AA1 – Life Sciences



The Spatio-Temporal Modelling of Mechanisms Underlying Pain Relief via the µ-Opioid Receptor

Project Heads

Martin Lohse, Christof Schütte, Christoph Stein, Marcus Weber, Stefanie Winkelmann (since January 2021)

Project Members

Vikram Sunkara (till January 2021, FU), Noureldin Saleh (till August 2019, ZIB), Sourav Ray (from January 2020, ZIB)

Project Duration

First funding period: 01.01.2019 – 31.12.2020; Second funding period: 01.01.21 – 31.12.2022

Located at

FU Berlin / ZIB


The project has shown that the chemical environment of µ-opioid receptors can play an important role for pain relief and for the clinical use of pain relief drugs. This not only includes the binding event of an opioid to the receptor, but it also shows changes in the downstream signaling cascade and reveals possible alternative ways of initiation of signaling. In this interdisciplinary project we combined experimental and mathematical research and now have at hand the possibility to optimize new drugs according to our holistic stochastic model that couples molecular and cellular effects across 18 orders of magnitude in time. This was made possible by significant progress in overcoming the timescale barrier in molecular dynamics.

Project Webpages

M. Weber and C. Stein have presented a common outreach talk at URANIA in 03/2020. The link is here.

There is a ZIB webpage about this project here.

Selected Publications

  • S. Ray, K. Fackeldey, C. Stein, M. Weber: Coarse-grained MD simulations of opioid interactions with the mu-opioid receptor and the surrounding lipid membrane. Biophysica, 3(2), 2023
  • A. Thies, V. Sunkara, S. Ray, H. Wulkow, M. Ö. Celik, F. Yergöz, C. Schütte, C. Stein, M. Weber and Stefanie Winkelmann: Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design. Scientific Reports, 13(607), 2023
  • M.Ö. Celik,  V. Seitz, F. Yergöz, S. Dembla, N.K. Blum, S. Schulz, C. Stein: Modulation of G-protein activation, calcium currents and opioid receptor phosphorylation by the pH-dependent antinociceptive agonist NFEPP. Frontiers in Molecular Neuroscience, 16, 2023
  • H.H. Boltz, A. Sirbu, N. Stelzer, P. de Lanerolle, S. Winkelmann, P. Annibale: The impact of membrane protein diffusion on GPCR signaling. Cells, 11(10), 2022
  • N.N. Jimenez-Vargas, Y. Yu, D.D. Jensen, D.D. Bok, M. Wisdom, R. Latorre, C. Lopez, J.O. Jaramillo-Polanco, C. Degro, M. Guzman-Rodriguez, Q. Tsang, Z. Snow, B.L. Schmidt, D. E. Reed, A. E. Lomax, K. G. Margolis, C. Stein, N. W. Bunnett, S. J. Vanner: Agonist that activates the μ-opioid receptor in acidified microenvironments inhibits colitis pain without side effects. Gut, 71(4), 2022
  • S. Roehl, M. Weber, K.Fackeldey: Computing the minimal rebinding effect for nonreversible processes. SIAM MMS, 19(1), 2021
  • A. Bittracher, C. Schütte: A probabilistic algorithm for aggregating vastly undersampled large Markov chains. Physica D, 416:132799, 2021
  • J. Möller, A. Isbilir, T. Sungkaworn, B. Osberg, C. Karathanasis, V. Sunkara, E.O. Grushevskyi, A. Bock, P. Annibale, M. Heilemann, C. Schuette, and M.J. Lohse: Single molecule mu-opioid receptor membrane-dynamics reveal agonist-specific dimer formation with super-resolved precision. Nature chemical biology, 16, 2020
  • S. Winkelmann, C. Schütte: Stochastic Dynamics in Computational Biology. Vol. 645. Cham: Springer, 2020
  • S. Ray, V. Sunkara, C. Schütte, M. Weber: How to calculate pH-dependent binding rates for receptor-ligand systems based on thermodynamic simulations with different binding motifs. Molecular Simulation, 46(18), 2020
  • R. J. Rabben, S. Ray, M. Weber: ISOKANN: Invariant subspaces of Koopman Operators learned by a Neural Network. The J. of Chem. Phys., 153(11):114109, 2020
  • Meyer J, Del Vecchio G, Seitz V, Massaly N, Stein C: Modulation of mu-opioid receptor activation by acidic pH is dependent on ligand structure and an ionizable amino acid residue. British Journal of Pharmacology, 176(23), 2019
  • Del Vecchio G, Labuz D, Temp J, Seitz V, Kloner M, Negrete R, Rodriguez-Gaztelumendi A, Weber M, Machelska H, Stein C: pKa of opioid ligands as a discriminating factor for side effects. Scientific Reports, 9(1), 2019
    correction: Scientific Reports 2020; 10:4366. doi.org/10.1038/s41598-020-61224-7
  • Lešnik S, Hodošček M, Bren U, Stein C, Bondar AN: Potential energy function for fentanyl-based opioid pain killers. J Chem Inf Model 2020; 60:3566−76; dx.doi.org/10.1021/acs.jcim.0c00185
  • Massaly N, Temp J, Machelska H, Stein C: Uncovering the analgesic effects of a pH-dependent mu-opioid receptor agonist using a model of non-evoked ongoing pain. Pain 2020; 161:2798–804. doi: 10.1097/j.pain.0000000000001968
  • Baamonde A, Menéndez L, González-Rodríguez S, Lastra A, Seitz V, Stein C, Machelska H: A low pKa ligand inhibits cancer-associated pain in mice by activating peripheral mu-opioid receptors. Sci Rep 2020; 10:18599; doi.org/10.1038/s41598-020-75509-4


  • Yergöz F, Çelik ÖM, Seitz V, Weber M, Stein C: Modulation of opioid receptor function by mediators of tissue injury and inflammation. International Narcotics Research Conference 2021; July 14; virtual
  • Ray S, Stein C, Weber M: Modulation of Receptor-Activation Due to Hydrogen Bond Formation. ICIAM 2021: XV. International Conference on Industrial and Applied Mathematics, Istanbul, Turkey, August 16, 2021; virtual (Best Presentation Award)

Review Articles:

  • Stein C:
    Schmerzinhibition durch Opioide – neue Konzepte.
    Der Schmerz 2019;33:295-302
    DOI: 10.1007/s00482-019-0386-y
  • Stein C, Kopf A:
    Pain therapy – are there new options on the horizon?
    Best Practice & Research Clinical Rheumatology 2019;33:101420
  • Stein C:
    Opioid analgesia: recent developments
    Curr Opin Supportive & Palliative Care 2020;14:112-117

Book Chapters:

  • Stein C, Gaveriaux-Ruff C:
    Opioids and Pain.
    In: The Oxford Handbook of the Neurobiology of Pain. ed. by Wood J. Oxford University Press, New York 2020: 729-769.
    DOI: 10.1093/oxfordhb/9780190860509.013.9
  • Stein C:
    In: Encyclopedia of Molecular Pharmacology 3rd Edition, ed. by Offermanns S, Rosenthal W. Springer, Berlin Heidelberg New York 2020: 1-6. doi.org/10.1007/978-3-030-21573-6_6-1
  • Stein C, Kopf A:
    Management of the patient with chronic pain.
    In: Miller’s Anesthesia 9th Edition. ed. by Gropper MA. Elsevier, Philadelphia 2020: 1604-21
  • Rittner HL, Oehler B, Stein C:
    Immune system, pain and analgesia.
    In: The Senses: A Comprehensive Reference; Vol. 6. Pain, ed. by Schaible HG, Pogatzki-Zahn E. Elsevier, Philadelphia 2020

Selected Pictures

Different binding modes at only one pH value

binding mode
Binding Mode of Fentanyl at pH7
The binding modes of opioids depend on the pH value of the environment. With changing the pH-value, the protonation state of the opioid and of the receptor changes, too. From a modelling point of view, each protonation event leads to a new mathematical model to describe the dynamics of the molecular system. I.e. for every protonation state of the system we end up with a different modelling and, thus, with a different resulting kinetics. The mathematical problem is given by the fact, that changes in pH-value do not simply change the protonation state, they change the probabilities for each of the states. Hence, the “correct” physical modelling of an opiod-receptor binding process is not given by one mathematical model, it is given by a set of different models combined with different statistical weights. One mathematical goal of this project was to find a way to simulate molecular processes, if the mathematical descripition of the process being used is a statistical mixture of different physical models.

Simulation of protonation states

Simulation of the opioid receptor and opioids
Simulation of the opioid receptor and opioids
In this project we created all possible different physical models (different protonation states) of the opoid receptor and its binding opioid molecule. Then we simulated the underlying Markov process for each of them separately. For the mixture of the different models, we clustered all Markov states of the different physical models together and created a transition rate matrix (a dicretized Fokker-Planck operator) for the entire process by regarding the probabilities for the single models. The last step of combining the single simulation results was possible by using a certain type of discretization of Fokker-Planck operators.
pH dependent binding rate of opioids
The outcome of our procedure revealed that Fentanyl compared to NFEPP  (two different opioids) have very different binding rates in inflamed compared to healthy tissue. For the first time in opioid research, we were able to plot a continuous curve which shows the pH-dependence of activation rates of opiod-receptors.

We were able to explain the outcome of clinical tests on the basis of this dependence.


There is a translational challenge in going from in vitro to in situ. We bridging this gap by developing mathematical models to capture the spatio-temporal dynamics of the opioid in situ.

Our recent in vitro studies on MOR expressed in transfected cells have yielded the following results: H2O2 did not interfere with binding of the standard MOR ligand DAMGO. Higher H2O2 concentrations decreased G-protein coupling (measured by binding of [35S]-GTPγS) induced by the standard MOR agonist fentanyl. At acidic pH, the pH-dependent ligand NFEPP (but not fentanyl) more potently activated MOR-dependent G-protein coupling. H2O2 did not influence fentanyl-induced inhibition of forskolin-stimulated cAMP production. These results will be complemented by measurements of membrane ion currents.

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