Large-scale neuronal network models based on a probabilistic connectivity principle

The use of models of large-scale neuronal networks has become indispensable in studying information processing in various brain areas, such as the hippocampus (Traub et al. 1994), the cortex (Traub et al. 1996), or the thalamocortical network (Destexhe & Sejnowski, 2001). At the same time, constructing and implementing such models is fraught with difficulties of both conceptual and technical nature because the exact connectivity of the network is usually not known, and because of the problems that arise when large systems of ordinary differential equations are to be solved. To avoid some of these problems, we used a novel approach based on a principle of probabilistic connectivity of the network. We thus obtained the mathematically expected (average) behaviour of neurones representing whole neurone pools. This method was tested on three network models of general nature, but with detailed biophysical neurone and synaptic models. The first simple example consists of one pool of 300 identical neurones that is connected with NMDA-type synapses to neurones of a second pool (of 300 neurones), and both pools receive independent afferent inputs. This model shows that the effect of the activities of all neurones of a pool are taken into account when computing the overall output of the pool. The second example demonstrates that computationally difficult cases, such as the behaviour of networks with mutually strong excitatory connections between two neurone pools can reliably be simulated. Finally, our method also works with a heterogeneous network of three neurone pools with different neurone types and excitatory (AMPA, NMDA) and inhibitory (GABAA) synaptic connections. These results suggest that models based on the probabilistic connectivity principle are a viable alternative to detailed deterministic network models