On the one hand, there are the individual nerve cells whose membrane depolarization is at the basis of everything and on the other hand, there’s lyric poetry, serial murder and the calculus. In between there are hundreds of billions of nerve cells, with hundreds of trillions of connections. Scientists understand the bottom end and can say useful things about the top end, but getting from one end to the other is another story…
…They devised a simple mathematical model that accurately represents a three-cell microcircuit in a chicken’s brain. They then found, to their surprise, that they could collapse their model mathematically to one equation with two parameters, which are derived from but not the same as the strength of the connections between neurons (the synaptic strength) that neural models usually emphasize…
one fruitful approach has been to analyze a microcircuit consisting of a few neurons all of whose interconnections can be traced.
Microcircuits that have been analyzed in this way include the network that controls the chewing rhythm of a lobster’s stomach (yes, it has teeth in its stomach), the reflex arc that allows a fruit fly to dodge a fly swatter and the timing network that controls the heartbeat of a medicinal leech.
Looking for a way to explain to the students in his Physics of the Brain class how delayed feedback produces complexity in a circuit, Ralf Wessel, Ph.D., associate professor of physics in Arts & Sciences, came up with a toy neural circuit simple enough to be stepped through time iterations at the blackboard. He used it to show his students that if there was feedback among the neurons, simple constant inputs could produce a long-period oscillation in their outputs.
Wessel then asked Matthew S. Caudill, Ph.D., graduate research assistant in physics, to create a computer model of the circuit so that it could be explored more thoroughly. As they worked with three-neuron microcircuit they realized it was very like one students in Wessel’s neurophysiology lab were studying.
That circuit, which consists of three neurons and their feedback projections, has a simple task: to detect motion in the chicken’s field of view. One neuron in the area called the optic tectum because it sits on the “roof” of the brain, sends axons to others in a knob of tissue called the nucleus isthmi. The neurons in the isthmi send projections back to the optic tectum, either directly to the neuron from which they got their input or back to the rest of the tectum (the crucial feedback loops). (This feedback resembles the loops between the cortex and thalamus in mammals, which are central components of consciousness.) There are similar microcircuits in the optical processing areas of reptilian and mammalian brains.
The microcircuit’s behavior could be captured mathematically by three equations, each of which describes one neuron’s output in terms of its inputs and parameters called synaptic weights, the standard way of expressing the strength of the connection between two neurons. Looking at the equations, Wessel and Caudill recognized that they could be reduced by algebraic substitution to one equation with two parameters (derived from the original five synaptic weights).
“It is as if,” says Caudill, “the system of three neurons was reduced to one abstract neuron that does the same thing, follows the same rule, as the more complicated circuit. “
…The finding also suggests why it might be difficult to achieve insight into neural circuits in the lab. Neurophysiologists probing neuronal circuits by inserting a glass electrode in one neuron, stimulating it, and recording the electrical activity of another neuron are likely to be baffled by physiological variations from animal to animal. The chicken microcircuit suggests that to understand a neural circuit they would have to measure combinations of synaptic weights. But the catch is they can’t know which ones to measure unless they already know the rule the circuit follows.