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ITRI and HP Collaborate in System Biology Bioinformatics Project.

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A macroscopic cable equation, which describes the passive linear ("electrotonic") response of a myelinated axon, was previously derived from a segmented cable equation using Keller's two-space homogenization method [Basser, PJ, Med. and Biol. Comput., 1993, Vol. 31, pp. S87–S92]. Here we use the space and length constants of this averaged cable equation to predict classical scaling laws that govern relationships among the inner and outer diameters of the axon's myelin sheath and the distance separating adjacent nodes of Ranvier. These laws are derived by maximizing the characteristic speed of an electrical disturbance along the axon, i.e., the ratio of the characteristic length and the characteristic time constants of the macroscopic cable, subject to the constraint that the nodal width is constant. Using this result, it is also possible to show that all myelinated axons are equally fault tolerant. No free parameters were used in this analysis; all variables and physical constants used in these calculations were taken from published experimental data.

A mathematical model is developed to describe and investigate interstitial branching of axonal networks during nervous system development. The model under consideration describes axonal network growth in which the concentration of axon guidance molecules controls axon's growth and interstitial branching from axon shaft. Numerical simulations show that in the model framework axonal networks branch similarly to real neural networks in vitro.

Two concepts have long dominated vertebrate nerve electrophysiology: (a) Schwann cell-formed myelin sheaths separated by minute non-myelinated nodal gaps and spiraling around axons of peripheral motor nerves reduce current leakage during propagation of trains of axon action potentials; (b) "jumping" by action potentials between successive nodes greatly increases signal conduction velocity. Long-held and more recent assumptions and issues underlying those concepts have been obscured by research emphasis on axon-sheath biochemical symbiosis and nerve regeneration. We hypothesize: mutual electromagnetic induction in the axon-glial sheath association, is fundamental in signal conduction in peripheral and central myelinated axons, explains the g-ratio and is relevant to animal navigation.