Appendix 4: Web access to correspondence with NATURE, including some detailed brain modeling.

Here are the neural logic pieces S.J. Kline and I submitted to NATURE in 1997. The derivation of the S-K equation is now more compact, but the neural logic now is as it was then, except for modifications to account for glial clefts that are set out in the last reference.

In response to the draft submissions referenced below, the editors of NATURE wrote a gracious, supportive, and seemingly reluctant rejection letter that I have made available on my website in two forms:

text at http://www.wisc.edu/rshowalt/natletshrt/

full facsimile at http://www.wisc.edu/rshowalt/naturlet/

NATURE's letter included this:

"         Although it is sadly the case that some studies simply do not lend themselves to the NATURE format, this need not mean that our readers are left in the dark about the latest developments.    As you know, we frequently discuss such work in the context of our News and Views section, and if you were to send us preprints of your present papers when they are finally accepted elsewhere for publication, we could explore the possibility of doing likewise with your work. "

NATURE's letter indicates that the editors of an outstanding journal that specializes in neurobiology found the material significant and plausible.

The neurophysiological papers below will be rewritten and submitted to a neurophysiological journal when the central mathematical foundation of the S-K derivation, the subject of this paper, is peer reviewed. The submissions to NATURE are referenced here to show the potential importance in neuroscience and neural medicine that the S-K equation has.

HYPOTHESIS: DENDRITES, DENDRITIC SPINES, AND STEREOCILIA HAVE RESONANT MODES UNDER S-K THEORY by M.R. Showalter

at http://www.wisc.edu/rshowalt/hypothesis/

REASONS TO DOUBT THE CURRENT NEURAL CONDUCTION MODEL by M.R. Showalter at http://www.wisc.edu/rshowalt/doubt/

A NEW PASSIVE NEURAL EQUATION. Part a: derivation by M.R. Showalter

at http://www.wisc.edu/rshowalt/deriva/

A PASSIVE NEURAL EQUATION: Part b: neural conduction properties by M.R. Showalter

at http://www.wisc.edu/rshowalt/derivb/

Here are the physical derivation (math) papers we submitted to NATURE.

MODELING OF PHYSICAL SYSTEMS ACCORDING TO MAXWELL'S FIRST METHOD by M.R.Showalter and S.J.Kline at http://www.wisc.edu/rshowalt/maxmeth/

EQUATIONS FROM COUPLED FINITE INCREMENT PHYSICAL MODELS MUST BE SIMPLIFIED IN INTENSIVE FORM by M.R.Showalter and

S.J.Kline at http://www.wisc.edu/rshowalt/pointfrm/

If equations derived according to Maxwell's 1st method are right, inferences from experiments are only valid over a RESTRICTED range.

by M.R. Showalter and S.J. Kline at http://www.wisc.edu/rshowalt/range/

For background, we also submitted an annotation of an excellent survey article, showing how the new theory fit what was known.

A verbatim copy of COMPUTATION AND THE SINGLE NEURON by Christof Koch taken from NATURE, 16 January, 1997 annotated and with two appendices by M.Robert Showalter at http://www.wisc.edu/rshowalt/kochanno/

The NATURE submissions fit data rather well, but should not have done so, because I'd used an inconsistent system of units (MKS units are needed for consistent crossterms.) I have since accounted for the effects of glial clefts that surround neural lines, using an analysis that depends on S-K. Results fit data well again:

" The Glial membrane-fluid cleft-neural membrane arrangement cuts effective neural capacitance, greatly increasing signal conduction velocity and greatly reducing the energy requirement per action potential. by M.R. Showalter at http://www.wisc.edu/rshowalt/cleft/