Proceedings of a Workshop on Statistics on Networks (CD-ROM) (2007) / Chapter Skim
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Keynote Address, Day 2--Variability, Homeostasis per Contents and Compensation in Rhythmic Motor Networks--Eve Marder, Brandeis University
Keynote Address, Day 2--Variability, Homeostasis per Contents and Compensation in Rhythmic Motor Networks--Eve Marder, Brandeis University
Pages 270-291
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From page 270... ...
Keynote Address, Day 2 270
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From page 271... ...
When we started thinking about this, and this goes back a number of years, Larry Abbott and I worked on a series of models that basically used very simple negative feedback homeostatic mechanisms to try and understand how you could get stable neuronal function despite turnover and perturbations. What that led to was going back to step one and saying, how well do negative-feedback self-tuning stability mechanisms have to work?
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From page 272... ...
Among adult animals, we ask how much animal-to-animal variation there is in network mechanisms and underlying parameters, and then we will talk about the problem of parameter tuning: how tightly the parameters that determine neuronal activity and network dynamics have to be tuned and whether stable network function arises from tightly controlled elements or because elements can compensate for each other. CPGs are groups of neurons in your spinal cord or brain stem.
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From page 273... ...
In these circuit diagrams, we use resister symbols to mean that cells are electrically coupled by gap junctions, so current can flow in both directions. These symbols are chemical inhibitory synapses, which means that when one cell is depolarized or fires, it will inhibit the follower cell.
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From page 274... ...
The short answer is that the AB neuron shown in Figure 2 is an oscillatory neuron that behaves a lot like this in isolation. It's electrically coupled to the PD neuron, and it's because of that electrical coupling that the PD neuron shows this depolarization burst of action potentials: hyperpolarization, depolarization, et cetera.
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From page 275... ...
FIGURE 3 Here in Figure 4 are some intracellular recordings, some made from a juvenile, some from an adult. You can see by your eye that the waveforms and patterns look virtually identical between that baby lobster and the big lobster, which tells you that there has to be a mechanism that maintains the stable function despite a massive amount of growth, and therefore a massive change in any one of those properties.
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From page 276... ...
To go beyond making the simple assertion, I would like to show you what we realized we have to do, which was to ask to what's the variation among individual animals. Basically, this defines the range of normal motor patterns in the population, and what we are going to do to quantify the motor patterns is look at these extracellular recordings form the motor nerves showing one-two-three, the discharge pattern we have been looking at, that triphasic motor pattern.
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From page 277... ...
FIGURE 5 The first thing I would like to show you is that if we look at different animals, the mean cycle periods vary about two-fold. Figure 6 shows a histogram of the cycle periods in 99 animals.
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From page 278... ...
It has to be put in place before the animals hatch, because these motor patterns need to be ready for the animal before it starts to eat. In the babies, we tend to see more variability, and to some degree slower patterns, which then consolidate so there is a whole other story about how things change very early in development.
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From page 279... ...
This in and of itself is actually a very challenging problem, because getting constant phase relationships over a large frequency range with constant time constant events, which is basically what you have, is tricky. Now, thanks to really beautiful work by one of my former postdocs, Farzan Nadim, I think we really do understand the mechanisms underlying this.
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From page 280... ...
Some of them will just fire single action potentials more or less randomly, and I we will call those tonically firing neurons. Other neurons will fire what I'll call bursts, that is to say they will depolarize, fire bursts of action potentials, and then they will hyperpolarize.
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From page 281... ...
Zheng made a model to make these traces that contained a sodium current, a conventional one, two different kinds of calcium currents, and three different kinds of potassium currents. Then he varied the relative density of those currents, and that's what gave these different characteristic amounts of activity.
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From page 282... ...
They represent a model very much like the one I just showed you, one with a sodium current, a calcium current, and three different kinds of potassium currents. What Mark found, and this is really quite interesting, is he could have silent cells that have either low or high sodium currents.
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From page 283... ...
So, even the values of those three potassium currents are insufficient to basically predict what the cell's behavior. On the other hand, the space partitions better if you plot one of those potassium currents against the calcium current and the sodium current.
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We have a leak current, and a current I haven't spoken to you about before. It's a hyperpolarization activated inward current, three different potassium currents, two different calcium currents and sodium current.
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What I'm going to do is very briefly show you a new way we can visualize what is going on in 8-dimensional spaces. It's useful to be able to bring eight dimensions down into 2-D, which we do through something called dimensional stacking.
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So if I start looking at any one of these currents, you can see that all of these models, which have very similar behavior, have nonetheless very different underlying structure. That says that widely disparate solutions producing similar behavior at the single cell level may be found in a continuous region of parameter space, and therefore that relatively simple tuning rules and targeting activity levels might be used to tune cells.
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From page 287... ...
If we go in and use the criteria from the biological database, and we use those to pick out all the model networks that meet all of these criteria, 2.4 percent of them were in the right frequency range, had the right duty cycles, the right phase relationships, and so on; there were something like 12 or 15 criteria that led us to that subset of networks. We can now ask of that 2.4 percent that fit within a range that we would expect to be relevant to the biological system, what do they look like in their underlying structure?
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From page 288... ...
And then we have to understand the rules that allow cells to wander around in their protected regions of parameter space as they are constantly rebuilding themselves to maintain our networks functioning throughout our life.
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DING: Okay. Another question is, for each of the model neurons that you studied, over a million neurons studied, presumably these neurons are very highly nonlinear units.
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In advanced technologies, like my digital watch, you use the network architecture to create extreme robustness to the things that are hard to regulate well. And you make extremely fragile architectures for things that are easy to regulate.
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From page 291... ...
1998. "A model neuron with activitydependent conductances regulated by multiple calcium sensors." Journal of Neuroscience 18:2309-2320.
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