Neuronal networks store information both in the spike rate and in the spike timing (i.e. the changes of the delay between two spikes belonging to the same or different neurons). The information is also transferred in a specific behaviour called "burst", a densely packed spike activity often encountered as pattern synchronized among different neuronal cells (Garaschuk et al 2000; Opitz et al 2001; Potter 2001; Kamioka, 1996; Jimbo, 1998; Jimbo, 1999; Shahaf and Marom, 2001).
In in vitro neuronal networks after approximately 8-10 DIV single spikes, spatially coordinated population bursts, temporally separated by periods of silence, are ubiquitously occurring firing patterns. While the oscillatory pattern as such is extremely stable, the precise onset of these patterns, as well as their actual individual burst rate and duration and their variability, crucially depend upon cell type, plating density, cell preparation and pharmacological environment (Opitz et al 2001; Wagenaar et al. 2005, 2006). Thus, networks of (e.g. rat or mouse cortical, striatal or hippocampal) neurons plated on MEAs can be considered as in vitro models of neuronal oscillators, and are sensitive to pharmacological manipulation.
The rich repertoire of spiking and bursting patterns observed in cultured neuronal networks can be described to astonishing accuracy within the framework of an extended mean field analysis, with numerical model parameters quantitatively determined from single-cell experiments (Giugliano et al. 2004; Amit and Brunel 1997). This mean field analysis relies upon the numerical solution of a stochastic differential equation in the presence of Gaussian noise. It can be complemented by numerical simulations of integrate-and-fire (IF) neurons.
Both in development and in maturity neuronal networks experience long-term variations of baseline activity. If, on one hand variations of baseline activity represents different opportunities for network precessing, then on the other hand, the variability imposes functional challenges to the neuronal homeostasis. Numerous open questions remain as to how spontaneous activity modes (homeostatic modes) affect the effectiveness of reinforcement signals, the rate of and capacity for associative memory formation, and the persistence of associative memories in the face of spontaneous activity and unrelated stimulation. The formation of associative memories for complex patterns by realistic networks with spiking neurons and bounded, bi-stable synapses is only beginning to be understood (Senn and Fusi, 2005). Many of these questions are difficult to address with mean-field analysis and software simulation.
In recurrent networks without pacemaker neurons, self-sustaining background activity can be modelled as a constant depolarizing input current (Latham2000a), a noisy input current (Ihzikevich2003), or a Poisson spike train (Ihzikevich2004). The activity dynamics and operating point of the network may assume different modes (synchronized bursing, asynchronous, etc) and are controlled by background activity (Ihzikevich2004).
Small networks of spiking neurons and plastic synapses can be realized in silico with suitably designed, analogue/digital hybrid circuits (Mead, 1988; Fusi, Mattia, 1999). Such systems offer considerable flexibility and convenience in setting connectivity, performing experiments, and analysing collective behaviour. Current electronic synapses incorporate some biological detail (Indiveri et al., 2006): (i) connection weight is bi-stable, bounded, and changes in a stochastic manner,
(ii) the modification of connection weight depends on the phase relation between a pre-synaptic spike and a post-synaptic activity variable (e.g., depolarization, Ca2+-analogue). Networks with such synapses can learn complex and highly correlated patterns in a semi-supervised fashion (Senn, Fusi, 2005).
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