@article{HaaseSunkaraKohletal., author = {Haase, Tobias and Sunkara, Vikram and Kohl, Benjamin and Meier, Carola and Bußmann, Patricia and Becker, Jessica and Jagielski, Michal and von Kleist, Max and Ertel, Wolfgang}, title = {Discerning the spatio-temporal disease patterns of surgically induced OA mouse models}, series = {PLOS One}, volume = {14}, journal = {PLOS One}, number = {4}, publisher = {PLOS One}, doi = {10.1371/journal.pone.0213734}, abstract = {Osteoarthritis (OA) is the most common cause of disability in ageing societies, with no effective therapies available to date. Two preclinical models are widely used to validate novel OA interventions (MCL-MM and DMM). Our aim is to discern disease dynamics in these models to provide a clear timeline in which various pathological changes occur. OA was surgically induced in mice by destabilisation of the medial meniscus. Analysis of OA progression revealed that the intensity and duration of chondrocyte loss and cartilage lesion formation were significantly different in MCL-MM vs DMM. Firstly, apoptosis was seen prior to week two and was narrowly restricted to the weight bearing area. Four weeks post injury the magnitude of apoptosis led to a 40-60\% reduction of chondrocytes in the non-calcified zone. Secondly, the progression of cell loss preceded the structural changes of the cartilage spatio-temporally. Lastly, while proteoglycan loss was similar in both models, collagen type II degradation only occurred more prominently in MCL-MM. Dynamics of chondrocyte loss and lesion formation in preclinical models has important implications for validating new therapeutic strategies. Our work could be helpful in assessing the feasibility and expected response of the DMM- and the MCL-MM models to chondrocyte mediated therapies.}, language = {en} } @article{Sunkara, author = {Sunkara, Vikram}, title = {On the Properties of the Reaction Counts Chemical Master Equation}, series = {Entropy}, volume = {21}, journal = {Entropy}, number = {6}, doi = {10.3390/e21060607}, pages = {607}, abstract = {The reaction counts chemical master equation (CME) is a high-dimensional variant of the classical population counts CME. In the reaction counts CME setting, we count the reactions which have fired over time rather than monitoring the population state over time. Since a reaction either fires or not, the reaction counts CME transitions are only forward stepping. Typically there are more reactions in a system than species, this results in the reaction counts CME being higher in dimension, but simpler in dynamics. In this work, we revisit the reaction counts CME framework and its key theoretical results. Then we will extend the theory by exploiting the reactions counts' forward stepping feature, by decomposing the state space into independent continuous-time Markov chains (CTMC). We extend the reaction counts CME theory to derive analytical forms and estimates for the CTMC decomposition of the CME. This new theory gives new insights into solving hitting times-, rare events-, and a priori domain construction problems.}, language = {en} } @article{TempLabuzNegreteetal., author = {Temp, Julia and Labuz, Dominika and Negrete, Roger and Sunkara, Vikram and Machelska, Halina}, title = {Pain and knee damage in male and female mice in the medial meniscal transection-induced osteoarthritis}, series = {Osteoarthritis and Cartilage}, journal = {Osteoarthritis and Cartilage}, doi = {10.1016/j.joca.2019.11.003}, language = {en} } @article{SunkaraHeinzHeinrichetal.2020, author = {Sunkara, Vikram and Heinz, Gitta A. and Heinrich, Frederik F. and Durek, Pawel and Mobasheri, Ali and Mashreghi, Mir-Farzin and Lang, Annemarie}, title = {Combining segmental bulk- and single-cell RNA-sequencing to define the chondrocyte gene expression signature in the murine knee joint}, series = {Osteoarthritis and Cartilage}, volume = {29}, journal = {Osteoarthritis and Cartilage}, number = {6}, doi = {10.1016/j.joca.2021.03.007}, pages = {905 -- 914}, year = {2020}, language = {en} } @article{LaydonSunkaraBoelenetal., author = {Laydon, Daniel J. and Sunkara, Vikram and Boelen, Lies and Bangham, Charles R. M. and Asquith, Becca}, title = {The relative contributions of infectious and mitotic spread to HTLV-1 persistence}, series = {PLOS Computational Biology}, journal = {PLOS Computational Biology}, doi = {10.1371/journal.pcbi.1007470}, language = {en} } @article{SunkaraHeinzHeinrichetal., author = {Sunkara, Vikram and Heinz, Gitta A. and Heinrich, Frederik F. and Durek, Pawel and Mobasheri, Ali and Mashreghi, Mir-Farzin and Lang, Annemarie}, title = {Combining segmental bulk- and single-cell RNA-sequencing to define the chondrocyte gene expression signature in the murine knee joint}, series = {bioarxiv (Accepted in Osteoarthr. Cartil.)}, journal = {bioarxiv (Accepted in Osteoarthr. Cartil.)}, doi = {10.1101/2020.06.13.148056}, language = {en} } @article{RettigHaasePletnyovetal., author = {Rettig, Anika and Haase, Tobias and Pletnyov, Alexandr and Kohl, Benjamin and Ertel, Wolfgang and von Kleist, Max and Sunkara, Vikram}, title = {SLCV - A Supervised Learning - Computer Vision combined strategy for automated muscle fibre detection in cross sectional images}, series = {PeerJ}, journal = {PeerJ}, publisher = {PeerJ}, address = {PeerJ}, doi = {10.7717/peerj.7053}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-72639}, abstract = {Muscle fibre cross sectional area (CSA) is an important biomedical measure used to determine the structural composition of skeletal muscle, and it is relevant for tackling research questions in many different fields of research. To date, time consuming and tedious manual delineation of muscle fibres is often used to determine the CSA. Few methods are able to automatically detect muscle fibres in muscle fibre cross sections to quantify CSA due to challenges posed by variation of bright- ness and noise in the staining images. In this paper, we introduce SLCV, a robust semi-automatic pipeline for muscle fibre detection, which combines supervised learning (SL) with computer vision (CV). SLCV is adaptable to different staining methods and is quickly and intuitively tunable by the user. We are the first to perform an error analysis with respect to cell count and area, based on which we compare SLCV to the best purely CV-based pipeline in order to identify the contribution of SL and CV steps to muscle fibre detection. Our results obtained on 27 fluorescence-stained cross sectional images of varying staining quality suggest that combining SL and CV performs signifi- cantly better than both SL based and CV based methods with regards to both the cell separation- and the area reconstruction error. Furthermore, applying SLCV to our test set images yielded fibre detection results of very high quality, with average sensitivity values of 0.93 or higher on different cluster sizes and an average Dice Similarity Coefficient (DSC) of 0.9778.}, language = {en} } @article{Sunkara2019, author = {Sunkara, Vikram}, title = {Algebraic Expressions of Conditional Expectations in Gene Regulatory Networks}, series = {Journal of Mathematical Biology}, journal = {Journal of Mathematical Biology}, number = {79}, publisher = {Journal of Mathematical Biology}, issn = {1438-0064}, doi = {10.1007/s00285-019-01410-y}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-70526}, pages = {1779 -- 1829}, year = {2019}, abstract = {Gene Regulatory Networks are powerful models for describing the mechanisms and dynamics inside a cell. These networks are generally large in dimension and seldom yield analytical formulations. It was shown that studying the conditional expectations between dimensions (vertices or species) of a network could lead to drastic dimension reduction. These conditional expectations were classically given by solving equations of motions derived from the Chemical Master Equation. In this paper we deviate from this convention and take an Algebraic approach instead. That is, we explore the consequences of conditional expectations being described by a polynomial function. There are two main results in this work. Firstly: if the conditional expectation can be described by a polynomial function, then coefficients of this polynomial function can be reconstructed using the classical moments. And secondly: there are dimensions in Gene Regulatory Networks which inherently have conditional expectations with algebraic forms. We demonstrate through examples, that the theory derived in this work can be used to develop new and effective numerical schemes for forward simulation and parameter inference. The algebraic line of investigation of conditional expectations has considerable scope to be applied to many different aspects of Gene Regulatory Networks; this paper serves as a preliminary commentary in this direction.}, language = {en} } @article{MoellerIsbilirSungkawornetal., author = {M{\"o}ller, Jan and Isbilir, Ali and Sungkaworn, Titiwat and Osberg, Brenda and Karathanasis, Christos and Sunkara, Vikram and Grushevsky, Eugene O and Bock, Andreas and Annibale, Paolo and Heilemann, Mike and Sch{\"u}tte, Christof and Lohse, Martin J.}, title = {Single molecule mu-opioid receptor membrane-dynamics reveal agonist-specific dimer formation with super-resolved precision}, series = {Nature Chemical Biology}, volume = {16}, journal = {Nature Chemical Biology}, doi = {10.1038/s41589-020-0566-1}, pages = {946 -- 954}, language = {en} } @article{LangVesterFerreiraGomesetal., author = {Lang, Annemarie and Vester, Antja and Ferreira-Gomes, M. and Guerra, G.M. and Heinrich, Fredrich R. and G{\"o}tzke, C.C. and Kurmies, Sebastian and Sunkara, Vikram and Durek, Pawel and Boerckel, Joel D. and Mashreghi, Mir-Farzin}, title = {PIPELINE FOR SINGLE CELL SEQUENCING OF HUMAN CHONDROCYTE PELLET CULTURES TO DELINEATE IL-1β MODULATED CHANGES IN CELL HETEROGENEITY}, series = {Osteoarthritis and Cartilage}, volume = {30}, journal = {Osteoarthritis and Cartilage}, number = {Supplement 1}, doi = {10.1016/j.joca.2022.02.112}, pages = {S90}, language = {en} } @article{SunkaraLewisNguyenetal., author = {Sunkara, Vikram and Lewis, Angus and Nguyen, Giang T. and O'Reilly, Malgorzata M. and Bean, Nigel}, title = {A discontinuous Galerkin method for approximating the stationary distribution of stochastic fluid-fluid processes}, series = {Methodology and Computing in Applied Probability}, journal = {Methodology and Computing in Applied Probability}, doi = {10.1007/s11009-022-09945-2}, language = {en} } @article{WulkowKoltaiSunkaraetal., 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}, series = {J. Stat. Phys.}, journal = {J. Stat. Phys.}, 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} } @article{LangHelfmeierStefanowskietal., author = {Lang, Annemarie and Helfmeier, Sarah and Stefanowski, Jonathan and Kuppe, Aditi and Sunkara, Vikram and Pfeiffenberger, Moritz and Wolter, Angelique and Damerau, Alexandra and Hemmati-Sadeghi, Shabnam and Ringe, Jochen and Haag, Rainer and Hauser, Anja E. and L{\"o}hning, Max and Perka, Carsten and Duda, Georg and Hoff, Paula and Schmidt-Bleek, Katharina and Gaber, Timo and Buttgereit, Frank}, title = {HIF-stabilization prevents delayed fracture healing}, series = {bioarxiv}, journal = {bioarxiv}, doi = {10.1101/2020.07.02.182832}, language = {en} } @misc{SunkaraRaharinirinaPeppertetal., author = {Sunkara, Vikram and Raharinirina, N. Alexia and Peppert, Felix and von Kleist, Max and Sch{\"u}tte, Christof}, title = {Inferring Gene Regulatory Networks from Single Cell RNA-seq Temporal Snapshot Data Requires Higher Order Moments}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-79664}, abstract = {Due to the increase in accessibility and robustness of sequencing technology, single cell RNA-seq (scRNA-seq) data has become abundant. The technology has made significant contributions to discovering novel phenotypes and heterogeneities of cells. Recently, there has been a push for using single-- or multiple scRNA-seq snapshots to infer the underlying gene regulatory networks (GRNs) steering the cells' biological functions. To date, this aspiration remains unrealised. In this paper, we took a bottom-up approach and curated a stochastic two gene interaction model capturing the dynamics of a complete system of genes, mRNAs, and proteins. In the model, the regulation was placed upstream from the mRNA on the gene level. We then inferred the underlying regulatory interactions from only the observation of the mRNA population through~time. We could detect signatures of the regulation by combining information of the mean, covariance, and the skewness of the mRNA counts through time. We also saw that reordering the observations using pseudo-time did not conserve the covariance and skewness of the true time course. The underlying GRN could be captured consistently when we fitted the moments up to degree three; however, this required a computationally expensive non-linear least squares minimisation solver. There are still major numerical challenges to overcome for inference of GRNs from scRNA-seq data. These challenges entail finding informative summary statistics of the data which capture the critical regulatory information. Furthermore, the statistics have to evolve linearly or piece-wise linearly through time to achieve computational feasibility and scalability.}, language = {en} } @article{RaharinirinaPeppertvonKleistetal., 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}, series = {Patterns}, volume = {2}, journal = {Patterns}, number = {9}, doi = {10.1016/j.patter.2021.100332}, 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} } @article{PeppertvonKleistSchuetteetal., 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}, series = {IEEE Transactions on Neural Networks and Learning Systems}, volume = {33}, journal = {IEEE Transactions on Neural Networks and Learning Systems}, number = {11}, doi = {10.1109/TNNLS.2021.3072746}, pages = {6194 -- 6205}, 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{SchulzePeppertSchuetteetal., author = {Schulze, Kenrick and Peppert, Felix and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {Chimeric U-Net-Modifying the standard U-Net towards Explainability}, series = {bioRxiv}, journal = {bioRxiv}, doi = {10.1101/2022.12.01.518699}, language = {en} } @inproceedings{ChaukairSchuetteSunkara, author = {Chaukair, Mustafa and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {On the Activation Space of ReLU Equipped Deep Neural Networks}, series = {Procedia Computer Science}, volume = {222}, booktitle = {Procedia Computer Science}, doi = {10.1016/j.procs.2023.08.200}, pages = {624 -- 635}, 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{HajarolasvadiSunkaraKhavnekaretal., author = {Hajarolasvadi, Noushin and Sunkara, Vikram and Khavnekar, Sagar and Beck, Florian and Brandt, Robert and Baum, Daniel}, title = {Volumetric macromolecule identification in cryo-electron tomograms using capsule networks}, series = {BMC Bioinformatics}, volume = {23}, journal = {BMC Bioinformatics}, number = {360}, doi = {10.1186/s12859-022-04901-w}, abstract = {Background: Despite recent advances in cellular cryo-electron tomography (CET), developing automated tools for macromolecule identification in submolecular resolution remains challenging due to the lack of annotated data and high structural complexities. To date, the extent of the deep learning methods constructed for this problem is limited to conventional Convolutional Neural Networks (CNNs). Identifying macromolecules of different types and sizes is a tedious and time-consuming task. In this paper, we employ a capsule-based architecture to automate the task of macro- molecule identification, that we refer to as 3D-UCaps. In particular, the architecture is composed of three components: feature extractor, capsule encoder, and CNN decoder. The feature extractor converts voxel intensities of input sub-tomograms to activities of local features. The encoder is a 3D Capsule Network (CapsNet) that takes local features to generate a low-dimensional representation of the input. Then, a 3D CNN decoder reconstructs the sub-tomograms from the given representation by upsampling. Results: We performed binary and multi-class localization and identification tasks on synthetic and experimental data. We observed that the 3D-UNet and the 3D-UCaps had an F1-score mostly above 60\% and 70\%, respectively, on the test data. In both network architectures, we observed degradation of at least 40\% in the F1-score when identifying very small particles (PDB entry 3GL1) compared to a large particle (PDB entry 4D8Q). In the multi-class identification task of experimental data, 3D-UCaps had an F1-score of 91\% on the test data in contrast to 64\% of the 3D-UNet. The better F1-score of 3D-UCaps compared to 3D-UNet is obtained by a higher precision score. We speculate this to be due to the capsule network employed in the encoder. To study the effect of the CapsNet-based encoder architecture further, we performed an ablation study and perceived that the F1-score is boosted as network depth is increased which is in contrast to the previously reported results for the 3D-UNet. To present a reproducible work, source code, trained models, data as well as visualization results are made publicly available. Conclusion: Quantitative and qualitative results show that 3D-UCaps successfully perform various downstream tasks including identification and localization of macro- molecules and can at least compete with CNN architectures for this task. Given that the capsule layers extract both the existence probability and the orientation of the molecules, this architecture has the potential to lead to representations of the data that are better interpretable than those of 3D-UNet.}, language = {en} } @article{BirkRaharinirinaFackeldeyetal., author = {Birk, Ralph and Raharinirina, N. Alexia and Fackeldey, Konstantin and Richter, Tonio Sebastian and Weber, Marcus}, title = {Inferring cultural and social processes based on patterns of statistical relationships between Synodal texts}, abstract = {In this paper, we explore the relationship patterns between Ancient Egyptian texts of the corpus ``Synodal decrees'', which are originating between 243 and 185 BCE, during the Ptolemaic period. Particularly, we are interested in analyzing the grammatical features of the different texts. Conventional data analysis methods such as correspondence Analysis are very useful to explore the patterns of statistical interdependence between categories of variables. However, it is based on a PCA-like dimension-reduction method and turned out to be unsuitable for our dataset due to the high dimensionality of our data representations. Additionally, the similarity between pairs of texts and pairs of grammatical features is observed through the distance between their representation, but the degree of association between a particular grammatical feature and a text is not. Here, we applied a qualitative Euclidean embedding method that provides a new Euclidean representation of the categories of variables. This new representation of the categories is constructed in such a way that all the patterns of statistical interdependence, similarity, and association, are seen through the Euclidean distance between them. Nevertheless, the PCA-like dimension-reduction method also performed poorly on our new representation. Therefore, we obtained a two-dimensional visualization using non-linear methods such UMAP or t-SNE. Although these dimension-reduction methods reduced the interpretability of interpoint distances, we were still able to identify important similarity patterns between the Synodal text as well as their association patterns with the grammatical features.}, language = {en} } @misc{KostreSunkaraSchuetteetal., author = {Kostr{\´e}, Margarita and Sunkara, Vikram and Sch{\"u}tte, Christof and Djurdjevac Conrad, Nataša}, title = {Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-86764}, abstract = {Spreading processes are important drivers of change in social systems. To understand the mechanisms of spreading it is fundamental to have information about the underlying contact network and the dynamical parameters of the process. However, in many real-wold examples, this information is not known and needs to be inferred from data. State-of-the-art spreading inference methods have mostly been applied to modern social systems, as they rely on availability of very detailed data. In this paper we study the inference challenges for historical spreading processes, for which only very fragmented information is available. To cope with this problem, we extend existing network models by formulating a model on a mesoscale with temporal spreading rate. Furthermore, we formulate the respective parameter inference problem for the extended model. We apply our approach to the romanization process of Northern Tunisia, a scarce dataset, and study properties of the inferred time-evolving interregional networks. As a result, we show that (1) optimal solutions consist of very different network structures and spreading rate functions; and that (2) these diverse solutions produce very similar spreading patterns. Finally, we discuss how inferred dominant interregional connections are related to available archaeological traces. Historical networks resulting from our approach can help understanding complex processes of cultural change in ancient times.}, language = {en} } @article{KostreSunkaraSchuetteetal.2022, author = {Kostr{\´e}, Margarita and Sunkara, Vikram and Sch{\"u}tte, Christof and Djurdjevac Conrad, Natasa}, title = {Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia}, series = {Applied Network Science}, volume = {7}, journal = {Applied Network Science}, publisher = {Springer Nature}, doi = {10.1007/s41109-022-00492-w}, pages = {18}, year = {2022}, abstract = {Spreading processes are important drivers of change in social systems. To understand the mechanisms of spreading it is fundamental to have information about the underlying contact network and the dynamical parameters of the process. However, in many real-wold examples, this information is not known and needs to be inferred from data. State-of-the-art spreading inference methods have mostly been applied to modern social systems, as they rely on availability of very detailed data. In this paper we study the inference challenges for historical spreading processes, for which only very fragmented information is available. To cope with this problem, we extend existing network models by formulating a model on a mesoscale with temporal spreading rate. Furthermore, we formulate the respective parameter inference problem for the extended model. We apply our approach to the romanization process of Northern Tunisia, a scarce dataset, and study properties of the inferred time-evolving interregional networks. As a result, we show that (1) optimal solutions consist of very different network structures and spreading rate functions; and that (2) these diverse solutions produce very similar spreading patterns. Finally, we discuss how inferred dominant interregional connections are related to available archaeological traces. Historical networks resulting from our approach can help understanding complex processes of cultural change in ancient times.}, language = {en} } @article{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}, series = {Molecular Simulation}, volume = {46}, journal = {Molecular Simulation}, number = {18}, publisher = {Taylor and Francis}, doi = {10.1080/08927022.2020.1839660}, pages = {1443 -- 1452}, 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. 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 μ-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.}, language = {en} } @misc{RayThiesSunkaraetal., 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}, 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} } @misc{RaySunkaraSchuetteetal., 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}, 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} } @inproceedings{KostreSunkaraDjurdjevacConrad, author = {Kostre, Margarita and Sunkara, Vikram and Djurdjevac Conrad, Natasa}, title = {Inference of historical influence networks}, series = {International Conference on Complex Networks \& Their Applications Proceedings}, booktitle = {International Conference on Complex Networks \& Their Applications Proceedings}, edition = {International Conference on Complex Networks \& Their Applications}, doi = {10.12752/8558}, pages = {110 -- 113}, abstract = {We study the romanization process of northern Africa from 50 BC till 300 AD. Our goal is to infer the communication strength between different subregions, based on the evolution of the status of cities. Herefore, we use the general inverse infection model, that infers the weights of a known underlying network, given observations of the spreading on this network. As infection process we choose the SI metapopulation model, where I stands for a city with a Roman status. To solve the minimization problem we use the particle swarm optimization algorithm with a specific choice of parameters.}, language = {de} } @article{ThiesSunkaraRayetal., 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}, series = {Scientific Reports}, volume = {13}, journal = {Scientific Reports}, number = {607}, doi = {10.1038/s41598-023-27699-w}, 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} } @article{Raharinirina, author = {Raharinirina, Nomenjanahary Alexia AND Sunkara, Vikram AND von Kleist, Max AND Fackeldey, Konstantin AND Weber, Marcus}, title = {Multi-Input data ASsembly for joint Analysis (MIASA): A framework for the joint analysis of disjoint sets of variables}, series = {PLOS ONE}, volume = {19}, journal = {PLOS ONE}, number = {5}, publisher = {Public Library of Science}, doi = {10.1371/journal.pone.0302425}, pages = {1 -- 26}, language = {en} }