Why do neurons act in unison?
Predictions from the model (black curves) correspond very well to actual correlations that were found in simulations of a neural network (red areas). The panels show three separate examples; a full explanation can be found in the original article.
Experimentalists often observe small correlations between spike trains of neurons (i.e. the sequence of action potentials over time) in local neural networks. These observations can be made in many different areas of the brain’s cortex. Intuitively, this is not surprising: Each neuron is connected to thousands of neighbours and reacts to their inputs, so we even would expect correlations in activity to occur. However, one of the things that remain unclear, is: To which extent do these correlations bear a significance for the function of the network as a processor of information? Or are they simply a natural consequence of the dense synaptic wiring? The answer to this question is still unknown.
Theoretical models have shown how the interplay of the activity of excitatory and inhibitory neurons keeps correlations small. This is an important prerequisite for the brain to fulfil its many tasks. Strong correlations – which could occur when inhibitory neurons do not balance their excitatory counterparts – would result in global, all-encompassing activations in which no meaningful processing would be possible any more. However, it has been difficult so far to understand how exactly the detailed pattern of connections between neurons affects or counteracts correlations between specific neuron pairs.
In an article published in the journal Physical Review E, Volker Pernice and colleagues from the Bernstein Center Freiburg have now shown that correlations can be traced back to the synaptic connections in a rather simple manner. Using simulations of networks of neurons described as “leaky integrate-and-fire neurons” – a widely used simplified model of neurons – they demonstrated that a mathematical framework called “linear response theory” can be applied in order to directly relate collective neural activity to synaptic connections. This mathematical theory is important to understand the effects of weak influences on a system, and is widely used, for example as the basic principle of many detection devices. This theory, newly applied to a model of large networks of neurons by the scientists in Freiburg, makes it possible to understand the influence of different connectivity patterns on the collective dynamics of the neurons.
The description of the network in the terms of linear response theory assumes an absence of specific external stimulation or on-going oscillations in the network. Therefore, it is able to provide a baseline model to experiments where researchers try to assess the origin of observed correlations in local networks: Whether these are an epiphenomenon that is purely resulting from the network structure, or if additional mechanisms are at work.
Original article (subscription required):
Volker Pernice, Benjamin Staude, Stefano Cardanobile, and Stefan Rotter (2012) Recurrent interactions in spiking networks with arbitrary topology. Phys. Rev. E 85, 031916