Network Analysis , Complexity , and Brain Function

T hroughout the early history of neurology and neuroscience, most theoretical accounts of brain function have emphasized either aspects of localization or distributed properties [1]. Instead, modern views focus extensively on the structure and dynamics of large-scale neuronal networks, especially those of the cerebral cortex and associated thalamocortical circuits whose activation underlies human perception and cognition [2,3]. Both, localized and distributed aspects of brain function naturally emerge from this network perspective. This essay highlights several unique characteristics of brain networks and explores how a computational analysis of these networks (see also [4]) may impact on our understanding of human brain function. With a few notable exceptions (such as diffusible messengers), all communication between nerve cells is carried out along physical connections, often linking cells that are separated by large distances. Signals within these connections consist of series of action potentials (spikes) of unit magnitude and duration. The arrival of an action potential at a synaptic junction triggers numerous biochemical and biophysical processes, ultimately resulting in transmission of electrical signals to the postsynaptic (receiving) cell, which may in turn generate an output spike transmitted along the neuron’s axon. Neurons in the cerebral cortex maintain thousands of input and output connections with other neurons, forming a dense network of connectivity spanning the entire thalamocortical system. According to a detailed quantitative study [5], the human cerebral cortex contains approximately 8.3 10 neurons and 6.7 10 connections. The length of all connections within a single human brain is estimated between 100,000 and 10,000,000 km [5]. Despite this massive connectivity, cortical networks are exceedingly sparse, with an overall connectivity factor (number of connections present out of all possible) of around 10 . Brain networks are not random, but form highly specific patterns. A predominant feature of brain networks is that neurons tend to connect predominantly with other neurons in local groups. Thus, local connectivity ratios can be significantly higher than those suggested by random topology. Networks in the brain can be analyzed at multiple levels of scale. Within small and localized region of the brain, neurons form characteristic sets of connections, socalled local circuits [6]. For example, neurons forming cortical columns show specific patterns of connectivity between morphologically and pharmacologically distinct classes of cells in different layers. At a higher level of scale, such columns communicate through “tangential” or “horizontal” connections, forming networks of columns within single cortical areas. Connection patterns formed by these local, intraareal networks are thought to be responsible for the specific processing requirements OLAF SPORNS