Introduction We study the role of interaction between synaptic plasticity rules and cellular physiology in producing useful connectivity in neural populations. We leverage two key aspects of biological neural networks: 1) neurons and the synapses connecting them are inherently diverse in their structure and electrophysiological properties, and 2) synapses are highly plastic and subject to activity-dependent changes in strength, which can be mathematically formalized by rules such as spike-timing-dependent plasticity.
Methods We address this question in networks of quadratic integrate-and-fire (QIF) neurons endowed with STDP. We develop a multi-population mean-field model [1] that incorporates spike synchronization, allowing it to reproduce synaptic weight evolution in heterogeneous spiking neural networks — something conventional rate models fail to capture. Mathematically, synaptic evolution is driven by variables that trace past spiking events with time constants determined by the respective learning rule [2].
Results We find that the evolving connectivity patterns are the natural result of an interaction between neural heterogeneity and STDP. The mean-field model captures complex network structure even when it is relatively coarse-grained compared to the network of QIF neurons. As potential applications, we demonstrate that this model can flexibly store associative memory items, and encode memory sequences with repeating items.
Discussion We conclude that the mean-field model can accurately predict synaptic pattern formation in heterogeneous spiking networks. Not only can the model be used for analysis methods such as bifurcation analysis that are not available for discontinuous spiking neuron models, but it should also be applicable for a larger family of synaptic plasticity rules [3].
References [1] Richard Gast, Thomas R. Knösche, and Helmut Schmidt (2021). Mean-field approximations of networks of spiking neurons with short-term synaptic plasticity. Physical Review E, 104(4):044310.
[2] Morrison, Abigail, Markus Diesmann, and Wulfram Gerstner (2008). Phenomenological models of synaptic plasticity based on spike timing. Biological Cybernetics 98(6): 459-478.
[3] Pfister, Jean-Pascal, and Wulfram Gerstner (2006). Triplets of spikes in a model of spike timing-dependent plasticity. Journal of Neuroscience 26(38): 9673-9682.
Acknowledgement This work was supported by a Lumina-Quaeruntur fellowship (LQ100302301 awarded to H.S.) founded by the Czech Academy of Sciences, the Czech Science Foundation (No. 25-15412L), and the Brain dynamics project (No. CZ.02.01.01/00/22_008/0004643) funded by the European Regional Development Fund.
