J Joep Vanlier

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

UNLABELLED 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.

Parameter uncertainty in biochemical models described by ordinary differential equations

Improved mechanistic understanding of biochemical networks is one of the driving ambitions of Systems Biology. Computational modeling allows the integration of various sources of experimental data in order to put this conceptual understanding to the test in a quantitative manner. The aim of computational modeling is to obtain both predictive as well as explanatory models for complex phenomena, hereby providing useful approximations of reality with varying levels of detail. As the complexity required to describe different system increases, so does the need for determining how well such predictions can be made. Despite efforts to make tools for uncertainty analysis available to the field, these methods have not yet found widespread use in the field of Systems Biology. Additionally, the suitability of the different methods strongly depends on the problem and system under investigation. This review provides an introduction to some of the techniques available as well as gives an overview of the state-of-the-art methods for parameter uncertainty analysis.

A Bayesian approach to targeted experiment design

Motivation: Systems biology employs mathematical modelling to further our understanding of biochemical pathways. Since the amount of experimental data on which the models are parameterized is often limited, these models exhibit large uncertainty in both parameters and predictions. Statistical methods can be used to select experiments that will reduce such uncertainty in an optimal manner. However, existing methods for optimal experiment design (OED) rely on assumptions that are inappropriate when data are scarce considering model complexity. Results: We have developed a novel method to perform OED for models that cope with large parameter uncertainty. We employ a Bayesian approach involving importance sampling of the posterior predictive distribution to predict the efficacy of a new measurement at reducing the uncertainty of a selected prediction. We demonstrate the method by applying it to a case where we show that specific combinations of experiments result in more precise predictions. Availability and implementation: Source code is available at: http://bmi.bmt.tue.nl/sysbio/software/pua.html Contact: j.vanlier@tue.nl; N.A.W.v.Riel@tue.nl Supplementary information: Supplementary data are available at Bioinformatics online.

An integrated strategy for prediction uncertainty analysis

Motivation: To further our understanding of the mechanisms underlying biochemical pathways mathematical modelling is used. Since many parameter values are unknown they need to be estimated using experimental observations. The complexity of models necessary to describe biological pathways in combination with the limited amount of quantitative data results in large parameter uncertainty which propagates into model predictions. Therefore prediction uncertainty analysis is an important topic that needs to be addressed in Systems Biology modelling. Results: We propose a strategy for model prediction uncertainty analysis by integrating profile likelihood analysis with Bayesian estimation. Our method is illustrated with an application to a model of the JAK-STAT signalling pathway. The analysis identified predictions on unobserved variables that could be made with a high level of confidence, despite that some parameters were non-identifiable. Availability and implementation: Source code is available at: http://bmi.bmt.tue.nl/sysbio/software/pua.html. Contact: j.vanlier@tue.nl Supplementary information: Supplementary data are available at Bioinformatics online.

Parameter adaptations during phenotype transitions in progressive diseases

BackgroundThe study of phenotype transitions is important to understand progressive diseases, e.g., diabetes mellitus, metabolic syndrome, and cardiovascular diseases. A challenge remains to explain phenotype transitions in terms of adaptations in molecular components and interactions in underlying biological systems.ResultsHere, mathematical modeling is used to describe the different phenotypes by integrating experimental data on metabolic pools and fluxes. Subsequently, trajectories of parameter adaptations are identified that are essential for the phenotypical changes. These changes in parameters reflect progressive adaptations at the transcriptome and proteome level, which occur at larger timescales. The approach was employed to study the metabolic processes underlying liver X receptor induced hepatic steatosis. Model analysis predicts which molecular processes adapt in time after pharmacological activation of the liver X receptor. Our results show that hepatic triglyceride fluxes are increased and triglycerides are especially stored in cytosolic fractions, rather than in endoplasmic reticulum fractions. Furthermore, the model reveals several possible scenarios for adaptations in cholesterol metabolism. According to the analysis, the additional quantification of one cholesterol flux is sufficient to exclude many of these hypotheses.ConclusionsWe propose a generic computational approach to analyze biological systems evolving through various phenotypes and to predict which molecular processes are responsible for the transition. For the case of liver X receptor induced hepatic steatosis the novel approach yields information about the redistribution of fluxes and pools of triglycerides and cholesterols that was not directly apparent from the experimental data. Model analysis provides guidance which specific molecular processes to study in more detail to obtain further understanding of the underlying biological system.

Optimal experiment design for model selection in biochemical networks

BackgroundMathematical modeling is often used to formalize hypotheses on how a biochemical network operates by discriminating between competing models. Bayesian model selection offers a way to determine the amount of evidence that data provides to support one model over the other while favoring simple models. In practice, the amount of experimental data is often insufficient to make a clear distinction between competing models. Often one would like to perform a new experiment which would discriminate between competing hypotheses.ResultsWe developed a novel method to perform Optimal Experiment Design to predict which experiments would most effectively allow model selection. A Bayesian approach is applied to infer model parameter distributions. These distributions are sampled and used to simulate from multivariate predictive densities. The method is based on a k-Nearest Neighbor estimate of the Jensen Shannon divergence between the multivariate predictive densities of competing models.ConclusionsWe show that the method successfully uses predictive differences to enable model selection by applying it to several test cases. Because the design criterion is based on predictive distributions, which can be computed for a wide range of model quantities, the approach is very flexible. The method reveals specific combinations of experiments which improve discriminability even in cases where data is scarce. The proposed approach can be used in conjunction with existing Bayesian methodologies where (approximate) posteriors have been determined, making use of relations that exist within the inferred posteriors.

BISEN: Biochemical simulation environment

SUMMARY The Biochemical Simulation Environment (BISEN) is a suite of tools for generating equations and associated computer programs for simulating biochemical systems in the MATLAB computing environment. This is the first package that can generate appropriate systems of differential equations for user-specified multi-compartment systems of enzymes and transporters accounting for detailed biochemical thermodynamics, rapid equilibria of multiple biochemical species and dynamic proton and metal ion buffering. AVAILABILITY The software and a user manual (including several tutorial examples) are available at bbc.mcw.edu/BISEN.

Driving the Model to Its Limit: Profile Likelihood Based Model Reduction.

In systems biology, one of the major tasks is to tailor model complexity to information content of the data. A useful model should describe the data and produce well-determined parameter estimates and predictions. Too small of a model will not be able to describe the data whereas a model which is too large tends to overfit measurement errors and does not provide precise predictions. Typically, the model is modified and tuned to fit the data, which often results in an oversized model. To restore the balance between model complexity and available measurements, either new data has to be gathered or the model has to be reduced. In this manuscript, we present a data-based method for reducing non-linear models. The profile likelihood is utilised to assess parameter identifiability and designate likely candidates for reduction. Parameter dependencies are analysed along profiles, providing context-dependent suggestions for the type of reduction. We discriminate four distinct scenarios, each associated with a specific model reduction strategy. Iterating the presented procedure eventually results in an identifiable model, which is capable of generating precise and testable predictions. Source code for all toy examples is provided within the freely available, open-source modelling environment Data2Dynamics based on MATLAB available at http://www.data2dynamics.org/, as well as the R packages dMod/cOde available at https://github.com/dkaschek/. Moreover, the concept is generally applicable and can readily be used with any software capable of calculating the profile likelihood.

Parameter trajectory analysis to identify treatment effects of pharmacological interventions

The field of medical systems biology aims to advance understanding of molecular mechanisms that drive disease progression and to translate this knowledge into therapies to effectively treat diseases. A challenging task is the investigation of long-term effects of a (pharmacological) treatment, to establish its applicability and to identify potential side effects. We present a new modeling approach, called Analysis of Dynamic Adaptations in Parameter Trajectories (ADAPT), to analyze the long-term effects of a pharmacological intervention. A concept of time-dependent evolution of model parameters is introduced to study the dynamics of molecular adaptations. The progression of these adaptations is predicted by identifying necessary dynamic changes in the model parameters to describe the transition between experimental data obtained during different stages of the treatment. The trajectories provide insight in the affected underlying biological systems and identify the molecular events that should be studied in more detail to unravel the mechanistic basis of treatment outcome. Modulating effects caused by interactions with the proteome and transcriptome levels, which are often less well understood, can be captured by the time-dependent descriptions of the parameters. ADAPT was employed to identify metabolic adaptations induced upon pharmacological activation of the liver X receptor (LXR), a potential drug target to treat or prevent atherosclerosis. The trajectories were investigated to study the cascade of adaptations. This provided a counter-intuitive insight concerning the function of scavenger receptor class B1 (SR-B1), a receptor that facilitates the hepatic uptake of cholesterol. Although activation of LXR promotes cholesterol efflux and -excretion, our computational analysis showed that the hepatic capacity to clear cholesterol was reduced upon prolonged treatment. This prediction was confirmed experimentally by immunoblotting measurements of SR-B1 in hepatic membranes. Next to the identification of potential unwanted side effects, we demonstrate how ADAPT can be used to design new target interventions to prevent these.

Applications of analysis of dynamic adaptations in parameter trajectories

Metabolic profiling in combination with pathway-based analyses and computational modelling are becoming increasingly important in clinical and preclinical research. Modelling multi-factorial, progressive diseases requires the integration of molecular data at the metabolome, proteome and transcriptome levels. Also the dynamic interaction of organs and tissues needs to be considered. The processes involved cover time scales that are several orders of magnitude different. We report applications of a computational approach to bridge the scales and different levels of biological detail. Analysis of dynamic adaptations in parameter trajectories (ADAPTs) aims to investigate phenotype transitions during disease development and after a therapeutic intervention. ADAPT is based on a time-dependent evolution of model parameters to describe the dynamics of metabolic adaptations. The progression of metabolic adaptations is predicted by identifying necessary dynamic changes in the model parameters to describe the transition between experimental data obtained during different stages. To get a better understanding of the concept, the ADAPT approach is illustrated in a theoretical study. Its application in research on progressive changes in lipoprotein metabolism is also discussed.