Electrotonic length estimates in neurons with dendritic tapering or somatic shunt.
1. Compartmental models were used to compute the time constants and coefficients of voltage and current transients in hypothetical neurons having tapering dendrites or soma shunt and in a serially reconstructed motoneuron with soma shunt. These time constants and coefficients were used in equivalent cylinder formulas for the electrotonic length, L, of a cell to assess the magnitude of the errors that result when the equivalent cylinder formulas are applied to neurons with dendritic tapering or soma shunt. 2. Of all the formulas for a cylinder (with sealed ends), the most commonly used formula, which we call L tau 0/tau 1 (the formula uses the current-clamp time constants tau 0 and tau 1), was the most robust estimator of L in structures that tapered linearly. When the diameter at the end of the cylinder was no less than 20% of the initial diameter, L tau 0/tau 1 underestimated the actual L by at most 10%. 3. The equivalent cylinder formulas for a cylinder were applied to neurons modeled as a cylinder with a shunted soma at one end. The formula for L based solely on voltage-clamp time constants gave an exact estimate of L. However, the second voltage-clamp time constant cannot be reliably obtained experimentally for neurons studied thus far. Of the remaining formulas, L tau 0/tau 1 was again the most robust estimator of L. This formula overestimated L with the size of the overestimates depending on beta, rho beta = 1, and the actual L of the cylinder, where beta is the soma shunt factor, and rho beta = 1 is the dendritic-to-somatic conductance ratio when beta = 1 (no shunt). When the actual L was 0.5 and the soma shunt was large, this formula overestimated L by two- to threefold, but when the actual L was 1.5, the overestimate was only 10-15% regardless of the size of the shunt. 4. In neurons modeled as two cylinders with soma shunt, the L tau 0/tau 1 value computed with the actual tau 0 and tau 1 values overestimated the average L by two to six times when soma shunt was large. However, the L tau 0/tau 1 estimates computed with tau 0 and tau 1 values estimated with the exponential fitting program DISCRETE from voltage transients computed for these neuron models were never this large because of inherent problems in estimating closely spaced time constants from data.(ABSTRACT TRUNCATED AT 400 WORDS)
Holmes
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WR
Mathematical Research Branch, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892.
Rall
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W
D000818:Animals; D003712:Dendrites / Q000502:physiology* / Q000648:ultrastructure*; D004553:Electric Conductivity; D004594:Electrophysiology; D008433:Mathematics; D008959:Models, Neurological; D009474:Neurons / Q000166:cytology* / Q000502:physiology* / Q000648:ultrastructure