An Electrically Interconnected Axon Microstructure Forms a Small World Network in the Brain

My blog post from four days ago was about a paper that described a previously unknown slow integration of action potentials that resulted in the abrupt appearance of action potentials in the distant segments of CA1 hippocampal interneuron axons that continued to fire for tens of seconds to minutes. Their preliminary evidence that gap junctions between axons may be involved led me to pioneering theoretical work by Dr. Roger Traub describing the dynamics of axo-axonal gap junctions and to the recent paper “Mechanisms of very fast oscillations in networks of axons coupled by gap junctions” (published 2010 in the Journal of Computational Neuroscience).

Experiments analyzing the dynamics of axons connected at distal segments by gap junctions were conducted using three different computational models:

  • Large network models that included 3,072 axons.
  • Small network models that included just a handful of axons for detailed analysis.
  • Cellular automata.

In addition, they reproduced and modified the large scale biologically detailed model of Dr. Traub and colleagues from 1999.

Note: All of the computational models, including the modified Traub model, are available from the SenseLab ModelDB repository in the “Mechanisms of very fast oscillations in axon networks coupled by gap junctions (Munro, Borgers 2010)” record. The computational models are all in the C language except for the cellular automata models, which are in MATLAB code. Data analysis code, which is included, is also written for MATLAB.

The network exhibited three different types of behavior, depending on the gap junction conductance and the fixed somatic voltage:

  • externally driven very fast oscillations
  • re-entrant activity
  • non-oscillatory noisy activity

The results of the large network simulations suggested that the axonal plexus exhibits different behaviors depending on the number of propagation failures in the network. There were a lot of propagation failures during noise, some during re-entrant activity, and none during externally driven very fast oscillations. The failure of action potentials in distant axon branches to reach the cell body has recently been hypothesized to be the cause of spikelets, which have been observed in many types of neurons (see “Axon Segments May Form Distinct Processing Units“).

A major finding of this paper was that highly interconnected distal axon segments (a small subgroup of the total population of axons) were necessary for the emergence of externally driven very fast oscillations and re-entrant activity. These distal axon segments acted as gates like a highly connected node in a small world network. Their results from model networks of electrically coupled cells predict that:

  • Target patterns appear across an axon plexus when signal propagation is always reliable.
  • Spiral waves appear when propagation fails occasionally.
  • Noise appears when propagation failures are frequent.

Interestingly, it’s when the propagation of action potentials fail frequently enough to effectively shut down the highly interconnected axons that the network exhibits noise. The simulations show an abrupt phase change from noise to the re-entrant activity that shows only occasional propagation failure. Re-entrant activity may appear as spiral waves, which have been observed in cerebral cortex of living mammals (see “Spiral Waves in the Brain“). Together these data point to the neuropil as the area where significant signal processing is taking place in the brain.


Other related blog posts:

Spiral Waves in the Brain

Axon Segments May Form Distinct Processing Units