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."

Comments

Wha?

[slashbob22]

Obligatory:

Prof. Farnsworth: Same thing I teach every semester: The Mathematics of Quantum Neutrino Fields. I made up the title so that no student would dare take it.
Fry: Mathematics of wanton burrito meals. I'll be there!
Prof. Farnsworth: Please, Fry, I don't know how to teach; I'm a professor!

old news and/or nsufficient evidence

[brother bloat]

none of this stuff is particularly new. here's a brief summary of the first linked-to article:

integrate-and-fire models are extremely simple -- the idea (as implied by their name) is that this neuron model spikes if the membrane voltage passes some set threshold, and otherwise doesn't fire. In response to input current, the cell's membrane voltage charges (depolarizes) or decays (hyperpolarizes) according to exponential time constants. the other spiking models discussed are similarily oversimplified. (these simple neuronal models can be useful, for example in models of neural networks.)

the second article (the main one) is extemely vague on (a) how their findings were verified in actual neurons and (b) whether their model was borne out in actual neurons. i love computational neuroscience, and i think it's an extremely useful tool. one major downside with almost all computational models, however, is that they rely on assumptions that the designers can't prove. designing these models is often an iterative process, where (1) experiments inspire creation of a new model, (2) the model simulates a new condition during which new predictions are made, and (3) new experiments are performed which require adjusting the model or running more simulations. thus, to conclude (as this article appears to) that the authors have "proved proved that the presence of more scaffolding proteins available at the far downstream end of the neuron (and into the synapse) to AMPA receptors increased during LTP..." is misleading, given the dirth of evidence presented in the article.

if scaffolding proteins end up being verified as the mechanism by which AMPA receptors are anchored in the way the authors propose, that might be pretty interesting -- but clearly much more work needs to be done to verify that this is actually the case. the idea that AMPA receptors are promoted during LTP (increasing synaptic strength) and "demoted" during LTD (decreasing synaptic strength) is quite old (for example, see The Cognitive Neuroscience of Memory, published in 2002, by Howard Eichenbaum for a review).

Re:old news and/or nsufficient evidence

[lukesl]

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).

The solution is easy..

[FrostyCoolSlug]

and how memories are held while synapses still fire.

It's called threading..

Research abstract; more info

[FleaPlus]

I'm not sure if the first link is correct -- it isn't a research paper, just an intro-level lecture to integrate-and-fire models, one of the topics covered in computational neuroscience. The actual research paper by Earnshaw & Bressloff requires a subscription, but here's the abstract:

Biophysical Model of AMPA Receptor Trafficking and Its Regulation during Long-Term Potentiation/Long-Term Depression

AMPA receptors mediate the majority of fast excitatory synaptic transmission in the CNS, and evidence suggests that AMPA receptor trafficking regulates synaptic strength, a phenomenon implicated in learning and memory. There are two major mechanisms of AMPA receptor trafficking: exocytic/endocytic exchange of surface receptors with intracellular receptor pools, and the lateral diffusion or hopping of surface receptors between the postsynaptic density and the surrounding extrasynaptic membrane. In this paper, we present a biophysical model of these trafficking mechanisms under basal conditions and during the expression of long-term potentiation (LTP) and depression (LTD). We show how our model reproduces a wide range of physiological data, and use this to make predictions regarding possible targets of second-messenger pathways activated during the induction phase of LTP/LTD.

Computational neuroscience is a great topic. If you're interested in learning more about it, there's a nice book by Gerstner & Kistler called Spiking Neuron Models, which can be purchased hard-copy or downloaded for free online. The wikipedia page is also pretty good, with plenty of links to fun neural simulation software.

(And yes, I Am A Computational Neuroscientist... or at least I'm in a computational neuroscience grad program ;)

Re:We'll see

[lukesl]

We absolutely can model neurons in silicon, and people do, but that's not the hard part. The problem is that there are so many free parameters, and there's no easy way to know what the correct values are. The rate limiting step right now is experimental, not theoretical (of course, this is just my opinion as an experimentalist--lots of reasonable people probably disagree).

Also, just because you can reduce neurons to a simplified model, it doesn't mean that these models, or the thing they're modeling, are simple phenomena. Condensed matter physics (for example) is full of simple toy models that become incredibly complex when they're scaled up, and neuroscience is very much the same way.

Theoreticians vs. experimentalists

[benhocking]

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.

memory in part

[picob]

A lot of knowledge about the working of memory comes from a snail called Aplysia californica. Surprisingly maybe, these snails already have the neural mechanism that works - allthough on a much larger scale - in our brains:

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:

The synapse allows two neurons to communicate with one another. Each synapse involves a transmission point that sends a signal across a small gap to a receiving area.

Signals are sent in the form of a chemical substance, known as a neurotransmitter. These chemicals move across the gap and bind to receptors embedded in the receiving area.

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/(vzapqd45k3ktbt qvphyzfm2y)/app/home/contribution.asp?referrer=par ent&backto=issue,22,30;journal,46,226;linkingpubli cationresults,1:102022,1
http://www.jneurosci.org/cgi/content/full/25/23/56 23

Hype out of nothing + Stealing other people's work

[phystor]

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

Re:I can't remember

[Taquoriaan]

Really? Funny... I'm member of the religious community AND studying cognitive neurosciences... :D