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!

I can't remember

[Micklewhite]

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.

Re: I can't remember

[Black Parrot]

> I recon this is probably going to throw the ol' religious community for a loop.

I doubt it. They don't tend to get their panties in a bunch over anything else coming out of neuroscience. (Though perhaps only because their oblivious to it. Maybe the next person who wants to compete for stardom in the anti-science profession will adopt this as his whipping horse; too much competition these days in the evolution-denial movement.)

You do encounter a lot of dyed-in-the-wool dualists on the 'net who should balk at this, but in my experience they're completely unfazed by the massive amounts of straightforward evidence that chemical imbalances in the brain, damage, aging, magnetic fields, medicinal or recreational drugs, etc. can affect decision making and behavior, some even to the point of complete personality changes, so I suspect that they will ignore these reports just as vigorously.

Re:I can't remember

[Maian]

This "ol' religious community" you speak of is only the religious right. I know of plenty of religious people who don't have anything against neuroscience as long as the research is ethical (i.e. no human babies chopped up). I'm not religious myself, so I don't understand their rationales and can't explain how they reconcile this matter of mind and soul.

P.S. It's "reckon" not "recon".

Re:I can't remember

[Micklewhite]

I was thinking of the ancient Egyptians, they're gaining a foothold in the american mid-west. They wouldn't be too pleased to find out they've been throwing an important vital organ in the garbage all these years.

It is 'recon' I was trying to make a joke.. Apparently references to Loradidine are dead.

Re:I can't remember

[Taquoriaan]

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

Re:I can't remember

[MillionthMonkey]

I've been an atheist since college.

I only ever have religious feelings, like I used to have when I was a kid, at one time, and that is during epileptic seizures. Along with a lot of other inappropriate emotions. Some nuclei in the limbic system get fried by the synchronized currents. Of course I'm always pretty out of it at that point, but that's about what you'd expect.

Re: I can't remember

[edschurr]

What about magnetic fields? Is it that temporary "autism" effect?

Re: I can't remember

[Black Parrot]

> What about magnetic fields? Is it that temporary "autism" effect?

I don't know much about it. Apparently 'they' have experimented with people playing a game designed to pit your greed against your sense of fair play, and people's decisions swing way in one direction when part of their brain is exposed to some kind of magnetic field while playing.

I read something about it very recently, but can't recall where.

Re: I can't remember

[aminorex]

I simply can't imagine what neuroscience has to do with religion. Or rather, I can
imagine what it has to do with religion in the mind of a person who regards materialistic
reductionism as a refutation of religion, but I can't imagine how anyone could take
such a view seriously, and simultaneously consider themselves intellectually honest.

Re: I can't remember

[XanBaldur]

You do encounter a lot of dyed-in-the-wool dualists on the 'net who should balk at this Cartesian dualists should certainly balk at this, but there are other schools of dualist thought which are compatible with this sort of scientific evidence. Some emergent dualists will argue (seemingly successfully) that even though it seems like most, if not all, cognitive function seems to reside in the brain, materialism can't account for issues such as qualia or free will (although many emergent dualists readily accept determinism).

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..

Re:The solution is easy..

[picob]

Memory in neurons, as shown by Kandel, requires changes in the synapse. For instance memory involves changes in the number and types of receptors. A synapse doesn't just transmit a zero or a one like computers, a synapse is a location where many signals collide. Although threading may be an interesting option for higher order memory, something like conscious memory, memory on a cellular level as known at this time works on a different level.

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:Research abstract; more info

[BWJones]

Thanks FleaPlus,

This is correct as the first link in the post is not directly concerned with the paper. I actually know Paul Bressloff pretty well and his work is pretty exciting. Of course the next step is biological validation of the data and we've talked a bit about how to go there. The trick will be to find funding in this current political climate for this work.....

Re:Research abstract; more info

[Anonymous Coward]

Actually, this paper can be accessed from Bressloff's publications page: http://www.math.utah.edu/~bresslof/papers.html

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.

"Academic Paper"??

[Anonymous Coward]

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.

Fromt the what .dept?

[geekster]

from the 1-+-1-=-thinking dept.

My neural network actually hurt trying to decipher that...

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.

Re:Theoreticians vs. experimentalists

[lukesl]

That sounds like a smart strategy. As a (theoretically-inclined) experimentalist, I'm working on developing new techniques for fast membrane potential measurement using light. Sounds like the same fundamental problem, but different approaches.

Re:Theoreticians vs. experimentalists

[iidoru]

While one can treat neurons (or a whole neuronal network) as a black box that produces output starting from a given input, this intentionally disregards the inner workings of the box (neuron or network). This however has been a successful strategy to model the bahaviour of a neuron with a single (set) of functions (which are admittedly complex) , but it is very hard to derive predictions for behaviour that is not within the range of the experimental data that is used to generate the model.

I concur that it is easy to model a simplified neuron, but a real neuron has regions of the cell body that react differently, it has dendrites, an axon and butons - which is where the real computational work in a neuron is performed. There are also some basic problems - last time I checked (which was about 4 years ago, if someone knows better please correct me) - there was not even a model that realistically simulated the eletrotonic response to current injections into the cell body in a cortical pyramidal cell - one of the more interesting cells to study..

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:Hype out of nothing + Stealing other people's w

[teslar]

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?

BT

[ivow]

The more AMPA receptors that are anchored in place, the stronger the synapse.So, our brain is a lot like bit torrent?

Re:Text for students, not academic paper

[Nefarious Wheel]

There's a big difference between ANONYMOUS COWARDS and people willing to SIGN THEIR WORK as it appears the former like to SHOUT IN ALL CAPS TO UNDERSCORE THEIR OPINIONS with only enough non-shouty text to get past the LAMENESS FILTERS.

Collaboration

[benhocking]

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.)

Re:Collaboration

[lukesl]

Right now, the Drosophila antennal lobe, which is their version of the olfactory bulb. To be honest, most of what I've done for the past few years is more like biophysics than neuroscience (the perils of technology development), but I'll be moving back towards actual neurophysiology after I defend my thesis next week.

So, the Izhikevich-type neurons...I actually used those once, a few years ago, when I was attempting to make a model of oscillations in the locust antennal lobe. I actually started with a Wilson-Cowan-type model, then moved on to the Izhikevich model when I couldn't get it to work. It was just a rotation project, so I never had time to make it pan out, but still, interesting stuff.

Re:We'll see

[kurzweilfreak]

I'll join that. I've yet to see any kind of response to his book yet, positive or negative. Anyone know of any? I'm currently reading for my second time right now, and his framework seems solid.

How many neurons are in Drosophila?

[benhocking]

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.)

Re:How many neurons are in Drosophila?

[lukesl]

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?

The Drosophila CNS is not like C. elegans, where every single neuron is specified, but in some brain regions it's close to that. Also, there are not very many neurons--I think something like 250,000 in the entire brain, and often as few as tens to hundreds of a certain class of neurons in a particular structure, such as the antennal lobe. The other advantages include the huge array of genetic and anatomical tools that can be readily borrowed from the fruit fly community, short generation times, and small brains that facilitate imaging (which is what I do). The one big drawback is the difficulty of doing traditional neurophysiology in the fly. Extracellular recordings are apparently very difficult, if not impossible, by traditional methods, since the neurons are so small. Doing intracellular recordings is also very difficult largely because the organism is so small--it takes skill even to open up the head and take the brain out. Behavioral assays are also a nightmare. So it depends what kind of work one is trying to do.

Detailed models of neurons

[benhocking]

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.

Re:Detailed models of neurons

[iidoru]

just to clarify maybe - and I apologize for not doing my homework right now by looking up what has been done in the last 4 years, which is a long time - Compartment models do not fall under the black box theory. Black boxes are for examples "neurons" that are represented from a more theoretical standpoint by a large matrix that describes the response function - disregarding the underlying biology of the model, yet doing a good job for some applications.
Yes I do know about the hippocampal models, and yes they are not that far off from cortical neurons. Most of these models model the "interesting behaviour" of neurons, i.e. supra-threshold behaviour, spikes, spike-trains, LTP and so on. In general this is been done well, and some interesting theories rest on these models. However, reading the fine print in the methods of some of these papers, a wide range, including unphysiological values, of basic parameters appears. Now having done this myself, it is necessary to tune certain parameters to make the model work and to make it simulate a certain behaviour that we have experimental data on, but it is hard to then go and derive conclusions about behaviour that is not supported by experimental data, since there is some uncertainty about some very basic stuff in the model.

*rimshot*

[benhocking]

The one big drawback is the difficulty of doing traditional neurophysiology in the fly.

So, do you find when you're working "on the fly" that you often have to just "wing it"?

TMS

[benhocking]

I'm guessing he's referring to Transcranial Magnetic Stimulation.