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LECTURE 4: MEASURING MEMBRANE CONDUCTANCE AND CAPACITANCE & VOLTAGE-CLAMP RECORDING REQUIRED...
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Transcript of LECTURE 4: MEASURING MEMBRANE CONDUCTANCE AND CAPACITANCE & VOLTAGE-CLAMP RECORDING REQUIRED...
LECTURE 4: MEASURING MEMBRANE CONDUCTANCE AND CAPACITANCE &VOLTAGE-CLAMP RECORDING
REQUIRED READING: Kandel text, Chapters 8, 9 (beginning), pgs 140-153
We have talked about the properties of solid-state RC electrical circuits.
We have also learned that the resting membrane consists of electrical components:The membrane is a capacitor
Channels create ion-specific conductancesConcentration gradients establish ion-specific battery potentials
We show here that a cell at rest exposed to a transition in transmembrane voltage responds as a simple RC circuit
SO LONG AS THE VOLTAGE CHANGES DO NOT ALTER THE OPEN/CLOSED STATES OF ANY MEMBRANE CHANNELS !!!
In an RC electrical circuit, we can measure the resistance (conductance) andcapacitance of components by analyzing currents and component voltages
induced by applying a voltage step.
RB
RA +
- VBat
SWITCH CLOSED t = 0 sec
C
IC
IA
IB
time 0
I A
time 0
I A
IA=10 mV/(RA + RB)
time 0
I A
IC
C= QC / VC = QC (RA + RB) /10 mV RB
WHEN RA <<< RB IA=10mV/RBC = QC / 10mV
AND
= 10 mV
GRAPHIC AND CIRCUIT REPRESENTATIONS OF ION FLOWSACROSS THE MEMBRANE AT THE RESTING POTENTIAL
inin
outout
K+
K+
+ + +
- - -
K+
K+
K+
K+
K+
K+ Na+
Na+
+ + ++ + ++ + +
- - - - - -- - - - - -- - -
+ + + + + +Vm = - 71 mV
EEKK = - 82 mV = - 82 mV EENaNa = + 85 mV = + 85 mV
IIK K = = - - IINaNa
AT STEADY STATE:
inin
outout
+
-EK = - 82 mV
gK = 2 nS
I K =
2
2
pA
RK = 0.5 G
inin
outout
-+ENa = + 85 mV
gNa = 0.14 nS
I Na =
-
22
p
A
RNa = 7.1 G
EEKK + I + IKKRRKK = Vm = EENaNa + I + INaNaRRNaNa-82 mV + (22 pA)(0.5 G-82 mV + (22 pA)(0.5 G)) = -71 mV = +85 mV + (-22 pA)(7.1 G+85 mV + (-22 pA)(7.1 G))
Vminin
outout
= -71 mV+++
-- -
GRAPHIC AND CIRCUIT REPRESENTATIONS OF ION FLOWSACROSS THE MEMBRANE AT THE RESTING POTENTIAL
inin
outout
K+
K+
+ + +
- - -
K+
K+
K+
K+
K+
K+ Na+
Na+
+ + ++ + ++ + +
- - - - - -- - - - - -- - -
+ + + + + +Vm = - 71 mV
EEKK = - 82 mV = - 82 mV EENaNa = + 85 mV = + 85 mV
IIK K = = - - IINaNa
AT STEADY STATE:
EErestrest + I + IleakleakRRleakleak = Vm -71 mV + (0 pA)(0.48 G-71 mV + (0 pA)(0.48 G)) = -71 mV
inin
outout
+
-Erest = - 71 mV
gleak = 2.14 nS
I leak =
0
p
A
Rleak = 0.48 G
Vminin
outout
= -71 mV+++
-- -
Vcommand
Ileak
Erest
slope = gleak
(Vcommand - Erest ) x gleak = Ileak
VOLTAGE STEP, TOTAL CHANNEL CONDUCTANCE, ANDLEAK CURRENT OBEY OHM’S LAW
For simplicity, we can combine all of thechannels and gradients contributing to
resting potential into one circuit containing:
a resting potential battery
Erest
and the total conductance of all channels
gtotal
gleak
Vc
om
man
d
Cmem +-
out
in
Erest
+-
Ileak
A VOLTAGE CHANGE ACROSS THE MEMBRANE ACTS INDEPENDENTLYON EACH COMPONENT OF THE MEMBRANE CIRCUIT
inin
outout
+
-EK = - 82 mV
gK = 2 nS
I K =
2
2
pA
RK = 0.5 G
inin
outout
-+ENa = + 85 mV
gNa = 0.14 nS
I Na =
-
22
p
A
RNa = 7.1 G
- -Vm =
inin
outout
-71 mV
+++
-+-
- 61 mV
IMPOSEIMPOSECOMMANDCOMMANDVOLTAGEVOLTAGE
10 mV10 mVABOVEABOVE
RESTINGRESTINGPOTENTIALPOTENTIAL
inin
outout
+
-EK = - 82 mV
gK = 2 nS
I K =
4
2
pA
RK = 0.5 G
inin
outout
-+ENa = + 85 mV
gNa = 0.14 nS
I Na =
-2
0.6
pA
RNa = 7.1 G
- -Vm =
inin
outout
-61 mV
++
+-
- 61 mV
inin
outout
+
-EK = - 82 mV
gK = 2 nS
I K =
4
2
pA
RK = 0.5 G
inin
outout
-+ENa = + 85 mV
gNa = 0.14 nS
I Na =
-2
0.6
pA
RNa = 7.1 G
- -Vm =
inin
outout
-61 mV
++
+-
- 61 mV
VOLTAGE STEP 10 mV
TOTAL CHANNEL CONDUCTANCE
gtotal(leak) 2.14 nS
NET STEADY STATECURRENT FLOW
Ileak 21.4 pA
DISCHARGE = 10 mV x C
V
g
I
x
=
VOLTAGE STEP FROM RESTING POTENTIAL INDUCES CAPACITANCETRANSIENT CURRENT AND STEADY-STATE LEAK CURRENT
time 0
I TO
TA
L
Ileak = (Vcommand - Vrest ) x gtotal(leak)
IC
0
x
=
EFFECT OF VOLTAGE STEP ON CURRENTS AND VOLTAGEAT A DIFFERENT SITE WITHIN NEURON
Rmem
+
-
Vc
om
- E
res
t
Cmem Rmem Cmem
out
in Raxial
SITE OF COMMAND DIFFERENT SITE
time 0
I TO
TA
L
Ileak = (Vcommand - Erest ) / Rmem
IC
0
time 0
I TO
TA
L
Ileak = (Vcommand - Erest )/
IC
0 (Rmem + Raxial )
If Raxial is significant, Ileak and voltage divergence from Erest at different site
is less and voltage divergence is delayed by Raxial x C time constant
DETERMINANTS OF AXIAL RESISTANCE
Raxial ~ Distanceaxial / Areacross-sectional
Cell soma has relatively large diameter (3 - 30 microns) and cross-sectional area,
so Raxial in soma is negligible. Therefore, transmembrane voltage will always be the same at all points around the soma, even during rapid current/voltage changes.
Raxial is significant along the axon and thin dendrites. The narrower an axon’s
diameter, the larger is Raxial, and the greater delay and attenuation of a voltage change occuring at a distance within the cell.
THE IDEAL VOLTAGE CLAMP
Voltage clamp is the ability to rapidly and stably fix a voltage difference between 2 points.
When used in conjunction with a whole-cell patch, voltage clamp allows forthe immediate and stable shift in the voltage across the cell membrane.
Voltage clamp allows for the measurement of passive membrane properties(leak conductance and membrane capacitance)
along with voltage- and time-dependent changes in ion-specific conductances
The ideal voltage clamp can be simulated as a “command” voltage battery connected to an on/off switch
Rleak
Vc
lam
p
Cmem +-
out
in
Erest
+- +-
+-
Vclamp
patchpipet
CELL
bath(grounded)
THE REAL VOLTAGE CLAMP
A real voltage clamp consists of a feedback amplifier which continuously compares the voltage across the membrane to a command voltage, and injects
sufficient current into the cell to make this voltage difference = 0
VB
VA
IC
C
B
A
SIMPLIFIED SCHEMATICOF A TRANSISTOR
AMPLIFIER
IICC ~~ VVBB -- VVAA +-patchpipet
CELL
bath(grounded)
Vmembrane
VcommandPOWERPOWERSOURCESOURCE
Iinject
IinjectCURRENTCURRENTMONITORMONITOR
Icap
Imem
ground
ground
If any changes occur in membrane channelscausing new currents and drift of Vm,
the voltage clamp very rapidly senses thisdrift and adjusts current injection to
maintain Vm = Vcommand
REAL VOLTAGE CLAMP ANALOGOUS TO“WATER LEVEL CONTROLLER” IN LEAKY TUB
Inside of tub (inside cell) has width and depth (capacitance) and has an open drain (leak conductance, gleak). Baseline water level (resting potential, Vrest) is set by water level (resting battery, Erest) outside the tub.
The water level controller (voltage clamp) measures water level in tub (Vmembrane) and compares it to an adjustable water level set value (Vcommand) and then injects or sucks water from the tub (current injection) with a pressure proportional to the difference in levels (Vcommand - Vmembrane).
When a new water level command is applied, the system first injects/sucks a large amount of water to reset water level (Iinject = IC) and then continues to inject/suck smaller amount of water to compensate for water passing through drain and thereby maintains command level (Iinject = Ileak). The flow of water through drain obeys “Ohm’s law”, determined by how much command level differs from resting level and by size of drain. Ileak = (Vcommand - Erest) x gleak