Abstract
Non-random connectivity can emerge without structured external input driven by activity-dependent mechanisms of synaptic plasticity based on precise spiking patterns. Here we analyze the emergence of global structures in recurrent networks based on a triplet model of spike timing dependent plasticity (STDP), which depends on the interactions of three precisely-timed spikes, and can describe plasticity experiments with varying spike frequency better than the classical pair-based STDP rule. We derive synaptic changes arising from correlations up to third-order and describe them as the sum of structural motifs, which determine how any spike in the network influences a given synaptic connection through possible connectivity paths. This motif expansion framework reveals novel structural motifs under the triplet STDP rule, which support the formation of bidirectional connections and ultimately the spontaneous emergence of global network structure in the form of self-connected groups of neurons, or assemblies. We propose that under triplet STDP assembly structure can emerge without the need for externally patterned inputs or assuming a symmetric pair-based STDP rule common in previous studies. The emergence of non-random network structure under triplet STDP occurs through internally-generated higher-order correlations, which are ubiquitous in natural stimuli and neuronal spiking activity, and important for coding. We further demonstrate how neuromodulatory mechanisms that modulate the shape of the triplet STDP rule or the synaptic transmission function differentially promote structural motifs underlying the emergence of assemblies, and quantify the differences using graph theoretic measures.
Highlights
The synaptic wiring between neurons—originally proposed as a mechanism for learning and memory—is sculpted by experience and has become a most relevant link between circuit structure and function [1]
We present two main results: first, we derive a formal analytical framework for the evolution of synaptic weights depending on the second- and third-order cumulants of spike time interactions under the triplet spike timing dependent plasticity (STDP) rule by expressing them as a sum of structural motifs; second, we discuss the functional implications of this framework and present the biological conditions which promote the formation of assemblies without external instruction
To study the autonomous emergence of assemblies in a recurrent network from a general form of STDP that includes the contribution of pairs and triplets of spikes to synaptic plasticity, we require a minimal theoretical representation of the network with plastic synapses driven by internal correlations in the spike timing statistics
Summary
The synaptic wiring between neurons—originally proposed as a mechanism for learning and memory—is sculpted by experience and has become a most relevant link between circuit structure and function [1]. The original formulation of Hebbian plasticity, whereby “cells that fire together, wire together” [2, 3], fostered the concept of ‘cell assemblies’ [4], defined as groups of neurons that are repeatedly co-activated leading to the strengthening of synaptic connectivity between individual neurons This has suggested that activity-dependent synaptic plasticity, including both long-term potentiation and long-term depression, is a key mechanism for the emergence of assemblies in the organization of neural circuits [5,6,7]. Experiments in sensory deprived larvae have demonstrated that the basic structure of spontaneous activity and functional connectivity emerges without intact retinal inputs, suggesting that neuronal assemblies are intrinsically generated in the tectum and not just the product of correlated external inputs [25,26,27] This raises the important question of what drives the emergence of these clustered structures, and whether patterned external input is necessary
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