Answered: A myelinated axon conducts nerve…

A myelinated axon conducts nerve impulses at a speed of 40 m/s. What is the signal speed if the thickness of the myelin sheath is halved but no other changes are made to the axon?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter29: Direct Current (dc) Circuits

Section: Chapter Questions

Problem 82PQ

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A myelinated axon conducts nerve impulses at a speed of 40 m/s. What is the signal speed if the thickness of the myelin sheath is halved but no other changes are made to the axon?

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Assume a length of axon membrane of about 0.10 m is excited by an action potential (length excited = nerve speed pulse duration = 50.0 m/s 2.0 103 s = 0.10 m). In the resting state, the outer surface of the axon wall is charged positively with K+ ions and the inner wall has an equal and opposite charge of negative organic ions, as shown in Figure P18.43. Model the axon as a parallel-plate capacitor and take C = 0A/d and Q = C V to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness d = 1.0 108 m, axon radius r = 1.0 101 m, and cell-wall dielectric constant = 3.0. (a) Calculate the positive charge on the outside of a 0.10-m piece of axon when it is not conducting an electric pulse. How many K+ ions are on the outside of the axon assuming an initial potential difference of 7.0 102 V? Is this a large charge per unit area? Hint: Calculate the charge per unit area in terms of electronic charge e per squared (2). An atom has a cross section of about 1 2 (1 = 1010 m). (b) How much positive charge must flow through the cell membrane to reach the excited state of + 3.0 102 V from the resting state of 7.0 102 V? How many sodium ions (Na+) is this? (c) If it takes 2.0 ms for the Na+ ions to enter the axon, what is the average current in the axon wall in this process? (d) How much energy does it take to raise the potential of the inner axon wall to + 3.0 102 V, starting from the resting potential of 7.0 102 V? Figure P18.43 Problem 43 and 44.
Assume a length of axon membrane of about 0.10 m is excited by an action potential (length excited = nerve speed × pulse duration = 50.0 m/s × 0.0020 s = 0.10 m). In the resting state, the outer surface of the axon wall is charged positively with K+ ions and the inner wall has an equal and opposite charge of negative organic ions, as shown in the figure below. Model the axon as a parallel-plate capacitor and take C = ??0A/d and Q = CΔV to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness d = 1.1 ✕ 10−8 m, axon radius r = 2.0 ✕ 101 ?m, and cell-wall dielectric constant ? = 2.7. A diagram shows a collection of positive and negative charges in and around an axon. The diagram is divided into three sections, one on top of the other. The top section is labeled "External fluid". A row of positive charges labeled "Positive charge layer" lies along the bottom side of this section. Above the row of positive charges, there is an even mixture of…
Calculate the capacitance of the myelinated neuron membrane (axon), if its thickness is 0.8 micrometres (um) using a value of area of 10-6 m2. The membrane wall is mainly lipids and you will need to find the value of the permittivity in your notes. Give your answer in picoFarads (10-12 F) NB 1um = 10-6 m
A particular myelinated axon has nodes spaced 0.80 mm apart. The resistance between nodes is 20 MΩ; the capacitance of each insulated segment is 1.2 pF. What is the conduction speed of a nerve impulse along this axon?
The giant axon of a squid is 0.5 mm in diameter, 10 cm long, and not myelinated. Unmyelinated cell membranes behave as capacitors with 1 μF of capacitance per square centimeter of membrane area. When the axon is charged to the -70 mV resting potential, what is the energy stored in this capacitance?
Consider the model of the axon as a capacitor from Figure P18.43. (a) How much energy doesit take to restore the inner wall of the axon to -7.0 x 10-2 V,starting from +3.0 x 10-2 V? (b) Find the average current inthe axon wall during this process.
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What is the magnitude of the electric field across an axon membrane 1.2×10−8 m thick if the resting potential is -70 mV ?
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In Example 23.14 we estimated the capacitance of the cell membrane to be 89 pF, and in Example 23.15 we found that approximately 10,000 Na+ ions flow through an ion channel when it opens. Based on this information and what you learned about the action potential, estimate the total number of sodium channels in the membrane of a nerve cell.
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