Tabak, Mascagni, Bertram, 2010
This CellML model runs in PCEnv, OpenCell and COR, and the units are consistent throughout. This is the mean field model with synaptic depression, and is only one of the five models described in the paper. However, the others describe networks of 100 linked cells, which is a simulation not inside the current scope of CellML. This model also features elements unsuitable to CellML, the variable "noise" is defined as an array of values around zero with a normal distribution, but it is simply set to zero for this simulation. This model comes close to reproducing figures 7A and 7B, although the slight oscillation in these figures arising from the variable "noise" is not present.
ABSTRACT: Spontaneous episodic activity is a fundamental mode of operation of developing networks. Surprisingly, the duration of an episode of activity correlates with the length of the silent interval that precedes it, but not with the interval that follows. Here we use a modeling approach to explain this characteristic but so far unexplained feature of developing networks. Because the correlation pattern is observed in networks with different structures and components, a satisfactory model needs to generate the right pattern of activity regardless of the details of network architecture or individual cell properties. We thus developed simple models incorporating excitatory coupling between heterogeneous neurons and activity-dependent synaptic depression. These models robustly generated episodic activity with the correct correlation pattern. The correlation pattern resulted from episodes being triggered at random levels of recovery from depression while they terminated around the same level of depression. To explain this fundamental difference between episode onset and termination, we then used a mean field model, where only average activity and average level of recovery from synaptic depression are considered. In this model, episode onset is highly sensitive to inputs. Thus, noise resulting from random coincidences in the spike times of individual neurons led to the high variability at episode onset and to the observed correlation pattern. This work further demonstrates that networks with widely different architectures, different cell types and different functions, all operate according to the same general mechanism early in their development.
The original paper reference is cited below:
Mechanism for the universal pattern of activity in developing neuronal networks, Joel Tabak, Michael Mascagni, Richard Bertram, 2010, Journal of Neurophysiology, volume 103, 2208-2221. PubMed ID: 20164396