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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."
If thinking is really so simple, we should be able to model it in silicon. That will be the real test of this idea.
I'm not saying we should necessarily expect human-or-better intelligence from an AI based on this. But I'd hope this would at least suggest a way to make more powerful classification systems than the present neural network models (and similar schemes).
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!
Proof by very large bribes. QED.
I recon this is probably going to throw the ol' religious community for a loop. I don't think there's anything in the bible about neuroscience, or proteins that fire when you remember things.
It really makes you think.
I don't own a snook, and if I did I wouldn't leave it cocked.
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) )) >
and how memories are held while synapses still fire.
It's called threading..
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
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.
Such research (although not as is) can increase our understand of how to store data intelligently (& efficiently) in the computer domain. Data mining research would greatly benefit from such modeling studies.
from the 1-+-1-=-thinking dept.
My neural network actually hurt trying to decipher that...
if we could model what the hell goes on in people's brains when they can't tell ITS from IT'S or write definately?
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
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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
dupe!
Which figure, what's the reference to your paper and shouldn't you be taking that up with him as opposed to complaining on Slashdot?
The more AMPA receptors that are anchored in place, the stronger the synapse.So, our brain is a lot like bit torrent?
There is a big difference between an academic paper published in a peer reviewed journal, WHICH REPORTS NEW RESULTS and a text for students WHICH DOES NOT REPORT NEW THINGS and is used in the teaching process. The audience of an academic paper is made of PROFESSIONAL SCIENTISTS and on the other hand a text for students is supposed to be used by people in training.
Although we're not there yet, we're currently in the process of trying to get a grant from NIH to work with experimentalists in using our GA tools. It's not necessarily germane, but what region of the brain do you study? We mainly model the hippocampus, although we've had a little experience with PFC, visual cortex, and neocortex in general. Our lab has done models from levels of abstraction down to ion channels (H-H variants mainly) up to models of a dozen or so brain regions (at very abstract levels), although most of my research has focused on models of Izhikevich-type neurons in the hippocampus. (Izhikevich neurons are about as computationally fast as integrate-and-fire neurons, but have been shown by Izhikevich (in his 2007 book) to map to H-H type models.)
Ben Hocking
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Leslie Valiant---he invented the PAC (probably approximate correct) model of machine learning back in 1984, if you'll recall---postulates an interesting model:
Memorization and association on a realistic neural model, Neural Computation, 17:3 (2005) 527-555.
They might actually have some advantage when it comes to early research with using GAs to reproduce NNs. Is the Drosophila nervous system consistent, or is there a certain amount of randomness to it? (For example, the human brain is far too large and complex to be fully specified by the genome. To a certain degree the genome must be coding something like, "grow a few tens of thousands of neurons here, and send the axons in this general direction and the dendrites in that general direction" - and by "coding" I'm not really being that literal, I realize that physics is also quite relevant, but that evolution takes advantage of that physics to code the "message". We model the CA3 region of the hippocampus on a small scale - 100,000 neurons or less - as being totally randomly connected - not that we believe that it's really 100% random, just that's our best first approximation.)
Ben Hocking
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I have not been personally involved in any detailed models of neurons, but there are models out there of single neurons with thousands of compartments. These definitely don't fit the "black box" description, IMO, and I think they do quite a good job of modeling the behavior of the neurons they're designed to model. I don't know if one has been worked out for a cortical pyramidal cell, but I do know they work quite well for hippocampal pyramidal cells, and I'd be very surprised if they hadn't been worked out for their cortical brethren.
One strategy we've explored is a merging of those detailed models with our simplified models. We've created a rudimentary interface that allows our neural network software package to write out data such that a Neuron script can read it in, thus allowing comparisons between the two levels of detail. We can also reverse the process (have our software package read in input from a Neuron simulation). What I could envision happening is that one uses GAs (or some other approach) to iron out some of the details of the detailed model (as the GP experimentalist admits there is unfortunately still a lot of unknowns about the in vivo behavior), and then use another GA (or Evolutionary Algorithm) to find a suitable simplified model of the detailed model - one that is simple enough to be run in a simulation of 100,000 neurons.
Ben Hocking
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Ben Hocking
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I'm guessing he's referring to Transcranial Magnetic Stimulation.
Ben Hocking
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This is Paul Bressloff (Professor of Mathematics, University of Utah)
I do not like beeing accused of stealing a figure by an anonymous person on a non-peer-reviewed website.
As someone else pointed out, the correct procedure is to email me directly. I am more than happy to
correct any errors in my lecture notes, particularly if I have not cited a figure correctly. It should also be noted that
the posted lecture notes are based on lectures I gave graduate students at the Math Institute. They differ significantly
from the final version that will appear in print
I also do not appreciate the snide comments about my work that appear to be based on a brief article
that I did not write in Sci Am. This article, which has nothing to do with my lectures, refers to
our recent modeling study of AMPAR trafficking that appeared in J. Neurosci. Our model provides a quantitative
framework for testing various hypotheses regarding the role of AMPAR trafficking in theexpression of synaptic plasticity.
If you believe that you can do a better job, then I encourage you to submit a research article to a peer reviewed journal. That is how
science progresses, not by unattributed criticism of researchers!
I will not be responding to further comments on this website but feel free to contact me directly if you have something constructive to say.