Space-time stochastic models for neurotransmission processes
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.
Basic function of a chemcial 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)
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.
Different voltage-clamp measured signals at drosophila NMJ: (A) Mini excitatory junction currents (mEJC) that occur stochastically without stimulation. (B) Evoked excitatory junction currents in response to stimulation. (eEJC). (C) eEJC from a two-pulse stimulation train showing synaptic facilitation. (A,B: T. Götz, C: Kobbersmed et al.)
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 varying 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. In this project, we have built on that work and have developed a method for direct computation of the exact first- and second-order moments for models that generate the postsynaptic current by convolving an impulse response function with the output signal of a linear reaction network. This renders expensive stochastic simulations obsolete. We are now investigating if a model extension could help explore the rate-limiting factor during sustained synaptic activity, which is currently an unsolved problem in biology.
Unpriming Model by Kobbersmed et al.: 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.)
See also:
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. https://doi.org/10.1016/j.mbs.2021.108760
Kobbersmed, Janus RL, Andreas T Grasskamp, Meida Jusyte, Mathias A Böhme, Susanne Ditlevsen, Jakob Balslev Sørensen, und Alexander M Walter. „Rapid regulation of vesicle priming explains synaptic facilitation despite heterogeneous vesicle:Ca2+ channel distances“. Herausgegeben von Mark CW van Rossum, Ronald L Calabrese, und Victor Matveev. eLife 9 (20. Februar 2020): e51032. https://doi.org/10.7554/eLife.51032.
