Understanding How the Brain is Wired Using Graph Theory

Morphological bias towards wire length optimization.
Figure 1. The graphs show the balance between path length economy (y-axis) and wire length economy (x-axis) in cerebral cortical spiny cells (left) and basket cells (right). Full path length optimization results in the star tree morphology (bright green). Full wire length optimization results in the minimal spanning tree morphology (blue). Reconstructed axons were found to have a bias towards wire length optimization (red). From Figure 4 in “Communication and wiring in the cortical connectome” (published October 16, 2012 in Frontiers in Neuroanatomy).

Understanding how the brain is wired is fundamental to understanding how the brain works. Graph Theory, used extensively in analyses of computer network related data, is one of the more recent mathematical tools applied to trying to understand how the brain is wired.

A paper published last month asks if brain wiring is optimized to balance the amount of material used to create a biological “wire” and the time it takes for a signal to go from one place to another. The authors of “Communication and wiring in the cortical connectome” (published October 16, 2012 in Frontiers in Neuroanatomy) apply graph theory to answer the question.

The authors address three different levels of structural brain organization:

  • the single cell
  • the local neural circuit
  • fiber tracts connecting cortical regions

The authors found that sufficient quantitative neuron morphology data and inter-regional cerebral cortical connectivity data exist to provide insight at these levels. However, they found that quantitative data were severely lacking for local cortical neuron circuits and they were unable to provide insight using their graph theory techniques at this level.

The investigation pointed to an optimization between the path length from one node to another and the length of the wire between the two nodes. There seems to be a bias towards wire length optimization (see Figure 1 above). These data suggest that recently developed tracing techniques (see Other related blog posts below) may provide the morphologically detailed data that will enable the discovery of general principles behind how the brain is wired.

Other related blog posts:

Peering into the Structure and Function of Brain Micro-Circuitry

The Connectome: Automated Submicron Reconstruction of Brain Circuitry

The Connectome: Video Journey Through Brain Microcircuitry