@article{GelssKlusEisertetal.2019, author = {Gelß, Patrick and Klus, Stefan and Eisert, Jens and Sch{\"u}tte, Christof}, title = {Multidimensional Approximation of Nonlinear Dynamical Systems}, volume = {14}, journal = {Journal of Computational and Nonlinear Dynamics}, number = {6}, doi = {10.1115/1.4043148}, year = {2019}, abstract = {A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system identification, ranging from industrial engineering and acoustic signal processing to stock market models. In order to find appropriate representations of underlying dynamical systems, various data-driven methods have been proposed by different communities. However, if the given data sets are high-dimensional, then these methods typically suffer from the curse of dimensionality. To significantly reduce the computational costs and storage consumption, we propose the method multidimensional approximation of nonlinear dynamical systems (MANDy) which combines data-driven methods with tensor network decompositions. The efficiency of the introduced approach will be illustrated with the aid of several high-dimensional nonlinear dynamical systems.}, language = {en} } @article{KoltaiSchuette2018, author = {Koltai, P{\´e}ter and Sch{\"u}tte, Christof}, title = {A multiscale perturbation expansion approach for Markov state modeling of non-stationary molecular dynamics}, volume = {16}, journal = {SIAM J. Multiscale Model. Simul.}, number = {4}, publisher = {SIAM}, doi = {10.1137/17M1146403}, pages = {1455 -- 1485}, year = {2018}, abstract = {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.}, language = {en} } @article{ShaoBjaanaesHellandetal.2019, author = {Shao, Borong and Bjaanaes, Maria and Helland, Aslaug and Sch{\"u}tte, Christof and Conrad, Tim}, title = {EMT network-based feature selection improves prognosis prediction in lung adenocarcinoma}, volume = {14}, journal = {PLOS ONE}, number = {1}, doi = {10.1371/journal.pone.0204186}, year = {2019}, abstract = {Various feature selection algorithms have been proposed to identify cancer prognostic biomarkers. In recent years, however, their reproducibility is criticized. The performance of feature selection algorithms is shown to be affected by the datasets, underlying networks and evaluation metrics. One of the causes is the curse of dimensionality, which makes it hard to select the features that generalize well on independent data. Even the integration of biological networks does not mitigate this issue because the networks are large and many of their components are not relevant for the phenotype of interest. With the availability of multi-omics data, integrative approaches are being developed to build more robust predictive models. In this scenario, the higher data dimensions create greater challenges. We proposed a phenotype relevant network-based feature selection (PRNFS) framework and demonstrated its advantages in lung cancer prognosis prediction. We constructed cancer prognosis relevant networks based on epithelial mesenchymal transition (EMT) and integrated them with different types of omics data for feature selection. With less than 2.5\% of the total dimensionality, we obtained EMT prognostic signatures that achieved remarkable prediction performance (average AUC values above 0.8), very significant sample stratifications, and meaningful biological interpretations. In addition to finding EMT signatures from different omics data levels, we combined these single-omics signatures into multi-omics signatures, which improved sample stratifications significantly. Both single- and multi-omics EMT signatures were tested on independent multi-omics lung cancer datasets and significant sample stratifications were obtained.}, language = {en} } @article{GuptaPeterJungetal.2019, author = {Gupta, Pooja and Peter, Sarah and Jung, Markus and Lewin, Astrid and Hemmrich-Stanisak, Georg and Franke, Andre and von Kleist, Max and Sch{\"u}tte, Christof and Einspanier, Ralf and Sharbati, Soroush and zur Bruegge, Jennifer}, title = {Analysis of long non-coding RNA and mRNA expression in bovine macrophages brings up novel 2 aspects of Mycobacterium avium subspecies paratuberculosis infections}, volume = {9}, journal = {Scientific Reports in Nature}, doi = {10.1038/s41598-018-38141-x}, year = {2019}, abstract = {Paratuberculosis is a major disease in cattle that severely affects animal welfare and causes huge economic losses worldwide. Development of alternative diagnostic methods is of urgent need to control the disease. Recent studies suggest that long non-coding RNAs (lncRNAs) play a crucial role in regulating immune function and may confer valuable information about the disease. However, their role has not yet been investigated in cattle with respect to infection towards Paratuberculosis. Therefore, we investigated the alteration in genomic expression profiles of mRNA and lncRNA in bovine macrophages in response to Paratuberculosis infection using RNA-Seq. We identified 397 potentially novel lncRNA candidates in macrophages of which 38 were differentially regulated by the infection. A total of 820 coding genes were also significantly altered by the infection. Co-expression analysis of lncRNAs and their neighbouring coding genes suggest regulatory functions of lncRNAs in pathways related to immune response. For example, this included protein coding genes such as TNIP3, TNFAIP3 and NF-κB2 that play a role in NF-κB2 signalling, a pathway associated with immune response. This study advances our understanding of lncRNA roles during Paratuberculosis infection.}, language = {en} } @article{WinkelmannSchuette2016, author = {Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {The Spatiotemporal Master Equation: Approximation of Reaction-Diffusion Dynamics via Markov State Modeling}, volume = {145}, journal = {Journal of Chemical Physics}, number = {21}, doi = {10.1063/1.4971163}, year = {2016}, abstract = {Accurate modeling and numerical simulation of reaction kinetics is a topic of steady interest.We consider the spatiotemporal chemical master equation (ST-CME) as a model for stochastic reaction-diffusion systems that exhibit properties of metastability. The space of motion is decomposed into metastable compartments and diffusive motion is approximated by jumps between these compartments. Treating these jumps as first-order reactions, simulation of the resulting stochastic system is possible by the Gillespie method. We present the theory of Markov state models (MSM) as a theoretical foundation of this intuitive approach. By means of Markov state modeling, both the number and shape of compartments and the transition rates between them can be determined. We consider the ST-CME for two reaction-diffusion systems and compare it to more detailed models. Moreover, a rigorous formal justification of the ST-CME by Galerkin projection methods is presented.}, language = {en} } @article{DuwalWinkelmannSchuetteetal.2015, author = {Duwal, Sulav and Winkelmann, Stefanie and Sch{\"u}tte, Christof and von Kleist, Max}, title = {Optimal Treatment Strategies in the Context of 'Treatment for Prevention' against HIV/1 in Resource-Poor Settings}, volume = {11}, journal = {PloS Computational Biology}, number = {4}, doi = {10.1371/journal.pcbi.1004200}, year = {2015}, abstract = {An estimated 2.7 million new HIV-1 infections occurred in 2010. `Treatment-for-prevention' may strongly prevent HIV-1 transmission. The basic idea is that immediate treatment initiation rapidly decreases virus burden, which reduces the number of transmittable viruses and thereby the probability of infection. However, HIV inevitably develops drug resistance, which leads to virus rebound and nullifies the effect of `treatment-for-prevention' for the time it remains unrecognized. While timely conducted treatment changes may avert periods of viral rebound, necessary treatment options and diagnostics may be lacking in resource-constrained settings. Within this work, we provide a mathematical platform for comparing different treatment paradigms that can be applied to many medical phenomena. We use this platform to optimize two distinct approaches for the treatment of HIV-1: (i) a diagnostic-guided treatment strategy, based on infrequent and patient-specific diagnostic schedules and (ii) a pro-active strategy that allows treatment adaptation prior to diagnostic ascertainment. Both strategies are compared to current clinical protocols (standard of care and the HPTN052 protocol) in terms of patient health, economic means and reduction in HIV-1 onward transmission exemplarily for South Africa. All therapeutic strategies are assessed using a coarse-grained stochastic model of within-host HIV dynamics and pseudo-codes for solving the respective optimal control problems are provided. Our mathematical model suggests that both optimal strategies (i)-(ii) perform better than the current clinical protocols and no treatment in terms of economic means, life prolongation and reduction of HIV-transmission. The optimal diagnostic-guided strategy suggests rare diagnostics and performs similar to the optimal pro-active strategy. Our results suggest that 'treatment-for-prevention' may be further improved using either of the two analyzed treatment paradigms.}, language = {en} } @article{SarichDjurdjevacConradBruckneretal.2014, author = {Sarich, Marco and Djurdjevac Conrad, Natasa and Bruckner, Sharon and Conrad, Tim and Sch{\"u}tte, Christof}, title = {Modularity revisited: A novel dynamics-based concept for decomposing complex networks}, volume = {1}, journal = {Journal of Computational Dynamics}, number = {1}, doi = {10.3934/jcd.2014.1.191}, pages = {191 -- 212}, year = {2014}, language = {en} } @article{DibakJdelRazoDeSanchoetal.2018, author = {Dibak, Manuel and J. del Razo, Mauricio and De Sancho, David and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations}, volume = {148}, journal = {Journal of Chemical Physics}, number = {214107}, doi = {10.1063/1.5020294}, year = {2018}, abstract = {Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long-timescale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large lengthscales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time- and lengthscales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step towards MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B <--> C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported.}, language = {en} } @article{KlusNueskePeitzetal.2020, author = {Klus, Stefan and N{\"u}ske, Feliks and Peitz, Sebastian and Niemann, Jan-Hendrik and Clementi, Cecilia and Sch{\"u}tte, Christof}, title = {Data-driven approximation of the Koopman generator: Model reduction, system identification, and control}, volume = {406}, journal = {Physica D: Nonlinear Phenomena}, doi = {10.1016/j.physd.2020.132416}, year = {2020}, language = {en} } @article{MusiałŻołnaczSrockaetal.2020, author = {Musiał, Anna and Żołnacz, Kinga and Srocka, Nicole and Kravets, Oleh and Große, Jan and Olszewski, Jacek and Poturaj, Krzysztof and Wojcik, Grzegorz and Mergo, Paweł and Kamil, Dybka and Dyrkacz, Mariusz and Dlubek, Michal and Lauritsen, Kristian and B{\"u}lter, Andreas and Schneider, Philipp-Immanuel and Zschiedrich, Lin and Burger, Sven and Rodt, Sven and Urbanczyk, Wacław and Sek, Grzegorz and Reitzenstein, Stephan}, title = {Plug\&play fibre-coupled 73 kHz single-photon source operating in the telecom O-band}, volume = {3}, journal = {Adv. Quantum Technol.}, arxiv = {http://arxiv.org/abs/1912.10351}, doi = {10.1002/qute.202000018}, pages = {2000018}, year = {2020}, language = {en} } @misc{MollenhauerSchusterKlusetal.2020, author = {Mollenhauer, Mattes and Schuster, Ingmar and Klus, Stefan and Sch{\"u}tte, Christof}, title = {Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces}, volume = {304}, journal = {Advances om Dynamics, Optimization and Computation. Series: Studies in Systems, Decision and Control. A volume dedicated to Michael Dellnitz on his 60th birthday}, editor = {Junge, Oliver and Sch{\"u}tze, O. and Froyland, Gary and Ober-Blobaum, S. and Padberg-Gehle, K.}, publisher = {Springer International}, isbn = {978-3-030-51264-4}, doi = {10.1007/978-3-030-51264-4_5}, pages = {109 -- 131}, year = {2020}, language = {en} }