Molecular Biology of the Cell by Bruce Alberts, Alexander Johnson, Julian Lewis, David Morgan, Martin Raff, Keith Roberts, Peter Walter by by Bruce Alberts, Alexander Johnson, Julian Lewis, David Morg

chapter 11 end-of-chapter problems
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21.4 nm
Table Q11–1 Ionic composition of seawater and of the
cytosol in the squid giant axon (Problem 11–10).
Ion Cytosol Seawater
Na + 65 mM 430 mM
Figure Q11–2 A “ball” tethered by a “chain” to a voltage-gated K +
channel (Problem 11–9).
K + 344 mM 9 mM
11–9 In a subset Problems of voltage-gated p11.11/11.10 K + channels, the
N-terminus of each subunit acts like a tethered ball that
occludes the cytoplasmic end of the pore soon after it
opens, thereby inactivating the channel. This “ball-andchain”
model for the rapid inactivation of voltage-gated
K + channels has been elegantly supported for the shaker
K + channel from Drosophila melanogaster. (The shaker
K + channel in Drosophila is named after a mutant form
that causes excitable behavior—even anesthetized flies
keep twitching.) Deletion of the N-terminal amino acids
from the normal shaker channel gives rise to a channel
that opens in response to membrane depolarization, but
stays open instead of rapidly closing as the normal channel
does. A peptide (MAAVAGLYGLGEDRQHRKKQ) that
corresponds to the deleted N-terminus can inactivate the
open channel at 100 µM.
Is the concentration of free peptide (100 µM) that
is required to inactivate the defective K + channel anywhere
near the local concentration of the tethered ball on a normal
channel? Assume that the tethered ball can explore a
hemisphere [volume = (2/3)πr 3 ] with a radius of 21.4 nm,
which is the length of the polypeptide “chain” (Figure
Q11–2). Calculate the concentration for one ball in this
hemisphere. How does that value compare with the concentration
of free peptide needed to inactivate the channel?
11–10 The giant axon of the squid (Figure Q11–3) occupies
a unique position in the history of our understanding
of cell membrane potentials and nerve action. When an
electrode is stuck into an intact giant axon, the membrane
potential registers –70 mV. When the axon, suspended in a
bath of seawater, is stimulated to conduct a nerve impulse,
the membrane potential changes transiently from –70 mV
to +40 mV.
For univalent ions and at 20°C (293 K), the Nernst equation
reduces to
V = 58 mV × log (C o /C i )
where C o and C i are the concentrations outside and inside,
respectively.
Using this equation, calculate the potential across
the resting membrane (1) assuming that it is due solely to
K + and (2) assuming that it is due solely to Na + . (The Na +
and K + concentrations in the axon cytosol and in seawater
are given in Table Q11–1.) Which calculation is closer
to the measured resting potential? Which calculation is
closer to the measured action potential? Explain why these
assumptions approximate the measured resting and action
potentials.
11–11 Acetylcholine-gated cation channels at the neuromuscular
junction open in response to acetylcholine
released by the nerve terminal and allow Na + ions to enter
the muscle cell, which causes membrane depolarization
and ultimately leads to muscle contraction.
A. Patch-clamp measurements show that young rat
muscles have cation channels that respond to acetylcholine
(Figure Q11–4). How many kinds of channel are there?
How can you tell?
B. For each kind of channel, calculate the number of
ions that enter in one millisecond. (One ampere is a current
of one coulomb per second; one pA equals 10 –12
ampere. An ion with a single charge such as Na + carries a
charge of 1.6 × 10 –19 coulomb.)
2 pA
40 msec
Figure Q11–4 Patch-clamp measurements of acetylcholine-gated
cation channels in young rat muscle (Problem 11–11).
Problems p11.12/11.11
Figure Q11–3 The squid Loligo (Problem 11–10). This squid is about
15 cm in length.