TY - JOUR A1 - Enciso, Marta A1 - Schütte, Christof A1 - Delle Site, Luigi T1 - A pH-dependent coarse-grained model for peptides JF - Soft Matter N2 - We propose the first, to our knowledge, coarse-grained modeling strategy for peptides where the effect of changes of the pH can be efficiently described. The idea is based on modeling the effects of the pH value on the main driving interactions. We use reference data from atomistic simulations and experimental databases and transfer their main physical features to the coarse-grained resolution according to the principle of “consistency across the scales”. The coarse-grained model is refined by finding a set of parameters that, when applied to peptides with different sequences and experimental properties, reproduces the experimental and atomistic data of reference. We use such a parameterized model for performing several numerical tests to check its transferability to other systems and to prove the universality of the related modeling strategy. We have tried systems with rather different responses to pH variations, showing a highly satisfactory performance of the model. Y1 - 2013 U6 - https://doi.org/10.1039/C3SM27893J VL - 9 IS - 26 SP - 6118 EP - 6127 ER - TY - JOUR A1 - Winkelmann, Stefanie A1 - Schütte, Christof A1 - von Kleist, Max T1 - Markov Control Processes with Rare State Observation: Sensitivity Analysis with Respect to Optimal Treatment Strategies against HIV-1 JF - International Journal of Biomathematics and Biostatistics N2 - We present the theory of “Markov decision processes (MDP) with rare state observation” and apply it to optimal treatment scheduling and diagnostic testing to mitigate HIV-1 drug resistance development in resource-poor countries. The developed theory assumes that the state of the process is hidden and can only be determined by making an examination. Each examination produces costs which enter into the considered cost functional so that the resulting optimization problem includes finding optimal examination times. This is a realistic ansatz: In many real world applications, like HIV-1 treatment scheduling, the information about the disease evolution involves substantial costs, such that examination and control are intimately connected. However, a perfect compliance with the optimal strategy can rarely be achieved. This may be particularly true for HIV-1 resistance testing in resource-constrained countries. In the present work, we therefore analyze the sensitivity of the costs with respect to deviations from the optimal examination times both analytically and for the considered application. We discover continuity in the cost-functional with respect to the examination times. For the HIV-application, moreover, sensitivity towards small deviations from the optimal examination rule depends on the disease state. Furthermore, we compare the optimal rare-control strategy to (i) constant control strategies (one action for the remaining time) and to (ii) the permanent control of the original, fully observed MDP. This comparison is done in terms of expected costs and in terms of life-prolongation. The proposed rare-control strategy offers a clear benefit over a constant control, stressing the usefulness of medical testing and informed decision making. This indicates that lower-priced medical tests could improve HIV treatment in resource-constrained settings and warrants further investigation. Y1 - 2013 VL - 2 IS - 1 ER - TY - JOUR A1 - Schütte, Christof A1 - Nielsen, Adam A1 - Weber, Marcus T1 - Markov State Models and Molecular Alchemy JF - Molecular Physics N2 - In recent years Markov State Models (MSMs) have attracted a consid- erable amount of attention with regard to modelling conformation changes and associated function of biomolecular systems. They have been used successfully, e.g., for peptides including time-resolved spectroscopic experiments, protein function and protein folding , DNA and RNA, and ligand-receptor interaction in drug design and more complicated multivalent scenarios. In this article a novel reweighting scheme is introduced that allows to construct an MSM for certain molecular system out of an MSM for a similar system. This permits studying how molecular properties on long timescales differ between similar molecular systems without performing full molecular dynamics simulations for each system under con- sideration. The performance of the reweighting scheme is illustrated for simple test cases including one where the main wells of the respective energy landscapes are located differently and an alchemical transformation of butane to pentane where the dimension of the state space is changed. KW - MSM KW - Reweighting KW - Girsanov Y1 - 2015 U6 - https://doi.org/10.1080/00268976.2014.944597 VL - 113 IS - 1 SP - 69 EP - 78 ER - TY - JOUR A1 - Agarwal, Animesh A1 - Wang, Han A1 - Schütte, Christof A1 - Delle Site, Luigi T1 - Chemical potential of liquids and mixtures via Adaptive Resolution Simulation JF - The Journal of Chemical Physics Y1 - 2014 U6 - https://doi.org/10.1063/1.4886807 VL - 141 SP - 034102 ER - TY - GEN A1 - Wang, Han A1 - Schütte, Christof T1 - Building Markov State Models for Periodically Driven Non-Equilibrium Systems N2 - Recent years have seen an increased interest in non-equilibrium molecular dynamics (NEMD) simulations, especially for molecular systems with periodic forcing by external fields, e.g., in the context of studying effects of electromagnetic radiation on the human body tissue. Lately, an NEMD methods with local thermostating has been proposed that allows for studying non-equilibrium processes in a statistically reliable and thermodynamically consistent way. In this article, we demonstrate how to construct Markov State Models (MSMs) for such NEMD simulations. MSM building has been well-established for systems in equilibrium where MSMs with just a few (macro-)states allow for accurate reproduction of the essential kinetics of the molecular system under consideration. Non-equilibrium MSMs have been lacking so far. The article presents how to construct such MSMs and illustrates their validity and usefulness for the case of conformation dynamics of alanine dipeptide in an external electric field. T3 - ZIB-Report - 14-46 KW - Non-equilibrium KW - Markov states model KW - Alanine dipeptide KW - Electric field KW - Floquet theory Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-53167 SN - 1438-0064 N1 - To appear in: Journal of Chemical Theory and Computation ER - TY - GEN A1 - Gul, Raheem A1 - Schütte, Christof A1 - Bernhard, Stefan T1 - Mathematical modeling and sensitivity analysis of arterial anastomosis in arm arteries N2 - Cardiovascular diseases are one of the major problems in medicine today and the number of patients increases worldwide. To find the most efficient treatment, prior knowledge about function and dysfunction of the cardiovas- cular system is required and methods need to be developed that identify the disease in an early stage. Mathematical modeling is a powerful tool for prediction and investigation of cardiovascular diseases. It has been shown that the Windkessel model, being based on an analogy between electrical circuits and fluid flow, is a simple but effective method to model the human cardiovascular system. In this paper, we have applied parametric local sensitivity analysis (LSA) to a linear elastic model of the arm arteries, to find and rank sensitive param- eters that may be helpful in clinical diagnosis. A computational model for end-to-side anastomosis (superior ulnar collateral anastomosis with posterior ulnar recurrent, SUC-PUR) is carried out to study the effects of some clinically relevant haemodynamic parameters like blood flow resistance and terminal re- sistance on pressure and flow at different locations of the arm artery. In this context, we also discuss the spatio-temporal dependency of local sensitivities. The sensitivities with respect to cardiovascular parameters reveal the flow resistance and diameter of the vessels as most sensitive parameters. These parameters play a key role in diagnosis of severe stenosis and aneurysms. In contrast, wall thickness and elastic modulus are found to be less sensitive. T3 - ZIB-Report - 15-22 KW - computational cardiovascular model KW - cardiovascular parameters KW - sensitivity analysis KW - anastomosis KW - Windkessel model Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-54339 SN - 1438-0064 ER - TY - BOOK ED - Ciccotti, Giovanni ED - Ferrario, Mauro ED - Schütte, Christof T1 - Molecular Dynamics Simulation T3 - Entropy (special issue) Y1 - 2014 PB - Multidisciplinary Digital Publishing Institute (MDPI) 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 -