TY - CONF AB - Universal differential equations (UDEs) leverage the respective advantages of mechanistic models and artificial neural networks and combine them into one dynamic model. However, these hybrid models can suffer from unrealistic solutions, such as negative values for biochemical quantities. We present non-negative UDE (nUDEs), a constrained UDE variant that guarantees non-negative values. Furthermore, we explore regularisation techniques to improve generalisation and interpretability of UDEs. AU - Philipps, M.* AU - Körner, A.* AU - Vanhoefer, J.* AU - Pathirana, D.* AU - Hasenauer, J. C1 - 72378 C2 - 56573 CY - Radarweg 29, 1043 Nx Amsterdam, Netherlands SP - 25-30 TI - Non-negative universal differential equations with applications in systems biology. JO - IFAC PapersOnline VL - 58 IS - 23 PB - Elsevier PY - 2024 SN - 2405-8963 ER - TY - JOUR AB - Mathematical models based on ordinary differential equations have been employed with great success to study complex biological systems. With soaring data availability, more and more models of increasing size are being developed. When working with these large-scale models, several challenges arise, such as high computation times or poor identifiability of model parameters. In this work, we review and illustrate the most common challenges using a published model of cellular metabolism. We summarize currently available methods to deal with some of these challenges while focusing on reproducibility and reusability of models, efficient and robust model simulation and parameter estimation. AU - Kapfer, E.M.* AU - Stapor, P. AU - Hasenauer, J. C1 - 58587 C2 - 48528 SP - 58-64 TI - Challenges in the calibration of large-scale ordinary differential equation models. JO - IFAC PapersOnline VL - 52 IS - 26 PY - 2019 SN - 2405-8963 ER - TY - JOUR AB - In systems and computational biology, ordinary differential equations are used for the mechaÂnistic modelling of biochemical networks. These models can easily have hundreds of states and parameters. Typically most parameters are unknown and estimated by fitting model output to observation. During parameter estimation the model needs to be solved repeatedly, sometimes millions of times. This can then be a computational bottleneck, and limits the employment of such models. In many situations the experimental data provides information about the steady state of the biochemical reaction network. In such cases one only needs to obtain the equilibrium state for a given set of model parameters. In this paper we exploit this fact and solve the steady state problem directly rather than integrating the ODE forward in time until steady state is reached. We use Newton's method-like some previous studies- A nd develop several improvements to achieve robust convergence. To address the reliance of Newtons method on good initial guesses, we propose a continuation method. We show that the method works robustly in this setting and achieves a speed up of up to 100 compared to using ODE solves. AU - Lines, G.T.* AU - Paszkowski, L.* AU - Schmiester, L. AU - Weindl, D. AU - Stapor, P. AU - Hasenauer, J. C1 - 58574 C2 - 48526 SP - 32-37 TI - Efficient computation of steady states in large-scale ODE models of biochemical reaction networks. JO - IFAC PapersOnline VL - 52 IS - 26 PY - 2019 SN - 2405-8963 ER - TY - JOUR AB - The parameters of dynamical models of biological processes always possess some degree of uncertainty. This parameter uncertainty translates into an uncertainty of model predictions. The trajectories of unmeasured state variables are examples of such predictions. Quantifying the uncertainty associated with a given prediction is an important problem for model developers and users. However, the nonlinearity and complexity of most dynamical models renders it nontrivial. Here, we evaluate three state-of-the-art approaches for prediction uncertainty quantification using two models of different sizes and computational complexities. We discuss the trade-offs between applicability and statistical interpretability of the different methods, and provide guidelines for their application. AU - Villaverde, A.F.* AU - Raimundez-Alvarez, E. AU - Hasenauer, J. AU - Banga, J.R.* C1 - 58588 C2 - 48529 SP - 45-51 TI - A comparison of methods for quantifying prediction uncertainty in systems biology. JO - IFAC PapersOnline VL - 52 IS - 26 PY - 2019 SN - 2405-8963 ER - TY - JOUR AB - Mixed effect modeling is widely used to study cell-to-cell and patient-to-patient variability. The population statistics of mixed effect models is usually approximated using Dirac mixture distributions obtained using Monte-Carlo, quasi Monte-Carlo, and sigma point methods. Here, we propose the use of a method based on the Cramér-von Mises Distance, which has been introduced in the context of filtering. We assess the accuracy of the different methods using several problems and provide the first scalability study for the Cramér-von Mises Distance method. Our results indicate that for a given number of points, the method based on the modified Cramér-von Mises Distance method tends to achieve a better approximation accuracy than Monte-Carlo and quasi Monte-Carlo methods. In contrast to sigma-point methods, the method based on the modified Cramér-von Mises Distance allows for a flexible number of points and a more accurate approximation for nonlinear problems. AU - Wang, D. AU - Stapor, P. AU - Hasenauer, J. C1 - 58589 C2 - 48530 SP - 200-206 TI - Dirac mixture distributions for the approximation of mixed effects models. JO - IFAC PapersOnline VL - 52 IS - 26 PY - 2019 SN - 2405-8963 ER - TY - JOUR AB - Derivative-free optimization can be used to estimate parameters without computing derivatives. As there exist many methods, it is unclear which to use in practice. Here, we present two comparative studies of 18 state-of-the-art methods: Firstly, we evaluate them on a set of 466 classic optimization test problems of dimension 2 to 300. Secondly, we study their performance in parameter estimation on 8 ODE models of biological processes, comparing them to state-of-the-art derivative-based optimization. We observe that different problem features necessitate the use of different methods, for which we can give suggestions based on our findings. Our analysis suggests that classic test problems are not representative for problems in systems biology. For ODE models, we find that purely derivative-free methods are for most problems not reliable or at least inferior to derivative-based methods. AU - Schälte, Y. AU - Stapor, P. AU - Hasenauer, J. C1 - 54529 C2 - 45629 SP - 98-101 TI - Evaluation of derivative-free optimizers for parameter estimation in systems biology. JO - IFAC PapersOnline VL - 51 IS - 19 PY - 2018 SN - 2405-8963 ER - TY - CONF AB - Gradient formation of Poml is a key regulator of cell cycle and cell growth in fission yeast (Schizosaccharomyces pombe). A variety of models to explain Poml gradient formation have been proposed, a quantitative analysis and comparison of these models is, however, still missing. In this work we present four models from the literature and perform a quantitative comparison using published single-cell images of the gradient formation process. For the comparison of these partial differential equation (PDE) models we use state-of-the-art techniques for parameter estimation together with model selection. The model selection supports the hypothesis that buffering of the gradient is achieved via clustering. The selected model does, however, not ensure mass conservation, which might be considered as problematic. AU - Hross, S. AU - Fiedler, A. AU - Theis, F.J. AU - Hasenauer, J. C1 - 50353 C2 - 42149 SP - 264-269 TI - Quantitative comparison of competing PDE models for Pomlp dynamics in fission yeast. JO - IFAC PapersOnline VL - 49-26 PY - 2016 SN - 2405-8963 ER - TY - JOUR AB - Biological processes exhibiting stochastic fluctuations are mainly modeled using the Chemical Master Equation (CME). As a direct simulation of the CME is often computationally intractable, we recently introduced the Method of Conditional Moments (MCM). The MCM is a hybrid approach to approximate the statistics of the CME solution. In this work, we provide a more comprehensive formulation of the MCM by using non-central conditional moments instead of central conditional moments. The modified formulation allows for additional insight into the model structure and for extensions to higher-order reactions and non-polynomial propensity functions. The properties of the non-central MCM are analyzed using a model for the regulation of pili formation on the surface of bacteria, which possesses rational propensity functions. AU - Kazeroonian, A. AU - Theis, F.J. AU - Hasenauer, J. A2 - Boje, E.* ; Xia, X.* C1 - 45066 C2 - 37220 CY - Laxenburg, Austria SP - 1729-1735 TI - Modeling of stochastic biological processes with non-polynomial propensities using non-central conditional moment equation. JO - IFAC PapersOnline VL - 19 PB - IFAC PY - 2014 SN - 2405-8963 ER -