@misc{AgarwalWangSchuetteetal.2014, author = {Agarwal, Animesh and Wang, Han and Sch{\"u}tte, Christof and Delle Site, Luigi}, title = {Chemical potential of liquids and mixtures via Adaptive Resolution Simulation}, issn = {1438-0064}, doi = {10.1063/1.4886807}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-50972}, year = {2014}, abstract = {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.}, language = {en} } @misc{BanischSchuetteDjurdjevacConrad2014, author = {Banisch, Ralf and Sch{\"u}tte, Christof and Djurdjevac Conrad, Natasa}, title = {Module Detection in Directed Real-World Networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-49849}, year = {2014}, abstract = {We investigate the problem of finding modules (or clusters, communities) in directed networks. Until now, most articles on this topic have been oriented towards finding complete network partitions despite the fact that this often is unwanted. We present a novel random walk based approach for non-complete partitions of the directed network into modules in which some nodes do not belong to only one of the modules but to several or to none at all. The new random walk process is reversible even for directed networks but inherits all necessary information about directions and structure of the original network. We demonstrate the performance of the new method in application to a real-world earthquake network.}, language = {en} } @misc{SchuetteDeuflhardNoeetal.2014, author = {Sch{\"u}tte, Christof and Deuflhard, Peter and No{\´e}, Frank and Weber, Marcus}, title = {Design of functional molecules}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {49 -- 65}, year = {2014}, language = {en} } @misc{DeuflhardSchuette2014, author = {Deuflhard, Peter and Sch{\"u}tte, Christof}, title = {Life Sciences}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {1 -- 5}, year = {2014}, language = {en} } @misc{SchuetteConrad2014, author = {Sch{\"u}tte, Christof and Conrad, Tim}, title = {Showcase 3: Information-based medicine}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {66 -- 67}, year = {2014}, language = {en} } @misc{ZhangWangHartmannetal.2014, author = {Zhang, Wei and Wang, Han and Hartmann, Carsten and Weber, Marcus and Sch{\"u}tte, Christof}, title = {Applications of the cross-entropy method to importance sampling and optimal control of diffusions}, issn = {1438-0064}, doi = {10.1137/14096493X}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-49720}, year = {2014}, abstract = {We study the cross-entropy method for diffusions. One of the results is a versatile cross-entropy algorithm that can be used to design efficient importance sampling strategies for rare events or to solve optimal control problems. The approach is based on the minimization of a suitable cross-entropy functional, with a parametric family of exponentially tilted probability distributions. We illustrate the new algorithm with several numerical examples and discuss algorithmic issues and possible extensions of the method.}, language = {en} } @misc{KlebanovSikorskiSchuetteetal.2016, author = {Klebanov, Ilja and Sikorski, Alexander and Sch{\"u}tte, Christof and R{\"o}blitz, Susanna}, title = {Prior estimation and Bayesian inference from large cohort data sets}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57475}, year = {2016}, abstract = {One of the main goals of mathematical modelling in systems biology related to medical applications is to obtain patient-specific parameterisations and model predictions. In clinical practice, however, the number of available measurements for single patients is usually limited due to time and cost restrictions. This hampers the process of making patient-specific predictions about the outcome of a treatment. On the other hand, data are often available for many patients, in particular if extensive clinical studies have been performed. Using these population data, we propose an iterative algorithm for contructing an informative prior distribution, which then serves as the basis for computing patient-specific posteriors and obtaining individual predictions. We demonsrate the performance of our method by applying it to a low-dimensional parameter estimation problem in a toy model as well as to a high-dimensional ODE model of the human menstrual cycle, which represents a typical example from systems biology modelling.}, language = {en} } @article{KryvenRoeblitzSchuette2015, author = {Kryven, Ivan and R{\"o}blitz, Susanna and Sch{\"u}tte, Christof}, title = {Solution of the chemical master equation by radial basis functions approximation with interface tracking}, volume = {9}, journal = {BMC Systems Biology}, number = {67}, doi = {10.1186/s12918-015-0210-y}, pages = {1 -- 12}, year = {2015}, abstract = {Background. The chemical master equation is the fundamental equation of stochastic chemical kinetics. This differential-difference equation describes temporal evolution of the probability density function for states of a chemical system. A state of the system, usually encoded as a vector, represents the number of entities or copy numbers of interacting species, which are changing according to a list of possible reactions. It is often the case, especially when the state vector is high-dimensional, that the number of possible states the system may occupy is too large to be handled computationally. One way to get around this problem is to consider only those states that are associated with probabilities that are greater than a certain threshold level. Results. We introduce an algorithm that significantly reduces computational resources and is especially powerful when dealing with multi-modal distributions. The algorithm is built according to two key principles. Firstly, when performing time integration, the algorithm keeps track of the subset of states with significant probabilities (essential support). Secondly, the probability distribution that solves the equation is parametrised with a small number of coefficients using collocation on Gaussian radial basis functions. The system of basis functions is chosen in such a way that the solution is approximated only on the essential support instead of the whole state space. Discussion. In order to demonstrate the effectiveness of the method, we consider four application examples: a) the self-regulating gene model, b) the 2-dimensional bistable toggle switch, c) a generalisation of the bistable switch to a 3-dimensional tristable problem, and d) a 3-dimensional cell differentiation model that, depending on parameter values, may operate in bistable or tristable modes. In all multidimensional examples the manifold containing the system states with significant probabilities undergoes drastic transformations over time. This fact makes the examples especially challenging for numerical methods. Conclusions. The proposed method is a new numerical approach permitting to approximately solve a wide range of problems that have been hard to tackle until now. A full representation of multi-dimensional distributions is recovered. The method is especially attractive when dealing with models that yield solutions of a complex structure, for instance, featuring multi-stability. Electronic version: http://www.biomedcentral.com/1752-0509/9/67}, language = {en} } @article{EncisoSchuetteDelleSite2015, author = {Enciso, Marta and Sch{\"u}tte, Christof and Delle Site, Luigi}, title = {Influence of pH and sequence in peptide aggregation via molecular simulation}, volume = {143}, journal = {Journal of Chemical Physics}, number = {24}, doi = {https://doi.org/10.1063/1.4935707}, year = {2015}, language = {en} } @article{SchuetteSarich2015, author = {Sch{\"u}tte, Christof and Sarich, Marco}, title = {A Critical Appraisal of Markov State Models}, volume = {224}, journal = {The European Physical Journal Special Topics}, number = {12}, doi = {10.1140/epjst/e2015-02421-0}, pages = {2445 -- 2462}, year = {2015}, abstract = {Markov State Modelling as a concept for a coarse grained description of the essential kinetics of a molecular system in equilibrium has gained a lot of atten- tion recently. The last 10 years have seen an ever increasing publication activity on how to construct Markov State Models (MSMs) for very different molecular systems ranging from peptides to proteins, from RNA to DNA, and via molecu- lar sensors to molecular aggregation. Simultaneously the accompanying theory behind MSM building and approximation quality has been developed well be- yond the concepts and ideas used in practical applications. This article reviews the main theoretical results, provides links to crucial new developments, outlines the full power of MSM building today, and discusses the essential limitations still to overcome.}, language = {en} } @misc{HartmannBanischSarichetal.2013, author = {Hartmann, Carsten and Banisch, Ralf and Sarich, Marco and Badowski, Thomas and Sch{\"u}tte, Christof}, title = {Characterization of Rare Events in Molecular Dynamics}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42410}, year = {2013}, abstract = {A good deal of molecular dynamics simulations aims at predicting and quantifying rare events, such as the folding of a protein or a phase transition. Simulating rare events is often prohibitive, especially if the equations of motion are high-dimensional, as is the case in molecular dynamics. Various algorithms have been proposed for efficiently computing mean first passage times, transition rates or reaction pathways. This article surveys and discusses recent developments in the field of rare event simulation and outlines a new approach that combines ideas from optimal control and statistical mechanics. The optimal control approach described in detail resembles the use of Jarzynski's equality for free energy calculations, but with an optimized protocol that speeds up the sampling, while (theoretically) giving variance-free estimators of the rare events statistics. We illustrate the new approach with two numerical examples and discuss its relation to existing methods.}, language = {en} } @misc{SarichBanischHartmannetal.2013, author = {Sarich, Marco and Banisch, Ralf and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Markov State Models for Rare Events in Molecular Dynamics}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42420}, year = {2013}, abstract = {Rare but important transition events between long lived states are a key feature of many molecular systems. In many cases the computation of rare event statistics by direct molecular dynamics (MD) simulations is infeasible even on the most powerful computers because of the immensely long simulation timescales needed. Recently a technique for spatial discretization of the molecular state space designed to help overcome such problems, so-called Markov State Models (MSMs), has attracted a lot of attention. We review the theoretical background and algorithmic realization of MSMs and illustrate their use by some numerical examples. Furthermore we introduce a novel approach to using MSMs for the efficient solution of optimal control problems that appear in applications where one desires to optimize molecular properties by means of external controls.}, language = {en} } @misc{SchuetteNielsenWeber2014, author = {Sch{\"u}tte, Christof and Nielsen, Adam and Weber, Marcus}, title = {Markov State Models and Molecular Alchemy}, issn = {1438-0064}, doi = {10.1080/00268976.2014.944597}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-46718}, year = {2014}, abstract = {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 ex- periments, protein function and protein folding , DNA and RNA, and ligand-receptor interaction in drug design and more complicated multi- valent 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 proper- ties 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 en- ergy landscapes are located differently and an alchemical transformation of butane to pentane where the dimension of the state space is changed.}, language = {en} } @misc{OsterlandBennProhaskaetal.2015, author = {Osterland, Marc and Benn, Andreas and Prohaska, Steffen and Sch{\"u}tte, Christof}, title = {Single Cell Tracking in Phase-Contrast Microscopy}, journal = {EMBL Symposium 2015 - Seeing is Believing - Imaging the Processes of Life}, year = {2015}, abstract = {In this work, we developed an automatic algorithm to analyze cell migration in chemotaxis assays, based on phase-contrast time-lapse microscopy. While manual approaches are still widely used in recent publications, our algorithm is able to track hundreds of single cells per frame. The extracted paths are analysed with traditional geometrical approaches as well as diffusion-driven Markov state models (MSM). Based on these models, a detailed view on spatial and temporal effects is possible. Using our new approach on experimental data, we are able to distinguish between directed migration (e.g. towards a VEGF gradient) and random migration without favored direction. A calculation of the committor probabilities reveals that cells of the whole image area are more likely to migrate directly towards the VEGF than away from it during the first four hours. However, in absence of a chemoattractant, cells migrate more likely to their nearest image border. These conclusions are supported by the spatial mean directions. In a next step, the cell-cell interaction during migration and the migration of cell clusters will be analyzed. Furthermore, we want to observe phenotypical changes during migration based on fluorescence microscopy and machine learning. The algorithm is part of a collaborative platform which brings the experimental expertise of scientists from life sciences and the analytical knowledge of computer scientists together. This platform is built using web-based technologies with a responsive real-time user interface. All data, including raw and metadata as well as the accompanying results, will be stored in a secure and scalable compute cluster. The compute cluster provides sufficient space and computational power for modern image-based experiments and their analyses. Specific versions of data and results can be tagged to keep immutable records for archival.}, language = {en} } @misc{KoltaiCiccottiSchuette2016, author = {Koltai, Peter and Ciccotti, Giovanni and Sch{\"u}tte, Christof}, title = {On metastability and Markov state models for non-stationary molecular dynamics}, volume = {174103}, journal = {The Journal of Chemical Physics}, edition = {145}, issn = {1438-0064}, doi = {10.1063/1.4966157}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57869}, year = {2016}, abstract = {We utilize the theory of coherent sets to build Markov state models for non- equilibrium molecular dynamical systems. Unlike for systems in equilibrium, "meta- stable" sets in the non-equilibrium case may move as time evolves. We formalize this concept by relying on the theory of coherent sets, based on this we derive finite-time non-stationary Markov state models, and illustrate the concept and its main differences to equilibrium Markov state modeling on simple, one-dimensional examples.}, language = {en} } @article{DjurdjevacConradWeberSchuette2016, author = {Djurdjevac Conrad, Natasa and Weber, Marcus and Sch{\"u}tte, Christof}, title = {Finding dominant structures of nonreversible Markov processes}, volume = {14}, journal = {Multiscale Modeling and Simulation}, number = {4}, doi = {10.1137/15M1032272}, pages = {1319 -- 1340}, year = {2016}, language = {en} } @misc{GuptaRoeblitzKrauseetal.2013, author = {Gupta, Pooja and R{\"o}blitz, Susanna and Krause, Carola and Knaus, Petra and Sch{\"u}tte, Christof}, title = {Mathematical modeling of the Smad and Non-Smad BMP signaling pathways in context of cell density}, journal = {Computational Models in biology and medicine, 2013, Dresden, Germany}, year = {2013}, language = {en} } @inproceedings{GuptaKrauseRikeitetal.2014, author = {Gupta, Pooja and Krause, Carola and Rikeit, Paul and R{\"o}blitz, Susanna and Knaus, Petra and Sch{\"u}tte, Christof}, title = {Modeling of the BMP mediated co-regulation of the Smad and Non-Smad pathways in the context of cell density}, booktitle = {10th International BMP conference, 2014, Berlin, Germany}, year = {2014}, language = {en} } @article{GulSchuetteBernhard2016, author = {Gul, Raheem and Sch{\"u}tte, Christof and Bernhard, Stefan}, title = {Mathematical modeling and sensitivity analysis of arterial anastomosis in arm arteries}, journal = {Applied Mathematical Modelling}, doi = {10.1016/j.apm.2016.03.041}, year = {2016}, language = {en} } @misc{BittracherBanischSchuette2017, author = {Bittracher, Andreas and Banisch, Ralf and Sch{\"u}tte, Christof}, title = {Data-driven Computation of Molecular Reaction Coordinates}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66179}, year = {2017}, abstract = {The identification of meaningful reaction coordinates plays a key role in the study of complex molecular systems whose essential dynamics is characterized by rare or slow transition events. In a recent publication, the authors identified a condition under which such reaction coordinates exist - the existence of a so-called transition manifold - and proposed a numerical method for their point-wise computation that relies on short bursts of MD simulations. This article represents an extension of the method towards practical applicability in computational chemistry. It describes an alternative computational scheme that instead relies on more commonly available types of simulation data, such as single long molecular trajectories, or the push-forward of arbitrary canonically-distributed point clouds. It is based on a Galerkin approximation of the transition manifold reaction coordinates, that can be tuned to individual requirements by the choice of the Galerkin ansatz functions. Moreover, we propose a ready-to-implement variant of the new scheme, that computes data-fitted, mesh-free ansatz functions directly from the available simulation data. The efficacy of the new method is demonstrated on a realistic peptide system.}, language = {en} } @phdthesis{Schuette1999, author = {Sch{\"u}tte, Christof}, title = {Conformational Dynamics: Modelling, Theory, Algorithm, and Application to Biomolecules}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4063}, number = {SC-99-18}, year = {1999}, abstract = {The function of many important biomolecules comes from their dynamic properties and their ability to switch between different {\em conformations}. In a conformation, the large scale geometric structure of the molecule is understood to be conserved, whereas on smaller scales the system may well rotate, oscillate or fluctuate. In a recent article [J. Comp. Phys., 151,1 (1999)], the present author and coworkers demonstrated that (a) conformations can be understood as almost invariant sets of some Markov chain being defined via the Hamiltonian system governing the molecular dynamics and that (b) these sets can efficiently be computed via eigenvectors of the corresponding Markov operator. The persent manuscript reviews the mathematical modelling steps behind the novel concept, includes a rigorous analytical justification of this approach and especially of the numerical details of the algorithm, and illustrates its performance when applied to realistic molecular systems.}, language = {en} } @misc{FischerSchuetteDeuflhardetal.2001, author = {Fischer, Alexander and Sch{\"u}tte, Christof and Deuflhard, Peter and Cordes, Frank}, title = {Hierarchical Uncoupling-Coupling of Metastable Conformations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6296}, number = {01-03}, year = {2001}, abstract = {Uncoupling-coupling Monte Carlo (UCMC) combines uncoupling techniques for finite Markov chains with Markov chain Monte Carlo methodology. UCMC aims at avoiding the typical metastable or trapping behavior of Monte Carlo techniques. From the viewpoint of Monte Carlo, a slowly converging long-time Markov chain is replaced by a limited number of rapidly mixing short-time ones. Therefore, the state space of the chain has to be hierarchically decomposed into its metastable conformations. This is done by means of combining the technique of conformation analysis as recently introduced by the authors, and appropriate annealing strategies. We present a detailed examination of the uncoupling-coupling procedure which uncovers its theoretical background, and illustrates the hierarchical algorithmic approach. Furthermore, application of the UCMC algorithm to the \$n\$-pentane molecule allows us to discuss the effect of its crucial steps in a typical molecular scenario.}, language = {en} } @article{WulkowKoltaiSunkaraetal.2021, author = {Wulkow, Niklas and Koltai, P{\´e}ter and Sunkara, Vikram and Sch{\"u}tte, Christof}, title = {Data-driven modelling of nonlinear dynamics by barycentric coordinates and memory}, journal = {J. Stat. Phys.}, arxiv = {http://arxiv.org/abs/2112.06742}, year = {2021}, abstract = {We present a numerical method to model dynamical systems from data. We use the recently introduced method Scalable Probabilistic Approximation (SPA) to project points from a Euclidean space to convex polytopes and represent these projected states of a system in new, lower-dimensional coordinates denoting their position in the polytope. We then introduce a specific nonlinear transformation to construct a model of the dynamics in the polytope and to transform back into the original state space. To overcome the potential loss of information from the projection to a lower-dimensional polytope, we use memory in the sense of the delay-embedding theorem of Takens. By construction, our method produces stable models. We illustrate the capacity of the method to reproduce even chaotic dynamics and attractors with multiple connected components on various examples.}, language = {en} } @misc{ErnstSchuetteSigristetal.2021, author = {Ernst, Ariane and Sch{\"u}tte, Christof and Sigrist, Stephan and Winkelmann, Stefanie}, title = {Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics}, issn = {1438-0064}, doi = {10.1016/j.mbs.2021.108760}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-82674}, year = {2021}, abstract = {Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance to the calcium channels determines the release probability and thereby the postsynaptic signal. Suitable models of the process need to capture both the mean and the variance observed in electrophysiological measurements of the postsynaptic current. In this work, we propose a method to directly compute the exact first- and second-order moments for signals generated by a linear reaction network under convolution with an impulse response function, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. We show that the autocorrelation of the process is central for the calculation of the filtered signal's second-order moments, and derive a system of PDEs for the cross-correlation functions (including the autocorrelations) of linear reaction networks with time-dependent rates. Finally, we employ our method to efficiently compare different spatial coarse graining approaches for a specific model of synaptic vesicle fusion. Beyond the application to neurotransmission processes, the developed theory can be applied to any linear reaction system that produces a filtered stochastic signal.}, language = {en} } @article{ErnstSchuetteSigristetal.2022, author = {Ernst, Ariane and Sch{\"u}tte, Christof and Sigrist, Stephan and Winkelmann, Stefanie}, title = {Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics}, volume = {343}, journal = {Mathematical Biosciences}, doi = {10.1016/j.mbs.2021.108760}, year = {2022}, abstract = {Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance to the calcium channels determines the release probability and thereby the postsynaptic signal. Suitable models of the process need to capture both the mean and the variance observed in electrophysiological measurements of the postsynaptic current. In this work, we propose a method to directly compute the exact first- and second-order moments for signals generated by a linear reaction network under convolution with an impulse response function, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. We show that the autocorrelation of the process is central for the calculation of the filtered signal's second-order moments, and derive a system of PDEs for the cross-correlation functions (including the autocorrelations) of linear reaction networks with time-dependent rates. Finally, we employ our method to efficiently compare different spatial coarse graining approaches for a specific model of synaptic vesicle fusion. Beyond the application to neurotransmission processes, the developed theory can be applied to any linear reaction system that produces a filtered stochastic signal.}, language = {en} } @article{ThiesSunkaraRayetal.2023, author = {Thies, Arne and Sunkara, Vikram and Ray, Sourav and Wulkow, Hanna and Celik, M. {\"O}zg{\"u}r and Yerg{\"o}z, Fatih and Sch{\"u}tte, Christof and Stein, Christoph and Weber, Marcus and Winkelmann, Stefanie}, title = {Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design}, volume = {13}, journal = {Scientific Reports}, number = {607}, doi = {10.1038/s41598-023-27699-w}, year = {2023}, abstract = {We previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. The design process of NFEPP was based on mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands, recognizing that GPCRs function differently under pathological versus healthy conditions. We now present an additional and novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels and their dependence on parameters of inflamed and healthy tissue (pH, radicals). The model is validated against in vitro experimental data for the ligands NFEPP and fentanyl at different pH values and radical concentrations. We observe markedly reduced binding affinity and calcium channel inhibition for NFEPP at normal pH compared to lower pH, in contrast to the effect of fentanyl. For increasing radical concentrations, we find enhanced constitutive G-protein activation but reduced ligand binding affinity. Assessing the different effects, the results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account.}, language = {en} } @misc{RayThiesSunkaraetal.2021, author = {Ray, Sourav and Thies, Arne and Sunkara, Vikram and Wulkow, Hanna and Celik, {\"O}zg{\"u}r and Yerg{\"o}z, Fatih and Sch{\"u}tte, Christof and Stein, Christoph and Weber, Marcus and Winkelmann, Stefanie}, title = {Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-82797}, year = {2021}, abstract = {Initiated by mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands in normal versus diseased (inflamed) environments, we previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. Uniquely, this design recognised that GPCRs function differently under pathological versus healthy conditions. We now present a novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels associated with parameters of inflamed tissue (pH, radicals). By means of molecular dynamics simulations, we also assessed qualitative changes of the reaction rates due to additional disulfide bridges inside the GPCR binding pocket and used these rates for stochastic simulations of the corresponding reaction jump process. The modelling results were validated with in vitro experiments measuring calcium currents and G-protein activation. We found markedly reduced G-protein dissociation and calcium channel inhibition induced by NFEPP at normal pH, and enhanced constitutive G-protein activation but lower probability of ligand binding with increasing radical concentrations. These results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account.}, language = {en} } @article{MontefuscoSchuetteWinkelmann2023, author = {Montefusco, Alberto and Sch{\"u}tte, Christof and Winkelmann, Stefanie}, title = {A route to the hydrodynamic limit of a reaction-diffusion master equation using gradient structures}, volume = {83}, journal = {SIAM Journal on Applied Mathematics}, number = {2}, arxiv = {http://arxiv.org/abs/2201.02613}, doi = {10.1137/22M1488831}, pages = {837 -- 861}, year = {2023}, abstract = {The reaction-diffusion master equation (RDME) is a lattice-based stochastic model for spatially resolved cellular processes. It is often interpreted as an approximation to spatially continuous reaction-diffusion models, which, in the limit of an infinitely large population, may be described by means of reaction-diffusion partial differential equations. Analyzing and understanding the relation between different mathematical models for reaction-diffusion dynamics is a research topic of steady interest. In this work, we explore a route to the hydrodynamic limit of the RDME which uses gradient structures. Specifically, we elaborate on a method introduced in [J. Maas and A. Mielke, J. Stat. Phys., 181 (2020), pp. 2257-2303] in the context of well-mixed reaction networks by showing that, once it is complemented with an appropriate limit procedure, it can be applied to spatially extended systems with diffusion. Under the assumption of detailed balance, we write down a gradient structure for the RDME and use the method in order to produce a gradient structure for its hydrodynamic limit, namely, for the corresponding RDPDE.}, language = {en} } @article{PeppertvonKleistSchuetteetal.2022, author = {Peppert, Felix and von Kleist, Max and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {On the Sufficient Condition for Solving the Gap-Filling Problem Using Deep Convolutional Neural Networks}, volume = {33}, journal = {IEEE Transactions on Neural Networks and Learning Systems}, number = {11}, doi = {10.1109/TNNLS.2021.3072746}, pages = {6194 -- 6205}, year = {2022}, abstract = {Deep convolutional neural networks (DCNNs) are routinely used for image segmentation of biomedical data sets to obtain quantitative measurements of cellular structures like tissues. These cellular structures often contain gaps in their boundaries, leading to poor segmentation performance when using DCNNs like the U-Net. The gaps can usually be corrected by post-hoc computer vision (CV) steps, which are specific to the data set and require a disproportionate amount of work. As DCNNs are Universal Function Approximators, it is conceivable that the corrections should be obsolete by selecting the appropriate architecture for the DCNN. In this article, we present a novel theoretical framework for the gap-filling problem in DCNNs that allows the selection of architecture to circumvent the CV steps. Combining information-theoretic measures of the data set with a fundamental property of DCNNs, the size of their receptive field, allows us to formulate statements about the solvability of the gap-filling problem independent of the specifics of model training. In particular, we obtain mathematical proof showing that the maximum proficiency of filling a gap by a DCNN is achieved if its receptive field is larger than the gap length. We then demonstrate the consequence of this result using numerical experiments on a synthetic and real data set and compare the gap-filling ability of the ubiquitous U-Net architecture with variable depths. Our code is available at https://github.com/ai-biology/dcnn-gap-filling.}, language = {en} } @article{BittracherMollenhauerKoltaietal.2023, author = {Bittracher, Andreas and Mollenhauer, Mattes and Koltai, P{\´e}ter and Sch{\"u}tte, Christof}, title = {Optimal Reaction Coordinates: Variational Characterization and Sparse Computation}, volume = {21}, journal = {Multiscale Modelling \& Simulation}, number = {2}, arxiv = {http://arxiv.org/abs/2107.10158}, doi = {10.1137/21M1448367}, pages = {449 -- 488}, year = {2023}, abstract = {Reaction coordinates (RCs) are indicators of hidden, low-dimensional mechanisms that govern the long-term behavior of high-dimensional stochastic processes. We present a novel and general variational characterization of optimal RCs and provide conditions for their existence. Optimal RCs are minimizers of a certain loss function, and reduced models based on them guarantee a good approximation of the statistical long-term properties of the original high-dimensional process. We show that for slow-fast systems, metastable systems, and other systems with known good RCs, the novel theory reproduces previous insight. Remarkably, for reversible systems, the numerical effort required to evaluate the loss function scales only with the variability of the underlying, low-dimensional mechanism, and not with that of the full system. The theory provided lays the foundation for an efficient and data-sparse computation of RCs via modern machine learning techniques.}, language = {en} } @article{MollenhauerKlusSchuetteetal.2022, author = {Mollenhauer, Mattes and Klus, Stefan and Sch{\"u}tte, Christof and Koltai, P{\´e}ter}, title = {Kernel Autocovariance Operators of Stationary Processes: Estimation and Convergence}, volume = {23}, journal = {Journal of Machine Learning Research}, number = {327}, arxiv = {http://arxiv.org/abs/2004.00891}, pages = {1 -- 34}, year = {2022}, abstract = {We consider autocovariance operators of a stationary stochastic process on a Polish space that is embedded into a reproducing kernel Hilbert space. We investigate how empirical estimates of these operators converge along realizations of the process under various conditions. In particular, we examine ergodic and strongly mixing processes and obtain several asymptotic results as well as finite sample error bounds. We provide applications of our theory in terms of consistency results for kernel PCA with dependent data and the conditional mean embedding of transition probabilities. Finally, we use our approach to examine the nonparametric estimation of Markov transition operators and highlight how our theory can give a consistency analysis for a large family of spectral analysis methods including kernel-based dynamic mode decomposition.}, language = {en} } @misc{HelfmannDjurdjevacConradLorenzSpreenetal.2023, author = {Helfmann, Luzie and Djurdjevac Conrad, Natasa and Lorenz-Spreen, Philipp and Sch{\"u}tte, Christof}, title = {Supplementary code for the paper Modelling opinion dynamics under the impact of influencer and media strategies}, doi = {10.12752/9267}, year = {2023}, abstract = {This repository contains the Julia code accompanying the paper "Modelling opinion dynamics under the impact of influencer and media strategies", Scientific Reports, Vol.13, p. 19375, 2023.}, language = {en} } @misc{Secker2023, author = {Secker, Christopher}, title = {Novel multi-objective affinity approach allows to identify pH-specific μ-opioid receptor agonists (Dataset)}, doi = {10.12752/9622}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-96220}, year = {2023}, abstract = {Virtual Screening Dataset for the paper "Novel multi-objective affinity approach allows to identify pH-specific μ-opioid receptor agonists" by Secker et al. (https://doi.org/10.1186/s13321-023-00746-4)}, language = {en} } @article{WehlitzSadeghiMontefuscoetal.2025, author = {Wehlitz, Nathalie and Sadeghi, Mohsen and Montefusco, Alberto and Sch{\"u}tte, Christof and Pavliotis, Grigorios A. and Winkelmann, Stefanie}, title = {Approximating particle-based clustering dynamics by stochastic PDEs}, volume = {24}, journal = {SIAM Journal on Applied Dynamical Systems}, number = {2}, arxiv = {http://arxiv.org/abs/2407.18952}, doi = {10.1137/24M1676661}, pages = {1231 -- 1250}, year = {2025}, abstract = {This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane mediated receptor dynamics on cell surfaces, we formulate a stochastic particle-based model for diffusion and pairwise interaction of particles, leading to intriguing clustering phenomena. Employing numerical simulation and cluster detection methods, we explore the approximation of the particle-based clustering dynamics through mean-field approaches. We find that SPDEs successfully reproduce spatiotemporal clustering dynamics, not only in the initial cluster formation period, but also on longer time scales where the successive merging of clusters cannot be tracked by deterministic mean-field models. The computational efficiency of the SPDE approach allows us to generate extensive statistical data for parameter estimation in a simpler model that uses a Markov jump process to capture the temporal evolution of the cluster number.}, language = {en} } @article{KostreDjurdjevacConradSchuetteetal.2024, author = {Kostr{\´e}, Margarita and Djurdjevac Conrad, Natasa and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {Exploration of Particle Swarm Optimisation Algorithm with Divergent Parameters}, journal = {Natural Computing}, year = {2024}, language = {en} } @article{RegenyiMashreghiSchuetteetal.2024, author = {Reg{\´e}nyi, Enikő and Mashreghi, Mir-Farzin and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {Exploring transcription modalities from bimodal, single-cell RNA sequencing data}, volume = {6}, journal = {NAR Genomics and Bioinformatics}, number = {4}, publisher = {Oxford University Press (OUP)}, issn = {2631-9268}, doi = {10.1093/nargab/lqae179}, year = {2024}, abstract = {Abstract There is a growing interest in generating bimodal, single-cell RNA sequencing (RNA-seq) data for studying biological pathways. These data are predominantly utilized in understanding phenotypic trajectories using RNA velocities; however, the shape information encoded in the two-dimensional resolution of such data is not yet exploited. In this paper, we present an elliptical parametrization of two-dimensional RNA-seq data, from which we derived statistics that reveal four different modalities. These modalities can be interpreted as manifestations of the changes in the rates of splicing, transcription or degradation. We performed our analysis on a cell cycle and a colorectal cancer dataset. In both datasets, we found genes that are not picked up by differential gene expression analysis (DGEA), and are consequently unnoticed, yet visibly delineate phenotypes. This indicates that, in addition to DGEA, searching for genes that exhibit the discovered modalities could aid recovering genes that set phenotypes apart. For communities studying biomarkers and cellular phenotyping, the modalities present in bimodal RNA-seq data broaden the search space of genes, and furthermore, allow for incorporating cellular RNA processing into regulatory analyses.}, language = {en} } @inproceedings{RiberaBorrellRichterSchuette2025, author = {Ribera Borrell, Enric and Richter, Lorenz and Sch{\"u}tte, Christof}, title = {Reinforcement Learning with Random Time Horizons}, volume = {267}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, arxiv = {http://arxiv.org/abs/2506.00962}, pages = {5101 -- 5123}, year = {2025}, language = {en} } @misc{RiberaBorrellQuerRichteretal.2021, author = {Ribera Borrell, Enric and Quer, Jannes and Richter, Lorenz and Sch{\"u}tte, Christof}, title = {Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics}, issn = {1438-0064}, year = {2021}, abstract = {Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal importance sampling controls as a stochastic optimization problem, this then brings additional numerical challenges and the convergence of corresponding algorithms might as well suffer from metastabilty. In this article we address this issue by combining systematic control approaches with the heuristic adaptive metadynamics method. Crucially, we approximate the importance sampling control by a neural network, which makes the algorithm in principle feasible for high dimensional applications. We can numerically demonstrate in relevant metastable problems that our algorithm is more effective than previous attempts and that only the combination of the two approaches leads to a satisfying convergence and therefore to an efficient sampling in certain metastable settings.}, language = {en} } @article{SchuetteKlusHartmann2023, author = {Sch{\"u}tte, Christof and Klus, Stefan and Hartmann, Carsten}, title = {Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning}, volume = {32}, journal = {Acta Numerica}, doi = {10.1017/S0962492923000016}, pages = {517 -- 673}, year = {2023}, abstract = {One of the main challenges in molecular dynamics is overcoming the 'timescale barrier': in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, even on the largest or specifically dedicated supercomputers. This article discusses how to circumvent the timescale barrier by a collection of transfer operator-based techniques that have emerged from dynamical systems theory, numerical mathematics and machine learning over the last two decades. We will focus on how transfer operators can be used to approximate the dynamical behaviour on long timescales, review the introduction of this approach into molecular dynamics, and outline the respective theory, as well as the algorithmic development, from the early numerics-based methods, via variational reformulations, to modern data-based techniques utilizing and improving concepts from machine learning. Furthermore, its relation to rare event simulation techniques will be explained, revealing a broad equivalence of variational principles for long-time quantities in molecular dynamics. The article will mainly take a mathematical perspective and will leave the application to real-world molecular systems to the more than 1000 research articles already written on this subject.}, language = {en} } @article{MontefuscoHelfmannOkunolaetal.2024, author = {Montefusco, Alberto and Helfmann, Luzie and Okunola, Toluwani and Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {Partial mean-field model for neurotransmission dynamics}, volume = {369}, journal = {Mathematical Biosciences}, arxiv = {http://arxiv.org/abs/2307.01737}, doi = {10.1016/j.mbs.2024.109143}, year = {2024}, abstract = {This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the stochastic-spatial particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios.}, language = {en} } @article{NiemannKlusConradetal.2024, author = {Niemann, Jan-Hendrik and Klus, Stefan and Conrad, Natasa Djurdjevac and Sch{\"u}tte, Christof}, title = {Koopman-Based Surrogate Models for Multi-Objective Optimization of Agent-Based Systems}, volume = {460}, journal = {Physica D: Nonlinear Phenomena}, arxiv = {http://arxiv.org/abs/2306.17666}, doi = {https://doi.org/10.1016/j.physd.2024.134052}, pages = {134052}, year = {2024}, abstract = {Agent-based models (ABMs) provide an intuitive and powerful framework for studying social dynamics by modeling the interactions of individuals from the perspective of each individual. In addition to simulating and forecasting the dynamics of ABMs, the demand to solve optimization problems to support, for example, decision-making processes naturally arises. Most ABMs, however, are non-deterministic, high-dimensional dynamical systems, so objectives defined in terms of their behavior are computationally expensive. In particular, if the number of agents is large, evaluating the objective functions often becomes prohibitively time-consuming. We consider data-driven reduced models based on the Koopman generator to enable the efficient solution of multi-objective optimization problems involving ABMs. In a first step, we show how to obtain data-driven reduced models of non-deterministic dynamical systems (such as ABMs) that depend on potentially nonlinear control inputs. We then use them in the second step as surrogate models to solve multi-objective optimal control problems. We first illustrate our approach using the example of a voter model, where we compute optimal controls to steer the agents to a predetermined majority, and then using the example of an epidemic ABM, where we compute optimal containment strategies in a prototypical situation. We demonstrate that the surrogate models effectively approximate the Pareto-optimal points of the ABM dynamics by comparing the surrogate-based results with test points, where the objectives are evaluated using the ABM. Our results show that when objectives are defined by the dynamic behavior of ABMs, data-driven surrogate models support or even enable the solution of multi-objective optimization problems.}, language = {en} } @article{DjurdjevacConradChemnitzKostreetal.2024, author = {Djurdjevac Conrad, Natasa and Chemnitz, Robin and Kostre, Margarita and Schweigart, Fleur and Fless, Friederike and Sch{\"u}tte, Christof and Ducke, Benjamin}, title = {A Mathematical perspective on Romanisation: Modelling the Roman road activation process in ancient Tunisia}, volume = {19}, journal = {PLoS ONE}, number = {9}, doi = {10.1371/journal.pone.0309752}, year = {2024}, abstract = {Romanisation is a multi-faceted historical phenomenon with profound and lasting cultural impact on the ancient world. In the modern-day territory of Tunisia, this is particularly manifest during the first four centuries AD, under the reign of the Roman Empire. We derive a reduced, operational concept of Romanisation as a cultural diffusion process that is observable in the archaeological remains of the Roman era settlement system. We then introduce a novel mathematical model that computes spatio-temporal approximations for the Romanisation of the settlement system. The model is based on the concept of temporal road activation and makes minimal assumptions regarding input data quality. The results of our study contribute to the understanding of the time dynamics of the region's road network, under the influence of Romanisation. Our model can be applied in similar archaeological research scenarios, to generate spatio-temporal backbones for the analysis of otherwise intractably complex social processes.}, language = {en} } @inproceedings{ChaukairSchuetteSunkara2023, author = {Chaukair, Mustafa and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {On the Activation Space of ReLU Equipped Deep Neural Networks}, volume = {222}, booktitle = {Procedia Computer Science}, doi = {10.1016/j.procs.2023.08.200}, pages = {624 -- 635}, year = {2023}, abstract = {Modern Deep Neural Networks are getting wider and deeper in their architecture design. However, with an increasing number of parameters the decision mechanisms becomes more opaque. Therefore, there is a need for understanding the structures arising in the hidden layers of deep neural networks. In this work, we present a new mathematical framework for describing the canonical polyhedral decomposition in the input space, and in addition, we introduce the notions of collapsing- and preserving patches, pertinent to understanding the forward map and the activation space they induce. The activation space can be seen as the output of a layer and, in the particular case of ReLU activations, we prove that this output has the structure of a polyhedral complex.}, language = {en} } @article{PlockHammerschmidtBurgeretal.2023, author = {Plock, Matthias and Hammerschmidt, Martin and Burger, Sven and Schneider, Philipp-Immanuel and Sch{\"u}tte, Christof}, title = {Impact Study of Numerical Discretization Accuracy on Parameter Reconstructions and Model Parameter Distributions}, volume = {60}, journal = {Metrologia}, arxiv = {http://arxiv.org/abs/2305.02663}, doi = {10.1088/1681-7575/ace4cd}, pages = {054001}, year = {2023}, abstract = {In optical nano metrology numerical models are used widely for parameter reconstructions. Using the Bayesian target vector optimization method we fit a finite element numerical model to a Grazing Incidence x-ray fluorescence data set in order to obtain the geometrical parameters of a nano structured line grating. Gaussian process, stochastic machine learning surrogate models, were trained during the reconstruction and afterwards sampled with a Markov chain Monte Carlo sampler to determine the distribution of the reconstructed model parameters. The numerical discretization parameters of the used finite element model impact the numerical discretization error of the forward model. We investigated the impact of the polynomial order of the finite element ansatz functions on the reconstructed parameters as well as on the model parameter distributions. We showed that such a convergence study allows to determine numerical parameters which allows for efficient and accurate reconstruction results.}, language = {en} } @article{CoomberChewleSeckeretal.2025, author = {Coomber, Celvic and Chewle, Surahit and Secker, Christopher and Fackeldey, Konstantin and Weber, Marcus and Winkelmann, Stefanie and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {Investigating Endogenous Opioids Unravels the Mechanisms Behind Opioid-Induced Constipation, a Mathematical Modeling Approach}, volume = {26}, journal = {International Journal of Molecular Sciences}, number = {13}, doi = {10.3390/ijms26136207}, year = {2025}, abstract = {Endogenous opioids, such as Endomorphin-2, are not typically associated with severe constipation, unlike pharmaceutical opioids, which induce opioid-induced constipation (OIC) by activating μ-opioid receptors in the gastrointestinal tract. In this study, we present a mathematical model, which integrates the serotonergic and opioid pathways, simulating the interaction between serotonin and opioid signaling within the enteric nervous system (ENS). The model explores the mechanisms underlying OIC, with a focus on the change in adenylyl cyclase (AC) activity, cAMP accumulation, and the distinct functionalities of Endomorphin-2 compared to commonly used pharmaceutical opioids. We study the effects of Morphine, Fentanyl, and Methadone and contrast them with Endomorphin-2. Our findings reveal that opioids do not perturb the signaling of serotonin, but only the activity of AC, suggesting that serotonin levels have no influence on improving opioid-induced constipation. Furthermore, this study reveals that the primary difference between endogenous and pharmaceutical opioids is their degradation rates. This finding shows that modulating opioid degradation rates significantly improves cAMP recovery. In conclusion, our insights steer towards exploring opioid degrading enzymes, localized to the gut, as a strategy for mitigating OIC.}, language = {en} } @article{WinkelmannZonkerSchuetteetal.2021, author = {Winkelmann, Stefanie and Zonker, Johannes and Sch{\"u}tte, Christof and Djurdjevac Conrad, Natasa}, title = {Mathematical modeling of spatio-temporal population dynamics and application to epidemic spreading}, volume = {336}, journal = {Mathematical Biosciences}, publisher = {Elsevier}, arxiv = {http://arxiv.org/abs/2205.05000}, doi = {10.1016/j.mbs.2021.108619}, year = {2021}, abstract = {Agent based models (ABMs) are a useful tool for modeling spatio-temporal population dynamics, where many details can be included in the model description. Their computational cost though is very high and for stochastic ABMs a lot of individual simulations are required to sample quantities of interest. Especially, large numbers of agents render the sampling infeasible. Model reduction to a metapopulation model leads to a significant gain in computational efficiency, while preserving important dynamical properties. Based on a precise mathematical description of spatio-temporal ABMs, we present two different metapopulation approaches (stochastic and piecewise deterministic) and discuss the approximation steps between the different models within this framework. Especially, we show how the stochastic metapopulation model results from a Galerkin projection of the underlying ABM onto a finite-dimensional ansatz space. Finally, we utilize our modeling framework to provide a conceptual model for the spreading of COVID-19 that can be scaled to real-world scenarios.}, language = {en} } @article{RaharinirinaPeppertvonKleistetal.2021, author = {Raharinirina, Alexia N. and Peppert, Felix and von Kleist, Max and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {Inferring gene regulatory networks from single-cell RNA-seq temporal snapshot data requires higher-order moments}, volume = {2}, journal = {Patterns}, number = {9}, doi = {10.1016/j.patter.2021.100332}, year = {2021}, abstract = {Single-cell RNA sequencing (scRNA-seq) has become ubiquitous in biology. Recently, there has been a push for using scRNA-seq snapshot data to infer the underlying gene regulatory networks (GRNs) steering cellular function. To date, this aspiration remains unrealized due to technical and computational challenges. In this work we focus on the latter, which is under-represented in the literature. We took a systemic approach by subdividing the GRN inference into three fundamental components: data pre-processing, feature extraction, and inference. We observed that the regulatory signature is captured in the statistical moments of scRNA-seq data and requires computationally intensive minimization solvers to extract it. Furthermore, current data pre-processing might not conserve these statistical moments. Although our moment-based approach is a didactic tool for understanding the different compartments of GRN inference, this line of thinking—finding computationally feasible multi-dimensional statistics of data—is imperative for designing GRN inference methods.}, language = {en} } @misc{NiemannSchuetteKlus2021, author = {Niemann, Jan-Hendrik and Sch{\"u}tte, Christof and Klus, Stefan}, title = {Simulation data: Data-driven model reduction of agent-based systems using the Koopman generator}, volume = {16}, journal = {PLOS ONE}, number = {5}, doi = {http://doi.org/10.5281/zenodo.4522119}, year = {2021}, language = {en} } @article{delRazoFroembergStraubeetal.2022, author = {del Razo, Mauricio and Fr{\"o}mberg, Daniela and Straube, Arthur and Sch{\"u}tte, Christof and H{\"o}fling, Felix and Winkelmann, Stefanie}, title = {A probabilistic framework for particle-based reaction-diffusion dynamics using classical Fock space representations}, volume = {112}, journal = {Letters in Mathematical Physics}, number = {49}, arxiv = {http://arxiv.org/abs/arXiv:2109.13616}, doi = {10.1007/s11005-022-01539-w}, year = {2022}, language = {en} } @article{StraubeWinkelmannSchuetteetal.2021, author = {Straube, Arthur and Winkelmann, Stefanie and Sch{\"u}tte, Christof and H{\"o}fling, Felix}, title = {Stochastic pH oscillations in a model of the urea-urease reaction confined to lipid vesicles}, volume = {12}, journal = {J. Phys. Chem. Lett.}, doi = {10.1021/acs.jpclett.1c03016}, pages = {9888 -- 9893}, year = {2021}, abstract = {The urea-urease clock reaction is a pH switch from acid to basic that can turn into a pH oscillator if it occurs inside a suitable open reactor. We numerically study the confinement of the reaction to lipid vesicles, which permit the exchange with an external reservoir by differential transport, enabling the recovery of the pH level and yielding a constant supply of urea molecules. For microscopically small vesicles, the discreteness of the number of molecules requires a stochastic treatment of the reaction dynamics. Our analysis shows that intrinsic noise induces a significant statistical variation of the oscillation period, which increases as the vesicles become smaller. The mean period, however, is found to be remarkably robust for vesicle sizes down to approximately 200 nm, but the periodicity of the rhythm is gradually destroyed for smaller vesicles. The observed oscillations are explained as a canard-like limit cycle that differs from the wide class of conventional feedback oscillators.}, language = {en} }