Comp. Neuro. introductory textbooks

nobahar

Hello!

I know some people on the forum are computational neuroscientists (or related fields), and I was wondering if anyone could recommend a good introductory book. One that goes step-by-step through how the equations come about and why they are the way they are. Rather than books that simply give the equations and say "...this models the neuron...", etc.
I'm guessing textbooks might be stronger on some topics than others. I found one that has a good introduction to the fundamentals of information theory quite well: the reasoning behind the equations, proofs, and so on; but it doesn't give a very good explanation of how neurons are modelled for some reason, and just tends to give the equations.

Anyone have any books they found particularly useful?

madness

The standard textbook:

http://www.amazon.co.uk/Theoretical-.../dp/0262041995

A good textbook on information theory applied to neuroscience:

http://www.amazon.co.uk/Spikes-Explo.../dp/0262681080

Dynamical systems applied to neuroscience:

http://www.amazon.co.uk/Dynamical-Sy...6501098&sr=1-1

I would say the first one is best for understanding how neurons are modelled biophysically. Perhaps this one would be even better for this but I haven't personally read it:

http://www.amazon.co.uk/Principles-C.../dp/0521877954

atyy

http://www.amazon.com/Cellular-Bioph.../dp/0262231840

http://www.sciencemag.org/content/326/5951/379.summary

Pythagorean

I am part of the Facebook 'Theoretical Neuroscience' group (including several instructors and well-knowns in the field like Bard Ermentrout and Peter Erdi) and they had this discussion some time ago. The general consensus was that Dayan & Abbott's Theoretical Neuroscience was okay, but all bottom-up (no top down approaches).

Neuroscience: A Mathematical Primer, by Alwyn Scott was mentioned, but not much appreciated by faculty, Dynamical Systems in Neuroscience by Eugene Izhikevich is one of my favorites, but again, to idiosyncratic for faculty teaching the course.

Ermentrout suggested Hugh Wilson's Spikes, Decisions, and Actions: The Dynamical Foundations of Neuroscience as the best book, but also mentioned his own book, Mathematical Foundations in Neuroscience.

Pythagorean

Here is Hugh Wilson's Book, free to download from Wilson himself (as Ermentrout had mentioned). It's being sold used for $1000 in hard cover (because it's out of print)!!! It's received excellent reviews at Amazon:

http://cvr.yorku.ca/webpages/wilson.htm#book

nobahar

Thanks for the suggestions. Some I can get hold of, some I can't. Thanks for the free online book Py; I had a brief look and it seems to take you through step-by-step, starting from 'simple' differentials. I also looked at Theoretical Neuroscience by Dayan, suggested by madness.
Differential equations, eigenvalues, eigenvectors... sheesh...

Anyway, thanks again for the recommendations.

Pythagorean

I think what I like about that free book is that it has the word "decisions" in the title, hinting that it might actually cover top-down models as well as the standard bottom-up models. I downloaded it, but haven't had the chance to flip through it yet.

nobahar

Hi py, what do you mean by "bottom-up" and "top-down" models? I'm new to this (obviously). I have to keep setting it aside to tackle the kind-of 'pre-requisites', like electrostatic interactions and circuits, and the maths.

Pythagorean

Say you have some behavior you observe that you want to model. Say that when you poke a creature, 70% of the time, it retracts a protruding appendage, but 30% of the time it doesn't.

There's two ways you can model this. The simple way would be to model it as a black box with an input and an output. The input would be the poke, and the output would be the retraction (or lack of retraction). You could simply model the black box to generate a random number between 1 and 0, with all numbers on that interval being equally probable. Then if the number is between 0 and .3, the output is no retraction, but if the number between .3 and 1, there is a retraction. This would be an example of a top-down model. You're modeling exactly what you observe, nothing more, and you're not asking about the mechanisms underlying it. This is maybe even too pure of an example of top-down modeling, since it doesn't really allow for you to learn anything about the system itself, but it can be used as a component in a bigger system.

A more complicated way to model it would be to model the neurons as differential equations with parameters tuned to the right values. This has the advantage of being able to talk about mechanisms, but it has the disadvantage that you may never find the regime of parameter sets and inputs that reproduces the behavior you observe because there's so much complexity. You may even be missing an important part of the story and end up forcing the neurons out of their natural paramter ranges to produce something like the behavior, when all along, you were missing another member or property of the ensemble (like astrocytes, or another bridging neuron, or a specific synapse).

Generally, the bottom-up model is preferred in the physical sciences, but if your system gets to complex with lots of interacting parts, it might be better to use a top-down model. Ultimately, the most complicated stuff uses both: you start with a top-down model of all the interacting black-boxes, but as you gain understanding, you replace the black boxes with components that are more bottom-up modeled.

atyy

Is that really a "model"? If I just put in what I observe, then it's just the data, which I guess is a "model". But it doesn't seem to make a prediction, since the input space is restricted exactly to stimuli already used in the experiments.

Do you happen to have Volterra series or an equivalent (for all practical purposes) representation in mind?

Pythagorean

You're right; I thought so too, which is why I put my last sentence. I went too much to the extreme of exactly modeling observations and no more.

Volterra-Lotka is a good example:

http://en.wikipedia.org/wiki/Lotka%E...terra_equation

We don't couple a bunch of bunnies and foxes together we just model the general population of each as a function of both the population of the other and the organisms own population.

atyy

I see. Let's see if I understand your terminology: an integrate and fire neuron would be both "bottom up" with respect to say decision making, and "top down" with respect to the Hodgkin-Huxley models, since eg. m,h,n are not explicitly modelled, and in fact will in general be less faithful to reality than the HH equations, but that error may not matter for one's purposes.

Pythagorean

With respect to decision making, I'd think a integrate and fire neuron would be bottom-up still because it says nothing about observations with respect to decision making. It's still a matter of putting integrate and fire neurons together and hoping some thing like decision making comes out of it.

You'd actually have to model the decision of a person as the particle in state space, rather than the state of the neuron, I'd think. So the VL models the statespace of the two populations as one particle; it doesn't take a bunch of rabbits and bunnies and couple them together and hope for the best.

atyy

Yes, that's what I meant to convey. Top-down would be like http://books.google.com/books?id=CM5...gbs_navlinks_s :)

Pythagorean

Ah yes, sorry. I reread your post. Yeah, that's consistent with my terminology. Will check out the book once I'm at a computer.

update: yeah, that fits the the stereotype I've developed that psychologists are more likely to utilize top-down models, neuroscientists bottom-up models. Nonlinear scientists both :)

madness

There is a bit of a problem with the definition of top-down and bottom-up in neuroscience, in my opinion. In the brain, top-down can refer to the modulation of low-level brain areas by high level brain areas, e.g. the influence of attention on perception. There is also the concept that a complex system can have emergent behaviour which influences its constituent components, similar to how society shapes an individual. These are both different from what you have discussed here - there are multiple uses of the term.

Pythagorean

Yes, we're taking about modeling theory specifically here, not the brain processes themselves.