First I should emphasize that this is a mathematical model, which cannot do more than approximate the brain, if that. But interesting nevertheless.

A team led by Marcelo O. Magnasco, head of the Laboratory of Mathematical Physics at The Rockefeller University, created a model to try to see how such a very complex and responsive network like the brain can balance the opposing forces of excitation and inhibition. “The defining characteristic of our system is that the unit of behavior is not the individual neuron or a local neural circuit but rather groups of neurons that can oscillate in synchrony,” Magnasco says. “The result is that the system is much more tolerant to faults: Individual neurons may or may not fire, individual connections may or may not transmit information to the next neuron, but the system keeps going.”

Most models of neural networks assume that each time a neuron fires and stimulates an adjoining neuron, the strength of the connection between the two increases. This is called the Hebbian theory of synaptic plasticity. “Our system is anti-Hebbian,” Magnasco says. “If the connections among any groups of neurons are strongly oscillating together, they are weakened because they threaten homeostasis. Instead of trying to learn, our neurons are trying to forget.” This anti-Hebbian model balances a network which has more of degrees of freedom than classical models can accommodate, which one presumes the brain might require.

Magnasco theorizes that the connections that balance excitation and inhibition often function at the brink of instability. The abstract model does not try to recreate any particular brain function such as memory formation. A systematic theory of how neurons communicate could help answer the questions of researchers exploring brain function, Magnasco hopes. “We’re trying to reverse-engineer the brain and clearly there are some concepts we’re missing,” he says. “This model could be one part of a better understanding. It has a large number of interesting properties that make it a suitable substrate for a large-scale computing device.”

Journal reference:

1. Magnasco et al. Self-Tuned Critical Anti-Hebbian Networks. Physical Review Letters, 2009; 102 (25): 258102 DOI: 10.1103/PhysRevLett.102.258102

Adapted from materials from Rockefeller University.

Tags: brain science, math model

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