# Computing The Path To Safety

April 18, 2012

When a locust jumps and flies away from potential danger, the insect is reacting through a complex mathematical computation of sensory inputs completed within the nervous system. Researchers at Baylor College of Medicine have pinpointed how and when that computation is completed, resulting in a safe get-away. In the current edition of The Journal of Neuroscience, the researchers show that it happens within a single neuron.

The locust uses two variables to determine when to jump — speed and size of an approaching object. The information is sent through the brain via electrical signals received by dendrites, the spiky offshoots of a neuron, and then passed along the axon, the long offshoot of a neuron that carries messages to the dendrites of other neurons. The firing rate of one neuron which determines the animal’s behavioral response can be charted, appearing as a bell-shaped curve with a single peak on a graph. The graph is a representation of the locust’s visual response to an approaching danger.

“As the rates increase, the curve will reach a peak, and shortly after that point we see the locust jump,” said Fabrizio Gabbiani, associate professor of neuroscience at BCM and co-author on the study. “The two variables must be combined together in the nervous system to obtain this visual response, but we did not know exactly how and at what location that was being carried out. Past studies suggest that both variables must be represented by their logarithms to complete the computation. What we show in this study is how and when a neuron actually computes this mathematical function of the input that it receives.” (In mathematics, the logarithm to base 10 represents the number of times 10 must be multiplied by itself to achieve an answer. For example Log10100=2 since 10 times 10 equals 100.)

Gabbiani and his co-author Peter W. Jones, a graduate student who worked with Gabbiani and is currently at Carnegie Mellon University in Pittsburgh, took the two variables and were able to work out the mathematical equation needed to obtain the same results as the curved peak on the graph. They then could look at the neuronal activity and actually see the events leading up to the peak, and at what point each step in the equation took place.

They found that the computations the locust’s brain needed to carry out happened within one neuron, before the information reached the next neurons’ dendrites.

“Using sensitive imaging techniques, we could see this outcome. When synapses are activated, calcium passes through synaptic channels. We could then see that the calcium influx really stops at a certain point,” he said. “The activity takes place within one neuron. The paper shows that the way the neuron is extracting the logarithm is by compressing the inputs coming into it from the dendrites. The message is not passing through until this process is complete”.

These findings supporting the belief that single neurons can complete sophisticated computations.

“Some believe that neurons are very simple and the majority of the excitatory communication and computations in the brain happen because of the intricate connections of the neurons. The other view is that single neurons can do fairly complicated operations and that we can show here in our study.”

Gabbiani said the findings suggest that these same processes happen within more sophisticated animals, including humans.

Funding for this research was through grants from the National Institute of Mental Health, the National Science Foundation, and a fellowship from the National Institute for Biomedical Imaging and Bioengineering.

Gabbiani is also an adjunct associate professor with the department of computational and applied mathematics at Rice University.

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