TY - JOUR A1 - Thies, Arne A1 - Sunkara, Vikram A1 - Ray, Sourav A1 - Wulkow, Hanna A1 - Celik, M. Özgür A1 - Yergöz, Fatih A1 - Schütte, Christof A1 - Stein, Christoph A1 - Weber, Marcus A1 - Winkelmann, Stefanie T1 - Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design JF - Scientific Reports N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1038/s41598-023-27699-w VL - 13 IS - 607 ER - TY - GEN A1 - Ray, Sourav A1 - Thies, Arne A1 - Sunkara, Vikram A1 - Wulkow, Hanna A1 - Celik, Özgür A1 - Yergöz, Fatih A1 - Schütte, Christof A1 - Stein, Christoph A1 - Weber, Marcus A1 - Winkelmann, Stefanie T1 - Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design N2 - 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. T3 - ZIB-Report - 21-19 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82797 SN - 1438-0064 ER - TY - JOUR A1 - Montefusco, Alberto A1 - Schütte, Christof A1 - Winkelmann, Stefanie T1 - A route to the hydrodynamic limit of a reaction-diffusion master equation using gradient structures JF - SIAM Journal on Applied Mathematics N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1137/22M1488831 VL - 83 IS - 2 SP - 837 EP - 861 ER - TY - JOUR A1 - Ernst, Ariane A1 - Falkenhagen, Undine A1 - Winkelmann, Stefanie T1 - Model reduction for calcium-induced vesicle fusion dynamics JF - Proceedings in Applied Mathematics & Mechanics N2 - In this work, we adapt an established model for the Ca2+-induced fusion dynamics of synaptic vesicles and employ a lumping method to reduce its complexity. In the reduced system, sequential Ca2+-binding steps are merged to a single releasable state, while keeping the important dependence of the reaction rates on the local Ca2+ concentration. We examine the feasibility of this model reduction for a representative stimulus train over the physiologically relevant site-channel distances. Our findings show that the approximation error is generally small and exhibits an interesting nonlinear and non-monotonic behavior where it vanishes for very low distances and is insignificant at intermediary distances. Furthermore, we give expressions for the reduced model’s reaction rates and suggest that our approach may be used to directly compute effective fusion rates for assessing the validity of a fusion model, thereby circumventing expensive simulations. Y1 - 2023 U6 - https://doi.org/10.1002/pamm.202300184 VL - 23 IS - 4 ER - TY - CHAP A1 - Lücke, Marvin A1 - Koltai, Peter A1 - Winkelmann, Stefanie A1 - Molkethin, Nora A1 - Heitzig, Jobst T1 - Discovering collective variable dynamics of agent-based models T2 - 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022 N2 - Analytical approximations of the macroscopic behavior of agent-based models (e.g. via mean-field theory) often introduce a significant error, especially in the transient phase. For an example model called continuous-time noisy voter model, we use two data-driven approaches to learn the evolution of collective variables instead. The first approach utilizes the SINDy method to approximate the macroscopic dynamics without prior knowledge, but has proven itself to be not particularly robust. The second approach employs an informed learning strategy which includes knowledge about the agent-based model. Both approaches exhibit a considerably smaller error than the conventional analytical approximation. Y1 - 2022 U6 - https://doi.org/https://doi.org/10.15495/EPub_UBT_00006809 ER - TY - JOUR A1 - Erban, Radek A1 - Winkelmann, Stefanie T1 - Multi-grid reaction-diffusion master equation: applications to morphogen gradient modelling JF - Bulletin of Mathematical Biology N2 - The multi-grid reaction-diffusion master equation (mgRDME) provides a generalization of stochastic compartment-based reaction-diffusion modelling described by the standard reaction-diffusion master equation (RDME). By enabling different resolutions on lattices for biochemical species with different diffusion constants, the mgRDME approach improves both accuracy and efficiency of compartment-based reaction-diffusion simulations. The mgRDME framework is examined through its application to morphogen gradient formation in stochastic reaction-diffusion scenarios, using both an analytically tractable first-order reaction network and a model with a second-order reaction. The results obtained by the mgRDME modelling are compared with the standard RDME model and with the (more detailed) particle-based Brownian dynamics simulations. The dependence of error and numerical cost on the compartment sizes is defined and investigated through a multi-objective optimization problem. Y1 - 2025 U6 - https://doi.org/10.1007/s11538-024-01377-y VL - 87 SP - 6 ER - TY - JOUR A1 - Wehlitz, Nathalie A1 - Sadeghi, Mohsen A1 - Montefusco, Alberto A1 - Schütte, Christof A1 - Pavliotis, Grigorios A. A1 - Winkelmann, Stefanie T1 - Approximating particle-based clustering dynamics by stochastic PDEs JF - SIAM Journal on Applied Dynamical Systems N2 - 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. Y1 - 2025 U6 - https://doi.org/10.1137/24M1676661 VL - 24 IS - 2 SP - 1231 EP - 1250 ER - TY - JOUR A1 - Berns, Manon A1 - Yildiz, Mirza A1 - Winkelmann, Stefanie A1 - Walter, Alexander T1 - Independently engaging protein tethers of different length enhance synaptic vesicle trafficking to the plasma membrane JF - The Journal of Physiology N2 - Synaptic vesicle (SV) trafficking toward the plasma membrane (PM) and subsequent SV maturation are essential for neurotransmitter release. These processes, including SV docking and priming, are coordinated by various proteins, such as SNAREs, Munc13, and Synaptotagmin (Syt), which connect—tether—the SV to the PM. Here, we investigated how tethers of varying lengths mediate SV docking using a simplified mathematical model. The heights of the three tether types—estimated from the structures of the SNARE complex, Munc13, and Syt—defined the SV-to-PM distance ranges for tether formation. Geometric considerations linked SV-to-PM distances to the probability and rate of tether formation. We assumed that SV tethering constrains SV motility and that multiple tethers associate by independent interactions. The model predicted that forming multiple tethers favors shorter SV-to-PM distances. Although tethers acted independently in the model, their geometrical properties often caused sequential assembly, from longer ones (Munc13/Syt), that accelerated SV movement towards the PM, to shorter ones (SNAREs) which stabilized PM-proximal SVs. Modifying tether lengths or numbers affected SV trafficking. The independent implementation of tethering proteins enabled their selective removal to mimic gene knockout situations. This showed that simulated SV-to-PM distance distributions qualitatively aligned with published EM studies upon removal of SNARE and Syt tethers, while Munc13 knockout data were best approximated when assuming additional disruption of SNARE tethers. Thus, while salient features of SV docking can be accounted for by independent tethering alone, our results suggest that functional tether interactions not yet featured in our model are crucial for biological function. Y1 - 2025 U6 - https://doi.org/10.1113/JP286651 VL - 603 IS - 20 SP - 6107 EP - 6134 ER - TY - JOUR A1 - Montefusco, Alberto A1 - Helfmann, Luzie A1 - Okunola, Toluwani A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - Partial mean-field model for neurotransmission dynamics JF - Mathematical Biosciences N2 - 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. Y1 - 2024 U6 - https://doi.org/10.1016/j.mbs.2024.109143 VL - 369 ER - TY - JOUR A1 - Lücke, Marvin A1 - Winkelmann, Stefanie A1 - Heitzig, Jobst A1 - Molkenthin, Nora A1 - Koltai, Péter T1 - Learning interpretable collective variables for spreading processes on networks JF - Physical Review E N2 - Collective variables (CVs) are low-dimensional projections of high-dimensional system states. They are used to gain insights into complex emergent dynamical behaviors of processes on networks. The relation between CVs and network measures is not well understood and its derivation typically requires detailed knowledge of both the dynamical system and the network topology. In this Letter, we present a data-driven method for algorithmically learning and understanding CVs for binary-state spreading processes on networks of arbitrary topology. We demonstrate our method using four example networks: the stochastic block model, a ring-shaped graph, a random regular graph, and a scale-free network generated by the Albert-Barabási model. Our results deliver evidence for the existence of low-dimensional CVs even in cases that are not yet understood theoretically. Y1 - 2024 U6 - https://doi.org/10.1103/PhysRevE.109.L022301 VL - 109 IS - 2 SP - L022301 ER - TY - JOUR A1 - Ernst, Ariane A1 - Bankowski, Anastasia A1 - Jusyte, Meida A1 - Okunola, Toluwani A1 - Petrov, Tino A1 - Walter, Alexander A1 - Winkelmann, Stefanie T1 - Parameter Optimization for a Neurotransmission Recovery Model JF - Bulletin of Mathematical Biology N2 - We assess the empirical applicability of a simplified model for neurotransmitter release that incorporates maturation, fusion, and recovery of both release sites and vesicles. Model parameters are optimized by fitting the model to experimental data obtained from neuromuscular junction synapses of 3rd-instar Drosophila melanogaster larvae. In particular, the mean-squared error between the local extrema of the simulated total junction current and its experimental counterpart is minimized. We compare three estimation approaches, differing in the choice of optimized parameters and the fusion rate function. Despite the model’s minimalistic structure, it demonstrates a compelling ability to replicate experimental data, yielding plausible parameter estimates for five different animals. An additional identifiability analysis based on the profile likelihood reveals practical non-identifiabilities for several parameters, highlighting the need for additional constraints or data to improve estimation accuracy. Y1 - 2025 U6 - https://doi.org/10.1007/s11538-025-01486-2 VL - 87 PB - Bulletin of Mathematical Biology ER - TY - JOUR A1 - Straube, Arthur A1 - Olicón Méndez, Guillermo A1 - Winkelmann, Stefanie A1 - Höfling, Felix A1 - Engel, Maximilian T1 - Unfolding the geometric structure and multiple timescales of the urea-urease pH oscillator N2 - We study a two-variable dynamical system modeling pH oscillations in the urea–urease reaction within giant lipid vesicles – a problem that intrinsically contains multiple, well-separated timescales. Building on an existing, deterministic formulation via ordinary differential equations, we resolve different orders of magnitude within a small parameter and analyze the system's limit cycle behavior using geometric singular perturbation theory (GSPT). By introducing two different coordinate scalings – each valid in a distinct region of the phase space – we resolve the local dynamics near critical fold points, using the extension of GSPT through such singular points due to Krupa and Szmolyan. This framework enables a geometric decomposition of the periodic orbits into slow and fast segments and yields closed-form estimates for the period of oscillation. In particular, we link the existence of such oscillations to an underlying biochemical asymmetry, namely, the differential transport across the vesicle membrane. Y1 - 2025 ER -