Proceedings of a Workshop on Statistics on Networks (CD-ROM) (2007) / Chapter Skim
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Neurons, Networks, and Noise: An Introduction--Nancy Kopell, Boston University
Neurons, Networks, and Noise: An Introduction--Nancy Kopell, Boston University
Pages 62-73
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From page 62... ...
These equations come from electrical circuit theory, and the major equation there is conservation of current, so it is talking about ionic currents that are going across the cell membrane and through little channels. Each ionic current is given by Ohm's law, E = IR.
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From page 63... ...
There are many characteristic time scales in there. Even when you are talking about a bit of a single neuron, you are talking potentially about a very large number of dimensions.
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From page 64... ...
For an excitatory synapse the current will drive the cell to a higher voltage, which will make it more likely for the cell to be able to produce an action potential and, for an inhibitory one, it does the opposite. There are also electrical synapses which depend on the difference in the voltages between the post-synaptic and presynaptic cells.
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From page 65... ...
The graph in Figure 3 shows how the voltage builds up and then decays in an action potential. This is the simplest kind of caricature with which people work.
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From page 66... ...
The mathematics that describe what it will do is called a spiketime difference map, which maps the timing difference between the two cells at a given cycle onto the timing difference between them at the next cycle, so that you can see if they will synchronize. It is simple algebra that takes you from one to another to get that map.
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From page 67... ...
By synchrony I mean zero phase. For the particular deterministic spike-time response curve in Figure 5 it turns out that, if you hook up two identical cells with that, they will synchronize, not go into anti-phase.
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From page 68... ...
You can predict what will happen statistically to the network when you actually hook up these two cells to real cells with the dynamic clamp. When cell fires you look up the spike-time response curve and realize it should advance this much with a certain random amount, and you make the other cell fire at that, and you keep doing that.
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From page 69... ...
This is all very contentious. There is a huge amount to be said about gamma rhythms and where they come from and why people think it is important to early sensory processing, to motor control, and to general cognitive processing.
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From page 70... ...
There seems to be a lot of noise in the physiological situations that correspond to this. One can produce this in slice, and many of us including this gang believe it is this kind of activity that is associated with a kind of background attention, a kind of vigilance that enables you to take inputs that are at low level and be able to perceive them much better than if this background activity were completely 70
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From page 71... ...
Now if there is input into a subset of the excitatory cells here, it will create a cell assembly in which the cells that are involved are producing a kind of PING rhythm and everything else here is more or less suppressed. In the larger story that I am not telling, this corresponds to inputs to a specific set of cells that are doing neural computations and that are responding in the presence of this kind of background activity.
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From page 72... ...
QUESTION: Like in a network model, how to go about from the single unit that is the basic building block, to a local field potential kind of measurement? Can that be done within the same mathematical network?
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From page 73... ...
2003. Synchronization of strongly coupled excitatory neurons: Relating network behavior to biophysics, Journal of Computational Neuroscience 15:71-90.
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