Modeling of superbursts in neuronal cultures: Which synaptic and cellular mechanisms are required?

The activity in neuronal cultures is dominated by the synchronized network bursts. The nature of these bursts is very varied: Their quantity and quality has been shown to depend on many variables, including the time in vitro, initial plating density, and extracellular ionic concentrations (Wagenaar et al., BMC Neurosci. 2006, Maeda et al., JNeurosci. 1995). Similar activity can be reproduced by simulating a network of point-neurons using many different approaches (see e.g. Tsodyks et al., JNeurosci. 2000; Gritsun et al., Biol. Cybern. 2010). Such models are often, however, restrictive by the range of dynamical regimes they are able to describe. Especially, the superbursts, i.e., prolonged network bursts that consist of tightly repeated short bursts (see e.g. Wagenaar et al., BMC Neurosci. 2006), propose a challenge to the models due to their variable nature and the wide temporal scale of the phenomenon. Understanding their contributors is important in order to analyze and understand the collective behavior of more complex neuronal systems.
In this work, we study computationally the contribution of different synaptic and cellular mechanisms to the network burst characteristics and to the emergence of the superbursts. In addition, the effect of the synaptic map is monitored by applying various types of connectivity graphs. We apply several point-neuron models, including a current-based leaky integrate-and-fire model (LIF) (Tsodyks et al., JNeurosci. 2000), a conductance-based leaky integrate-and-fire model (CLIF) (Compte et al., Cereb. Cortex 2000), and a Hodgkin-Huxley type of model (HH) (Golomb et al., JNeurophysiol. 2006). The synapses are modeled as chemical synapses with or without synaptic depression. Using the LIF model, the synaptic properties are extensively varied and their contributions to the network bursting are studied, both in excitatory-only and excitatory-inhibitory networks. Ceaseless bursts, in other words the runaway excitation, can be produced by recurrent networks without dynamical synapses, but for the cessation of the bursts either synaptic depression or strong enough recurrent inhibition has to be applied. In the CLIF model, the synaptic properties are held fixed, but the effect of inclusion of different excitatory synaptic currents (AMPA and NMDA) is monitored. The results are compared with the dynamics produced by the LIF and HH model. Using all above neuron models, we also monitor the effect of the network structure on the bursting activity. We show that certain structural classes promote the emergence of the superbursts, while certain structural classes more effectively restrict their lengths.