Title: Network Structures Arising from Spike-Timing Dependent Plasticity
Description: Spike-timing dependent plasticity (STDP), a widespread synaptic modification mechanism, is sensitive to correlations between presynaptic spike trains, and organizes neural circuits in functionally useful ways. In this dissertation, I study the structures arising from STDP in a population of synapses with an emphasis on the interplay between synaptic stability and Hebbian competition, explained in Chapter 1. Starting from the simplest description of STDP which relates synaptic modification to the intervals between pairs of pre- and postsynaptic spikes, I show in Chapter 2 that stability and Hebbian competition are incompatible in this class of ``pair-based'' STDP models, either when hard bounds or soft bounds are imposed to the synapses. In chapter 3, I propose an alternative biophysically inspired method for imposing bounds to synapses, i.e. introducing a small temporal shift in the STDP window. Shifted STDP overcomes the incompatibility of synaptic stability and competition and can implement both Hebbian and anti-Hebbian forms of competitive plasticity.

In light of experiments the explored a variety of spike patterns, STDP models have been augmented to account for interactions between multiple pre- and postsynaptic action potentials. In chapter 4, I study the stability/competition interplay in three different proposed multi-spike models of STDP. I show that the ``triplet model'' leads to a partially steady-state distribution of synaptic weights and induces Hebbian competition. The ``suppression model'' develops a stable distribution of weights when the average weight is high and shows predominantly anti-Hebbian competition. The "NMDAR-based" model can lead to either stable or partially stable synaptic weight distribution and exhibits both Hebbian and anti-Hebbian competition, depending on the parameters. I conclude that multi-spike STDP models can produce radically different effects at the population level depending on how they implement multi-spike interactions. Finally in chapter 5, I focus on the types of global structures that arise from STDP in a recurrent network.

By analyzing pairwise interactions of neurons through STDP and also numerical simulations of a large network, I show that conventional pair-based STDP functions as a loop-eliminating mechanism in a network of spiking neurons and organizes neurons into in- and out-hubs. Loop-elimination increases when depression dominates and decreases when potentiation dominates. STDP with dominant depression implements a buffering mechanism for network firing rates, and shifted STDP can generate recurrent connections in a network, and also functions as a homeostatic mechanism that maintains a roughly constant average value of the synaptic strengths. In conclusion, studying pairwise interactions of neurons through STDP provides a number of important insights about the structures that arise from this plasticity rule in large networks. This approach can be extended to networks with more complex STDP models and more structured external input.