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 - 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 - Zhang, Wei A1 - Schütte, Christof T1 - Reliable approximation of long relaxation timescales in molecular dynamics N2 - Many interesting rare events in molecular systems like ligand association, protein folding or con- formational changes happen on timescales that often are not accessible by direct numerical simulation. Therefore rare event approximation approaches like interface sampling, Markov state model building or advanced reaction coordinate based free energy estimation have attracted huge attention recently. In this article we analyze the reliability of such approaches: How precise is an estimate of long relaxation timescales of molecular systems resulting from various forms of rare event approximation methods? Our results give a theoretical answer to this question by relating it with the transfer operator approach to molecular dynamics. By doing so they also allow for understanding deep connections between the different approaches. T3 - ZIB-Report - 17-19 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63718 SN - 1438-0064 ER - TY - JOUR A1 - Koltai, Peter A1 - Ciccotti, Giovanni A1 - Schütte, Christof T1 - On Markov state models for non-equilibrium molecular dynamics JF - The Journal of Chemical Physics Y1 - 2016 U6 - https://doi.org/10.1063/1.4966157 N1 - 2016 Editor's Choice of The Journal of Chemical Physics VL - 145 IS - 174103 ER - TY - JOUR A1 - Klus, Stefan A1 - Nüske, Feliks A1 - Koltai, Peter A1 - Wu, Hao A1 - Kevrekidis, Ioannis A1 - Schütte, Christof A1 - Noé, Frank T1 - Data-driven model reduction and transfer operator approximation JF - Journal of Nonlinear Science Y1 - 2018 UR - https://link.springer.com/article/10.1007/s00332-017-9437-7 U6 - https://doi.org/10.1007/s00332-017-9437-7 VL - 28 IS - 3 SP - 985 EP - 1010 ER - TY - GEN A1 - Gupta, Pooja A1 - Gramatke, Annika A1 - Einspanier, Ralf A1 - Schütte, Christof A1 - von Kleist, Max A1 - Sharbati, Jutta T1 - In silicio cytotoxicity assessment on cultured rat intestinal cells deduced from cellular impedance measurements 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 IC_{50} 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. IC_{50} 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. T3 - ZIB-Report - 17-08 KW - Real-time cell analyzer KW - Toxicity KW - Mathematical modeling KW - IC_{50} Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62666 SN - 1438-0064 ER - TY - JOUR A1 - Huttary, Rudolf A1 - Goubergrits, Leonid A1 - Schütte, Christof A1 - Bernhard, Stefan T1 - Simulation, Identification and Statistical Variation in Cardiovascular Analysis (SISCA) - a Software Framework for Multi-compartment Lumped Modeling JF - Computers in Biology and Medicine Y1 - 2017 U6 - https://doi.org/10.1016/j.compbiomed.2017.05.021 VL - 87 SP - 104 EP - 123 ER - TY - JOUR A1 - von Kleist, Max A1 - Schütte, Christof A1 - Zhang, Wei T1 - Statistical analysis of the first passage path ensemble of jump processes JF - Journal of Statistical Physics N2 - The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study the first passage path ensemble of both discrete-time and continuous-time jump processes on a finite state space. The main approach is to divide each first passage path into nonreactive and reactive segments and to study them separately. The analysis can be applied to jump processes which are non-ergodic, as well as continuous-time jump processes where the waiting time distributions are non-exponential. In the particular case that the jump processes are both Markovian and ergodic, our analysis elucidates the relations between the study of the first passage paths and the study of the transition paths in transition path theory. We provide algorithms to numerically compute statistics of the first passage path ensemble. The computational complexity of these algorithms scales with the complexity of solving a linear system, for which efficient methods are available. Several examples demonstrate the wide applicability of the derived results across research areas. Y1 - 2018 U6 - https://doi.org/10.1007/s10955-017-1949-x VL - 170 SP - 809 EP - 843 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 - 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 - 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 - 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 - 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 - 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 - Gelß, Patrick A1 - Matera, Sebastian A1 - Schütte, Christof T1 - Solving the master equation without kinetic Monte Carlo: Tensor train approximations for a CO oxidation model JF - Journal of Computational Physics N2 - In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO2(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased Y1 - 2016 U6 - https://doi.org/10.1016/j.jcp.2016.03.025 VL - 314 SP - 489 EP - 502 ER - TY - JOUR A1 - Klus, Stefan A1 - Koltai, Peter A1 - Schütte, Christof T1 - On the numerical approximation of the Perron-Frobenius and Koopman operator JF - Journal of Computational Dynamics N2 - Information about the behavior of dynamical systems can often be obtained by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with a dynamical system. Examples of such operators are the Perron-Frobenius and the Koopman operator. In this paper, we will review di� fferent methods that have been developed over the last decades to compute � infinite-dimensional approximations of these in� finite-dimensional operators - in particular Ulam's method and Extended Dynamic Mode Decomposition (EDMD) - and highlight the similarities and di� fferences between these approaches. The results will be illustrated using simple stochastic di� fferential equations and molecular dynamics examples. Y1 - 2016 U6 - https://doi.org/10.3934/jcd.2016003 VL - 3 IS - 1 SP - 51 EP - 77 ER - TY - JOUR A1 - Hartmann, Carsten A1 - Schütte, Christof A1 - Zhang, Wei T1 - Model reduction algorithms for optimal control and importance sampling of diffusions JF - Nonlinearity N2 - We propose numerical algorithms for solving optimal control and importance sampling problems based on simplified models. The algorithms combine model reduction techniques for multiscale diffusions and stochastic optimization tools, with the aim of reducing the original, possibly high-dimensional problem to a lower dimensional representation of the dynamics, in which only a few relevant degrees of freedom are controlled or biased. Specifically, we study situations in which either a reaction coordinate onto which the dynamics can be projected is known, or situations in which the dynamics shows strongly localized behavior in the small noise regime. No explicit assumptions about small parameters or scale separation have to be made. We illustrate the approach with simple, but paradigmatic numerical examples. Y1 - 2016 U6 - https://doi.org/10.1088/0951-7715/29/8/2298 VL - 29 IS - 8 SP - 2298 EP - 2326 ER - TY - JOUR A1 - Klus, Stefan A1 - Schütte, Christof T1 - Towards tensor-based methods for the numerical approximation of the Perron-Frobenius and Koopman operator JF - Journal of Computational Dynamics N2 - The global behavior of dynamical systems can be studied by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with the system. Two important operators which are frequently used to gain insight into the system's behavior are the Perron-Frobenius operator and the Koopman operator. Due to the curse of dimensionality, computing the eigenfunctions of high-dimensional systems is in general infeasible. We will propose a tensor-based reformulation of two numerical methods for computing finite-dimensional approximations of the aforementioned infinite-dimensional operators, namely Ulam's method and Extended Dynamic Mode Decomposition (EDMD). The aim of the tensor formulation is to approximate the eigenfunctions by low-rank tensors, potentially resulting in a significant reduction of the time and memory required to solve the resulting eigenvalue problems, provided that such a low-rank tensor decomposition exists. Typically, not all variables of a high-dimensional dynamical system contribute equally to the system's behavior, often the dynamics can be decomposed into slow and fast processes, which is also reflected in the eigenfunctions. Thus, the weak coupling between different variables might be approximated by low-rank tensor cores. We will illustrate the efficiency of the tensor-based formulation of Ulam's method and EDMD using simple stochastic differential equations. Y1 - 2016 U6 - https://doi.org/10.3934/jcd.2016007 VL - 3 IS - 2 SP - 139 EP - 161 ER - TY - GEN A1 - Weber, Marcus A1 - Fackeldey, Konstantin A1 - Schütte, Christof T1 - Set-free Markov State Building N2 - Molecular dynamics (MD) simulations face challenging problems since the timescales of interest often are much longer than what is possible to simulate and even if sufficiently long simulation are possible the complex nature of the resulting simulation data makes interpretation difficult. Markov State Models (MSMs) help to overcome these problems by making experimentally relevant timescales accessible via coarse grained representations that also allows for convenient interpretation. However, standard set-based MSMs exhibit some caveats limiting their approximation quality and statistical significance. One of the main caveats results from the fact that typical MD trajectories repeatedly re-cross the boundary between the sets used to build the MSM which causes statistical bias in estimating the transition probabilities between these sets. In this article, we present a set-free approach to MSM building utilizing smooth overlapping ansatz functions instead of sets and an adaptive refinement approach. This kind of meshless discretization helps to overcome the recrossing problem and yields an adaptive refinement procedure that allows to improve the quality of the model while exploring state space and inserting new ansatz functions into the MSM. T3 - ZIB-Report - 17-10 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62167 SN - 1438-0064 ER -