Project
AA1-5
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
ZIB
Description
Neurotransmission denotes the process by which a chemical or electrical signal is passed from a neuron to a target cell. At chemical synapses, the input signal is translated into the release of neurotransmitters that rapidly diffuse over the synaptic cleft and elicit a postsynaptic response by binding to receptors in the target cell membrane, see the figures below for an illustration. Before being released into the cleft, the molecules are contained in synaptic vesicles that can dock to protein clusters called release sites. Once a vesicle binds to a site it is primed for release: The release sites sit in a region of the cell membrane called the active zone close to voltage-gated calcium-channels. The arriving signal triggers the opening of the channels, leading to an influx of calcium-ions. These ions bind to receptors on the vesicle surface and thus provokes the fusion of vesicles with the presynaptic membrane, thereby releasing neurotransmitters into the synaptic cleft. The entire mechanism is inherently of stochastic nature: vesicle fusion is not triggered reliably (but with a certain release probability) and the entire chain of events depends on molecular interactions and diffusion processes. The aim of this project was to increase our understanding of this mechanism by employing space-time stochastic modeling and in turn use the biology as a motivation to advance stochastic modeling and simulation.
In this project, a method for the direct computation of variances for signals generated by a reaction network under convolution with an impulse response function was developed, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. The identity of the rate-limiting recovery process during neurotransmission has been investigated by means of sensitivity analysis of a novel non-linear ODE and stochastic jump model. Moreover, a textbook on stochastic models for biochemical reaction processes has been written and a probabilistic framework for particle-based reaction-diffusion dynamics has been derived.
Selected Publications
- A. Montefusco, L. Helfmann, T. Okunola, S. Winkelmann, C. Schütte. Partial mean-field model for neurotransmission dynamics. Mathematical Biosciences, 369, 2024.
- M. Engel, G. Olicón-Méndez, N. Wehlitz, S. Winkelmann. Synchronization and random attractors in reaction jump processes. Journal of Dynamics and Differential Equations, 1-36, 2024
- A. Ernst, N. Unger, C. Schütte, A. Walter, S. Winkelmann. Rate-limiting recovery processes in neurotransmission under sustained stimulation. Mathematical Biosciences, 362:109023, 2023
- M. J. del Razo, S. Winkelmann, R. Klein, and F. Höfling. Chemical diffusion master equation: formulations of reaction–diffusion processes on the molecular level. Journal of Mathematical Physics, 64(1), 2023
- A. Ernst, U. Falkenhagen, S. Winkelmann. Model reduction for calcium-induced vesicle fusion dynamics. Proceedings in Applied Mathematics & Mechanics, 23(4), 2023
- A. Montefusco, C. Schütte, and S. Winkelmann. A route to the hydrodynamic limit of a reaction-diffusion master equation using gradient structures. SIAM Journal on Applied Mathematics, 83(2):837-861, 2023
- A. Thies, V. Sunkara, S. Ray, H. Wulkow, M. O. Celik, F. Yergöz, C. Schütte, 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. Frömberg, A. V. Straube, C. Schütte, F. Höfling, 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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