Recently, many experimental results have supported the idea that the brain operates
near a critical point [1-5], as reflected by the power laws of avalanche size distributions
and maximization of fluctuations. Several models have been proposed as explanations
for the power law distributions that emerge in spontaneous cortical activity [6,5].
Models based on branching processes and on self-organized criticality are the most
relevant. However, there are additional features of neuronal avalanches that are not
captured in these models, such as the stable recurrence of particular spatiotemporal
patterns and the conditions under which these precise and diverse patterns can be
retrieved [4]. Indeed, neuronal avalanches are highly repeatable and can be clustered
into statistically significant families of activity patterns that satisfy several
requirements of a memory substrate. In many areas of the brain having different brain
functionality, repeatable precise spatiotemporal patterns of spikes seem to play a
crucial role in the coding and storage of information. Many in vitro and in vivo studies
have demonstrated that cortical spontaneous activity occurs in precise spatiotemporal
patterns, which often reflect the activity produced by external or sensory inputs.
The temporally structured replay of spatiotemporal patterns has been observed to occur,
both in the cortex and hippocampus, during sleep and in the awake state, and it has
been hypothesized that this replay may subserve memory consolidation.
Previous studies have separately addressed the topics of phase-coded memory storage
and neuronal avalanches, but our work is the first to show how these ideas converge
in a single cortical model. We study a network of leaky integrate- and-fire (LIF)
neurons, whose synaptic connections are designed with a rule based on spike-timing
dependent plasticity (STDP). The network works as an associative memory of phase-coded
spatiotemporal patterns, whose storage capacity has been studied in [7]. In this paper,
we study the spontaneous dynamics when the excitability of the model is tuned to be
at the critical point of a phase transition, between the successful persistent replay
and non-replay of encoded patterns. We introduce an order parameter, which measures
the overlap (similarity) between the activity of the network and the stored patterns.
We find that, depending on the excitability of the network, different working regimes
are possible. For high excitability, the dynamical attractors are stable, and a collective
activity that replays one of the stored patterns emerges spontaneously, while for
low excitability, no replay is induced. Between these two regimes, there is a critical
region in which the dynamical attractors are unstable, and intermittent short replays
are induced by noise. At the critical spiking threshold, the order parameter goes
from zero to one, and its fluctuations are maximized, as expected for a phase transition
(and as observed in recent experimental results in the brain [5]). Notably, in this
critical region, the avalanche size and duration distributions follow power laws.
Critical exponents are consistent with a scaling relationship observed recently in
neural avalanches measurements. In conclusion, our simple model suggests that avalanche
power laws in cortical spontaneous activity may be the effect of a network at the
critical point between the replay and non-replay of spatiotemporal patterns. Interestingly
in the cortex, the emergence of power law distributions of avalanche sizes depends
on an optimal concentration of dopamine and on the balance of excitation and inhibition,
suggesting that particular parameters must be appropriately tuned. This may suggest
that the cortex operates near the critical point of a phase transition, characterized
by a critical value of excitability.