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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 = {2014-01-24 15:16:37 +0000},
	Date-Modified = {2014-01-24 15:16:37 +0000},
	Journal = {PLOS ONE},
	Number = {9},
	Pages = {e74335},
	Pdf = {Raue/Lessons Learned from Quantitative Dynamical.pdf},
	Title = {Lessons Learned from Quantitative Dynamical Modeling in Systems Biology},
	Url = {http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0074335},
	Volume = {8},
	Year = {2013},
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@article{Raue:2009ec,
	Abstract = {Motivation: Mathematical description of biological reaction networks by differential equations leads to large models whose parameters are calibrated in order to optimally explain experimental data. Often only parts of the model can be observed directly. Given a model that sufficiently describes the measured data, it is important to infer how well model parameters are determined by the amount and quality of experimental data. This knowledge is essential for further investigation of model predictions. For this reason a major topic in modeling is identifiability analysis.

Results: We suggest an approach that exploits the profile likelihood. It enables to detect structural non-identifiabilities, which manifest in functionally related model parameters. Furthermore, practical non-identifiabilities are detected, that might arise due to limited amount and quality of experimental data. Last but not least confidence intervals can be derived. The results are easy to interpret and can be used for experimental planning and for model reduction.},
	Author = {Raue, A and Kreutz, C and Maiwald, T and Bachmann, J and Schilling, M and Klingm{\"u}ller, U and Timmer, J},
	Date-Added = {2014-01-24 15:11:14 +0000},
	Date-Modified = {2014-01-24 15:11:14 +0000},
	Journal = {Bioinformatics},
	Number = {15},
	Pages = {1923--1929},
	Pdf = {Raue/Structural and practical identifiability analysis of partially0.pdf},
	Pdfsupplement = {Raue/Structural and practical identifiability analysis of partially1.pdf},
	Title = {Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood},
	Url = {http://bioinformatics.oxfordjournals.org/cgi/content/abstract/btp358v1},
	Volume = {25},
	Year = {2009},
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@article{Hindmarsh:2005fb,
	Abstract = {SUNDIALS is a suite of advanced computational codes for solving large-scale problems that can be modeled as a system of nonlinear algebraic equations, or as initial-value problems in ordinary differential or differential-algebraic equations. The basic versions of these codes are called KINSOL, CVODE, and IDA, respectively. The codes are written in ANSI standard C and are suitable for either serial or parallel machine environments. Common and notable features of these codes include inexact Newton-Krylov methods for solving large-scale nonlinear systems; linear multistep methods for time-dependent problems; a highly modular structure to allow incorporation of different preconditioning and/or linear solver methods; and clear interfaces allowing for users to provide their own data structures underneath the solvers. We describe the current capabilities of the codes, along with some of the algorithms and heuristics used to achieve efficiency and robustness. We also describe how the codes stem from previous and widely used Fortran 77 solvers, and how the codes have been augmented with forward and adjoint methods for carrying out first-order sensitivity analysis with respect to model parameters or initial conditions.},
	Author = {Hindmarsh, AC and Brown, PN and Grant, KE and Lee, SL and Serban, R and Shumaker, DE and Woodward, CS},
	Date-Added = {2014-01-24 15:10:58 +0000},
	Date-Modified = {2014-01-24 15:10:58 +0000},
	Journal = {ACM T Math Software},
	Number = {3},
	Pages = {363--396},
	Title = {{SUNDIALS}: Suite of nonlinear and differential/algebraic equation solvers},
	Volume = {31},
	Year = {2005}}