chord conductance equation

Basics of electrophysiology
Objectives
1. Know the meaning of Ohm’s Law
2. Know the meaning of ionic current
3. Know the basic electrophysiology terms
4. Know the effects of changing membrane potential in excitable cells
5. Know the effects of changing ionic conductances in excitable cells
6. Understand the terms ‘activation’ and ‘inactivation’
What do the following categories of drugs
have in common?
antiarrhythmics
antihypertensives
anxiolytics
anticonvulsants
sedatives/hypnotics
antidiabetics
anesthetics
They all include drugs that act on ion channels
Therefore...
Ion channels are interesting to pharmacists
Channel
selectivity
Na+
Ca2+
Cl-
K+
molecules
Channel gating
Voltage
Extracellular
ligand
Intracellular
ligand
Ligand-gated ion channels
(Dr. Ishmael)
Voltage-gated ion channels
Voltage-gated ion channels
• Voltage sensor
• Inactivation
• Voltage-dependent block
Voltage sensor
Inactivation
extracellular
+
intracellular
Voltage-dependent block
extracellular
+
+
intracellular
+
A guide to “Electrophysiologese”
Membrane potential (Em): The voltage difference across
the cell membrane (inside vs outside) (millivolts)
Resting potential: The membrane potential at which the
membrane spends most of its time
Action potential: The transient change in membrane
potential due to active properties of the membrane
Electrotonic potential: A change in membrane potential
due to passive properties of the membrane
A guide to “Electrophysiologese”
Depolarization: A change of membrane potential in the
positive direction.
Repolarization: Return of the membrane potential to the
resting potential after a depolarization.
Hyperpolarization: A change of membrane potential to a
more negative value than the normal resting potential.
A guide to “Electrophysiologese”
Inward current: Net movement of positive ions into the
cell, or net movement of negative ions out of the cell.
By convention, plotted as negative current.
Inward current causes depolarization
Outward current: Net movement of positive ions out of the
cell, or net movement of negative ions into the cell.
By convention, plotted as positive current.
Outward current causes repolarization/hyperpolarization
A guide to “Electrophysiologese”
Excitable cell: A cell that can fire action potentials
Excitability: The ability to fire action potentials
Threshold potential: The membrane potential at which
an action potential fires
Excitable cells fire action potentials
mV
2 msec
A nerve cell (neuron)
axon
Cell body
Hodgkin and Huxley
Voltage clamp
Depolarization changes the conductance of the membrane
Inward current is carried by Na+ ions
Outward current is carried by K+ ions
Hodgkin & Huxley reconstructed the action potential
Electrochemical gradients
Ion channels allow ions to pass through
Why would ions want to pass through?
Which way will they go?
At what rate will they go through?
Concentration gradient (chemical gradient)
Net flow
Membrane potential (electrical gradient)
Cation
channel
Anion
channel
+
-
+
-
Membrane potential (electrical gradient)
Cation
channel
Anion
channel
-
+
+
Electrochemical gradient
-
+
+
-
+
+
+
-
-
+
+
+
-
+
+
-
+
-
-
-
-
-
+
+
+
-
+
+
-
+
- +-
-
+
+
+
+
-
+
-
-
The Nernst potential
EX =
60
zX
.
log
( )
[Xo]
[Xi]
(At physiological temperature)
[Xi] = Ionic concentration inside the cell
[Xo] = Ionic concentration outside the cell
zX = ionic valence (number and sign (+ or -) of charges on ion)
EX is in millivolts (mV)
[Xo] and [Xi] are in millimolar (mM)
ion
Extracellular
concentration
(mM)
Na+
145
12
67
K+
4
155
-98
Ca2+
1.5
Cl-
123
Intracellular
concentration
(mM)
0.0001
4.2
Nernst
potential
(mV)
129
-90
If Cl- is passively distributed (not pumped), ECl = resting potential
The different concentrations of physiological ions means that they
have different Nernst potentials.
Therefore, at any membrane potential, there is a driving force on
at least some of the ions.
(driving force = membrane potential – Nernst potential)
At physiological membrane potentials, the driving force is
inward for Na+ and Ca2+ ions and outward for K+ ions.
Therefore, at physiological membrane potentials, there are inward
Na+ and Ca2+ currents and outward K+ currents.
Ohm’s law: V=IR; I=GV
V or E = potential (Volts); I = current (Amps);
R = resistance (Ohms); G = 1/R = conductance (Siemens)
The cell membrane is a resistor
Ohm’s Law
I=GV
I
High G
Low G
V
Slope = conductance (G)
Ohm’s Law
I
IK=G(Em-EK)
EK = -98 mV
V
ENa = 67 mV
INa=G(Em-ENa)
At rest, ionic gradients are maintained by the Na+-K+ ATPase
INa
2 K+
+ ++++ ++++
ATPase
- - -------IK
ICl
3 Na+
membrane potential = -90 mV
GNa is low
GK is high
INa
outside
+ ++++ ++++
inside
- - --------
ICl
IK
If the membrane potential is not changing,
-INa = -((-90mV)-ENa) x GNa = (IK) = ((-90mV)-EK) x GK
ECl = -90 mV
(Ca2+ channels not shown)
Na+ channels just opened
membrane is depolarizing
GNa is very high
GK is high
INa
IK
INa > -(IK)
outside
+ + + + +
inside
-----
ICl
(no significant effect on concentration)
membrane potential = +30 mV
GNa is very high
GK is high
ICl
INa
IK
outside
-----
inside
+ + + + +
(outward current,
inward Cl flow)
INa = (30mV-ENa) x GNa = -(IK + ICl)
= -[(30mV-EK) x GK + (30mV-ECl) x GCl ]
membrane potential = -90 mV
ECl = -90 mV
INa
IK
outside
+ ++++ ++++
inside
- - --------
ICl
What will happen to the membrane potential if we open
more Cl- channels?
What will happen to excitability if we open more Clchannels?
chord conductance equation
g2
gX
g1
Em  (E1)  (E2) ... (EX)
gT
gT
gT
gK
gCl
gNa
gCa
(ECl) 
(ENa ) 
(ECa )
Em  (EK ) 
gT
gT
gT
gT
Electrical signaling changes intracellular Ca2+
[Na+]i, [K+]i, [Cl-]i don’t change significantly.
Depolarization opens Ca2+ channels. [Ca2+]i increases.
Ca2+
Action potential
axon
Postsynaptic
cell
Neurotransmitter
receptor
Here are the main points again:
Nerves, muscles and other excitable cells use electrical signaling
Physiologically, Na+ channels always pass inward current;
K+ channels always pass outward current.
Inward current depolarizes the membrane.
Outward current repolarizes/hyperpolarizes the membrane.
In an excitable cell, depolarization causes activation
of Na+ channels, followed by inactivation of Na+
channels and activation of K+ channels.
These processes underlie the action potential of the nerve axon.
Net movement of ions through channels is always down the
electrochemical gradient.
Concentration gradients are maintained by ATPases and ion exchangers
The membrane potential depends on the relative conductance
of the membrane for K+, Na+, Cl- and Ca2+ ions.
Ion selectivity varies among ion channels.
In cells that don’t actively transport Cl-, opening Cl- channels
decreases excitability by stabilizing the membrane potential.
The intracellular response to electrical signaling is a change in
cytoplasmic Ca2+.