Researchers have found the first evidence that chemical activity within networks of brain cells displays behavior that is characteristic of self-organized criticality. Previously seen only in physical processes, self-organized criticality describes complex systems far from equilibrium that spontaneously move toward a critical state without external tuning.
While the implications of the work remain unclear, the researchers believe further study could lead to new insights into disease processes, improved techniques for diagnosing diseases of the brain, and perhaps even new treatment options. Modelling techniques developed for the work could also give neuroscientists a new way to study long-range signalling in the brain.
"This work makes a connection between physics -- where we understand self-organized criticality -- and complex biological systems," said Dr. Peter Jung, a visiting physicist at the Georgia Institute of Technology. "It is a starting point for a complete new way of thinking about waves in the brain and disease processes."
Jung and Dr. Ann Cornell-Bell of Connecticut-based Viatech Imaging, combined theoretical modeling with experimental observation of chemical activity in cells taken from the hippocampal area of a rat brain. Their collaboration began after another researcher, Dr. Frank Moss from the University of Missouri at St. Louis, noticed similarities between calcium ion waves that Cornell-Bell observed and mathematical models of noise-enhanced pattern formation developed by Jung.
Development of Imbalance Makes Waves More Likely
The calcium ion waves studied by Jung, Cornell-Bell, Moss and collaborator Dr. Kathleen Shaver Madden arise randomly in brain cells known as astrocytes, whose normal task is to regulate the flow of ions and neurotransmitters in the neuronal cells that transmit signals in the brain. The astrocytes can become chemically unbalanced if levels of a neurotransmitter kainate exceed a critical threshold. Kainate is generated by the random firing of neurons that is part of the normal "noise" in the brain.
When one astrocyte becomes unbalanced, it lowers the critical threshold of one or more neighboring cells, increasing the likelihood that they will also become unbalanced. This process in many interconnected cells allows the system to reach a critical state, permitting propagation of a spiral-like wave of calcium and other ions throughout the network. The spontaneous formation of calcium waves is controlled by the amount of kainate present at the cells.
Experimental Work Agrees with Modelling
In experimental work using the hippocampus of day-old rats, Cornell-Bell observed the formation and movement of these waves using a dye that fluoresces in the presence of calcium ions. By accurately recording the wave propagation using a video camera, she generated data from which the wave patterns could be mathematically analyzed.
The cell networks produce waves in a wide range of sizes and durations. Jung and Cornell-Bell found that the distribution of sizes and durations follows a "power" law; that is, the number of waves of a certain size or time duration observed within a time interval is proportional to that size or duration raised to a specific exponent. Adherence to such a power law is the signature of self-organized criticality.
To simulate the brain network under study, Jung created computer models composed of between 10,000 and one million "excitable" units. Each of these units could exist in one of three states: quiet, excited, or quiescent (recovery). The units are weakly coupled to one another, modeling the relationship between brain astrocytes.
Introducing random thermal noise into Jung's model creates noise-sustained waves similar to those seen by Cornell-Bell in the brain tissue. Jung's model obeys the same power law observed experimentally in the rat brain.
"The graph from the model and the graph from the experiment could lie on top of one another," Jung said. "The experiment fits the model very well, so we know we are in the right class of systems."
Origins of Self-Organized Criticality
Physicists Per Bak, Chao Tang and Kurt Wiesenfeld first described the phenomenon of self-organized criticality in physical systems ten years ago. The best-known example involves sandpiles that gradually reach a critical state -- leading to avalanches of varying sizes -- as grains of sand are slowly added. The work and its implications remain controversial in the physics community.
In brain cells, random firing of neurons creates noise that moves the system toward criticality, Jung explained. Without the noise, the system would remain balanced and create no waves. Adding quantities of neurotransmitter to the brain system increases the firing rate and therefore the formation of calcium ion waves.
"The noise is self-organizing," Jung explained. "It's like the gasoline that keeps a car going. Even if you have a very nice car, you still need the gasoline to get it going. The noise gives you the push to get the system into criticality."
What role the chemical waves play in the brain is uncertain, though the researchers believe they may help communicate information about the state of excitability of the astrocytes. But the self-organized criticality they display could provide a "fingerprint" to help identify disease processes.
"The waves are the fingerprint showing that the system has organized itself into criticality," said Jung. "This appears to be the natural state of brain tissue. The question is what happens if there is something wrong with the tissue."
Phenomena May Provide Clues to Disease Processes
Preliminary study of brain tissue removed from epileptic patients suggests that diseased tissue may in fact produce wave patterns that are dramatically different from the waves produced by healthy tissue.
"We have seen very rapid local oscillations in the calcium ions of epileptic cells, which may correspond to a very noisy field with low coherence," Cornell-Bell explained. "We hope to analyze these preliminary observations. What we hope will develop from all of this is a diagnostic tool that has not existed before."
In addition to epilepsy, such a diagnostic tool could also apply to other brain disorders, including Alzheimer's Disease, slow brain viruses, and even psychiatric problems such as depression, she said.
Information on the experimental and theoretical work was presented at the March meeting of the American Physical Society. Jung's work on "Thermal Waves, Criticality and Self Organization in Excitable Media" has been published in Physical Review Letters.
The work has been sponsored by Deutsche Forshungsgemeinschaft, the U.S. National Institutes of Health, and the U.S. Office of Naval Research.
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