@article{RabbenRayWeber2020, author = {Rabben, Robert Julian and Ray, Sourav and Weber, Marcus}, title = {ISOKANN: Invariant subspaces of Koopman operators learned by a neural network}, volume = {153}, journal = {The Journal of Chemical Physics}, number = {11}, doi = {10.1063/5.0015132}, pages = {114109}, year = {2020}, abstract = {The problem of determining the rate of rare events in dynamical systems is quite well-known but still difficult to solve. Recent attempts to overcome this problem exploit the fact that dynamic systems can be represented by a linear operator, such as the Koopman operator. Mathematically, the rare event problem comes down to the difficulty in finding invariant subspaces of these Koopman operators K. In this article, we describe a method to learn basis functions of invariant subspaces using an artificial neural Network.}, language = {en} } @misc{RaySunkaraSchuetteetal.2020, author = {Ray, Sourav and Sunkara, Vikram and Sch{\"u}tte, Christof and Weber, Marcus}, title = {How to calculate pH-dependent binding rates for receptor-ligand systems based on thermodynamic simulations with different binding motifs}, issn = {1438-0064}, doi = {10.1080/08927022.2020.1839660}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-78437}, year = {2020}, abstract = {Molecular simulations of ligand-receptor interactions are a computational challenge, especially when their association- (``on''-rate) and dissociation- (``off''-rate) mechanisms are working on vastly differing timescales. In addition, the timescale of the simulations themselves is, in practice, orders of magnitudes smaller than that of the mechanisms; which further adds to the complexity of observing these mechanisms, and of drawing meaningful and significant biological insights from the simulation. One way of tackling this multiscale problem is to compute the free-energy landscapes, where molecular dynamics (MD) trajectories are used to only produce certain statistical ensembles. The approach allows for deriving the transition rates between energy states as a function of the height of the activation-energy barriers. In this article, we derive the association rates of the opioids fentanyl and N-(3-fluoro-1-phenethylpiperidin-4-yl)- N-phenyl propionamide (NFEPP) in a \$\mu\$-opioid receptor by combining the free-energy landscape approach with the square-root-approximation method (SQRA), which is a particularly robust version of Markov modelling. The novelty of this work is that we derive the association rates as a function of the pH level using only an ensemble of MD simulations. We also verify our MD-derived insights by reproducing the in vitro study performed by the Stein Lab, who investigated the influence of pH on the inhibitory constant of fentanyl and NFEPP (Spahn et al. 2017). MD simulations are far more accessible and cost-effective than in vitro and in vivo studies. Especially in the context of the current opioid crisis, MD simulations can aid in unravelling molecular functionality and assist in clinical decision-making; the approaches presented in this paper are a pertinent step forward in this direction.}, language = {en} } @article{RoehlWeberFackeldey2021, author = {R{\"o}hl, Susanne and Weber, Marcus and Fackeldey, Konstantin}, title = {Computing the minimal rebinding effect for non-reversible processes}, volume = {19}, journal = {Multiscale Modeling and Simulation}, number = {1}, arxiv = {http://arxiv.org/abs/2007.08403}, doi = {https://doi.org/10.1137/20M1334966}, pages = {460 -- 477}, year = {2021}, abstract = {The aim of this paper is to investigate the rebinding effect, a phenomenon describing a "short-time memory" which can occur when projecting a Markov process onto a smaller state space. For guaranteeing a correct mapping by the Markov State Model, we assume a fuzzy clustering in terms of membership functions, assigning degrees of membership to each state. The macro states are represented by the membership functions and may be overlapping. The magnitude of this overlap is a measure for the strength of the rebinding effect, caused by the projection and stabilizing the system. A minimal bound for the rebinding effect included in a given system is computed as the solution of an optimization problem. Based on membership functions chosen as a linear combination of Schur vectors, this generalized approach includes reversible as well as non-reversible processes.}, 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{BauerWeberDiehlWieseneckeretal.2021, author = {Bauer, Wolfgang and Weber, Marcus and Diehl-Wiesenecker, Eva and Galtung, Noa and Prpic, Monika and Somasundaram, Rajan and Tauber, Rudolf and Schwenk, Jochen and Micke, Patrick and Kappert, Kai}, title = {Plasma Proteome Fingerprints Reveal Distinctiveness and Clinical Outcome of SARS-CoV-2 Infection}, volume = {13}, journal = {Viruses}, number = {12}, doi = {10.3390/v13122456}, pages = {2456}, year = {2021}, abstract = {We evaluated how plasma proteomic signatures in patients with suspected COVID-19 can unravel the pathophysiology, and determine kinetics and clinical outcome of the infection. We identified distinct plasma proteins linked to the presence and course of COVID-19. These plasma proteomic findings may translate to a protein fingerprint, helping to assist clinical management decisions.}, language = {en} } @book{TernesBauerBraueretal.2023, author = {Ternes, Thomas and Bauer, Karl-Heinz and Brauer, Frank and Drewes, J{\"o}rg and Joss, Adriano and Hiller, Georg and Jewell, Kevin and Oehlmann, J{\"o}rg and Radke, Michael and Schulte-Oehlmann, Ulrike and Schwartz, Thomas and Seel, Peter and V{\"o}lker, Jeanette and Weber, Lilo and Weber, Marcus}, title = {Handlungsempfehlung zur integrativen Bewertung der weitergehenden Abwasserbehandlung von kommunalen Kl{\"a}ranlagen}, volume = {T1/2023}, editor = {Wilhelm, Christian}, publisher = {DWA / GDCh}, isbn = {978-3-96862-563-8}, year = {2023}, abstract = {Das vorliegende Statuspapier beschreibt ein Konzept zur weitergehenden Abwasserbehandlung f{\"u}r die Bewertung von Aufbereitungsverfahren, sowohl in einer Pilotphase zur Auswahl von Verfah- rensoptionen als auch f{\"u}r die Bewertung großtechnischer Anlagen.}, language = {de} } @article{FernandesChaowdharySalehetal.2022, author = {Fernandes, Rita and Chaowdhary, Suvrat and Saleh, Noureldin and Mikula, Natalia and Kanevche, Katerina and Berlepsch, Hans and Hosogi, Naoki and Heberle, Joachim and Weber, Marcus and B{\"o}ttcher, Christoph and Koksch, Beate}, title = {Cyanine Dye Coupling Mediates Self-assembly of a pH Sensitive Peptide into Novel 3D Architectures}, volume = {61}, journal = {Angewandte Chemie}, number = {48}, pages = {e202208647}, year = {2022}, abstract = {A conjugated Cy5 dye-peptide system reveals the formation of two novel and structurally distinct supramolecular assemblies with photo-physical characteristics of H-type dimers or tetramers, respectively. The molecular ultrastructures are triggered by the complementary interplay of mutual chromophore coupling and pH induced changes in the peptide charge pattern.}, language = {en} } @article{SechiFackeldeyChewleetal.2022, author = {Sechi, Renata and Fackeldey, Konstantin and Chewle, Surahit and Weber, Marcus}, title = {SepFree NMF: A Toolbox for Analyzing the Kinetics of Sequential Spectroscopic Data}, volume = {15}, journal = {Algorithms}, number = {9}, doi = {10.3390/a15090297}, pages = {297}, year = {2022}, abstract = {This work addresses the problem of determining the number of components from sequential spectroscopic data analyzed by non-negative matrix factorization without separability assumption (SepFree NMF). These data are stored in a matrix M of dimension "measured times" versus "measured wavenumbers" and can be decomposed to obtain the spectral fingerprints of the states and their evolution over time. SepFree NMF assumes a memoryless (Markovian) process to underline the dynamics and decomposes M so that M=WH, with W representing the components' fingerprints and H their kinetics. However, the rank of this decomposition (i.e., the number of physical states in the process) has to be guessed from pre-existing knowledge on the observed process. We propose a measure for determining the number of components with the computation of the minimal memory effect resulting from the decomposition; by quantifying how much the obtained factorization is deviating from the Markovian property, we are able to score factorizations of a different number of components. In this way, we estimate the number of different entities which contribute to the observed system, and we can extract kinetic information without knowing the characteristic spectra of the single components. This manuscript provides the mathematical background as well as an analysis of computer generated and experimental sequentially measured Raman spectra.}, language = {en} } @article{RayFackeldeySteinetal.2023, author = {Ray, Sourav and Fackeldey, Konstantin and Stein, Christoph and Weber, Marcus}, title = {Coarse Grained MD Simulations of Opioid interactions with the µ-opioid receptor and the surrounding lipid membrane}, volume = {3}, journal = {Biophysica}, number = {2}, doi = {10.3390/biophysica3020017}, pages = {263 -- 275}, year = {2023}, abstract = {In our previous studies, a new opioid (NFEPP) was developed to only selectively bind to the 𝜇-opoid receptor (MOR) in inflamed tissue and thus avoid the severe side effects of fentanyl. We know that NFEPP has a reduced binding affinity to MOR in healthy tissue. Inspired by the modelling and simulations performed by Sutcliffe et al., we present our own results of coarse-grained molecular dynamics simulations of fentanyl and NFEPP with regards to their interaction with the 𝜇-opioid receptor embedded within the lipid cell membrane. For technical reasons, we have slightly modified Sutcliffe's parametrisation of opioids. The pH-dependent opioid simulations are of interest because while fentanyl is protonated at the physiological pH, NFEPP is deprotonated due to its lower pKa value than that of fentanyl. Here, we analyse for the first time whether pH changes have an effect on the dynamical behaviour of NFEPP when it is inside the cell membrane. Besides these changes, our analysis shows a possible alternative interaction of NFEPP at pH 7.4 outside the binding region of the MOR. The interaction potential of NFEPP with MOR is also depicted by analysing the provided statistical molecular dynamics simulations with the aid of an eigenvector analysis of a transition rate matrix. In our modelling, we see differences in the XY-diffusion profiles of NFEPP compared with fentanyl in the cell membrane.}, language = {en} }