Dynamics of pruning in simulated large-scale spiking neural networks

Abstract

Massive synaptic pruning following over-growth is a general feature of mammalian brain maturation. This article studies the synaptic pruning that occurs in large networks of simulated spiking neurons in the absence of specific input patterns of activity. The evolution of connections between neurons were governed by an original bioinspired spike-timing-dependent synaptic plasticity (STDP) modification rule which included a slow decay term. The network reached a steady state with a bimodal distribution of the synaptic weights that were either incremented to the maximum value or decremented to the lowest value. After $1\times 10^6$ time steps the final number of synapses that remained active was below 10% of the number of initially active synapses independently of network size. The synaptic modification rule did not introduce spurious biases in the geometrical distribution of the remaining active projections. The results show that, under certain conditions, the model is capable of generating spontaneously emergent cell assemblies.

Introduction

Massive synaptic pruning following over-growth is a general feature of mammalian brain maturation Rakic et al., 1986, Zecevic and Rakic, 1991. Pruning starts near time of birth and is completed by time of sexual maturation. Biological mechanisms that regulate pruning mechanisms involve complex neurochemical pathways of cell signaling and are not intended to be reviewed here. Trigger signals able to induce synaptic pruning could be related to dynamic functions that depend on the timing of action potentials. Spike-timing-dependent synaptic plasticity (STDP) is a change in the synaptic strength based on the ordering of pre- and post-synaptic spikes. This mechanism has been proposed to explain the origin of long-term potentiation (LTP), i.e. a mechanism for reinforcement of synapses repeatedly activated shortly before the occurrence of a post-synaptic spike Kelso et al., 1986, Bi and Poo, 1998, Froemke and Dan, 2002, Kepecs et al., 2002, Markram et al., 1997. STDP has also been proposed to explain long-term depression (LTD), which corresponds to the weakening of synapses strength whenever the pre-synaptic cell is repeatedly activated shortly after the occurrence of a post-synaptic spike (Karmarkar and Buonomano, 2002).

The glutamatergic NMDA receptors were initially identified as the receptor site with all biological features compatible with LTP induced by coincident pre- and post-synaptic cell discharges (Wigstrom and Gustafsson, 1986). The involvement of NMDA receptors in timing-dependent long-term depression (tLTD) has been recently described (Sjstrm et al., 2003). Recent investigations suggest that glutamatergic receptors with AMPA channels and GABAergic receptors may also undergo modifications of the corresponding post-synaptic potentials as a function of the timing of pre- and post-synaptic activities Engel et al., 2001, Woodin et al., 2003. These studies suggest that several mechanisms mediated by several neurotransmitters may exist at the synaptic level for changing the post-synaptic potential, either excitatory or inhibitory, as a function of the relative timing of pre- and post-synaptic spikes.

The important consequences that changes in synaptic strength may produce for information transmission, and subsequently for synaptic pruning, have raised an interest to simulate the activity of neural networks with embedded synapses characterized by STDP Lumer et al., 1997, Fusi et al., 2000, Hopfield and Brody, 2004 The relation between synaptic efficacy and synaptic pruning Chechik et al., 1999, Mimura et al., 2003, suggest that the weak synapses may be modified and removed through competitive “learning” rules. Competitive synaptic modification rules maintain the average neuronal input to a post-synaptic neuron, but provoke selective synaptic pruning in the sense that converging synapses are competing for control of the timing of post-synaptic action potentials Song et al., 2000, Song and Abbott, 2001.

This article studies the synaptic pruning that occurs in a large network of simulated spiking neurons in the absence of specific input patterns. The originality of our study stands on the size of the network, up to 10,000 units, the duration of the experiment, 1,000,000 time units (one time unit corresponding to the duration of a spike), and the application of an original bioinspired STDP modification rule compatible with hardware implementation Eriksson et al., 2003, Tyrrell et al., 2003. The network is composed of a mixture of excitatory and inhibitory connections that maintain a balanced input locally connected in a random way.

STDP is considered an important mechanism that modifies the gain of several types of synapses in the brain. In this study the synaptic modification rule was applied only to the excitatory–excitatory connections. This plasticity rule might produce the strengthening of the connections among neurons that belong to cell assemblies characterized by recurrent patterns of firing. Conversely, those connections that are not recurrently activated might decrease in efficiency and eventually be eliminated. The main goal of our study is to determine whether or not, and under which conditions, such cell assemblies may emerge from a large neural network receiving background noise and content-related input organized in both temporal and spatial dimension. In order to reach this goal the first step consisted in characterizing the dynamics of synaptic pruning in absence of content-related input. This first step is described here.