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The Mathematics of Neuroscience
eldavojohn writes "An academic paper on math [PDF] has been released by Paul Bressloff, resulting in much ado about the mathematical modeling of the brain's memory storage. The paper deals with specific receptors called AMPA and how memories are held while synapses still fire. Scientific American is running a more detailed report on the subject." From the article "At any given time, some AMPA receptors are moving inside the nerve cell where they are unable to receive signals. But to maintain memory, a number of AMPA receptors are anchored in place with what are known as scaffolding proteins, Bressloff said. The computer models examined how many AMPA receptors are anchored at the receiving area on the surface as opposed to those found elsewhere in the nerve cell. The more AMPA receptors that are anchored in place, the stronger the synapse."
The "academic paper" linked to has nothing to do with memory formation or AMPA receptors. It is merely a subset of Bressloff's lecture notes about classic neuronal models.
one major downside with almost all computational models, however, is that they rely on assumptions that the designers can't prove.
I think this is the key. Laypeople think that the reason we don't understand the brain is because it's too complicated. It is complicated, but the main difficulty is the inconvenience of the brain as an experimental system. It's very hard to see what's going on inside a brain without damaging it so it doesn't work any more, so we're stuck using experimental tools that answer the questions we can answer instead of the questions we want to answer. So basically what I think you're saying (and I agree) is that the problem with modeling approaches is that the data isn't there to back them up. I would argue that means the real problem is not with the modeling, but with the experimental side (and I say this as an experimentalist, so it isn't meant in any derogatory way).
Well, as a theoretician in computational neuroscience, I concur (on all of your points). One step I've taken along this path is to use genetic algorithms to augment my search through parameter space. It still requires quite a few answers from experimentalists to usefully reduce parameter space, though, as well as verification.
Ben Hocking
Need a professional organizer?
Nobel-prize winner Kandel elucidated a mechanism of memory with the gill reflex in Aplysia: the response to a water jet on the gill which could lead to long term- and short term memory. Two possible 'directions' of memory are habituation and sensitization.
Habituation is a downregulation of the response to a signal. In snails the response of the gill reflex will decrease over time, just like you forget a source of noise if you hear it long enough.
Sensitization is a mechanism in which the response to a signal is increased. The response of the gill reflex can be increased when it is coupled by another stimulation. For instance a small electrical shock on the head. This model was already known from Pavlov's studies on dogs: a bell can induce a 'food' response when previously associated with food. The aplysia model was more suitable for study on a cellular scale, however.
to quote the article this is how communication between neurons work:
Here I should mention the transmission at a synapse involves many signals, not just one. The synapse is a location that is carefully regulated. Sensitization and habituation occur at the synapse. The synapse changes physiologically in these events.
This AMPA receptor is one of the receptors that is associated with the learning response. It isn't the only receptor, though, and signals in the synapse are very complex and regulated through many signaling pathways.
Here's more about memory:
http://www.journals.royalsoc.ac.uk/(vzapqd45k3ktb
http://www.jneurosci.org/cgi/content/full/25/23/5
As a computational neuroscientist let me add my 2 cents:
(1) The topic treated is old stuff, there is plenty of evidence for it, for instance see Roberto Malinow's beautiful work on this subject. Unfortunately the model does not add anything.
(2) I have no idea how they got themselves into Scientific American, clearly its quality is going down.
(2) The posted link is to a text-book with little relevance to the actual research. However, I was very surprised to find an unattributed figure in the text made by me!!! He doesn't even cite my paper... out his 150 or so references. This really shows who this Bressloff guy is. Oh well. -phystor
Really? Funny... I'm member of the religious community AND studying cognitive neurosciences... :D
Actually, this paper can be accessed from Bressloff's publications page: http://www.math.utah.edu/~bresslof/papers.html