Dynamic Mathematical Modeling of IL13-Induced Signaling in Hodgkin and Primary Mediastinal B-Cell Lymphoma Allows Prediction of Therapeutic Targets

Efficient parameter estimation for ODE models of cellular processes using semi-quantitative data

MOTIVATION

Quantitative dynamical models facilitate the understanding of biological processes and the prediction of their dynamics. The parameters of these models are commonly estimated from experimental data. Yet, experimental data generated from different techniques do not provide direct information about the state of the system but a nonlinear (monotonic) transformation of it. For such semi-quantitative data, when this transformation is unknown, it is not apparent how the model simulations and the experimental data can be compared.

RESULTS

We propose a versatile spline-based approach for the integration of a broad spectrum of semi-quantitative data into parameter estimation. We derive analytical formulas for the gradients of the hierarchical objective function and show that this substantially increases the estimation efficiency. Subsequently, we demonstrate that the method allows for the reliable discovery of unknown measurement transformations. Furthermore, we show that this approach can significantly improve the parameter inference based on semi-quantitative data in comparison to available methods.

AVAILABILITY AND IMPLEMENTATION

Modelers can easily apply our method by using our implementation in the open-source Python Parameter EStimation TOolbox (pyPESTO) available at https://github.com/ICB-DCM/pyPESTO.

Controllability and accessibility analysis of nonlinear biosystems

BACKGROUND

We address the problem of determining the controllability and accessibility of nonlinear biosystems. We consider models described by affine-in-inputs ordinary differential equations, which are adequate for a wide array of biological processes. Roughly speaking, the controllability of a dynamical system determines the possibility of steering it from an initial state to any point in its neighbourhood; accessibility is a weaker form of controllability.

METHODS

While the methodology for analysing the controllability of linear systems is well established, its generalization to the nonlinear case has proven elusive. Thus, a number of related but different properties - including different versions of accessibility, reachability or weak local controllability - have been defined to approach its study, and several partial results exist in lieu of a general test. Here, leveraging the applicable results from differential geometric control theory, we source sufficient conditions to assess nonlinear controllability, as well as a necessary and sufficient condition for accessibility.

RESULTS

We develop an algorithmic procedure to evaluate these conditions efficiently, and we provide its open source implementation. Using this software tool, we analyse the accessibility and controllability of a number of models of biomedical interest. While some of them are fully controllable, we find others that are not, as is the case of some models of EGF and NFκB signalling networks.

CONCLUSIONS

The contributions in this paper facilitate the accessibility and controllability analysis of nonlinear models, not only in biomedicine but also in other areas in which they have been rarely performed to date.

Likelihood-ratio test statistic for the finite-sample case in nonlinear ordinary differential equation models

Likelihood ratios are frequently utilized as basis for statistical tests, for model selection criteria and for assessing parameter and prediction uncertainties, e.g. using the profile likelihood. However, translating these likelihood ratios into p-values or confidence intervals requires the exact form of the test statistic's distribution. The lack of knowledge about this distribution for nonlinear ordinary differential equation (ODE) models requires an approximation which assumes the so-called asymptotic setting, i.e. a sufficiently large amount of data. Since the amount of data from quantitative molecular biology is typically limited in applications, this finite-sample case regularly occurs for mechanistic models of dynamical systems, e.g. biochemical reaction networks or infectious disease models. Thus, it is unclear whether the standard approach of using statistical thresholds derived for the asymptotic large-sample setting in realistic applications results in valid conclusions. In this study, empirical likelihood ratios for parameters from 19 published nonlinear ODE benchmark models are investigated using a resampling approach for the original data designs. Their distributions are compared to the asymptotic approximation and statistical thresholds are checked for conservativeness. It turns out, that corrections of the likelihood ratios in such finite-sample applications are required in order to avoid anti-conservative results.

JAK/STAT blockade reverses the malignant phenotype of Hodgkin and Reed-Sternberg cells

Constitutive activation of the JAK/STAT pathway is a common phenomenon in classic Hodgkin lymphoma (cHL). The clinical potential of anti-JAK/STAT therapy is being explored in early-stage clinical trials. Notwithstanding, very little information is available about the complex biological consequences of this blockade. Here, we investigated the effects of JAK/STAT pharmacological inhibition on cHL cell models using ruxolitinib, a JAK 1/2 inhibitor that induces apoptosis by concentration- and time-dependent mechanisms. An unbiased whole-transcriptome approach identified expression of the anti-GCSF receptor (CSF3R) as a potential surrogate biomarker of JAK/STAT overactivation. In addition, longitudinal gene expression analyses provided further mechanistic information about pertinent biological pathways involved, including 37 gene pathways distributed in 3 main clusters: cluster 1 was characterized by upregulation of the G2/M checkpoint and major histocompatibility complex-related clusters; 2 additional clusters (2 and 3) showed a progressive downregulation of the tumor-promoting inflammation signatures: JAK/STAT and interleukin 1 (IL-1)/IL-4/IL-13/IL-17. Together, our results confirm the therapeutic potential of JAK/STAT inhibitors in cHL, identify CSF3R as a new biomarker, and provide supporting genetic data and mechanistic understanding.

Structural identifiability of biomolecular controller motifs with and without flow measurements as model output

Controller motifs are simple biomolecular reaction networks with negative feedback. They can explain how regulatory function is achieved and are often used as building blocks in mathematical models of biological systems. In this paper we perform an extensive investigation into structural identifiability of controller motifs, specifically the so-called basic and antithetic controller motifs. Structural identifiability analysis is a useful tool in the creation and evaluation of mathematical models: it can be used to ensure that model parameters can be determined uniquely and to examine which measurements are necessary for this purpose. This is especially useful for biological models where parameter estimation can be difficult due to limited availability of measureable outputs. Our aim with this work is to investigate how structural identifiability is affected by controller motif complexity and choice of measurements. To increase the number of potential outputs we propose two methods for including flow measurements and show how this affects structural identifiability in combination with, or in the absence of, concentration measurements. In our investigation, we analyze 128 different controller motif structures using a combination of flow and/or concentration measurements, giving a total of 3648 instances. Among all instances, 34% of the measurement combinations provided structural identifiability. Our main findings for the controller motifs include: i) a single measurement is insufficient for structural identifiability, ii) measurements related to different chemical species are necessary for structural identifiability. Applying these findings result in a reduced subset of 1568 instances, where 80% are structurally identifiable, and more complex/interconnected motifs appear easier to structurally identify. The model structures we have investigated are commonly used in models of biological systems, and our results demonstrate how different model structures and measurement combinations affect structural identifiability of controller motifs.

Dynamic modelling predicts lactate and IL-1β as interventional targets in metabolic-inflammation-clock regulatory loop in glioma

In an attempt to understand the role of dysregulated circadian rhythm in glioma, our recent findings highlighted the existence of a feed-forward loop between tumour metabolite lactate, pro-inflammatory cytokine IL-1β and circadian CLOCK. To further elucidate the implication of this complex interplay, we developed a mathematical model that quantitatively describes this lactate dehydrogenase A (LDHA)-IL-1β-CLOCK/BMAL1 circuit and predicts potential therapeutic targets. The model was calibrated on quantitative western blotting data in two glioma cell lines in response to either lactate inhibition or IL-1β stimulation. The calibrated model described the experimental data well and most of the parameters were identifiable, thus the model was predictive. Sensitivity analysis identified IL-1β and LDHA as potential intervention points. Mathematical models described here can be useful to understand the complex interrelationship between metabolism, inflammation and circadian rhythm, and in designing effective therapeutic strategies. Our findings underscore the importance of including the circadian clock when developing pharmacological approaches that target aberrant tumour metabolism and inflammation. Insight box  The complex interplay of metabolism-inflammation-circadian rhythm in tumours is not well understood. Our recent findings provided evidence of a feed-forward loop between tumour metabolite lactate, pro-inflammatory cytokine IL-1β and circadian CLOCK/BMAL1 in glioma. To elucidate the implication of this complex interplay, we developed a mathematical model that quantitatively describes this LDHA-IL-1β-CLOCK/BMAL1 circuit and integrates experimental data to predict potential therapeutic targets. The study employed a multi-start optimization strategy and profile likelihood estimations for parameter estimation and assessing identifiability. The simulations are in reasonable agreement with the experimental data. Sensitivity analysis found LDHA and IL-1β as potential therapeutic points. Mathematical models described here can provide insights to understand the complex interrelationship between metabolism, inflammation and circadian rhythm, and in identifying effective therapeutic targets.

Realistic simulation of time-course measurements in systems biology

In systems biology, the analysis of complex nonlinear systems faces many methodological challenges. For the evaluation and comparison of the performances of novel and competing computational methods, one major bottleneck is the availability of realistic test problems. We present an approach for performing realistic simulation studies for analyses of time course data as they are typically measured in systems biology. Since the design of experiments in practice depends on the process of interest, our approach considers the size and the dynamics of the mathematical model which is intended to be used for the simulation study. To this end, we used 19 published systems biology models with experimental data and evaluated the relationship between model features (e.g., the size and the dynamics) and features of the measurements such as the number and type of observed quantities, the number and the selection of measurement times, and the magnitude of measurement errors. Based on these typical relationships, our novel approach enables suggestions of realistic simulation study designs in the systems biology context and the realistic generation of simulated data for any dynamic model. The approach is demonstrated on three models in detail and its performance is validated on nine models by comparing ODE integration, parameter optimization, and parameter identifiability. The presented approach enables more realistic and less biased benchmark studies and thereby constitutes an important tool for the development of novel methods for dynamic modeling.

Benchmarking tools for a priori identifiability analysis

MOTIVATION

The theoretical possibility of determining the state and parameters of a dynamic model by measuring its outputs is given by its structural identifiability and its observability. These properties should be analysed before attempting to calibrate a model, but their a priori analysis can be challenging, requiring symbolic calculations that often have a high computational cost. In recent years, a number of software tools have been developed for this task, mostly in the systems biology community. These tools have vastly different features and capabilities, and a critical assessment of their performance is still lacking.

RESULTS

Here, we present a comprehensive study of the computational resources available for analysing structural identifiability. We consider 13 software tools developed in 7 programming languages and evaluate their performance using a set of 25 case studies created from 21 models. Our results reveal their strengths and weaknesses, provide guidelines for choosing the most appropriate tool for a given problem and highlight opportunities for future developments.

AVAILABILITY AND IMPLEMENTATION

https://github.com/Xabo-RB/Benchmarking_files.

Multiscale modeling of collective cell migration elucidates the mechanism underlying tumor-stromal interactions in different spatiotemporal scales

Metastasis is the pathogenic spread of cancer cells from a primary tumor to a secondary site which happens at the late stages of cancer. It is caused by a variety of biological, chemical, and physical processes, such as molecular interactions, intercellular communications, and tissue-level activities. Complex interactions of cancer cells with their microenvironment components such as cancer associated fibroblasts (CAFs) and extracellular matrix (ECM) cause them to adopt an invasive phenotype that promotes tumor growth and migration. This paper presents a multiscale model for integrating a wide range of time and space interactions at the molecular, cellular, and tissue levels in a three-dimensional domain. The modeling procedure starts with presenting nonlinear dynamics of cancer cells and CAFs using ordinary differential equations based on TGFβ, CXCL12, and LIF signaling pathways. Unknown kinetic parameters in these models are estimated using hybrid unscented Kalman filter and the models are validated using experimental data. Then, the principal role of CAFs on metastasis is revealed by spatial-temporal modeling of circulating signals throughout the TME. At this stage, the model has evolved into a coupled ODE-PDE system that is capable of determining cancer cells' status in one of the quiescent, proliferating or migratory conditions due to certain metastasis factors and ECM characteristics. At the tissue level, we consider a force-based framework to model the cancer cell proliferation and migration as the final step towards cancer cell metastasis. The ability of the multiscale model to depict cancer cells' behavior in different levels of modeling is confirmed by comparing its outputs with the results of RT PCR and wound scratch assay techniques. Performance evaluation of the model indicates that the proposed multiscale model can pave the way for improving the efficiency of therapeutic methods in metastasis prevention.

Efficient gradient-based parameter estimation for dynamic models using qualitative data

MOTIVATION

Unknown parameters of dynamical models are commonly estimated from experimental data. However, while various efficient optimization and uncertainty analysis methods have been proposed for quantitative data, methods for qualitative data are rare and suffer from bad scaling and convergence.

RESULTS

Here, we propose an efficient and reliable framework for estimating the parameters of ordinary differential equation models from qualitative data. In this framework, we derive a semi-analytical algorithm for gradient calculation of the optimal scaling method developed for qualitative data. This enables the use of efficient gradient-based optimization algorithms. We demonstrate that the use of gradient information improves performance of optimization and uncertainty quantification on several application examples. On average, we achieve a speedup of more than one order of magnitude compared to gradient-free optimization. In addition, in some examples, the gradient-based approach yields substantially improved objective function values and quality of the fits. Accordingly, the proposed framework substantially improves the parameterization of models from qualitative data.

AVAILABILITY AND IMPLEMENTATION

The proposed approach is implemented in the open-source Python Parameter EStimation TOolbox (pyPESTO). pyPESTO is available at https://github.com/ICB-DCM/pyPESTO. All application examples and code to reproduce this study are available at https://doi.org/10.5281/zenodo.4507613.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Efficient gradient-based parameter estimation for dynamic models using qualitative data

Motivation

Unknown parameters of dynamical models are commonly estimated from experimental data. However, while various efficient optimization and uncertainty analysis methods have been proposed for quantitative data, methods for qualitative data are rare and suffer from bad scaling and convergence.

Results

Here, we propose an efficient and reliable framework for estimating the parameters of ordinary differential equation models from qualitative data. In this framework, we derive a semi-analytical algorithm for gradient calculation of the optimal scaling method developed for qualitative data. This enables the use of efficient gradient-based optimization algorithms. We demonstrate that the use of gradient information improves performance of optimization and uncertainty quantification on several application examples. On average, we achieve a speedup of more than one order of magnitude compared to gradient-free optimization. In addition, in some examples, the gradient-based approach yields substantially improved objective function values and quality of the fits. Accordingly, the proposed framework substantially improves the parameterization of models from qualitative data.

Availability and implementation

The proposed approach is implemented in the open-source Python Parameter EStimation TOolbox (pyPESTO). pyPESTO is available at https://github.com/ICB-DCM/pyPESTO. All application examples and code to reproduce this study are available at https://doi.org/10.5281/zenodo.4507613.

Supplementary information

Supplementary data are available at Bioinformatics online.

Parameterization of mechanistic models from qualitative data using an efficient optimal scaling approach

Quantitative dynamical models facilitate the understanding of biological processes and the prediction of their dynamics. These models usually comprise unknown parameters, which have to be inferred from experimental data. For quantitative experimental data, there are several methods and software tools available. However, for qualitative data the available approaches are limited and computationally demanding. Here, we consider the optimal scaling method which has been developed in statistics for categorical data and has been applied to dynamical systems. This approach turns qualitative variables into quantitative ones, accounting for constraints on their relation. We derive a reduced formulation for the optimization problem defining the optimal scaling. The reduced formulation possesses the same optimal points as the established formulation but requires less degrees of freedom. Parameter estimation for dynamical models of cellular pathways revealed that the reduced formulation improves the robustness and convergence of optimizers. This resulted in substantially reduced computation times. We implemented the proposed approach in the open-source Python Parameter EStimation TOolbox (pyPESTO) to facilitate reuse and extension. The proposed approach enables efficient parameterization of quantitative dynamical models using qualitative data.

Perturbation biology links temporal protein changes to drug responses in a melanoma cell line

Cancer cells have genetic alterations that often directly affect intracellular protein signaling processes allowing them to bypass control mechanisms for cell death, growth and division. Cancer drugs targeting these alterations often work initially, but resistance is common. Combinations of targeted drugs may overcome or prevent resistance, but their selection requires context-specific knowledge of signaling pathways including complex interactions such as feedback loops and crosstalk. To infer quantitative pathway models, we collected a rich dataset on a melanoma cell line: Following perturbation with 54 drug combinations, we measured 124 (phospho-)protein levels and phenotypic response (cell growth, apoptosis) in a time series from 10 minutes to 67 hours. From these data, we trained time-resolved mathematical models that capture molecular interactions and the coupling of molecular levels to cellular phenotype, which in turn reveal the main direct or indirect molecular responses to each drug. Systematic model simulations identified novel combinations of drugs predicted to reduce the survival of melanoma cells, with partial experimental verification. This particular application of perturbation biology demonstrates the potential impact of combining time-resolved data with modeling for the discovery of new combinations of cancer drugs.

Disentangling molecular mechanisms regulating sensitization of interferon alpha signal transduction

Tightly interlinked feedback regulators control the dynamics of intracellular responses elicited by the activation of signal transduction pathways. Interferon alpha (IFNα) orchestrates antiviral responses in hepatocytes, yet mechanisms that define pathway sensitization in response to prestimulation with different IFNα doses remained unresolved. We establish, based on quantitative measurements obtained for the hepatoma cell line Huh7.5, an ordinary differential equation model for IFNα signal transduction that comprises the feedback regulators STAT1, STAT2, IRF9, USP18, SOCS1, SOCS3, and IRF2. The model-based analysis shows that, mediated by the signaling proteins STAT2 and IRF9, prestimulation with a low IFNα dose hypersensitizes the pathway. In contrast, prestimulation with a high dose of IFNα leads to a dose-dependent desensitization, mediated by the negative regulators USP18 and SOCS1 that act at the receptor. The analysis of basal protein abundance in primary human hepatocytes reveals high heterogeneity in patient-specific amounts of STAT1, STAT2, IRF9, and USP18. The mathematical modeling approach shows that the basal amount of USP18 determines patient-specific pathway desensitization, while the abundance of STAT2 predicts the patient-specific IFNα signal response.

Benchmark problems for dynamic modeling of intracellular processes

Motivation

Dynamic models are used in systems biology to study and understand cellular processes like gene regulation or signal transduction. Frequently, ordinary differential equation (ODE) models are used to model the time and dose dependency of the abundances of molecular compounds as well as interactions and translocations. A multitude of computational approaches, e.g. for parameter estimation or uncertainty analysis have been developed within recent years. However, many of these approaches lack proper testing in application settings because a comprehensive set of benchmark problems is yet missing.

Results

We present a collection of 20 benchmark problems in order to evaluate new and existing methodologies, where an ODE model with corresponding experimental data is referred to as problem. In addition to the equations of the dynamical system, the benchmark collection provides observation functions as well as assumptions about measurement noise distributions and parameters. The presented benchmark models comprise problems of different size, complexity and numerical demands. Important characteristics of the models and methodological requirements are summarized, estimated parameters are provided, and some example studies were performed for illustrating the capabilities of the presented benchmark collection.

Availability and implementation

The models are provided in several standardized formats, including an easy-to-use human readable form and machine-readable SBML files. The data is provided as Excel sheets. All files are available at https://github.com/Benchmarking-Initiative/Benchmark-Models, including step-by-step explanations and MATLAB code to process and simulate the models.

Supplementary information

Supplementary data are available at Bioinformatics online.

An efficient procedure to assist in the re-parametrization of structurally unidentifiable models

An efficient method that assists in the re-parametrization of structurally unidentifiable models is introduced. It significantly reduces computational demand by combining numerical and symbolic identifiability calculations. This hybrid approach facilitates the re-parametrization of large unidentifiable ordinary differential equation models, including models where state transformations are required. A model is first assessed numerically, to discover potential structurally unidentifiable parameters. We then use symbolic calculations to confirm the numerical results, after which we describe the algebraic relationships between the unidentifiable parameters. Finally, the unidentifiable parameters are substituted with new parameters and simplification ensures that all the unidentifiable parameters are eliminated from the original model structure. The novelty of this method is its utilisation of numerical results, which notably reduces the number of symbolic calculations required. We illustrate our procedure and the detailed re-parametrization process in 5 examples: (1) an immunological model, (2) a microbial growth model, (3) a lung cancer model, (4) a JAK/STAT model, and (5) a small linear model with a non-scalable re-parametrization.

Parameter Estimation and Uncertainty Quantification for Systems Biology Models

Mathematical models can provide quantitative insights into immunoreceptor signaling, and other biological processes, but require parameterization and uncertainty quantification before reliable predictions become possible. We review currently available methods and software tools to address these problems. We consider gradient-based and gradient-free methods for point estimation of parameter values, and methods of profile likelihood, bootstrapping, and Bayesian inference for uncertainty quantification. We consider recent and potential future applications of these methods to systems-level modeling of immune-related phenomena.

An easy and efficient approach for testing identifiability

Motivation

The feasibility of uniquely estimating parameters of dynamical systems from observations is a widely discussed aspect of mathematical modelling. Several approaches have been published for analyzing this so-called identifiability of model parameters. However, they are typically computationally demanding, difficult to perform and/or not applicable in many application settings.

Results

Here, an approach is presented which enables quickly testing of parameter identifiability. Numerical optimization with a penalty in radial direction enforcing displacement of the parameters is used to check whether estimated parameters are unique, or whether the parameters can be altered without loss of agreement with the data indicating non-identifiability. This Identifiability-Test by Radial Penalization (ITRP) can be employed for every model where optimization-based parameter estimation like least-squares or maximum likelihood is feasible and is therefore applicable for all typical systems biology models. The approach is illustrated and tested using 11 ordinary differential equation (ODE) models.

Availability and implementation

The presented approach can be implemented without great efforts in any modelling framework. It is available within the free Matlab-based modelling toolbox Data2Dynamics. Source code is available at https://github.com/Data2Dynamics.

Contact

ckreutz@fdm.uni-freiburg.de.

Supplementary information

Supplementary data are available at Bioinformatics online.

Robustness and Information Transfer within IL-6-induced JAK/STAT Signalling

Cellular communication via intracellular signalling pathways is crucial. Expression and activation of signalling proteins is heterogenous between isogenic cells of the same cell-type. However, mechanisms evolved to enable sufficient communication and to ensure cellular functions. We use information theory to clarify mechanisms facilitating IL-6-induced JAK/STAT signalling despite cell-to-cell variability. We show that different mechanisms enabling robustness against variability complement each other. Early STAT3 activation is robust as long as cytokine concentrations are low. Robustness at high cytokine concentrations is ensured by high STAT3 expression or serine phosphorylation. Later the feedback-inhibitor SOCS3 increases robustness. Channel Capacity of JAK/STAT signalling is limited by cell-to-cell variability in STAT3 expression and is affected by the same mechanisms governing robustness. Increasing STAT3 amount increases Channel Capacity and robustness, whereas increasing STAT3 tyrosine phosphorylation reduces robustness but increases Channel Capacity. In summary, we elucidate mechanisms preventing dysregulated signalling by enabling reliable JAK/STAT signalling despite cell-to-cell heterogeneity.

Determining minimal output sets that ensure structural identifiability

The process of inferring parameter values from experimental data can be a cumbersome task. In addition, the collection of experimental data can be time consuming and costly. This paper covers both these issues by addressing the following question: “Which experimental outputs should be measured to ensure that unique model parameters can be calculated?”. Stated formally, we examine the topic of minimal output sets that guarantee a model’s structural identifiability. To that end, we introduce an algorithm that guides a researcher as to which model outputs to measure. Our algorithm consists of an iterative structural identifiability analysis and can determine multiple minimal output sets of a model. This choice in different output sets offers researchers flexibility during experimental design. Our method can determine minimal output sets of large differential equation models within short computational times.

Integrative workflows for network analysis

Due to genetic heterogeneity across patients, the identification of effective disease signatures and therapeutic targets is challenging. Addressing this challenge, we have previously developed a network-based approach, which integrates heterogeneous sources of biological information to identify disease specific core-regulatory networks. In particular, our workflow uses a multi-objective optimization function to calculate a ranking score for network components (e.g. feedback/feedforward loops) based on network properties, biomedical and high-throughput expression data. High ranked network components are merged to identify the core-regulatory network(s) that is then subjected to dynamical analysis using stimulus–response and in silico perturbation experiments for the identification of disease gene signatures and therapeutic targets. In a case study, we implemented our workflow to identify bladder and breast cancer specific core-regulatory networks underlying epithelial–mesenchymal transition from the E2F1 molecular interaction map.

In this study, we review our workflow and described how it has developed over time to understand the mechanisms underlying disease progression and prediction of signatures for clinical decision making.

IL-13 and IL-13Rα1 are overexpressed in extranodal natural killer/T cell lymphoma and mediate tumor cell proliferation

Extranodal NK/T cell lymphoma (NKTCL) is a rare but aggressive subtype of non-Hodgkin lymphoma. Multi-agent chemotherapy and involved-field radiotherapy are used to treat this disease, but the prognosis remains poor. Interleukin 13 and its receptors (IL-13Rs) are correlated with the pathogenesis and progression of various malignances. However, their roles in NKTCL have not been evaluated. In this study, we examined the roles of IL-13 and IL-13Rs in NKTCL and the underlying mechanisms. We found significantly higher serum IL-13 levels (p < 0.001) and IL-13Rα1 expression in tumor tissues (36 of 40, p < 0.001) in patients with NKTCL than in control cohort. IL-13 secretion was observed in tumor tissues (30 of 40, p < 0.001) and several cell lines of NKTCL. However, we did not detect significant associations between clinical characteristics and the expression levels of IL-13 or IL-13Rs. In vitro, IL-13 activated Stat6 and promoted cell proliferation in a dose-dependent manner. In addition, blocking IL-13 exerted a negative effect on tumor cell growth. We conclude that IL-13 functions as an autocrine growth factor in NKTCL and contributes to its pathogenesis. Blocking IL-13 is thus a potential therapeutic approach for NKTCL.

Profile likelihood-based analyses of infectious disease models

Ordinary differential equation models are frequently applied to describe the temporal evolution of epidemics. However, ordinary differential equation models are also utilized in other scientific fields. We summarize and transfer state-of-the art approaches from other fields like Systems Biology to infectious disease models. For this purpose, we use a simple SIR model with data from an influenza outbreak at an English boarding school in 1978 and a more complex model of a vector-borne disease with data from the Zika virus outbreak in Colombia in 2015-2016. Besides parameter estimation using a deterministic multistart optimization approach, a multitude of analyses based on the profile likelihood are presented comprising identifiability analysis and model reduction. The analyses were performed using the freely available modeling framework Data2Dynamics (data2dynamics.org) which has been awarded as best performing within the DREAM6 parameter estimation challenge and in the DREAM7 network reconstruction challenge.

A Network-Based Integrative Workflow to Unravel Mechanisms Underlying Disease Progression

Unraveling mechanisms underlying diseases has motivated the development of systems biology approaches. The key challenges for the development of mathematical models and computational tool are (1) the size of molecular networks, (2) the nonlinear nature of spatio-temporal interactions, and (3) feedback loops in the structure of interaction networks. We here propose an integrative workflow that combines structural analyses of networks, high-throughput data, and mechanistic modeling. As an illustration of the workflow, we use prostate cancer as a case study with the aim of identifying key functional components associated with primary to metastasis transitions. Analysis carried out by the workflow revealed that HOXD10, BCL2, and PGR are the most important factors affected in primary prostate samples, whereas, in the metastatic state, STAT3, JUN, and JUNB are playing a central role. The identified key elements of each network are validated using patient survival analysis. The workflow presented here allows experimentalists to use heterogeneous data sources for the identification of diagnostic and prognostic signatures.

Diffuse large B-cell lymphoma: can genomics improve treatment options for a curable cancer?

Gene-expression profiling and next-generation sequencing have defined diffuse large B-cell lymphoma (DLBCL), the most common lymphoma diagnosis, as a heterogeneous group of subentities. Despite ongoing explosions of data illuminating disparate pathogenic mechanisms, however, the five-drug chemoimmunotherapy combination R-CHOP remains the frontline standard treatment. This has not changed in 15 years, since the anti-CD20 monoclonal antibody rituximab was added to the CHOP backbone, which first entered use in the 1970s. At least a third of patients are not cured by R-CHOP, and relapsed or refractory DLBCL is fatal in ∼90%. Targeted small-molecule inhibitors against distinct molecular pathways activated in different subgroups of DLBCL have so far translated poorly into the clinic, justifying the ongoing reliance on R-CHOP and other long-established chemotherapy-driven combinations. New drugs and improved identification of biomarkers in real time, however, show potential to change the situation eventually, despite some recent setbacks. Here, we review established and putative molecular drivers of DLBCL identified through large-scale genomics, highlighting among other things the care that must be taken when differentiating drivers from passengers, which is influenced by the promiscuity of activation-induced cytidine deaminase. Furthermore, we discuss why, despite having so much genomic data available, it has been difficult to move toward personalized medicine for this umbrella disorder and some steps that may be taken to hasten the process.

Model Based Targeting of IL-6-Induced Inflammatory Responses in Cultured Primary Hepatocytes to Improve Application of the JAK Inhibitor Ruxolitinib

IL-6 is a central mediator of the immediate induction of hepatic acute phase proteins (APP) in the liver during infection and after injury, but increased IL-6 activity has been associated with multiple pathological conditions. In hepatocytes, IL-6 activates JAK1-STAT3 signaling that induces the negative feedback regulator SOCS3 and expression of APPs. While different inhibitors of IL-6-induced JAK1-STAT3-signaling have been developed, understanding their precise impact on signaling dynamics requires a systems biology approach. Here we present a mathematical model of IL-6-induced JAK1-STAT3 signaling that quantitatively links physiological IL-6 concentrations to the dynamics of IL-6-induced signal transduction and expression of target genes in hepatocytes. The mathematical model consists of coupled ordinary differential equations (ODE) and the model parameters were estimated by a maximum likelihood approach, whereas identifiability of the dynamic model parameters was ensured by the Profile Likelihood. Using model simulations coupled with experimental validation we could optimize the long-term impact of the JAK-inhibitor Ruxolitinib, a therapeutic compound that is quickly metabolized. Model-predicted doses and timing of treatments helps to improve the reduction of inflammatory APP gene expression in primary mouse hepatocytes close to levels observed during regenerative conditions. The concept of improved efficacy of the inhibitor through multiple treatments at optimized time intervals was confirmed in primary human hepatocytes. Thus, combining quantitative data generation with mathematical modeling suggests that repetitive treatment with Ruxolitinib is required to effectively target excessive inflammatory responses without exceeding doses recommended by the clinical guidelines.

MDM4 genetic variants and risk of gastric cancer in an Eastern Chinese population

MDM4 is a p53-interacting protein and plays an important role in carcinogenesis. In this study of 1,077 gastric cancer (GCa) cases and 1,173 matched cancer-free controls, we investigated associations between three tagging single nucleotide polymorphisms (SNPs) (rs11801299 G>A, rs1380576 C>G and rs10900598 G>T) in MDM4 and gastric cancer risk in an Eastern Chinese Population. In logistic regression analysis, a significantly decreased GCa risk was associated with the rs1380576 GG variant genotype (adjusted odds ratio [OR] =0.74, 95% confidence interval [CI] =0.56-0.98) under a recessive model, which remained significant after correction by the false-positive reporting probability. This risk was more evident in subgroups of older subjects, males, never smokers, never drinkers and cancers of non-cardia. We then performed SNP-mRNA expression correlation analysis and found that the GG variant genotype was associated with significantly decreased expression of MDM4 mRNA in normal cell lines for 44 Chinese (P=0.032 for GG vs. CC) as well as for 269 multi-ethnic subjects (P<0.0001 for GG vs. CC). Our results suggest that the MDM4 rs1380576 G variant may be markers for GCa susceptibility. Larger, independent studies are warranted to validate our findings.

Delineating parameter unidentifiabilities in complex models

Scientists use mathematical modeling as a tool for understanding and predicting the properties of complex physical systems. In highly parametrized models there often exist relationships between parameters over which model predictions are identical, or nearly identical. These are known as structural or practical unidentifiabilities, respectively. They are hard to diagnose and make reliable parameter estimation from data impossible. They furthermore imply the existence of an underlying model simplification. We describe a scalable method for detecting unidentifiabilities, as well as the functional relations defining them, for generic models. This allows for model simplification, and appreciation of which parameters (or functions thereof) cannot be estimated from data. Our algorithm can identify features such as redundant mechanisms and fast time-scale subsystems, as well as the regimes in parameter space over which such approximations are valid. We base our algorithm on a quantification of regional parametric sensitivity that we call 'multiscale sloppiness'. Traditionally, the link between parametric sensitivity and the conditioning of the parameter estimation problem is made locally, through the Fisher information matrix. This is valid in the regime of infinitesimal measurement uncertainty. We demonstrate the duality between multiscale sloppiness and the geometry of confidence regions surrounding parameter estimates made where measurement uncertainty is non-negligible. Further theoretical relationships are provided linking multiscale sloppiness to the likelihood-ratio test. From this, we show that a local sensitivity analysis (as typically done) is insufficient for determining the reliability of parameter estimation, even with simple (non)linear systems. Our algorithm can provide a tractable alternative. We finally apply our methods to a large-scale, benchmark systems biology model of necrosis factor (NF)-κB, uncovering unidentifiabilities.

Demystifying the cytokine network: Mathematical models point the way

Cytokines provide the means by which immune cells communicate with each other and with parenchymal cells. There are over one hundred cytokines and many exist in families that share receptor components and signal transduction pathways, creating complex networks. Reductionist approaches to understanding the role of specific cytokines, through the use of gene-targeted mice, have revealed further complexity in the form of redundancy and pleiotropy in cytokine function. Creating an understanding of the complex interactions between cytokines and their target cells is challenging experimentally. Mathematical and computational modeling provides a robust set of tools by which complex interactions between cytokines can be studied and analyzed, in the process creating novel insights that can be further tested experimentally. This review will discuss and provide examples of the different modeling approaches that have been used to increase our understanding of cytokine networks. This includes discussion of knowledge-based and data-driven modeling approaches and the recent advance in single-cell analysis. The use of modeling to optimize cytokine-based therapies will also be discussed.

Structural Identifiability of Dynamic Systems Biology Models

A powerful way of gaining insight into biological systems is by creating a nonlinear differential equation model, which usually contains many unknown parameters. Such a model is called structurally identifiable if it is possible to determine the values of its parameters from measurements of the model outputs. Structural identifiability is a prerequisite for parameter estimation, and should be assessed before exploiting a model. However, this analysis is seldom performed due to the high computational cost involved in the necessary symbolic calculations, which quickly becomes prohibitive as the problem size increases. In this paper we show how to analyse the structural identifiability of a very general class of nonlinear models by extending methods originally developed for studying observability. We present results about models whose identifiability had not been previously determined, report unidentifiabilities that had not been found before, and show how to modify those unidentifiable models to make them identifiable. This method helps prevent problems caused by lack of identifiability analysis, which can compromise the success of tasks such as experiment design, parameter estimation, and model-based optimization. The procedure is called STRIKE-GOLDD (STRuctural Identifiability taKen as Extended-Generalized Observability with Lie Derivatives and Decomposition), and it is implemented in a MATLAB toolbox which is available as open source software. The broad applicability of this approach facilitates the analysis of the increasingly complex models used in systems biology and other areas.

Identification of Cell Type-Specific Differences in Erythropoietin Receptor Signaling in Primary Erythroid and Lung Cancer Cells

Lung cancer, with its most prevalent form non-small-cell lung carcinoma (NSCLC), is one of the leading causes of cancer-related deaths worldwide, and is commonly treated with chemotherapeutic drugs such as cisplatin. Lung cancer patients frequently suffer from chemotherapy-induced anemia, which can be treated with erythropoietin (EPO). However, studies have indicated that EPO not only promotes erythropoiesis in hematopoietic cells, but may also enhance survival of NSCLC cells. Here, we verified that the NSCLC cell line H838 expresses functional erythropoietin receptors (EPOR) and that treatment with EPO reduces cisplatin-induced apoptosis. To pinpoint differences in EPO-induced survival signaling in erythroid progenitor cells (CFU-E, colony forming unit-erythroid) and H838 cells, we combined mathematical modeling with a method for feature selection, the L₁ regularization. Utilizing an example model and simulated data, we demonstrated that this approach enables the accurate identification and quantification of cell type-specific parameters. We applied our strategy to quantitative time-resolved data of EPO-induced JAK/STAT signaling generated by quantitative immunoblotting, mass spectrometry and quantitative real-time PCR (qRT-PCR) in CFU-E and H838 cells as well as H838 cells overexpressing human EPOR (H838-HA-hEPOR). The established parsimonious mathematical model was able to simultaneously describe the data sets of CFU-E, H838 and H838-HA-hEPOR cells. Seven cell type-specific parameters were identified that included for example parameters for nuclear translocation of STAT5 and target gene induction. Cell type-specific differences in target gene induction were experimentally validated by qRT-PCR experiments. The systematic identification of pathway differences and sensitivities of EPOR signaling in CFU-E and H838 cells revealed potential targets for intervention to selectively inhibit EPO-induced signaling in the tumor cells but leave the responses in erythroid progenitor cells unaffected. Thus, the proposed modeling strategy can be employed as a general procedure to identify cell type-specific parameters and to recommend treatment strategies for the selective targeting of specific cell types.

A major challenge in the development of therapeutic interventions is the selective inhibition of a signal transduction pathway in one cell type such as a cancer cell leaving the other cell type such as a healthy cell as unaffected as possible. Here, we propose a new approach that combines mathematical modeling based on quantitative experimental data with statistical methods. We demonstrate based on simulated data that our approach can determine which parameters are the same and which parameters differ in two exemplary cell types. We compare a lung cancer cell line to the precursor cells of red blood cells. We show that the same signal transduction network induced by erythropoietin (EPO), a hormone that is frequently employed to treat anemia in cancer patients, regulates survival of both cell types. Based on our experimental data in combination with our computational approach, we identify seven cell type-specific differences in this signaling pathway. Our strategy allows predicting therapeutic targets that could be inhibited to interfere with survival of lung cancer cells while leaving production of red blood cells unaffected.

T160‐phosphorylated CDK2 defines threshold for HGF dependent proliferation in primary hepatocytes

Liver regeneration is a tightly controlled process mainly achieved by proliferation of usually quiescent hepatocytes. The specific molecular mechanisms ensuring cell division only in response to proliferative signals such as hepatocyte growth factor (HGF) are not fully understood. Here, we combined quantitative time-resolved analysis of primary mouse hepatocyte proliferation at the single cell and at the population level with mathematical modeling. We showed that numerous G1/S transition components are activated upon hepatocyte isolation whereas DNA replication only occurs upon additional HGF stimulation. In response to HGF, Cyclin:CDK complex formation was increased, p21 rather than p27 was regulated, and Rb expression was enhanced. Quantification of protein levels at the restriction point showed an excess of CDK2 over CDK4 and limiting amounts of the transcription factor E2F-1. Analysis with our mathematical model revealed that T160 phosphorylation of CDK2 correlated best with growth factor-dependent proliferation, which we validated experimentally on both the population and the single cell level. In conclusion, we identified CDK2 phosphorylation as a gate-keeping mechanism to maintain hepatocyte quiescence in the absence of HGF.

Fast integration-based prediction bands for ordinary differential equation models

MOTIVATION

To gain a deeper understanding of biological processes and their relevance in disease, mathematical models are built upon experimental data. Uncertainty in the data leads to uncertainties of the model's parameters and in turn to uncertainties of predictions. Mechanistic dynamic models of biochemical networks are frequently based on nonlinear differential equation systems and feature a large number of parameters, sparse observations of the model components and lack of information in the available data. Due to the curse of dimensionality, classical and sampling approaches propagating parameter uncertainties to predictions are hardly feasible and insufficient. However, for experimental design and to discriminate between competing models, prediction and confidence bands are essential. To circumvent the hurdles of the former methods, an approach to calculate a profile likelihood on arbitrary observations for a specific time point has been introduced, which provides accurate confidence and prediction intervals for nonlinear models and is computationally feasible for high-dimensional models.

RESULTS

In this article, reliable and smooth point-wise prediction and confidence bands to assess the model's uncertainty on the whole time-course are achieved via explicit integration with elaborate correction mechanisms. The corresponding system of ordinary differential equations is derived and tested on three established models for cellular signalling. An efficiency analysis is performed to illustrate the computational benefit compared with repeated profile likelihood calculations at multiple time points.

AVAILABILITY AND IMPLEMENTATION

The integration framework and the examples used in this article are provided with the software package Data2Dynamics, which is based on MATLAB and freely available at http://www.data2dynamics.org

CONTACT

helge.hass@fdm.uni-freiburg.de

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Systems biology of IL-6, IL-12 family cytokines

Interleukin-6-type cytokines play important roles in the communication between cells of multicellular organisms. They are involved in the regulation of complex cellular processes such as proliferation and differentiation and act as key player during inflammation and immune response. A major challenge is to understand how these complex non-linear processes are connected and regulated. Systems biology approaches are used to tackle this challenge in an iterative process of quantitative experimental and mathematical analyses. Here we review quantitative experimental studies and systems biology approaches dealing with the function of Interleukin-6-type cytokines in physiological and pathophysiological conditions. These approaches cover the analyses of signal transduction on a cellular level up to pharmacokinetic and pharmacodynamic studies on a whole organism level.

Data2Dynamics: a modeling environment tailored to parameter estimation in dynamical systems

Modeling of dynamical systems using ordinary differential equations is a popular approach in the field of systems biology. Two of the most critical steps in this approach are to construct dynamical models of biochemical reaction networks for large datasets and complex experimental conditions and to perform efficient and reliable parameter estimation for model fitting. We present a modeling environment for MATLAB that pioneers these challenges. The numerically expensive parts of the calculations such as the solving of the differential equations and of the associated sensitivity system are parallelized and automatically compiled into efficient C code. A variety of parameter estimation algorithms as well as frequentist and Bayesian methods for uncertainty analysis have been implemented and used on a range of applications that lead to publications.

AVAILABILITY AND IMPLEMENTATION

The Data2Dynamics modeling environment is MATLAB based, open source and freely available at http://www.data2dynamics.org.

CONTACT

andreas.raue@fdm.uni-freiburg.de

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Histone H3k9 and H3k27 Acetylation Regulates IL-4/STAT6-Mediated Igε Transcription in B Lymphocytes

IL-4 activates STAT6 and causes the subsequent up-regulation of Ig heavy chain germline Igε via chromatin remodeling involved in B lymphocytes development. STAT6 acts as a molecular switch to regulate the higher-order chromatin remodeling via dynamically orchestrating co-activators (CBP/Tudor-SN) and co-repressors (HDAC1/PSF). Here, we demonstrated that STAT6/Tudor-SN/PSF form a complex, balancing the acetylation and deacetylation states to co-regulate IL-4/STAT6 gene transcription. In addition, we confirmed that IL-4 treatment increased the HATs activity in Ramos cells. As "active" markers, the expression of H3K9ac and H3K27ac increased after treatment with IL-4. However, transcriptional repressors such as H3K9me3 and H3K27me3 decreased in response to IL-4 stimulation. Moreover, IL-4 treatment enhanced H3 acetylation at the Igε promoter regions. Our results revealed that the Igε gene transcription is regulated by histone modifications in the IL-4/STAT6 pathway. The study will provide novel insights into the pathogenesis of allergic diseases.

Malignant hematopoietic cell lines: in vitro models for the study of primary mediastinal B-cell lymphomas

Primary mediastinal B-cell lymphoma (PMBL) is a highly aggressive disease with a unique set of biological, clinical, morphological, immunological and in particular genetic features that in the molecular era of defining lymphomas clearly distinguishes it as a separate entity from other diffuse large B-cell lymphomas (DLBCL). A precise molecular diagnosis of PMBL can be achieved by gene expression profiling. The signature gene expression profile of PMBL is more closely related to classic Hodgkin lymphoma (cHL) than to other DLBCL subgroups. A number of common genetic aberrations in PMBL and cHL further underscore their close relationship. To investigate the pathobiology of lymphomas in depth, many groups have turned to cell lines that are suitable models facilitating molecular studies and providing unique insights. For the purposes of the current perspective, we focus on four bona fide PMBL-derived cell lines (FARAGE, KARPAS-1106, MEDB-1, U-2940) that we identified and validated as such through hierarchical cluster analysis among a large collection of leukemia-lymphoma cell lines. These gene expression profiles showed that the four PMBL cell lines represent a distinct entity and are most similar to cHL cell lines, confirming derivation from a related cell type. A validated cell line resource for PMBL should assist those seeking druggable targets in this entity. This review aims to provide a comprehensive overview of the currently available cellular models for the study of PMBL.

The potential for genetically altered microglia to influence glioma treatment

Diffuse and unstoppable infiltration of brain and spinal cord tissue by neoplastic glial cells is the single most important therapeutic problem posed by the common glioma group of tumors: astrocytoma, oligoastrocytoma, oligodendroglioma, their malignant variants and glioblastoma. These neoplasms account for more than two thirds of all malignant central nervous system tumors. However, most glioma research focuses on an examination of the tumor cells rather than on host-specific, tumor micro-environmental cells and factors. This can explain why existing diffuse glioma therapies fail and why these tumors have remained incurable. Thus, there is a great need for innovation. We describe a novel strategy for the development of a more effective treatment of diffuse glioma. Our approach centers on gaining control over the behavior of the microglia, the defense cells of the CNS, which are manipulated by malignant glioma and support its growth. Armoring microglia against the influences from glioma is one of our research goals. We further discuss how microglia precursors may be genetically enhanced to track down infiltrating glioma cells.

One-source peptide/phosphopeptide ratio standards for accurate and site-specific determination of the degree of phosphorylation

Reversible protein phosphorylation is a key mediator for intracellular signal transduction. Here we describe an innovative method for the production of pairs of peptide standards designed for quantitative mass spectrometry. These standard pairs can be used for site-specific analysis of the degree of phosphorylation of proteins in a bottom-up approach. The method starts from an isotopically labeled phosphopeptide analogue of the analyte phosphopeptide and ends up with a labeled peptide/phosphopeptide ratio standard in which the molar ratio between the phosphorylated and the unphosphorylated form is exactly defined. The signals of the ratio standard are used to standardize the corresponding analyte signals. This compensates for differences in LC recovery or ionization efficiency between the phosphorylated and unphosphorylated forms. The method can also be extended to quantitative analysis of multisite phosphorylation in a single peptide, which is exemplified for the presence of two phosphorylation sites. Peptide/phosphopeptide ratio standards exhibit high ratio accuracy, since ratio adjustment is performed by volumetric operations only.

New types of experimental data shape the use of enzyme kinetics for dynamic network modeling

Since the publication of Leonor Michaelis and Maude Menten's paper on the reaction kinetics of the enzyme invertase in 1913, molecular biology has evolved tremendously. New measurement techniques allow in vivo characterization of the whole genome, proteome or transcriptome of cells, whereas the classical enzyme essay only allows determination of the two Michaelis-Menten parameters V and K(m). Nevertheless, Michaelis-Menten kinetics are still commonly used, not only in the in vitro context of enzyme characterization but also as a rate law for enzymatic reactions in larger biochemical reaction networks. In this review, we give an overview of the historical development of kinetic rate laws originating from Michaelis-Menten kinetics over the past 100 years. Furthermore, we briefly summarize the experimental techniques used for the characterization of enzymes, and discuss web resources that systematically store kinetic parameters and related information. Finally, describe the novel opportunities that arise from using these data in dynamic mathematical modeling. In this framework, traditional in vitro approaches may be combined with modern genome-scale measurements to foster thorough understanding of the underlying complex mechanisms.

Parameter identifiability and sensitivity analysis predict targets for enhancement of STAT1 activity in pancreatic cancer and stellate cells

The present work exemplifies how parameter identifiability analysis can be used to gain insights into differences in experimental systems and how uncertainty in parameter estimates can be handled. The case study, presented here, investigates interferon-gamma (IFNγ) induced STAT1 signalling in two cell types that play a key role in pancreatic cancer development: pancreatic stellate and cancer cells. IFNγ inhibits the growth for both types of cells and may be prototypic of agents that simultaneously hit cancer and stroma cells. We combined time-course experiments with mathematical modelling to focus on the common situation in which variations between profiles of experimental time series, from different cell types, are observed. To understand how biochemical reactions are causing the observed variations, we performed a parameter identifiability analysis. We successfully identified reactions that differ in pancreatic stellate cells and cancer cells, by comparing confidence intervals of parameter value estimates and the variability of model trajectories. Our analysis shows that useful information can also be obtained from nonidentifiable parameters. For the prediction of potential therapeutic targets we studied the consequences of uncertainty in the values of identifiable and nonidentifiable parameters. Interestingly, the sensitivity of model variables is robust against parameter variations and against differences between IFNγ induced STAT1 signalling in pancreatic stellate and cancer cells. This provides the basis for a prediction of therapeutic targets that are valid for both cell types.

Bayesian model selection validates a biokinetic model for zirconium processing in humans

BACKGROUND

In radiation protection, biokinetic models for zirconium processing are of crucial importance in dose estimation and further risk analysis for humans exposed to this radioactive substance. They provide limiting values of detrimental effects and build the basis for applications in internal dosimetry, the prediction for radioactive zirconium retention in various organs as well as retrospective dosimetry. Multi-compartmental models are the tool of choice for simulating the processing of zirconium. Although easily interpretable, determining the exact compartment structure and interaction mechanisms is generally daunting. In the context of observing the dynamics of multiple compartments, Bayesian methods provide efficient tools for model inference and selection.

RESULTS

We are the first to apply a Markov chain Monte Carlo approach to compute Bayes factors for the evaluation of two competing models for zirconium processing in the human body after ingestion. Based on in vivo measurements of human plasma and urine levels we were able to show that a recently published model is superior to the standard model of the International Commission on Radiological Protection. The Bayes factors were estimated by means of the numerically stable thermodynamic integration in combination with a recently developed copula-based Metropolis-Hastings sampler.

CONCLUSIONS

In contrast to the standard model the novel model predicts lower accretion of zirconium in bones. This results in lower levels of noxious doses for exposed individuals. Moreover, the Bayesian approach allows for retrospective dose assessment, including credible intervals for the initially ingested zirconium, in a significantly more reliable fashion than previously possible. All methods presented here are readily applicable to many modeling tasks in systems biology.

Bayesian model selection validates a biokinetic model for zirconium processing in humans

BACKGROUND

In radiation protection, biokinetic models for zirconium processing are of crucial importance in dose estimation and further risk analysis for humans exposed to this radioactive substance. They provide limiting values of detrimental effects and build the basis for applications in internal dosimetry, the prediction for radioactive zirconium retention in various organs as well as retrospective dosimetry. Multi-compartmental models are the tool of choice for simulating the processing of zirconium. Although easily interpretable, determining the exact compartment structure and interaction mechanisms is generally daunting. In the context of observing the dynamics of multiple compartments, Bayesian methods provide efficient tools for model inference and selection.

RESULTS

We are the first to apply a Markov chain Monte Carlo approach to compute Bayes factors for the evaluation of two competing models for zirconium processing in the human body after ingestion. Based on in vivo measurements of human plasma and urine levels we were able to show that a recently published model is superior to the standard model of the International Commission on Radiological Protection. The Bayes factors were estimated by means of the numerically stable thermodynamic integration in combination with a recently developed copula-based Metropolis-Hastings sampler.

CONCLUSIONS

In contrast to the standard model the novel model predicts lower accretion of zirconium in bones. This results in lower levels of noxious doses for exposed individuals. Moreover, the Bayesian approach allows for retrospective dose assessment, including credible intervals for the initially ingested zirconium, in a significantly more reliable fashion than previously possible. All methods presented here are readily applicable to many modeling tasks in systems biology.

Systems biology of JAK-STAT signalling in human malignancies

Originally implicated in the regulation of survival, proliferation and differentiation of haematopoietic cells, the JAK-STAT pathway has also been linked to developmental processes, growth control and maintenance of homeostasis in a variety of other cells and tissues. Although it remains a complex system, its relative simplicity and the availability of molecular data makes it particularly attractive for modelling approaches. In this review, we will focus on JAK-STAT signalling in the context of cancer and present efforts to investigate signalling dynamics with the help of mathematical models. We describe the modelling workflow that realises a systems biology approach and give an example for interferon-γ signalling in pancreatic stellate cells.