  Living neuronal networks in dissociated neuronal cultures are widely known
for their ability to generate highly robust spatiotemporal activity patterns in
various experimental conditions. These include neuronal avalanches satisfying
the power scaling law and thereby exemplifying self-organized criticality in
living systems. A crucial question is how these patterns can be explained and
modeled in a way that is biologically meaningful, mathematically tractable and
yet broad enough to account for neuronal heterogeneity and complexity. Here we
propose a simple model which may offer an answer to this question. Our
derivations are based on just few phenomenological observations concerning
input-output behavior of an isolated neuron. A distinctive feature of the model
is that at the simplest level of description it comprises of only two
variables, a network activity variable and an exogenous variable corresponding
to energy needed to sustain the activity and modulate the efficacy of signal
transmission. Strikingly, this simple model is already capable of explaining
emergence of network spikes and bursts in developing neuronal cultures. The
model behavior and predictions are supported by empirical observations and
published experimental evidence on cultured neurons behavior exposed to oxygen
and energy deprivation. At the larger, network scale, introduction of the
energy-dependent regulatory mechanism enables the network to balance on the
edge of the network percolation transition. Network activity in this state
shows population bursts satisfying the scaling avalanche conditions. This
network state is self-sustainable and represents a balance between global
network-wide processes and spontaneous activity of individual elements.
