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We assess the empirical applicability of a simplified model for neurotransmitter release that incorporates maturation, fusion, and recovery of both release sites and vesicles. Model parameters are optimized by fitting the model to experimental data obtained from neuromuscular junction synapses of 3rd-instar Drosophila melanogaster larvae. In particular, the mean-squared error between the local extrema of the simulated total junction current and its experimental counterpart is minimized. We compare three estimation approaches, differing in the choice of optimized parameters and the fusion rate function. Despite the model’s minimalistic structure, it demonstrates a compelling ability to replicate experimental data, yielding plausible parameter estimates for five different animals. An additional identifiability analysis based on the profile likelihood reveals practical non-identifiabilities for several parameters, highlighting the need for additional constraints or data to improve estimation accuracy.
Integrating neural networks into mechanistic, equation-based models is a field of growing scientific interest, yet it lacks consistent terminology and a unified mathematical framework. We systematise existing approaches and establish new connections between hybrid modelling, differential equations theory, and deep learning. We clarify the roles of inference, prediction, and generalisation in hybrid models, showing how neural components can capture mathematical structures within and across datasets, and we connect these questions to structural identifiability theory. We further interpret hybrid models through a manifold-learning lens, demonstrating how parametric spaces of missing information can be learned, thereby providing an alternative approach to uncertainty quantification.
