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@article{raue2015data2dynamics,
	Author = {Raue, Andreas and Steiert, Bernhard and Schelker, Max and Kreutz, Clemens and Maiwald, Tim and Hass, Helge and Vanlier, Joep and T{\"o}nsing, Christian and Adlung, Lorenz and Engesser, Raphael and Mader, Wolfgang and Heinemann, Tim and Hasenauer, Jan and Schilling, Marcel and H{\"o}fer, Thomas and Klipp, Edda and Theis, Fabian and Klingm{\"{u}}ller, Ursula and Schoeberl, Birgit and Timmer, Jens},
	Date-Added = {2018-04-05 09:15:29 +0000},
	Date-Modified = {2018-04-05 11:57:32 +0000},
	Journal = {Bioinformatics},
	Number = {21},
	Pages = {3558--3560},
	Publisher = {Oxford Univ Press},
	Title = {{Data2Dynamics: A modeling environment tailored to parameter estimation in dynamical systems}},
	Volume = {31},
	Year = {2015}}

@article{Hug:2012fk,
	Abstract = {In this work we present results of a detailed Bayesian parameter estima- tion for an analysis of ordinary differential equation models. These depend on many unknown parameters that have to be inferred from experimental data. The statistical inference in a high-dimensional parameter space is however conceptually and computationally challenging. To ensure rigorous assess- ment of model and prediction uncertainties we take advantage of both a profile posterior approach and Markov chain Monte Carlo sampling.
We analyzed a dynamical model of the JAK2/STAT5 signal transduc- tion pathway that contains more than one hundred parameters. Using the profile posterior we found that the corresponding posterior distribution is bimodal. To guarantee efficient mixing in the presence of multimodal poste- rior distributions we applied a multi-chain sampling approach. The Bayesian parameter estimation enables the assessment of prediction uncertainties and the design of additional experiments that enhance the explanatory power of the model.},
	Author = {Hug, S and Raue, A and Hasenauer, J and Bachmann, J and Klingm{\"u}ller, U and Timmer, J and Theis, F},
	Date-Added = {2018-04-05 09:04:37 +0000},
	Date-Modified = {2018-04-05 12:00:49 +0000},
	Journal = {Mathematical Biosciences},
	Number = {2},
	Pages = {293--304},
	Title = {{High-dimensional Bayesian parameter estimation: Case study for a model of JAK2/\-STAT5 signaling}},
	Volume = {246},
	Year = {2013},
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@article{Raue:2010fk,
	Abstract = {Dynamical models of cellular processes promise to yield new insights into the underlying systems and their biological interpretation. The processes are usually nonlinear, high dimensional, and time-resolved experimental data of the processes are sparse. Therefore, parameter estimation faces the challenges of structural and practical nonidentifiability. Nonidentifiability of parameters induces nonobservability of trajectories, reducing the predictive power of the model. We will discuss a generic approach for nonlinear models that allows for identifiability and observability analysis by means of a realistic example from systems biology. The results will be utilized to design new experiments that enhance model predictiveness, illustrating the iterative cycle between modeling and experimentation in systems biology.},
	Author = {Raue, A and Becker, V and Klingm{\"u}ller, U and Timmer, J},
	Date-Added = {2018-04-05 09:03:37 +0000},
	Date-Modified = {2018-04-05 12:02:21 +0000},
	Journal = {Chaos},
	Number = {4},
	Pages = {045105},
	Title = {{Identifiability and observability analysis for experimental design in non-linear dynamical models}},
	Volume = {20},
	Year = {2010},
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@article{Raue:2010ys,
	Abstract = {Mathematical description of biological processes such as gene regulatory networks or signalling pathways by dynamic models utilising ordinary differential equations faces challenges if the model parameters like rate constants are estimated from incomplete and noisy experimental data. Typically, biological networks are only partially observed. Only a fraction of the modelled molecular species is measurable directly. This can result in structurally non-identifiable model parameters. Furthermore, practical non-identifiability can arise from limited amount and quality of experimental data. In the challenge of growing model complexity on one side, and experimental limitations on the other side, both types of non-identifiability arise frequently in systems biological applications often prohibiting reliable prediction of system dynamics. On theoretical grounds this article summarises how and why both types of non-identifiability arise. It exemplifies pitfalls where models do not yield reliable predictions of system dynamics because of non-identifiabilities. Subsequently, several approaches for identifiability analysis proposed in the literature are discussed. The aim is to provide an overview of applicable methods for detecting parameter identifiability issues. Once non-identifiability is detected, it can be resolved either by experimental design, measuring additional data under suitable conditions; or by model reduction, tailoring the size of the model to the information content provided by the experimental data. Both strategies enhance model predictability and will be elucidated by an example application.},
	Author = {Raue, A. and Kreutz, C. and Maiwald, T. and Klingm{\"u}ller, U. and Timmer, J.},
	Date-Added = {2018-04-05 09:03:35 +0000},
	Date-Modified = {2018-04-05 12:02:38 +0000},
	Journal = {IET Systems Biology},
	Number = {2},
	Pages = {120-130},
	Title = {Addressing parameter identifiability by model-based experimentation},
	Volume = {5},
	Year = {2011},
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@article{Kreutz:2011kx,
	Abstract = {Background
Predicting a system's behavior based on a mathematical model is a primary task in Systems Biology. If the model parameters are estimated from experimental data, the parameter uncertainty has to be translated into confidence intervals for model predictions. For dynamic models of biochemical networks, the nonlinearity in combination with the large number of parameters hampers the calculation of prediction confidence intervals and renders classical approaches as hardly feasible.

Results
In this article reliable confidence intervals are calculated based on the prediction profile likelihood. Such prediction confidence intervals of the dynamic states can be utilized for a data-based observability analysis. The method is also applicable if there are non-identifiable parameters yielding to some insufficiently specified modelpredictions that can be interpreted as non-observability. Moreover, a validation profile likelihood is introduced that should be applied when noisy validation experiments are to be interpreted.

Conclusions
The presented methodology allows the propagation of uncertainty from experimental to model pre-dictions. Although presented in the context of ordinary differential equations, the concept is general and also applicable to other types of models. Matlab code which can be used as a template to implement the method is provided at http://www.fdmold.uni-freiburg.de/~ckreutz/PPL .},
	Author = {Kreutz, C and Raue, A and Timmer, J},
	Date-Added = {2018-04-05 09:03:33 +0000},
	Date-Modified = {2018-04-05 12:01:09 +0000},
	Journal = {BMC Systems Biology},
	Pages = {120},
	Title = {Likelihood based observability analysis and confidence intervals for predictions of dynamic models},
	Volume = {6},
	Year = {2012},
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@article{Schelker:2012uq,
	Abstract = {Motivation: Cellular information processing can be described mathematically using differential equations. Often, external stimulation of cells by compounds such as drugs or hormones leading to activation has to be considered. Mathematically, the stimulus is represented by a time-dependent input function.
Parameters such as rate constants of the molecular interactions are often unknown and need to be estimated from experimental data, e.g. by maximum likelihood estimation. For this purpose, the input function has to be defined for all times of the integration interval. This is usually achieved by approximating the input by interpolation or smoothing of the measured data. This procedure is suboptimal since the input uncertainties are not considered in the estimation process which often leads to overoptimistic confidence intervals of the inferred parameters and the model dynamics.
Results: This article presents a new approach which includes the input estimation into the estimation process of the dynamical model parameters by minimizing an objective function containing all parameters simultaneously. We applied this comprehensive approach to an illustrative model with simulated data and compared it to alternative methods. Statistical analyses revealed that our method improves the prediction of the model dynamics and the confidence intervals leading to a proper coverage of the confidence intervals of the dynamic parameters. The method was applied to the JAK-STAT signaling pathway.},
	Author = {Schelker, M and Raue, A and Timmer, J and Kreutz, C},
	Date-Added = {2018-04-05 09:03:23 +0000},
	Date-Modified = {2018-04-05 12:04:54 +0000},
	Journal = {Bioinformatics},
	Number = {18},
	Pages = {i522-i528},
	Title = {Comprehensive estimation of input signals and dynamical parameters in biochemical reaction networks},
	Volume = {28},
	Year = {2012},
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@article{Kreutz:2013uq,
	Abstract = {Inferring knowledge about biological processes by a mathematical description is a major characteristic of Systems Biology. To understand and predict system's behavior the available experimental information is translated into a mathematical model. Since the availability of experimental data is often limited and measurements contain noise, it is essential to appropriately translate experimental uncertainty to model parameters as well as to model predictions. This is especially important in Systems Biology because typically large and complex models are applied and therefore the limited experimental knowledge might yield weakly specified model components.
Likelihood profiles have been recently suggested and applied in the Systems Biology for as- sessing parameter and prediction uncertainty. In this article, the profile likelihood concept is reviewed and the potential of the approach is demonstrated for a model of the erythropoietin (EPO) receptor.},
	Author = {Kreutz, C and Raue, A and Kaschek, D and Timmer, J},
	Date-Added = {2018-04-05 09:03:18 +0000},
	Date-Modified = {2018-04-05 12:01:22 +0000},
	Journal = {FEBS Journal},
	Number = {11},
	Pages = {2564-2571},
	Title = {Profile likelihood in systems biology},
	Volume = {280},
	Year = {2013},
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@article{Raue:2012zt,
	Abstract = {Due to the high complexity of biological data it is difficult to disentangle cellular processes relying only on intuitive interpretation of measurements. A Systems Biology approach that combines quantitative experimental data with dynamic mathematical modeling promises to yield deeper insights into these processes. Nevertheless, with growing complexity and increasing amount of quantitative experimental data, building realistic and reliable mathematical models can become a challenging task: the quality of experimental data has to be assessed objectively, unknown model parameters need to be estimated from the experimental data, and numerical calculations need to be precise and efficient.

Here, we discuss, compare and characterize the performance of computational methods throughout the process of quantitative dynamic modeling using two previously established examples, for which quantitative, dose- and time-resolved experimental data are available. In particular, we present an approach that allows to determine the quality of experimental data in an efficient, objective and automated manner. Using this approach data generated by different measurement techniques and even in single replicates can be reliably used for mathematical modeling. For the estimation of unknown model parameters, the performance of different optimization algorithms was compared systematically. Our results show that deterministic derivative-based optimization employing the sensitivity equations in combination with a multi-start strategy based on latin hypercube sampling outperforms the other methods by orders of magnitude in accuracy and speed. Finally, we investigated transformations that yield a more efficient parameterization of the model and therefore lead to a further enhancement in optimization performance. We provide a freely available open source software package that implements the algorithms and examples compared here.},
	Author = {Raue, A and Schilling, M and Bachmann, J and Matteson, A and Schelker, M and Kaschek, D and Hug, S and Kreutz, C and Harms, BD and Theis, F and Klingm{\"u}ller, U and Timmer, J},
	Date-Added = {2018-04-05 09:03:15 +0000},
	Date-Modified = {2018-04-05 12:03:26 +0000},
	Journal = {PLoS ONE},
	Number = {9},
	Pages = {e74335},
	Title = {Lessons learned from quantitative dynamical modeling in systems biology},
	Volume = {8},
	Year = {2013},
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@article{Raue:2013fk,
	Abstract = {Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take advantage of both Bayesian and frequentist methods. The elegance of Bayesian methodology is founded in the propagation of information content provided by experimental data and prior assumptions to the posterior probability distribution of model predictions. However, for complex applications experimental data and prior assumptions potentially constrain the posterior probability distribution insufficiently. In these situations Bayesian Markov chain Monte Carlo sampling can be infeasible. From a frequentist point of view insufficient experimental data and prior assumptions can be interpreted as non-identifiability. The profile likelihood approach offers to detect and to resolve non-identifiability by experimental design iteratively. Therefore, it allows one to better constrain the posterior probability distribution until Markov chain Monte Carlo sampling can be used securely. Using an application from cell biology we compare both methods and show that a successive application of both methods facilitates a realistic assessment of uncertainty in model predictions.},
	Author = {Raue, A. and Kreutz, C. and Theis, F. and Timmer, J.},
	Date-Added = {2018-04-05 09:03:13 +0000},
	Date-Modified = {2018-04-05 12:04:36 +0000},
	Journal = {Philosophical Transactions of the Royal Society A},
	Pages = {20110544},
	Title = {{Joining forces of Bayesian and frequentist methodology: A study for inference in the presence of non-identifiability}},
	Volume = {371},
	Year = {2013},
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	Bdsk-Url-1 = {http://arxiv.org/abs/1202.4605}}

@article{Raue:2014mz,
	Abstract = {Motivation: Modeling of dynamical systems using ordinary differential equations is a popular approach in the field of Systems Biology. The amount of experimental data that are used to build and calibrate these models is often limited. In this setting, the model parameters may not be uniquely determinable. Structural or a priori identifiability is a prop- erty of the system equations that indicates whether, in principle, the unknown model parameters can be determined from the available data.
Results: We performed a case study using three current approaches for structural identifiability analysis for an application from cell biology. The approaches are conceptually different and are developed inde- pendently. The results of the three approaches are in agreement. We discuss strength and weaknesses of each of them and illustrate how they can be applied to real world problems.},
	Author = {Raue, A and Karlsson, J and Saccomani, MP and Jirstrand, M and Timmer, J},
	Date-Added = {2018-04-05 09:01:49 +0000},
	Date-Modified = {2018-04-05 12:04:42 +0000},
	Journal = {Bioinformatics},
	Number = {10},
	Pages = {1440-1448},
	Title = {Comparison of approaches for parameter identifiability analysis of biological systems},
	Volume = {30},
	Year = {2014},
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@article{Toensing:2014,
	Author = {Toensing, C and Timmer, J and Kreutz, C},
	Date-Added = {2018-04-05 09:01:45 +0000},
	Date-Modified = {2018-04-05 12:05:27 +0000},
	Journal = {Physical Review E},
	Pages = {023303},
	Title = {Cause and cure of sloppiness in ordinary differential equation models},
	Volume = {90},
	Year = {2014}}

@incollection{kreutz2015statistics,
	Author = {Kreutz, Clemens and Raue, Andreas and Timmer, Jens},
	Booktitle = {Multiple Shooting and Time Domain Decomposition Methods},
	Date-Added = {2018-04-05 09:01:34 +0000},
	Date-Modified = {2018-04-05 12:01:45 +0000},
	Pages = {355--375},
	Publisher = {Springer},
	Title = {Statistics for model calibration},
	Year = {2015}}

@article{hass2015fast,
	Author = {Hass, Helge and Kreutz, Clemens and Timmer, Jens and Kaschek, Daniel},
	Date-Added = {2018-04-05 09:01:22 +0000},
	Date-Modified = {2018-04-05 09:01:22 +0000},
	Journal = {Bioinformatics},
	Number = {8},
	Pages = {1204--1210},
	Publisher = {Oxford University Press},
	Title = {Fast integration-based prediction bands for ordinary differential equation models},
	Volume = {32},
	Year = {2015}}

@article{steiert20161,
	Author = {Steiert, Bernhard and Timmer, Jens and Kreutz, Clemens},
	Date-Added = {2018-04-05 09:01:15 +0000},
	Date-Modified = {2018-04-05 12:05:03 +0000},
	Journal = {Bioinformatics},
	Number = {17},
	Pages = {i718--i726},
	Publisher = {Oxford University Press},
	Title = {L1 regularization facilitates detection of cell type-specific parameters in dynamical systems},
	Volume = {32},
	Year = {2016}}

@article{maiwald2016driving,
	Author = {Maiwald, Tim and Hass, Helge and Steiert, Bernhard and Vanlier, Joep and Engesser, Raphael and Raue, Andreas and Kipkeew, Friederike and Bock, Hans H and Kaschek, Daniel and Kreutz, Clemens and others},
	Date-Added = {2018-04-05 09:01:09 +0000},
	Date-Modified = {2018-04-05 12:01:59 +0000},
	Journal = {PloS ONE},
	Number = {9},
	Pages = {e0162366},
	Publisher = {Public Library of Science},
	Title = {{Driving the model to its limit: Profile likelihood based model reduction}},
	Volume = {11},
	Year = {2016}}

@article{kreutz2018easy,
	Author = {Kreutz, Clemens},
	Date-Added = {2018-04-05 09:00:57 +0000},
	Date-Modified = {2018-04-05 09:00:57 +0000},
	Journal = {Bioinformatics},
	Pages = {9},
	Publisher = {Oxford University Press},
	Title = {An easy and efficient approach for testing identifiability},
	Volume = {1},
	Year = {2018}}

@article{kazeroonian2016cerena,
	Author = {Kazeroonian, Atefeh and Fr{\"o}hlich, Fabian and Raue, Andreas and Theis, Fabian J and Hasenauer, Jan},
	Date-Added = {2018-04-05 09:00:51 +0000},
	Date-Modified = {2018-04-05 12:01:00 +0000},
	Journal = {PloS ONE},
	Number = {1},
	Pages = {e0146732},
	Publisher = {Public Library of Science},
	Title = {{CERENA: ChEmical REaction Network Analyzer---a toolbox for the simulation and analysis of stochastic chemical kinetics}},
	Volume = {11},
	Year = {2016}}