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Bi 1 Lecture 6

Thursday, April 6, 2006

Action Potentials and Single Channels

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[neurotransmitter]

openclosed

chemical transmission atsynapses:

electric field

openclosed

electrical transmission inaxons:

actually, E

Major Roles for Ion Channels

Monday:

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The electric field across a biological membrane, compared with other electric fields in the modern world

1. A “high-voltage” transmission line1 megavolt = 106 V.The ceramic insulators have a length of ~ 1 m.The field is ~ 106 V/m.

2. A biological membraneThe “resting potential” ~ the Nernst potential for K+, -60 mV.The membrane thickness is ~ 3 nm = 30 Å.The field is (6 x 10-2 V) / (3 x 10-9 m) = 2 x 107 V/m !!!

Dielectric breakdown voltages (V/m)

Ceramic 8 x 107

Silicone Rubber 3 x 107

Polyvinyl chloride 7 x 106

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Little Alberts 12-32© Garland

= IMPULSE

The action potential (the nerve impulse)

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http://www.theory.caltech.edu/people/politzer/syll1c/syll1c.html

Today’s reasoning employs electrical circuits

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open channel = conductor

=

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The miniature single-channel conductors add in parallel

ENa

(+60 mV)

GNa = Na

=GNa

Na

Na

outside

cytosol = inside

mostly K+mostly Na+

GK = K

EK (- 60 mV)

GKK

K

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C

E

G

Na+

VE G E G E G

G G GK K Na Na Cl Cl

K Na Cl

K+

At DC, IC = CdV/dt = 0,

so

Cl-

peak of action

potential: Na+ channels

open too

resting potential:

K+ channels open

outside

cytosol = inside

The membrane potential at steady state(not at equilibrium)

“after-hyperpolarization”: more K+ channels open

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The “Na+ pump” splits ATP to make a Na+ and K+ concentration gradient

A transporter protein moves a few ions for each conformational change

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2

Little Alberts 12-10 © Garland

from Lecture 5

What are the electrical consequences of the charge imbalance?

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Every large

Rvery large= =

Na pump = current source

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pump

channel

To understand the Na pump’s action on the membrane potential, we treat the pump as a current source . . .

and we treat the channels as resistors

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ATP

pump

channel

V

+

-

V = IR

Because of the charge imbalance,

The Na pump drives the membrane potential

more negative(the cell “hyperpolarizes”

= the pump is “electrogenic”)

. . . and we invoke Kirchoff’s law

C

E

G

Na+ K+ Cl-

outside

cytosol = inside

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All I really need to know about lifeI learned in Bi 1

1. If you want a job done right, get a protein (Lecture 3)

2. Electrical circuits explain many processes

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Channel opening and closing rate constants are functions of voltage--not of time:

The conformational changes are “Markov processes”.

The rate constants depend instantaneously on the voltage--not on the

history of the voltage.

These same rate constants govern both the macroscopic (summed) behavior and

the single-molecule behavior.

In a real neuron, the opening and closing of the channels changes the voltage, and it

takes a while to charge up the membrane capacitance (see QP1).

As result, impulse propagation is solved numerically--but on the basis of rate

constants derived from experiments where the voltage is held constant (“clamped”).

The Hodgkin-Huxley formulation of the nerve impulse

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http://nerve.bsd.uchicago.edu/nerve1.html

1. Waveform at one point (V vs t)2. Hyperpolarization3. “Refractory” period (30 ms total time, vary pulse 2 duration, pulse 3 = 30 A)5. Propagation (V vs. x)6. Repetitive firing: the frequency code (lengthen pulse 1)

(For robust frequency encoding, we require one additional type of K+ channel.)

Simulation of the nerve impulse (“unclamped”)

Francisco Bezanilla's simulation program at the Univ of Chicago:

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1973

Max Delbruck

Richard Feynman

H. A. L

Carver Mead

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Intracellular recording with sharp glass electrodes

V

= RC = 10 ms; too large!

C = 1 F/cm2

E

R = 104 -cm2

intracellular

extracellular

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A better way: record the current from channels directly?

Feynman’s idea

A

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5 pA = 104 ions/ms

20 ms

A single voltage-gated Na+ channel

-80 mV

-20 mV

A

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http://www.nobel.se/medicine/laureates/1991/press.html

Press release for 1991 Nobel Prize in Physiology or Medicine:

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Simulation of a voltage-gated K+ channel

http://nerve.bsd.uchicago.edu/model/rotmodel.html

Francisco Bezanilla's simulation program at the Univ. of Chicago:

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action potentialnounDate: 1926

: a momentary change in electrical potential (as between the inside of a nerve cell and the extracellular medium) that occurs

when a cell or tissue has been activated by a stimulus.

H. A. L. prefers “impulse”

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-from sense organs to the brain (Thanos Siapas, lecture 4)

-within the brain

-from the brain to muscles

-even in a muscle or in the heart

-even in the pancreas

The frequency of impulses represents signaling among cells

in the

nervous system.

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End of Lecture 6