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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."
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).
(( (CRAYON) )) >
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
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.