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.

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.

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.

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.

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.

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/.

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.

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.

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.

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/.

A20/TNFAIP3 Discriminates Tumor Necrosis Factor (TNF)-Induced NF-κB from JNK Pathway Activation in Hepatocytes.

In the liver tumor necrosis factor (TNF)-induced signaling critically regulates the immune response of non-parenchymal cells as well as proliferation and apoptosis of hepatocytes via activation of the NF-κB and JNK pathways. Especially, the induction of negative feedback regulators, such as IκBα and A20 is responsible for the dynamic and time-restricted response of these important pathways. However, the precise mechanisms responsible for different TNF-induced phenotypes under physiological stimulation conditions are not completely understood so far. In addition, it is not known if varying TNF concentrations may differentially affect the desensitization properties of both pathways. By using computational modeling, we first showed that TNF-induced activation and downstream signaling is qualitatively comparable between primary mouse hepatocytes and immortalized hepatocellular carcinoma (HCC) cells. In order to define physiologically relevant TNF levels, which allow for an adjustable and dynamic NF-κB/JNK pathway response in parenchymal liver cells, a range of cytokine concentrations was defined that led to gradual pathway responses in HCC cells (1-5 ng/ml). Repeated stimulations with low (1 ng/ml), medium (2.5 ng/ml) and high (5 ng/ml) TNF amounts demonstrated that JNK signaling was still active at cytokine concentrations, which led to dampened NF-κB signaling illustrating differential pathway responsiveness depending on TNF input dynamics. SiRNA-mediated inhibition of the negative feedback regulator A20 (syn. TNFAIP3) or its overexpression did not significantly affect the NF-κB response. In contrast, A20 silencing increased the JNK response, while its overexpression dampened JNK phosphorylation. In addition, the A20 knockdown sensitized hepatocellular cells to TNF-induced cleavage and activity of the effector caspase-3. In conclusion, a mathematical model-based approach shows that the TNF-induced pathway responses are qualitatively comparable in primary and immortalized mouse hepatocytes. The cytokine amount defines the pathway responsiveness under repeated treatment conditions with NF-κB signaling being dampened 'earlier' than JNK. A20 appears to be the molecular switch discriminating between NF-κB and JNK signaling when stimulating with varying physiological cytokine concentrations.

COPASI and its applications in biotechnology.

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.

Quantitative and integrative analysis of paracrine hepatocyte activation by nonparenchymal cells upon lipopolysaccharide induction.

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. DATABASE: The computational models described in this manuscript are available in the JWS database via the following link: https://jjj.bio.vu.nl/database/beuke.

Comparison of approaches for parameter estimation on stochastic models: Generic least squares versus specialized approaches.

Parameter estimation for models with intrinsic stochasticity poses specific challenges that do not exist for deterministic models. Therefore, specialized numerical methods for parameter estimation in stochastic models have been developed. Here, we study whether dedicated algorithms for stochastic models are indeed superior to the naive approach of applying the readily available least squares algorithm designed for deterministic models. We compare the performance of the recently developed multiple shooting for stochastic systems (MSS) method designed for parameter estimation in stochastic models, a stochastic differential equations based Bayesian approach and a chemical master equation based techniques with the least squares approach for parameter estimation in models of ordinary differential equations (ODE). As test data, 1000 realizations of the stochastic models are simulated. For each realization an estimation is performed with each method, resulting in 1000 estimates for each approach. These are compared with respect to their deviation to the true parameter and, for the genetic toggle switch, also their ability to reproduce the symmetry of the switching behavior. Results are shown for different set of parameter values of a genetic toggle switch leading to symmetric and asymmetric switching behavior as well as an immigration-death and a susceptible-infected-recovered model. This comparison shows that it is important to choose a parameter estimation technique that can treat intrinsic stochasticity and that the specific choice of this algorithm shows only minor performance differences.

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.

Exploiting intrinsic fluctuations to identify model parameters.

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.

The Systems Biology Markup Language (SBML): Language Specification for Level 3 Version 1 Core.

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/.