Neuron Conduction
Casey Adamson
Physics 212X
April 16, 2003
Contents
The Resting Potential
of the Nerve Cell
Introduction
During a thunderstorm in 1786, Luigi Galvani touched a frogâs leg with a metal instrument and noticed the muscles twitching. He concluded that the storm had generated electricity, which conducted through the frogâs nerves and caused the muscles to contract. Nerves do transmit impulses from one part of the body to another, but in a different way than in an ordinary conductor. The electrical properties are different in neural conduction because it is slower and does not very in strength (it is a all-or-nothing conduction).
A nerve cell (neuron) is the basic building block of the nervous system and is specialized to transmit information. It consists of a cell body and two types of branchlike fibers, dendrites and axons (top of Figure 1). Dendrites, along with the cell body, receive information in the form of stimuli from sensory receptors or from other nerve cells. The axon is a long, thin cellular extension responsible for transmitting information to other nerve cells, and is filled with a viscous intracellular fluid called the axoplasm. If stimuli received by the dendrites or the cell body is above the cellâs intensity threshold, a nerve impulse is initiated which propagates along the axon. It flows along the axon away from the cell body toward the terminal branches. Once a nerve impulse reaches the terminal branches, neurotransmitter substances release, conveying the impulse to receptors on the next cell.
Figure 1
The Resting Potential of the Nerve Cell
Critical to the function of the nerve cell, the cell
membrane maintains intracellular conditions that differ from those of the
extracellular environment. There is an excess of negative ions inside the cell
membrane and an excess of positive ions outside (middle of Figure 1). The
electrochemical gradient across the membrane is the means of nerve impulse transmission.
The concentration of potassium (K+) is 30 times greater in the fluid
inside the cell than outside and the concentration of sodium ions (Na+)
is nearly 10 times greater in the fluid outside the cell than inside (See Table
1). Anions, particularly chloride (Cl--), are also unevenly
distributed. Nerve cells use both passive diffusion and active transport to
maintain these differentials across their cell membranes. The unequal
distribution of Na+ and K+ is established by an
energy-dependant Na+-K+ ăpumpä, moving Na+ out
of the cell and K+ into the cell. Specialized proteins embedded in
the nerve cell membrane function as voltage-dependant channels, passing through
Na+ and K+ during nerve impulse transmission.
Table1
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Ion
Concentration Inside and Outside a Typical Resting Nerve Cell |
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Concentration
(mmol/L) |
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Inside |
Outside |
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Na+ |
15 |
145 |
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K+ |
150 |
5 |
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Cl––––- |
9 |
120 |
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Other |
156 |
30 |
The voltage-dependant Na+ channels are closed when the nerve cell is in its resting state, maintaining the unequal distribution of Na+. Impermeable to large anions (or other large negatively charged species, such as proteins), an excess of negative charge builds up immediately inside the cell membrane. The potential difference across the membrane is about 70 mV. If the electric potential outside the cell is taken to be zero, the electric potential inside is ö70 mV. This is the nerve cellâs resting potential (dV) (see bottom of Figure 3).
The arrangement of charge on each surface of the nerve cell membrane resembles that of a charged capacitor. The electric field (E) across a parallel-plate capacitor is uniform, so we can calculate the electric field across a cell membrane of 7 nm in thickness (dL):
E = -dV/dL = -(-70 x 10-3 V)/(7.0 x 10-9 m) = 1.0 x 107 V/m (inward)
The inward force (F) due to this field on a positive ion (q) would be:
F = qE = (1.6 x 10-19 C)(1.0 x 107 V/m) = 1.6 x 10-12 N
The force competes against the concentration gradient for K+, while it supports the effect of the concentration gradient for Na+.
The Stimulated Nerve Cell
If a physical or chemical stimulus is strong enough to cause depolarization from the resting potential of ö70 mV to around ö50 mV, the voltage-dependant Na+ transmembrane channels open. Favored by both the concentration gradient (see Table 1) and the electric gradient, Na+ ions flow into the cell, creating an electric current (I = ΔQ/Δt). The influx of Na+ causes a local reversal of electric polarity of the membrane, changing the electric potential to about +40 mV (a swing of 110 mV from the resting potential. The small cross-sectional area (A) of an axon and high resistivity (ρ) of the axoplasm yield an extremely high resistance (R = ρL/A).Ę A piece of nerve axon 1 cm in length (L) has an electrical resistance of about 2.5 x 108 Ω (comparable to that of wood). The produced electrical current:
I = V/R = (110 x 10-3 V)/(2.5 x 108 Ω) = 4.4 x 10-10 A
The Na+ concentration gradient (outside > inside) becomes balanced by the electric gradient (due to the membrane potential now having become positive on the inside), depolarization is complete at the site of the original stimulus. The Na+ channels then close again. The K+ channels respond to the changes in polarity, sending K+ flowing out of the cell. The movement of K+ ions and slower action of the Na+-K+ pump soon restore concentration differentials and electric gradient to the resting state. The transient change in the electric potential across the membrane is the action potential. After depolarization, for a brief period (milliseconds), the Na+ channels cannot be stimulated. This is called the refractory period.
Nerve Impulse Propagation
The local depolarization at the site of the original stimulus causes movement ö passive diffusion ö of ions into areas adjacent to the site of the stimulus. The potential in the adjacent area reaching the threshold level of ö50 mV, increases the permeability of Na+ and propagates the action potential of +40 mV in a wavelike manner along the length of the nerve cell. Because of the refractory period, the nerve impulse can only be propagated in one direction, away from the nerve cell body towards the terminal branches, to release neurotransmitter substances. These cross the gap (synapse) to the next nerve cell, allowing the process to be repeated.
A
discontinuous multilayered sheath, the myelin sheath, surrounds some
axons, formed when Schwann cells wrap around the axon (Figure 2). Gaps
about 1 µm wide in the
myelin sheath called nodes of Ranvier occur at regular intervals of 1 to
2 mm along the length of the axon. Propagation of a nerve impulse along a
myelinated axon differs somewhat from unmyelinated axons.
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Figure 2. Structure of the Neuron
(A) axon; (B) myelin
sheath; (C) nodes of Ranvier; (D) synapse; (E) dendrites
The myelin sheath is a good insulator, so ions cannot flow through it. Electric activity in myelinated nerve cells is confined to the nodes of Ranvier, where there are dense contractions of voltage-dependant ion channels. Action potentials can be generated only at the nodes of Ranvier and ăjumpä rapidly from one node to the next along the nerve axon due to the rapid diffusion of ions through axoplasm and extracellular fluid. The conduction velocity in a typical myelinated nerve axon is 12 m/s.
Conduction velocity depends on resistivity of the axoplasm and on the membrane capacitance. As resistance is inversely proportional to the cross-sectional area, an axon with a large diameter has a lower resistance and a higher conduction velocity. For a parallel-plate capacitor, capacitance is inversely proportional to the separation of the plates. It follows that myelinated axons have a lower capacitance than unmyelinated axons. The lower the membrane capacitance, the smaller the charge, and the less time the membrane will take both to depolarize and to repolarize. This is one explanation for the higher conduction velocity observed in myelinated axons. Measurements of conduction velocities in a wide range of nerve cells have been shown to correlate closely to their calculated resistances and capacitances.
The mechanism of electrical impulse transmission in nerve cells is certainly quite different from electric conduction in metals, but physics also has an important role to play in the understanding of this process.
Reference
Nickles, Elizabeth Pflegl. ăConduction in Nerve Cellsä (1991). Tipler, Paul A. Physics for Scientists and Engineers. Ch. 22, pp.740-743. Worth Publishers, Inc., U.S.A
ăNerve Cell, Structure.ä http://www.compuserve.co.uk/sciencecontent/dictionaryofscience/06/P0001863.stm (16 Apr. 2003).
ăStructure of the Neuron.ă http://psyc.athabascau.ca/html/Psych289/Biotutorials/1/part1.html (16 Apr. 2003).