Computation of high safety factor impulse propagation at axonal branch points

Goldfinger, Melvyn D.

doi:10.1097/00001756-200002280-00005

Cited by 16 publications

(19 citation statements)

References 16 publications

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“…In fact, the interplay between the total longitudinal current produced by the action potential and the input impedance of the axon segments ahead of the action potential determines the fate of the propagating action potential. The case of the branch point has been studied in detail (219,221,583). The so-called 3/2 power law developed by Rall describes an ideal relationship between the geometry of mother and daughter branches (221,424,426).…”

Section: A Geometrical Factors: Branch Points and Swellingsmentioning

confidence: 99%

Axon Physiology

Debanne

Campanac

Bialowas

et al. 2011

Physiological Reviews

557

492

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Axons are generally considered as reliable transmission cables in which stable propagation occurs once an action potential is generated. Axon dysfunction occupies a central position in many inherited and acquired neurological disorders that affect both peripheral and central neurons. Recent findings suggest that the functional and computational repertoire of the axon is much richer than traditionally thought. Beyond classical axonal propagation, intrinsic voltage-gated ionic currents together with the geometrical properties of the axon determine several complex operations that not only control signal processing in brain circuits but also neuronal timing and synaptic efficacy. Recent evidence for the implication of these forms of axonal computation in the short-term dynamics of neuronal communication is discussed. Finally, we review how neuronal activity regulates both axon morphology and axonal function on a long-term time scale during development and adulthood.

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Section: A Geometrical Factors: Branch Points and Swellingsmentioning

confidence: 99%

Axon Physiology

Debanne

Campanac

Bialowas

et al. 2011

Physiological Reviews

557

492

View full text Add to dashboard Cite

show abstract

“…The case of the branch point has been studied in detail 105,139,140 . The so-called 3/2 power law that was developed by Rall describes an ideal relationship between the geometry of mother and daughter branches 105 Several recent studies indicate that the hyperpolarization that is produced by repetitive stimulation could be dampened by hyperpolarization-induced cationic current (I h ) 26,81 .…”

Section: Box 1 | Theory Of Geometrical Constraints On Axonal Propagationmentioning

confidence: 99%

Information processing in the axon

2004

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“…[116,38,36]. The axial point-to-point conduction velocity computed in terms of electrotonic distance z (where z = x/λ d ) was:…”

Section: Generalmentioning

confidence: 99%

“…This validation testing was performed using two computational tools: (1) numerical compartmental cable modeling (introduced to neuroscience by Rall [111]), and (2) analog compartmental computation, as described previously [36]. The arborizations tested consisted of a parent fiber and two symmetrical daughter processes, with or without axonal-type voltage-dependent conductances.…”

Section: Introductionmentioning

confidence: 99%

Rallian "Equivalent" Cylinders Reconsidered: Comparisons With Literal Compartments

Goldfinger

2005

J. Integr. Neurosci.

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In Rall's "equivalent" cylinder morphological-to-electrical transformation, neuronal arborizations are reduced to single unbranched core-conductors. The conventional assumption that such an "equivalent" reconstructs the electrical properties of the fibers it represents was tested directly; electrical properties and responses of "equivalent" cylinders were compared with those of their literal branch constituents for fibers with a single symmetrical bifurcation. The numerical solution methods were validated independently by their accurate reconstruction of the responses of an analog circuit configured with compartmental architecture to solve the cable equation for passive fibers with a symmetrical bifurcation. In passive fibers, "equivalent" cylinders misestimated the spatial distribution of voltage amplitudes and steady-state input resistance, partly due to the lack of axial current bifurcation. In active fibers with a single propagating action potential, the spatial distributions of point-to-point conduction velocity values (measured in meters/second) for a literal branch point differed significantly from those of their "equivalent" cylinders. "Equivalent" cylinders also underestimated the diameter-dependent delay in propagation through the branch point and branches, due to the larger "equivalent" diameter. Corrections to the "equivalent" cylinder did not reconcile differences between "equivalent" and literal models. However, "equivalent" and literal branch fibers had the same (a) steady-state resistance "looking into" an isolated symmetrical branch point and (b) geometry-independent point-to-point propagation velocity when measured in space constants per millisecond except within +/-1 space constant from the geometrical inhomogeneity. In summary, Rall's "equivalent" cylinders did not accurately reconstruct all passive or active electrophysiological properties and responses of their literal compartments. For the modeling of individual neurons, the requirement of single-branch resolution is discussed.

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Computation of high safety factor impulse propagation at axonal branch points

Cited by 16 publications

References 16 publications

Axon Physiology

Axon Physiology

Information processing in the axon

Rallian "Equivalent" Cylinders Reconsidered: Comparisons With Literal Compartments

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