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Jonathan D. Lettvin

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neuron modeling

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Home page for a 见义勇为 and 愚公移山

Scientific Visualization

I like to produce both structural and functional displays of mathematical ideas sufficiently clearly to obviate the need for verbal/written explanation. Where necessary, I hand-draw GIF animations. Where possible, I compute visual displays with technologies like Three.js.

HOBBY: Modeling nervous systems

A project for a 愚公移山. My goal is to assemble a Brain Building Kit Where there's a will there's a way.

My personal goal is to answer Cajal's three questions about nervous systems (ISBN 0-19-507401-7 Histology of the Nervous System): "Practitioners will only be able to claim that a valid explanation of a histological observation has been provided if three questions can be answered satisfactorily: what is the functional role of the arrangement in the animal; what mechanisms underlie this function; and what sequence of chemical and mechanical events during evolution and development gave rise to these mechanisms." Santiago Ramón y Cajal

Principally, I work on the first two questions: I model observed groups of shaped neurons. I model observed signal propagation and expression. I replicate observed functional roles.

Brain Information constraints

I am an amateur scientist (BS Physics) without official credentials in neuroscience. Yet I spent my entire grammar school through high school years apprenticing in a well-known wet neuroscience lab, so review the literature I reference if you do not believe what I say here. The views expressed here are entirely my own except where I make reference.

Let's say that we take 100% brain use seriously. All synapses of all neurons are activated at the same time. On the face of it, an undifferentiated global pulse in the brain has no value at all, informationally similar to no activity at all. So 100% must mean something else.

There must be patterns of activity. A pattern means a volume of activity next to a volume of inactivity. A naive view would choose 50%/50% active/inactive as 100% use of the brain. However, this fails horribly. Consider that an image filled with white noise is essentially as useful as no activity at all.

Then, what makes activity informationally rich? I propose that one should expect something like a volume diffraction pattern expressing activity identifying sharp boundaries between adjacent fields of undifferentiated inactivity. The ability for these boundaries to migrate as activity surfaces through a field of inactivity seems like a viable starting hypothesis for making best use of neural organs. So, if this hypothesis were reasonable, and we wanted to be able to move an activity surface over 10 times its surface depth as wiggle-room, that would already cut down useful activity to no more than 1/10th of the cells in the brain. But this presupposes that one has a laminated layer-cake of activity as best use. This makes no sense either since there is little informational richness in moving layers up and down relative to each other. So, a more informationally appropriate use would be bubbles of activity where the surface of activity surrounds a volume of inactivity and which bubble is sufficiently distant from other bubbles. Still using the factor of 10 suggested before, and a volume containing bubbles of radius 10 and kept a distance 10 away from nearest neighbors, the unit activity surface is r2 and the volume is 2 \frac{4}{3}\pi r^3 for a active/total population ratio of 1/60th of the cells in the brain. So, for any more than 1 out of every 60 cells to be active would support this second approximation of informationally useful activity. But this, also, is inappropriate because a box full of same size bubbles is still informationally poor. This is where we come back to the idea of "3D diffraction patterns". The original holograms had a peculiar zebra-stripe appearance where shining a reference laser at an angle caused a 3D image of a scene to be visible. These holograms were 2D diffraction patterns capable of storing 3D information. My third hypothesis is that 3D diffraction patterns supported by neural organs are capable of reproducing 3D images with acceptable time-transitions. Such a scheme would require the wiggle-room to be larger in places, such that the likely population of active neurons could be cut possible by an order of magnitude. So, now we are down to 1 in every 600-1000 brain cells active at any given time.

My guess is that more "intelligent" people are the ones capable of performing more transforms on these activity surfaces to achieve a more varied outcome while less "intelligent" people use a more limited set of transforms. But this is rank speculation with no foundation in existing literature. I am conducting experiments to collect anecdotal evidence that the hypothesis is plausible. The experiments involve rote training to install alternative dissimilar reflex pathways for people presented with situations in which their prior reflexes were monotonous.

Sherrington, who won the Nobel Prize for his work in neuroscience proposed that there is no single neuron unaffected by every other neuron in the nervous system. All activity is as a contributing member of a community and all neurons contribute. Since all cells are autonomous cells, they perform normal cellular functions as well as providing signals to distant cells when necessary and sufficient conditions are met. The notion of using only 10% is difficult to understand. "They also serve who only stand and wait" (Churchill).

The vast majority (perhaps 97% or more) of axons are fully insulated without nodes of Ranvier (no access to external ions needed for Hodgkin&Huxley membrane pulse propagation) and therefore not carriers of membrane pulses. To see how the ubiquitous "unmyelinated" axons are insulated, review the image in Grays Anatomy 35th British Edition, W.B. Saunders Company, Philadelphia, 1973, pg 782. To justify the 97%, see "Functional properties of regenerated optic axons terminating in the primary olfactory cortex", Scalia, Brain Research, 685 (1995) 187-197 (speculation: Lissauer's tract in the spinal cord is vanishingly small yet may contain more axons than the entire rest of the spinal cord). The reason investigators prefer experiments on myelinated axons is that they are larger and easier to investigate; which means only 3% of axons generate the "pulses" used for the modern practice of brain mapping. Measuring gross signals in the smaller axons is published in the Gasser and Erlanger 1944 Nobel lectures. Measuring them individually is published in "What the Frog's Eye Tells the Frog's Brain", Lettvin, Proceedings of the IRE, November 1959, pg 1940-1951.

From what I have been able to interpret, a lot of the activity of the brain is the attempt to inhibit activity (bulbar inhibitory system). The inhibitory system is extraordinarily powerful with much global general inhibition preventing excitations and more focal inhibitions constraining excitations in more specific ways. Strychnine, apparently, increases activity in the central nervous system. An animal with strychnine poisoning was relieved of seizures by stimulating the bulbar inhibitory system (private communication with J. Y. Lettvin).

It gets even more interesting when you consider that instead of the estimated 1e11 neurons it is reasonable to consider information to be expressed over the estimated 1e15 synapses. My "activity surfaces" could be as thin as two synapses deep, separating a featureless "more" field from a featureless "less" field. That is on the order of between 0.1micron to 1.0 micron according to the http://book.bionumbers.org/how-big-is-a-synapse/ web page.

All this is purely my own personal interpretation of informational necessities in nervous systems. It may be wholly unsupportable when reviewed by a professional, but then again, it may not. Errors in factual material are my own and I invite clear non-ad-hominem corrections.

I welcome feedback and discussion on this material.

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