Download LECTURE.4.Gm.Cm.Vclamp

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 conductances
Concentration 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) and
capacitance of components by analyzing currents and component voltages
induced by applying a voltage step.
IA
RA
+
IC
RB
IB
VBat
-= 10
mV
IA
SWITCH CLOSED t = 0 sec
C
0
time
IA
IA
IC
C= QC / VC = QC (RA + RB) /10 mV RB
IA=10 mV/(RA + RB)
0
0
time
WHEN RA <<< RB
IA=10mV/RB
AND
time
C = QC / 10mV
GRAPHIC AND CIRCUIT REPRESENTATIONS OF ION FLOWS
ACROSS THE MEMBRANE AT THE RESTING POTENTIAL
K+
K+
K+
Na+
K+
out
+++
+++
+++
+++
+++
+++
in
- - -
- - -
- - -
- - -
- - -
- - -
K+
K+
EK = - 82 mV
K+
Na+
AT STEADY STATE:
ENa = + 85 mV
IK = - INa
gK = 2 nS
RK = 0.5 GW
+
-
EK = - 82 mV
+++ out
---
in
Vm = -71 mV
out
INa = - 22 pA
out
IK = 22 pA
K+
Vm = - 71 mV
gNa = 0.14 nS
RNa = 7.1 GW
+
in
in
EK + IKRK = Vm = ENa + INaRNa
-82 mV + (22 pA)(0.5 GW) = -71 mV = +85 mV + (-22 pA)(7.1 GW)
ENa = + 85 mV
GRAPHIC AND CIRCUIT REPRESENTATIONS OF ION FLOWS
ACROSS THE MEMBRANE AT THE RESTING POTENTIAL
K+
K+
K+
Na+
K+
out
+++
+++
+++
+++
+++
+++
in
- - -
- - -
- - -
- - -
- - -
- - -
K+
K+
K+
EK = - 82 mV
K+
Na+
ENa = + 85 mV
AT STEADY STATE:
IK = - INa
Ileak = 0 pA
out
gleak = 2.14 nS
Rleak = 0.48 GW
+
in
Erest = - 71 mV
Vm = - 71 mV
+++ out
---
in
Erest + IleakRleak = Vm
-71 mV + (0 pA)(0.48 GW) = -71 mV
Vm = -71 mV
VOLTAGE STEP, TOTAL CHANNEL CONDUCTANCE, AND
LEAK CURRENT OBEY OHM’S LAW
Ileak
For simplicity, we can combine all of the
channels and gradients contributing to
resting potential into one circuit containing:
a resting potential battery
slope = gleak
Erest
and the total conductance of all channels
Vcommand
gtotal
Erest
Vcommand
out
Ileak
+
-
gleak
+
-
Cmem
Erest
in
(Vcommand - Erest ) x gleak = Ileak
A VOLTAGE CHANGE ACROSS THE MEMBRANE ACTS INDEPENDENTLY
ON EACH COMPONENT OF THE MEMBRANE CIRCUIT
out
gK = 2 nS
RK =
+
-
out
0.5 GW +++
V
---
+
-
- 61 mV
EK = - 82 mV
m=
in
-71 mV
INa = - 22 pA
IK = 22 pA
out
gNa = 0.14 nS
RNa = 7.1 GW
+
in
in
10 mV
out
out
IK = 42 pA
ABOVE
RESTING
POTENTIAL
gK = 2 nS
RK = 0.5 GW
+
-
- -
+
-
- 61 mV
in
+ + out
EK = - 82 mV
in
Vm =
-61 mV
INa = -20.6 pA
IMPOSE
COMMAND
VOLTAGE
ENa = + 85 mV
gNa = 0.14 nS
RNa = 7.1 GW
+
in
ENa = + 85 mV
VOLTAGE STEP FROM RESTING POTENTIAL INDUCES CAPACITANCE
TRANSIENT CURRENT AND STEADY-STATE LEAK CURRENT
out
gK = 2 nS
RK = 0.5 GW
+
-
- -
+
-
- 61 mV
+ + out
EK = - 82 mV
in
Vm =
-61 mV
g
=
I
-
ENa = + 85 mV
in
10 mV
TOTAL CHANNEL
CONDUCTANCE
gtotal(leak)
RNa = 7.1 GW
IC
x
2.14 nS
NET STEADY STATE
=
CURRENT FLOW
Ileak
21.4 pA
DISCHARGE = 10 mV x C
ITOTAL
x
VOLTAGE STEP
gNa = 0.14 nS
+
in
DV
INa = -20.6 pA
IK = 42 pA
out
Ileak = (Vcommand - Vrest ) x gtotal(leak)
0
0
time
EFFECT OF VOLTAGE STEP ON CURRENTS AND VOLTAGE
AT A DIFFERENT SITE WITHIN NEURON
Vcom - Erest
SITE OF COMMAND
DIFFERENT SITE
out
+
Rmem
-
Cmem
in
Rmem
Cmem
Raxial
IC
ITOTAL
ITOTAL
IC
Ileak = (Vcommand - Erest ) / Rmem
0
0
time
/
Ileak = (Vcommand - Erest ) (Rmem + Raxial
0
0
time
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 for
the 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
+
-
Vclamp
Vclamp
out
Rleak
+
-
+
-
Cmem
bath
(grounded)
patch
pipet
Erest
in
CELL
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
SIMPLIFIED SCHEMATIC
OF A TRANSISTOR
AMPLIFIER
VB
POWER
SOURCE
Vcommand
Iinject
Vmembrane
ground
B
ground
C
VA
A
IC
IC ~ VB - VA
If any changes occur in membrane channels
causing new currents and drift of Vm,
the voltage clamp very rapidly senses this
drift and adjusts current injection to
maintain Vm = Vcommand
Iinject
CURRENT
MONITOR
Imem
bath
(grounded)
patch
pipet
Icap
CELL
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
Next Lecture: ION CHANNELS: STRUCTURES AND FUNCTIONS
REQUIRED READING: Kandel text, Chapters 6,9