Stochastic dynamics of Type-I interferon responses.

Interferon (IFN) activates the transcription of several hundred of IFN stimulated genes (ISGs) that constitute a highly effective antiviral defense program. Cell-to-cell variability in the induction of ISGs is well documented, but its source and effects are not completely understood. The molecular mechanisms behind this heterogeneity have been related to randomness in molecular events taking place during the JAK-STAT signaling pathway. Here, we study the sources of variability in the induction of the IFN-alpha response by using MxA and IFIT1 activation as read-out. To this end, we integrate time-resolved flow cytometry data and stochastic modeling of the JAK-STAT signaling pathway. The complexity of the IFN response was matched by fitting probability distributions to time-course flow cytometry snapshots. Both, experimental data and simulations confirmed that the MxA and IFIT1 induction circuits generate graded responses rather than all-or-none responses. Subsequently, we quantify the size of the intrinsic variability at different steps in the pathway. We found that stochastic effects are transiently strong during the ligand-receptor activation steps and the formation of the ISGF3 complex, but negligible for the final induction of the studied ISGs. We conclude that the JAK-STAT signaling pathway is a robust biological circuit that efficiently transmits information under stochastic environments.

PEtab-Interoperable specification of parameter estimation problems in systems biology.

Reproducibility and reusability of the results of data-based modeling studies are essential. Yet, there has been-so far-no broadly supported format for the specification of parameter estimation problems in systems biology. Here, we introduce PEtab, a format which facilitates the specification of parameter estimation problems using Systems Biology Markup Language (SBML) models and a set of tab-separated value files describing the observation model and experimental data as well as parameters to be estimated. We already implemented PEtab support into eight well-established model simulation and parameter estimation toolboxes with hundreds of users in total. We provide a Python library for validation and modification of a PEtab problem and currently 20 example parameter estimation problems based on recent studies.

SBML Level 3: an extensible format for the exchange and reuse of biological models.

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.

Piecewise parameter estimation for stochastic models in COPASI.

MOTIVATION: Computational modeling is widely used for deepening the understanding of biological processes. Parameterizing models to experimental data needs computationally efficient techniques for parameter estimation. Challenges for parameter estimation include in general the high dimensionality of the parameter space with local minima and in specific for stochastic modeling the intrinsic stochasticity. RESULTS: We implemented the recently suggested multiple shooting for stochastic systems (MSS) objective function for parameter estimation in stochastic models into COPASI. This MSS objective function can be used for parameter estimation in stochastic models but also shows beneficial properties when used for ordinary differential equation models. The method can be applied with all of COPASI's optimization algorithms, and can be used for SBML models as well. AVAILABILITY AND IMPLEMENTATION: The methodology is available in COPASI as of version 4.15.95 and can be downloaded from http://www.copasi.org CONTACT: frank.bergmann@bioquant.uni-heidelberg.de or fbergman@caltech.edu SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The pH-dependent lactose metabolism of Lactobacillus delbrueckii subsp. bulgaricus: An integrative view through a mechanistic computational model.

The fermentation process of milk to yoghurt using Lactobacillus delbrueckii subsp. bulgaricus in co-culture with Streptococcus thermophilus is hallmarked by the breakdown of lactose to organic acids such as lactate. This leads to a substantial decrease in pH - both in the medium, as well as cytosolic. The latter impairs metabolic activities due to the pH-dependence of enzymes, which compromises microbial growth. To quantitatively elucidate the impact of the acidification on metabolism of L. bulgaricus in an integrated way, we have developed a proton-dependent computational model of lactose metabolism and casein degradation based on experimental data. The model accounts for the influence of pH on enzyme activities as well as cellular growth and proliferation of the bacterial population. We used a machine learning approach to quantify the cell volume throughout fermentation. Simulation results show a decrease in metabolic flux with acidification of the cytosol. Additionally, the validated model predicts a similar metabolic behaviour within a wide range of non-limiting substrate concentrations. This computational model provides a deeper understanding of the intricate relationships between metabolic activity and acidification and paves the way for further optimization of yoghurt production under industrial settings.

Inspecting the Solution Space of Genome-Scale Metabolic Models.

Genome-scale metabolic models are frequently used in computational biology. They offer an integrative view on the metabolic network of an organism without the need to know kinetic information in detail. However, the huge solution space which comes with the analysis of genome-scale models by using, e.g., Flux Balance Analysis (FBA) poses a problem, since it is hard to thoroughly investigate and often only an arbitrarily selected individual flux distribution is discussed as an outcome of FBA. Here, we introduce a new approach to inspect the solution space and we compare it with other approaches, namely Flux Variability Analysis (FVA) and CoPE-FBA, using several different genome-scale models of lactic acid bacteria. We examine the extent to which different types of experimental data limit the solution space and how the robustness of the system increases as a result. We find that our new approach to inspect the solution space is a good complementary method that offers additional insights into the variance of biological phenotypes and can help to prevent wrong conclusions in the analysis of FBA results.

Spatial modeling reveals nuclear phosphorylation and subcellular shuttling of YAP upon drug-induced liver injury.

The Hippo signaling pathway controls cell proliferation and tissue regeneration via its transcriptional effectors yes-associated protein (YAP) and transcriptional coactivator with PDZ-binding motif (TAZ). The canonical pathway topology is characterized by sequential phosphorylation of kinases in the cytoplasm that defines the subcellular localization of YAP and TAZ. However, the molecular mechanisms controlling the nuclear/cytoplasmic shuttling dynamics of both factors under physiological and tissue-damaging conditions are poorly understood. By implementing experimental in vitro data, partial differential equation modeling, as well as automated image analysis, we demonstrate that nuclear phosphorylation contributes to differences between YAP and TAZ localization in the nucleus and cytoplasm. Treatment of hepatocyte-derived cells with hepatotoxic acetaminophen (APAP) induces a biphasic protein phosphorylation eventually leading to nuclear protein enrichment of YAP but not TAZ. APAP-dependent regulation of nuclear/cytoplasmic YAP shuttling is not an unspecific cellular response but relies on the sequential induction of reactive oxygen species (ROS), RAC-alpha serine/threonine-protein kinase (AKT, synonym: protein kinase B), as well as elevated nuclear interaction between YAP and AKT. Mouse experiments confirm this sequence of events illustrated by the expression of ROS-, AKT-, and YAP-specific gene signatures upon APAP administration. In summary, our data illustrate the importance of nuclear processes in the regulation of Hippo pathway activity. YAP and TAZ exhibit different shuttling dynamics, which explains distinct cellular responses of both factors under physiological and tissue-damaging conditions.

Accessible methods for the dynamic time-scale decomposition of biochemical systems.

MOTIVATION: The growing complexity of biochemical models asks for means to rationally dissect the networks into meaningful and rather independent subnetworks. Such foregoing should ensure an understanding of the system without any heuristics employed. Important for the success of such an approach is its accessibility and the clarity of the presentation of the results. RESULTS: In order to achieve this goal, we developed a method which is a modification of the classical approach of time-scale separation. This modified method as well as the more classical approach have been implemented for time-dependent application within the widely used software COPASI. The implementation includes different possibilities for the representation of the results including 3D-visualization. AVAILABILITY: The methods are included in COPASI which is free for academic use and available at www.copasi.org. CONTACT: irina.surovtsova@bioquant.uni-heidelberg.de SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

SYCAMORE--a systems biology computational analysis and modeling research environment.

UNLABELLED: SYCAMORE is a browser-based application that facilitates construction, simulation and analysis of kinetic models in systems biology. Thus, it allows e.g. database supported modelling, basic model checking and the estimation of unknown kinetic parameters based on protein structures. In addition, it offers some guidance in order to allow non-expert users to perform basic computational modelling tasks. AVAILABILITY: SYCAMORE is freely available for academic use at http://sycamore.eml.org. Commercial users may acquire a license. CONTACT: ursula.kummer@bioquant.uni-heidelberg.de.

Computational modeling of biochemical networks using COPASI.

Computational modeling and simulation of biochemical networks is at the core of systems biology and this includes many types of analyses that can aid understanding of how these systems work. COPASI is a generic software package for modeling and simulation of biochemical networks which provides many of these analyses in convenient ways that do not require the user to program or to have deep knowledge of the numerical algorithms. Here we provide a description of how these modeling techniques can be applied to biochemical models using COPASI. The focus is both on practical aspects of software usage as well as on the utility of these analyses in aiding biological understanding. Practical examples are described for steady-state and time-course simulations, stoichiometric analyses, parameter scanning, sensitivity analysis (including metabolic control analysis), global optimization, parameter estimation, and stochastic simulation. The examples used are all published models that are available in the BioModels database in SBML format.

Misinterpretation risks of global stochastic optimisation of kinetic models revealed by multiple optimisation runs.

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.

Quantitative systems pharmacology of interferon alpha administration: A multi-scale approach.

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.

Robustness of frequency vs. amplitude coding of calcium oscillations during changing temperatures.

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 Systems Biology Markup Language (SBML): Language Specification for Level 3 Version 2 Core Release 2.

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/.

SBML Level 3 package: Render, Version 1, Release 1.

Many software tools provide facilities for depicting reaction network diagrams in a visual form. Two aspects of such a visual diagram can be distinguished: the layout (i.e.: the positioning and connections) of the elements in the diagram, and the graphical form of the elements (for example, the glyphs used for symbols, the properties of the lines connecting them, and so on). This document describes the SBML Level 3 Render package that complements the SBML Level 3 Layout package and provides a means of capturing the precise rendering of the elements in a diagram. The SBML Level 3 Render package provides a flexible approach to rendering that is independent of both the underlying SBML model and the Layout information. There can be one block of render information that applies to all layouts or an additional block for each layout. Many of the elements used in the current render specification are based on corresponding elements from the SVG specification. This allows us to easily convert a combination of layout information and render information into a SVG drawing.

Simulation Experiment Description Markup Language (SED-ML) Level 1 Version 3 (L1V3).

The creation of computational simulation experiments to inform modern biological research poses challenges to reproduce, annotate, archive, and share such experiments. Efforts such as SBML or CellML standardize the formal representation of computational models in various areas of biology. The Simulation Experiment Description Markup Language (SED-ML) describes what procedures the models are subjected to, and the details of those procedures. These standards, together with further COMBINE standards, describe models sufficiently well for the reproduction of simulation studies among users and software tools. The Simulation Experiment Description Markup Language (SED-ML) is an XML-based format that encodes, for a given simulation experiment, (i) which models to use; (ii) which modifications to apply to models before simulation; (iii) which simulation procedures to run on each model; (iv) how to post-process the data; and (v) how these results should be plotted and reported. SED-ML Level 1 Version 1 (L1V1) implemented support for the encoding of basic time course simulations. SED-ML L1V2 added support for more complex types of simulations, specifically repeated tasks and chained simulation procedures. SED-ML L1V3 extends L1V2 by means to describe which datasets and subsets thereof to use within a simulation experiment.

The Systems Biology Markup Language (SBML): Language Specification for Level 3 Version 2 Core.

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 Version 2 of SBML Level 3 Core. The specification defines the data structures prescribed by SBML, their encoding in XML (the eXtensible Markup Language), validation rules that determine the validity of an SBML document, and examples of models in SBML form. The design of Version 2 differs from Version 1 principally in allowing new MathML constructs, making more child elements optional, and adding identifiers to all SBML elements instead of only selected elements. Other materials and software are available from the SBML project website at http://sbml.org/.

A model diagram layout extension for SBML.

MOTIVATION: Since the knowledge about processes in living cells is increasing, modelling and simulation techniques are used to get new insights into these complex processes. During the last few years, the SBML file format has gained in popularity and support as a means of exchanging model data between the different modelling and simulation tools. In addition to specifying the model as a set of equations, many modern modelling tools allow the user to create and to interact with the model in the form of a reaction graph. Unfortunately, the SBML file format does not provide for the storage of this graph data along with the mathematical description of the model. RESULTS: Therefore, we developed an extension to the SBML file format that makes it possible to store such layout information which describes position and size of objects in the graphical representation. AVAILABILITY: The complete specification can be found on (http://projects.villa-bosch.de/bcb/sbml/ (SBML Layout Extension documentation, 2005). Additionally, a complete implementation exists as part of libSBML (2006, http://www.sbml.org/software/libsbml/).

COPASI--a COmplex PAthway SImulator.

MOTIVATION: Simulation and modeling is becoming a standard approach to understand complex biochemical processes. Therefore, there is a big need for software tools that allow access to diverse simulation and modeling methods as well as support for the usage of these methods. RESULTS: Here, we present COPASI, a platform-independent and user-friendly biochemical simulator that offers several unique features. We discuss numerical issues with these features; in particular, the criteria to switch between stochastic and deterministic simulation methods, hybrid deterministic-stochastic methods, and the importance of random number generator numerical resolution in stochastic simulation. AVAILABILITY: The complete software is available in binary (executable) for MS Windows, OS X, Linux (Intel) and Sun Solaris (SPARC), as well as the full source code under an open source license from http://www.copasi.org.