TY - JOUR A1 - Vega, Iliusi A1 - Schütte, Christof A1 - Conrad, Tim T1 - Finding metastable states in real-world time series with recurrence networks JF - Physica A: Statistical Mechanics and its Applications N2 - In the framework of time series analysis with recurrence networks, we introduce a self-adaptive method that determines the elusive recurrence threshold and identifies metastable states in complex real-world time series. As initial step, we introduce a way to set the embedding parameters used to reconstruct the state space from the time series. We set them as the ones giving the maximum Shannon entropy of the diagonal line length distribution for the first simultaneous minima of recurrence rate and Shannon entropy. To identify metastable states, as well as the transitions between them, we use a soft partitioning algorithm for module finding which is specifically developed for the case in which a system shows metastability. We illustrate our method with a complex time series example. Finally, we show the robustness of our method for identifying metastable states. Our results suggest that our method is robust for identifying metastable states in complex time series, even when introducing considerable levels of noise and missing data points. Y1 - 2016 U6 - https://doi.org/10.1016/j.physa.2015.10.041 VL - 445 SP - 1 EP - 17 ER - TY - JOUR A1 - Conrad, Tim A1 - Genzel, Martin A1 - Cvetkovic, Nada A1 - Wulkow, Niklas A1 - Leichtle, Alexander Benedikt A1 - Vybiral, Jan A1 - Kytyniok, Gitta A1 - Schütte, Christof T1 - Sparse Proteomics Analysis – a compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data JF - BMC Bioinfomatics N2 - Background: High-throughput proteomics techniques, such as mass spectrometry (MS)-based approaches, produce very high-dimensional data-sets. In a clinical setting one is often interested in how mass spectra differ between patients of different classes, for example spectra from healthy patients vs. spectra from patients having a particular disease. Machine learning algorithms are needed to (a) identify these discriminating features and (b) classify unknown spectra based on this feature set. Since the acquired data is usually noisy, the algorithms should be robust against noise and outliers, while the identified feature set should be as small as possible. Results: We present a new algorithm, Sparse Proteomics Analysis (SPA),based on thet heory of compressed sensing that allows us to identify a minimal discriminating set of features from mass spectrometry data-sets. We show (1) how our method performs on artificial and real-world data-sets, (2) that its performance is competitive with standard (and widely used) algorithms for analyzing proteomics data, and (3) that it is robust against random and systematic noise. We further demonstrate the applicability of our algorithm to two previously published clinical data-sets. Y1 - 2017 U6 - https://doi.org/10.1186/s12859-017-1565-4 VL - 18 IS - 160 ER - TY - JOUR A1 - Rüdrich, S. A1 - Sarich, Marco A1 - Schütte, Christof T1 - Utilizing hitting times for finding metastable sets in non-reversible Markov chains JF - Journal of Comp. Dynamics Y1 - 2017 ER - TY - JOUR A1 - Gupta, Pooja A1 - Gramatke, Annika A1 - Einspanier, Ralf A1 - Schütte, Christof A1 - von Kleist, Max A1 - Sharbati, Jutta T1 - In silico cytotoxicity assessment on cultured rat intestinal cells deduced from cellular impedance measurements JF - Toxicology in Vitro N2 - Early and reliable identification of chemical toxicity is of utmost importance. At the same time, reduction of animal testing is paramount. Therefore, methods that improve the interpretability and usability of in vitro assays are essential. xCELLigence’s real-time cell analyzer (RTCA) provides a novel, fast and cost effective in vitro method to probe compound toxicity. We developed a simple mathematical framework for the qualitative and quantitative assessment of toxicity for RTCA measurements. Compound toxicity, in terms of its 50% inhibitory concentration IC50 on cell growth, and parameters related to cell turnover were estimated on cultured IEC-6 cells exposed to 10 chemicals at varying concentrations. Our method estimated IC50 values of 113.05, 7.16, 28.69 and 725.15 μM for the apparently toxic compounds 2-acetylamino-fluorene, aflatoxin B1, benzo-[a]-pyrene and chloramphenicol in the tested cell line, in agreement with literature knowledge. IC50 values of all apparent in vivo non-toxic compounds were estimated to be non-toxic by our method. Corresponding estimates from RTCA’s in-built model gave false positive (toxicity) predictions in 5/10 cases. Taken together, our proposed method reduces false positive predictions and reliably identifies chemical toxicity based on impedance measurements. The source code for the developed method including instructions is available at https://git.zib.de/bzfgupta/toxfit/tree/master. KW - Real-time cell analyzer KW - Toxicity KW - Mathematical modeling Y1 - 2017 SN - 1438-0064 VL - 41 SP - 179 EP - 188 ER - TY - JOUR A1 - Klus, Stefan A1 - Gelß, Patrick A1 - Peitz, Sebastian A1 - Schütte, Christof T1 - Tensor-based dynamic mode decomposition JF - Nonlinearity Y1 - 2018 U6 - https://doi.org/10.1088/1361-6544/aabc8f VL - 31 IS - 7 PB - IOP Publishing Ltd & London Mathematical Society ER - TY - JOUR A1 - Weber, Marcus A1 - Fackeldey, Konstantin A1 - Schütte, Christof T1 - Set-Free Markov State Model Building JF - Journal of Chemical Physics Y1 - 2017 U6 - https://doi.org/10.1063/1.4978501 VL - 146 IS - 12 ER - TY - GEN A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - Hybrid Models for Chemical Reaction Networks: Multiscale Theory and Application to Gene Regulatory Systems N2 - Well-mixed stochastic chemical kinetics are properly modelled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows to express various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. T3 - ZIB-Report - 17-29 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64264 ER - TY - GEN A1 - Bittracher, Andreas A1 - Koltai, Péter A1 - Klus, Stefan A1 - Banisch, Ralf A1 - Dellnitz, Michael A1 - Schütte, Christof T1 - Transition manifolds of complex metastable systems: Theory and data-driven computation of effective dynamics N2 - We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics. T3 - ZIB-Report - 17-22 KW - metastability KW - slow dynamics KW - effective dynamics KW - transition manifold KW - embedding KW - transfer operator KW - reaction coordinate Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63822 SN - 1438-0064 ER - TY - GEN A1 - Koltai, Péter A1 - Schütte, Christof T1 - A multi scale perturbation expansion approach for Markov state modeling of non-stationary molecular dynamics N2 - We investigate metastable dynamical systems subject to non-stationary forcing as they appear in molecular dynamics for systems driven by external fields. We show, that if the strength of the forcing is inversely proportional to the length of the slow metastable time scales of the unforced system, then the effective behavior of the forced system on slow time scales can be described by a low-dimensional reduced master equation. Our construction is explicit and uses the multiscale perturbation expansion method called two-timing, or method of multiple scales. The reduced master equation—a Markov state model—can be assembled by constructing two equilibrium Markov state models; one for the unforced system, and one for a slightly perturbed one. T3 - ZIB-Report - 17-49 KW - Markov state model KW - non-equilibrium molecular dynamics KW - two timescale master equation KW - non-stationary forcing KW - metastability Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64868 SN - 1438-0064 ER - TY - JOUR A1 - Benn, Andreas A1 - Hiepen, Christian A1 - Osterland, Marc A1 - Schütte, Christof A1 - Zwijsen, An A1 - Knaus, Petra T1 - Role of bone morphogenetic proteins in sprouting angiogenesis: differential BMP receptor-dependent signaling pathways balance stalk vs. tip cell competence JF - FASEB Journal N2 - Before the onset of sprouting angiogenesis, the endothelium is prepatterned for the positioning of tip and stalk cells. Both cell identities are not static, as endothelial cells (ECs) constantly compete for the tip cell position in a dynamic fashion. Here, we show that both bone morphogenetic protein (BMP) 2 and BMP6 are proangiogenic in vitro and ex vivo and that the BMP type I receptors, activin receptor-like kinase (ALK)3 and ALK2, play crucial and distinct roles in this process. BMP2 activates the expression of tip cell–associated genes, such as DLL4 (delta-like ligand 4) and KDR (kinase insert domain receptor), and p38-heat shock protein 27 (HSP27)–dependent cell migration, thereby generating tip cell competence. Whereas BMP6 also triggers collective cell migration via the p38-HSP27 signaling axis, BMP6 induces in addition SMAD1/5 signaling, thereby promoting the expression of stalk cell–associated genes, such as HES1 (hairy and enhancer of split 1) and FLT1 (fms-like tyrosine kinase 1). Specifically, ALK3 is required for sprouting from HUVEC spheroids, whereas ALK2 represses sprout formation. We demonstrate that expression levels and respective complex formation of BMP type I receptors in ECs determine stalk vs. tip cell identity, thus contributing to endothelial plasticity during sprouting angiogenesis. As antiangiogenic monotherapies that target the VEGF or ALK1 pathways have not fulfilled efficacy objectives in clinical trials, the selective targeting of the ALK2/3 pathways may be an attractive new approach. Y1 - 2017 U6 - https://doi.org/10.1096/fj.201700193RR VL - 31 IS - 11 SP - 4720 EP - 4733 ER - TY - JOUR A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems JF - The Journal of Chemical Physics N2 - Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations. Y1 - 2017 U6 - https://doi.org/10.1063/1.4986560 VL - 147 IS - 11 SP - 114115-1 EP - 114115-18 ER - TY - GEN A1 - Vega, Iliusi A1 - Schütte, Christof A1 - Conrad, Tim T1 - SAIMeR: Self-adapted method for the identification of metastable states in real-world time series N2 - In the framework of time series analysis with recurrence networks, we introduce SAIMeR, a heuristic self-adapted method that determines the elusive recurrence threshold and identifies metastable states in complex time series. To identify metastable states as well as the transitions between them, we use graph theory concepts and a fuzzy partitioning clustering algorithm. We illustrate SAIMeR by applying it to three real-world time series and show that it is able to identify metastable states in real-world data with noise and missing data points. Finally, we suggest a way to choose the embedding parameters used to construct the state space in which this method is performed, based on the analysis of how the values of these parameters affect two recurrence quantitative measurements: recurrence rate and entropy. T3 - ZIB-Report - 14-16 KW - time series analysis KW - application in statistical physics KW - recurrence quantification analysis KW - threshold KW - metastability KW - non-linear dynamics Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-50130 SN - 1438-0064 ER - TY - GEN A1 - Bockmayr, Alexander A1 - Siebert, Heike A1 - Röblitz, Susanna A1 - Schütte, Christof A1 - Deuflhard, Peter ED - Deuflhard, Peter ED - Grötschel, Martin ED - Hömberg, Dietmar ED - Kramer, Jürg ED - Mehrmann, Volker ED - Polthier, Konrad ED - Schmidt, Frank ED - Schütte, Christof ED - Skutela, Martin ED - Sprekels, Jürgen T1 - Advanced mathematical modeling in systems biology T2 - MATHEON-Mathematics for Key Technologies Y1 - 2014 VL - 1 SP - 29 EP - 44 PB - European Mathematical Society ER - TY - GEN A1 - Agarwal, Animesh A1 - Wang, Han A1 - Schütte, Christof A1 - Delle Site, Luigi T1 - Chemical potential of liquids and mixtures via Adaptive Resolution Simulation N2 - We employ the adaptive resolution approach AdResS, in its recently developed Grand Canonicallike version (GC-AdResS) [Wang et al. Phys.Rev.X 3, 011018 (2013)], to calculate the excess chemical potential, $μ^{ex}$, of various liquids and mixtures. We compare our results with those obtained from full atomistic simulations using the technique of thermodynamic integration and show a satisfactory agreement. In GC-AdResS the procedure to calculate $μ^{ex}$ corresponds to the process of standard initial equilibration of the system; this implies that, independently of the specific aim of the study, $μ^{ex}$, for each molecular species, is automatically calculated every time a GC-AdResS simulation is performed. T3 - ZIB-Report - 14-25 KW - Coarse graining KW - adaptive resolution KW - molecular dynamics KW - chemical potential Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-50972 SN - 1438-0064 ER -