compute. This optimisation can be realised in a classical or Bayesian fashion.

Estimating model parameters from experimental data is a crucial technique for working with computational models in systems biology. Since stochastic models are increasingly important, parameter estimation methods for stochastic modelling are also of increasing interest. This study presents an extension to the 'multiple shooting for stochastic systems (MSS)' method for parameter estimation. The transition probabilities of the likelihood function are approximated with normal distributions. Means and variances are calculated with a linear noise approximation on the interval between succeeding measurements. The fact that the system is only approximated on intervals which are short in comparison with the total observation horizon allows to deal with effects of the intrinsic stochasticity. The study presents scenarios in which the extension is essential for successfully estimating the parameters and scenarios in which the extension is of modest benefit. Furthermore, it compares the estimation results with reversible jump techniques showing that the approximation does not lead to a loss of accuracy. Since the method is not based on stochastic simulations or approximative sampling of distributions, its computational speed is comparable with conventional least-squares parameter estimation methods.

Summary Computational models can help researchers to interpret data, understand biological function, and make quantitative predictions. The Systems Biology Markup Language (SBML) is a file format for representing computational models in a declarative form that can be exchanged between different software systems. SBML is oriented towards describing biological processes of the sort common in research on a number of topics, including metabolic pathways, cell signaling pathways, and many others. By supporting SBML as an input/output format, different tools can all operate on an identical representation of a model, removing opportunities for translation errors and assuring a common starting point for analyses and simulations. This document provides the specification for Version 1 of SBML Level 3 Core. The specification defines the data structures prescribed by SBML as well as their encoding in XML, the eXtensible Markup Language. This specification also defines validation rules that determine the validity of an SBML document, and provides many examples of models in SBML form. Other materials and software are available from the SBML project web site, http://sbml.org/.

An enhanced version of the well known Wolf algorithm for the estimation of the Lyapunov characteristic exponents (LCEs) is proposed. It permits interpretation of the local behavior of non-linear flows. The new variant allows for reliable calculation of the non-uniformity-factors (NUFs). The NUFs can be interpreted as standard deviations of the LCEs. Since the latter can also be estimated by the Wolf algorithm, however, without local information on the flow, the new version ensures local interpretability and therefore allows the calculation of the NUFs. The local contributions to the LCEs which we call “local LCEs” can at least be calculated up to three dimensions. Application of the modified method to a hyperchaotic flow in four dimensions shows that an extension to many dimensions is possible and promises new insight into so far not fully understood high-dimensional non-linear systems.

We introduce an adaptive system for dynamics recognition. Thereby, an externally presented dynamics (stimulus) is mapped onto a mirror dynamics which is capable to simulate (simulus). A sudden change of the external dynamics leads to an surprisingly quick re-adaptation of the simulus, even if the presented dynamics is chaotic. The system consists of an internal pool of dynamical modules. The modules are forced to the latter dynamics in the sense of Pyragas' control mechanism by the stimulus. The control term, i.e. the strength of forcing, is used as a measure for which modules fit best to the external dynamics. In a sense, this defines a “dynamics-gradient” within the pool. The mirror dynamics now can be constructed by a linear combination of the best fitting modules with weights given by the control term amplitudes. If one adds the so-constructed mirror dynamics to the pool, one has a representation of the corresponding external dynamics within the pool. Later if the same external dynamics is presented again an even quicker adaptation is possible since a well-fitting module is already present. In order not to blow up the dimensionality of the pool, one can eliminate modules that have not been used for a long time. In principle, the modules can undergo an internal control. In addition, one principally can introduce evolution within the pool. Therefore, the system is able to show what sometimes is called a “second cybernetics”, i.e. a hyper-dynamics of the dynamics modules.