AA1 – Life Sciences



Space-Time Stochastic Models for Neurotransmission Processes

Project Heads

Christof Schütte, Stephan Sigrist, Stefanie Winkelmann

Project Members

Ariane Ernst (ZIB), Alexander Walter (FMP), Torsten Götz (Charité)

Project Duration

01.01.2019 – 30.09.2022

Located at



Neurotransmission denotes the passing of stimuli from a neural cell to a target cell at specific junction points called synapses. The aim of this project is to increase our understanding of the underlying processes via spatiotemporal deterministic and stochastic modelling.


At chemical synapses, neurotransmission is based on the action potential-triggered opening of voltage-gated Calcium channels. The inflowing Ca2+-ions bind to proteins on the surface of primed (docked and prepared) synaptic vesicles, causing them to release neurotransmitters into the synaptic cleft. After diffusing across the cleft, the molecules activate receptors in the postsynaptic membrane, triggering a new action potential. The process is of fundamentally stochastic nature not only because it relies on diffusion and binding of different molecules, but also because the vesicle release itself has proven to be failure-prone and varying in vesicle number. On top of that, synaptic strength changes with repeated use in the short as well as the long term, a phenomenon termed synaptic plasticity.

Despite — or rather, because! – of its unrelieable and plastic nature, synaptic function is a key player in almost all neural activity and suspected to be of great importance especially for learning processes in the brain. This makes it a very attractive area of research not only for neuroscientists, but also physicists, mathematicians and information scientists.  Since the size scale of vesicles as well as the synaptic cleft is in the order of few nanometers, well below the diffraction limit, dynamic and precise imaging of neurotransmission processes is currently very difficult. We can however measure the excitatory junction currents resulting from many synaptic contact points in the postsynaptic cell using voltage- or patch-clamp mehtod. In order to gain information from these currents, mathematical modelling is needed.


While many different models of varyig mathematical complexity have been published in order to characterize and categorize different synapses according to parameters such as e.g. release probability or synaptic strength, hardly any of them have helped our understanding of the molecular processes responsible for neurotransmission along. Only very recently, Kobbersmed et al. released an article proving the importance of Calcium-dependent priming/unpriming mechanisms in order to achieve realistic short-term plasticity as well as eEJC variances using realistic spatial vesicle distributions. We are aiming to build on that work using SDEs for a more efficient simulation of longer pulse trains and to explore the possibility of reducing the number of involved equations/steps in the model, both while still achieving high accordance with experimental eEJC amplitudes and variances.

Selected Publications

  • A. Ernst, N. Unger, C. Schütte, A. Walter, S. Winkelmann. Rate-limiting recovery processes in neurotransmission under sustained stimulation. Submitted, 2023
  • M. J. del Razo, S. Winkelmann, R. Klein, and F. H ̈ofling. Chemical diffusion master equation: formulations of reaction–diffusion processes on the molecular level. Cascades of Scales: Applications and Mathematical Methodologies, to appear 2023
  • A. Montefusco, C. Sch ̈utte, and S. Winkelmann. A route to the hydrodynamic limit of a reaction-diffusion master equation using gradient structures. SIAM Journal on Applied Mathematics, to appear 2023
  • A. Thies, V. Sunkara, S. Ray, H. Wulkow, M. ̈O. Celik, F. Yerg ̈oz, C. Sch ̈utte, C. Stein, M. Weber, and S. Winkelmann. Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design. Scientific Reports, 13(607), 2023
  • A. Ernst, C. Schütte, S. Sigrist, S. Winkelmann. Variance of filtered signals: characterization for linear reaction networks and application to neurotransmission dynamics. Mathematical Biosciences, 343, 2022
  • H.-H. Boltz, A. Sirbu, N. Stelzer, P. de Lanerolle, S. Winkelmann, and P. Annibale. The impact of membrane protein diffusion on GPCR signaling. Cells, 11(10):1660, 2022
  • M. J. del Razo, D. Fr ̈omberg, A. V. Straube, C. Sch ̈utte, F. H ̈ofling, and S. Winkelmann. A probabilistic framework for particle-based reaction–diffusion dynamics using classical Fock space representations. Letters in Mathematical Physics, 112(3):1–59, 2022
  • S. Winkelmann, C. Schütte. Stochastic Dynamics in Computational Biology. Springer, 2020

Selected Pictures



Basic function of a chemical synapse: upon arrival of an action potential, voltage-gated Calcium channels open in the active zone. The inflowing Ca2+-ions bind to proteins on the surface of primed (docked and prepared) vesicles, causing them to release neurotransmitters into the synaptic cleft. After diffusing across the cleft, the molecules activate receptors in the postsynaptic membrane, triggering a new action potential. (S. Winkelmann)

Unpriming Model: vesicles are primed for fusion with rate k_rep. Binding of Ca2+-ions increases release (fusion) probability, up to five ions can be bound. However, primed vesicles can also become unprimed depending on the local Calcium-concentration, where more Calcium decreases the unpriming rate. (Kobbersmed et al.)

Different voltage-clamp measured signals at drosophila NMJ: (A) Mini excitatory junction currents (mEJC). (B) Evoked excitatory junction currents. (eEJC). (C) eEJC from a two-pulse train showing synaptic facilitation. (A,B: T. Götz, C: Kobbersmed et al.)

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