P311 Adjustment of Vesicle Equation in the Modified Stochastic Synaptic Model to Correct Unexpected Behaviour in Frequency Response of Synaptic Efficacy
Ferney Beltran-Velandia*1,2,3, Nico Scherf2,3, Martin Bogdan1,2
1Neuromorphic Information Processing department, Leipzig University, Leipzig, Germany
2Center for Scalable Data Analytics and Artificial Intelligence ScaDS.AI, Dresden/Leipzig, Humboltstrasse 25, Leipzig, Germany
3Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstrasse 1a, Leipzig, Germany
*Email:beltran@informatik.uni-leipzig.de
Introduction
Synaptic Dynamics (SD) describes the plasticity properties of synapses in the timescale of milliseconds. Among different SD models, The Modified Stochastic Synaptic Model (MSSM) is a biophysical one that can simulate the SD mechanisms of facilitation and depression [1]. Further analysis of the parameters found in [2] points at an unexpected behaviour in the frequency response of the MSSM. This behaviour is also studied in the time-domain, which points to an adjustment in the dynamics of the vesicle release. This correction leads to a version of the MSSM without the unexpected behaviour, balancing better the equations and allowing to find new sets of parameters to simulate examples of facilitation and depression.
Methods
The MSSM represents the dynamics of synapses by modelling the dynamics of Calcium, Vesicles release, Probability of release, Neurotransmitters buffering and postsynaptic contribution with differential equations and 10 parameters. In previous work [2], a pipeline was used to tune the parameters of the MSSM when simulating two types of synapses: pyramidal to interneuron (facilitation) and Calyx of Held (depression). The parameters are analysed using the frequency response of the synaptic efficacy, ranging from 1-100Hz [3]. The unexpected behaviour is defined as the frequency from where a discontinuity appears. Further analysis in the time-domain allows to propose the adjusted MSSM, which corrects this behaviour and balances its equations.
Results
Applying the frequency response analysis to the parameters for the studied SD mechanisms shows that some responses exhibit the unexpected behaviour (Fig. 1a-b). This behaviour is associated in the time-domain with the increment of neurotransmitters released even though the number of vesicles is in its steady-state (Fig. 1c). An adjustment on the equation of Vesicles release corrects this behaviour by making the input contribution dependent on the current number of vesicles release (Fig. 1d). To validate our approach, the pipeline is run for the adjusted MSSM, finding 6000 new sets of parameters for both SD mechanisms. The frequency response for the new parameters is depicted in Fig. 1e-f, showing the expected behaviour.
Discussion
The adjustment of the MSSM not only corrects the unexpected behaviour in the frequency- and time-domains but also balances the equation of Vesicle release: In the original model, the probability of release had the same units as the vesicles. With the adjustment, the probability of release recovers its dimensionless nature. The new distributions of parameters show that some parameters have more influence to distinguish between facilitation and depression, especially the ones associated to Probability of release and Neurotransmitters buffering. Finally, this work represents a step forward to the integration of the MSSM into Spiking Neural Networks, enhancing their computationalcapabilitieswith the properties of Synaptic Dynamics.
Figure 1. Figure 1. Unexpected behaviour of the MSSM: a-b) frequency responses with unexpected behaviour. In red, an example of the discontinuity of the efficacy. c) Time response: N(t) increase even if V(t) is in steady-state, causing the unexpected behaviour. d) Time response of the adjusted MSSM showing the correction. e-f) Frequency response of new parameters with the unexpected behaviour corrected.
Acknowledgements
I want to thank the team of the Neuromorphic Information Processing Group, specially Patrick Schoefer and Dominik Krenzer for all the fruitful discussions.This work was partially funded by the German Federal Ministry of Education and Research (BMBF) within the project (ScaDS.AI) Dresden/Leipzig (BMBF grant 01IS18026B).
References
[1] El-Laithy, K. (2012). Towards a brain-inspired information processing system: Modelling and analysis of synaptic dynamics. LAP Lambert Academic Publishing.
[2] Beltran, F., Scherf, N., & Bogdan, M. (2025). A pipeline based on differential evolution for tuning parameters of synaptic dynamics models. (To appear in Proceedings of the 33rd ESANN)
[3] Markram, H., Wang, Y., & Tsodyks, M. (1998). Differential signaling via the same axon of neocortical pyramidal neurons. Proceedings of the National Academy of Sciences, 95 (9), 5323-5328. doi: 10.1073/pnas.95.9.5323
