USC Brain Scientists Do the Math
Their findings — appearing in this month’s issue of the journal Nature Neuroscience — contradict a widely accepted idea regarding the “arithmetic” neurons use to process information.
“It’s amazing that after a hundred years of modern neuroscience research, we still don’t know the basic information processing functions of a neuron,” said Bartlett Mel, an associate professor in the USC Viterbi School of Engineering and contributing author of the journal’s article.
“Historically, it has most often been assumed that a brain cell sums up its excitatory inputs linearly, meaning that the excitation caused by two inputs A and B activated together equals the sum of excitations caused by A and B presented separately.”
“We show that the cell significantly violates that rule,” Mel said.
The team found that the summation of information within an individual neuron depends on where the inputs occur, relative to each other, on the surface of the cell.
To understand the team’s work and the significance of its findings, it helps to know a little more about a brain cell.
All of the information processing that take place in the brain is managed by a web of neurons. These living cells come in a variety of shapes and sizes, often resembling trees or bushes.
A neuron receives input from other neurons at thousands of sites — called synapses — scattered across its surface. Each of the synapses generate a small local voltage response when activated.
According to the classical view of the neuron, synaptic responses flow down the cell’s branch-like dendrites, which act like electrical cables and accumulate at the cell body. If the overall voltage response there is sufficient, an electrical spike is fired, carried down the cell’s axon and communicated to hundreds or thousands of other neurons.
“Recent evidence suggests the story is not quite that simple, though,” Mel said. “The input signals may interact with each other in the dendrites and may be profoundly transformed on their way to the cell body.”
“In particular,” Mel added, “individual branches of the dendritic tree can, under certain circumstances, generate local spikes that greatly amplify synaptic responses locally within the dendritic tree.”
The team set out to establish the “arithmetic” used by the neuron to combine its many synaptic inputs, focusing on the pyramid-shaped neuron that makes up the bulk of the brain’s cortical gray matter.
The experiments were conducted in Haifa, Israel by Alon Polsky, lead author of the paper and graduate student at Technion, and Jackie Schiller, contributing author and co-principal investigator.
Using slices of cortical brain tissue from rats, Polsky and Schiller located individual pyramidal neurons, filled them with dye for visualization purposes (cells are otherwise transparent) and, using extracellular electrodes, stimulated the cells very close to their dendritic branches.
While recording the voltage at the cell body, the team would deliver shocks through one or two stimulating electrodes directed to different locations in the dendritic tree, for example, to the same or different dendritic branches.
They would then compare the voltage response at the cell body as the two inputs were activated first separately and then together.
“The powerful thing about [Schiller’s] method is that you can see where you’re stimulating because the dye grows a little brighter wherever synapses are activated,” said Mel, who worked with the team remotely from USC by collaborating on the experiment design and data analysis.
“You can direct the stimuli to very specific spatial locations on the cell and start to look at what a difference location makes. That old real estate phrase ‘location, location, location’ holds true for neurons as well.”
The data showed that three different scenarios could occur when two electrodes A and B were used to stimulate the same dendritic branch:
• If the total response to the two inputs (electrodes A and B) falls below the branch’s local firing threshold, the summation looks linear - A plus B.
• If the two inputs are just strong enough that together they cross the local threshold, the summation looks superlinear — more than A plus B.
• If each individual input is strong enough to cross the local threshold by itself, the summation is sublinear — less than A plus B.
Mel explained the last point in this way: “If two people are trying to build a fire together and they each have a match, the fire isn’t going burn twice as bright or twice as hot thanks to the second match, once it’s already been started with the first. The second match is irrelevant.”
In contrast to summation of inputs delivered to the same branch, the researchers found that summation of inputs on different dendritic branches always looked linear — like lighting two separate fires.
The findings support a 2003 modeling study carried out in Mel’s lab, in which he and graduate student Panayiota Poirazi predicted that pyramidal neurons would behave in this way. This was the first experimental test of those predictions.
“So, we now think of the neuron in terms of a two-layer model,” Mel said. “The first layer of processing occurs within separate dendritic branches. Each branch independently adds up the inputs to that branch, and then applies its own local thresholding non-linearity.”
“In the second layer of processing,” Mel added, “the results from all the different branches are added together linearly at the cell body, where they help to determine the cell’s overall firing rate.”
While the results are promising, the team is certain this is not the final word on the pyramidal neuron.
“Undoubtedly, this is still too simple a model,” Mel said. “But the two-layer model is a better description, it seems, than to assume that the neuron is simply combining everything linearly from everywhere. That’s clearly not what these data show.”
According to Mel, one additional complexity that must eventually be dealt with is that synaptic inputs arriving at the most remote part of the neuron — called the apical tuft — may interact in subtle ways with inputs arriving on the basal dendrites, closer to the cell body.
“We’d now like to see if we need to extend the two-layer model in to a three-layer model,” Mel said. “It may be that the basal and apical dendrites each behave as we’ve been saying, but when they interact with each other there’s an additional nonlinear interaction that occurs between them.”
Mel emphasizes that the “arithmetic” rules he and his colleagues found in pyramidal neurons may not apply to all neurons in the brain.
“There are other neurons that have different shapes, inputs, morphologies and ion channels,” he said. “There might be a dozen different answers to the question, depending on what neuron you’re looking at.”
While much more work lies ahead, new imaging techniques, lifelike models and modern laboratory procedures are making the task of understanding the brain’s complicated neurons a whole lot easier.
In the end, Mel said, the lessons learned from individual neurons will be crucial to advance researchers’ understanding of the brain as a whole.
“We tend to view the brain as a computer,” he said. “If we want to figure out how this computer works, we must first know how its separate parts function.”