Transcript Physical Mechanism of Calcium Pump Regulation by Phospholamban

Electrophysiology of Cell Membranes
Lecture 19
Reference: Class Notes
(Optional: Guyton and Hall, 11th Ed., Chapter 5)
Edward Via College of Osteopathic Medicine
Cell Biology and Physiology: Biochemistry, Block 1
Jim Mahaney, PhD
Copyright 2010
2
Long QT syndrome and…Deafness?
• Longer than normal interval in the
electrocardiogram
• Due to a longer than normal action potential in
cardiac muscle
• Caused by faulty Na+ currents or K+ currents
• Congenital deafness commonly caused by faulty
K+ currents due to abnormal K+ channels.
3
Ion Channels
Pure phospholipid bilayer
++ +
-+ - -+ - ++
-+ - ++ - -
Gf
+
-++ - -+
-+ - ++
-+ - ++ - -
Pure phospholipid bilayer
+ ion channel
+
+
-+ - -+ - +
-+ - + - -
+
+
+ +
-++ - -+
-+ - ++
-+ - ++ - -
ΔG
ΔG
Ion channels are enzymes which catalyze the passive movement of ions
across membranes by providing a polar pathway for ions to pass through
the lipid core of the membrane
4
Ion Channel Properties
Structural Components
Basic Properties
• Pore: provides a polar
pathway for movement of
ions
• Permeation: properties
describing the movement
of ions through a pore
• Gate: regulates the
movement of ions through
the pore
• Gating: properties
describing the opening
and closing of the pore
5
Ion Channels: Ion Permeability
• Channel gating: greatly
increase the time the channel
is open or closed
– Ligand binding
– Voltage change
• Selectivity:
– Single ion type (only K+)
– Multiple ion types (all +)
– Random (everything passes)
6
Channel Opening and Closing
• First order process:
ko
Closed
Open, where ki is the rate of the step.
kc
• Reversible process: channels freely open and close – conformational
changes
• Dictated by probability: there is a probability that the channel will be
open or closed at any given time.
• Membrane stimuli (ligand binding, voltage change, etc) change the
probability that the channel will be open or closed.
7
Channel Two-State Model
• For a two state model
– The opening rate is kf and the
closing rate is kb
– The opening and closing rates are
proportional to the probabilities of
each conformational transition
– Each opening and closing is termed
an event
• Channels usually have multiple
states (or degrees) of open or
closed
closed
open
kf
kb
8
Opening and Closing: the dwell time
closed
open
Dwell time open
Simulated single-channel current
kf
kb
Current
No current
Time 
Dwell time
closed
• The duration of each event is the dwell
time: how much time is spent open or
closed
– The average dwell time in the open state
is 1/kb
– The average dwell time in the closed
state is 1/kf
Open dwell time distribution
Τ = 1 / kb
Dwell time (sec)
9
Channel Open and Closed Probabilities
• For the two state model:
– The probability of being in the open state is
kf / (kf + kb)
– The probability of being in the closed state is
kb / (kf + kb)
• Voltage- and Ligand-gating increase the rate of
opening or closing, hence the dwell time for either
state, hence the probability of being in either state.
10
Voltage Gating
• Below the voltage
required to open the gate
of the channel, the channel
is closed…no current
• Above the gating voltage,
the channel opens and
closes freely, so current
flows
Open
Closed
Time 
Open
Closed
11
Ligand Gating
• In the absence of ligand,
the channel is closed…no
current
No Ligand
Open
Closed
1 X Ligand
• In the presence of ligand,
the channel opens and
closes freely, so current
flows
• More ligand binding
increases open probability
Open
Closed
5 X Ligand
Open
Closed
Time 
12
Channels and Saturation
• Since channels bind ions, their
conductance displays saturation
kinetics
• Obeys Michaelis-Mention
equation 
• gmax = maximum conductance;
Km = [ion] where g = ½ gmax and
Cion is the concentration of the
ion
gmax
g
Km
Cion
g max
g
Km
1
Cion
13
Cell Membrane Potentials
• Called transmembrane voltage (or
potential).
• Vm = Vinside – Voutside
• Most cells have a negative Vm
• Potential is an electric force which
moves from low to high by definition:
Voltage (mV)
• Every cell has an electrical potential
difference across its cell membrane.
0
-70
Intracellular
Extracellular
Membrane
– Anions (– charge, z) move with the
field
– Cations (+ charge, z) move against
the field
Force
Fe = - z (Vm / d)
14
The Electrochemical Potential
• Unequal [KCl], equal osmolarity:
charge is balanced on each side
• Add a K+ channel, for example
• K+ ions will move from areas of
higher to lower concentration.
• Electrical potential develops
• Eventually, electrical potential
will balance the diffusion potential
according the Nernst Equation
15
Cell Membrane Potentials Depend
on Ionic Concentration Gradients
• Typically, [KCl]out is 4.5 mM,
and [KCl]in is 155 mM (muscle)
• Resting potential of -95 mV
according to Nernst Equation
• Change [KCl]out, Vm changes:
RT [ X ]in
Ex  
ln
z x F [ X ]out
– Increased? Vm gets less negative =
depolarized
– Decreased? Vm gets more negative =
hyperpolarized
Key: Change ion gradients? Vm will change; change Vm? Ion gradients will change
16
Parameters Controlling Electrodiffusion
• Key is balance
• Ions will reach
electrochemical
equilibrium where the
movement of ions due to
diffusion and charge is
balanced
• Steady-state: ions move,
but no net change in [X]
or Vm
17
Ion Currents
• If there is a voltage across a
membrane, ions will move across the
membrane if a path is available (i.e.,
an ion channel).
• An unbalanced movement of charge
over time is a current (I, units =
Amps).
• By convention, current is in the
direction of positive charge (i.e.,
cations) movement
• One coulomb of positive charge per
second = 1 Amp
+
+
-+ - -+ - +
-+ - + - -
+
+
+ +
Current, I
-++ - -+
-+ - ++
-+ - ++ - -
18
Definitions and Conventions
• Direction of current flow is
defined by the direction of the
movement of positive charge.
Vin
V
Vout
• Positive charge out is an
outward current, also called a
positive current
• Positive charge in is an
inward charge, also called a
negative current.
• Opposite convention is true
for negative charges
+
+
-
Outward
Inward
Current
Current
(Positive)
(Negative)
19
Depolarizing…Hyperpolarizing
• Cell interior more negative than exterior,
making the cell polarized.
Vm = -70 mV
V
• Move cations in (inward or negative current)
to make the interior more positive (Vm less
negative): depolarizing
• Move cations out (outward or positive
current) to make the interior more negative
(Vm more negative): hyperpolarizing
• Consider anions…same principle but
opposite
-
+
+
-
Hyperpolarizing
Depolarizing
20
Ion Gradients in Mammalian Cells
ION
Out
Skeletal Muscle
Na+
145
K+
4.5
Ca2+
1
Cl116
In
Out/In
ENernst (mV), 37C
12
155
10-4
4.2
12
0.026
104
29
+ 67
- 95
+ 123
- 89
Most other cells
Na+
145
K+
4.5
Ca2+
1
Cl116
15
120
10-4
20
9.7
0.038
104
5.8
+ 61
- 88
+ 123
- 47
21
Ion Currents Depend on the
Electrochemical Driving Force
• V = IR or V = I / G
• Current for individual
ions: Ix = Gx(Vm – Ex)
• Vm – EX is called the
driving force for ion
currents
• For a given Vm = -80 mV,
can predict the driving
force for each ion
Arrows show the direction and magnitude of each current
22
Current-Voltage Plot
• Ohm’s Law: I = V/R or V = I*R
I
• Therefore: I = G*V
outward
• Reversal potential (Vr ) is voltage at
which the curve crosses the voltage axis:
zero current at this point
Inward
R is resistance (ohms)
• Conductance: G = 1/R (siemens)
• Linear plot says currents (i.e., ions) flow
equally well in both directions: Vr tells
position where current direction changes
ohmic
V
reverse
potential
23
• Outward rectification: large change in
outward current for a small change in V,
very little change in inward current for
change in V
I
V
Inward
outward
• Inward rectification: large change in
inward current for a small change in V,
very little change in outward current for
change in V
Inward
• If current flows more easily in one
direction or the other, I-V plots will not
be linear: Called rectification
outward
Non-Linear Current-Voltage Plots
Inward
rectification
I
V
Outward
rectification
24
The Goldman-Hodgkin-Katz Current
Equation
Don’t
memorize this
equation!
z 2 F 2Vm Px  [ X ]i  [ X ]o e(  zFVm / RT ) 


Ix 
(  zFVm / RT )
RT
1 e


• Predicts current for a single ion
• Incorporates diffusion, movement of an ion in an electric field,
and the current-voltage relationship.
• Set Ix = 0, equation reduces to the Nerst Equation and provides
the reversal potential: Vr
– When Vm is more positive than Vr, outward current
– When Vm is more negative than Vr, inward current
• However, this does not explain the curvature of the I-V plot
25
The Goldman-Hodgkin-Katz
Voltage Equation
Don’t
memorize this
equation!
•
•
•
•
Vrev
RT  PK [ K  ]i  PNa [ Na  ]i  PCl [Cl  ]o 


ln 



F  PK [ K ]o  PNa [ Na ]o  PCl [Cl ]i 
Itotal = IK + INa + ICl
Combine with GHK Current Equation
– Set total current to zero
– Solve for Vrev
Valid only when net current is zero
This is the key to understanding curved I-V
plots
– Vrev depends on individual ion
concentrations and how permeant each
ion is (a weighted value)
– Ion permeability changes dramatically
with changes in Vm so the effect of each
ion current on the cell changes, too
A channel that is "inwardlyrectifying" is one that passes
current (positive charge) more
easily in the inward direction (into
the cell). It is thought that this
current may play an important role
in regulating neuronal activity, by
helping to establish the resting
membrane potential of the cell.
26
Membrane Potential, Ion Gradients
and Permeabilities
• Consider the two major ions that contribute
current in muscle: K+ and Na+
• Simplify the GHK Voltage equation
– Divide numerator and denominator by PK
– Define PNa/PK as “α”
Vrev
 [ K  ]o   [ Na  ]o 

 (61.5 mV ) x log 10  

 [ K ]i   [ Na ]i 
27
Permeability and Ion Currents
• K+ currents are outward
rectifying (i.e., large
outward I when Vm is more
positive than Vr)
• Na+ currents are inward
rectifying (i.e., large inward
I when Vm is more negative
than Vr)
• PNa and PK change with Vm
Vrev
 [ K  ]o   [ Na  ]o 

 (61.5 mV ) x log 10  

 [ K ]i   [ Na ]i 
28
Ion Currents: Conceptual
Conceptual Framework:
[K+] is higher inside cell than outside, so it is difficult to have K+ current sending more K+
ions into the cell.
Likewise, [Na+] is higher outside cell than inside, so it is difficult to have Na+ current
sending more Na+ ions out of the cell.
29
Electrical Model
of a Cell Membrane
• Membranes are like capacitors: able
keep charges separated = stored
energy
• Membrane potential is like a battery:
able to drive a current if a pathway is
present.
• Ion channels are like resistors: ions
can flow through them but not
freely. Usually described by their
conductance (Gx) since in series.
Vm 
G
G
G
GK
EK  Na E Na  Ca ECa  Cl ECl ...
Gm
Gm
Gm
Gm
30
Membrane Capacitance
• Ions possess charge (q, units =
coulombs)
• Separation of charge creates
voltage: more charge separation
= greater voltage difference
• Ability to separate charge
depends on capacitance (Cm,
units = farads)
• Ions can’t pass bilayer freely, so
it has good capacitance
Vm = (1/Cm) x q
V
Slope = 1/C
q
31
Total Membrane Current
• Ionic Current: current from individual ions
– Directly proportional to electrochemical driving
force
• Capacitive Current: current from stored
charge across membrane
– Proportional to the rate of voltage change
32
Capacitive Current
• Charge separation across
membrane sets up a
voltage: Membrane is a
capacitor
• Current can’t flow across
membrane itself (the
capacitor, Cm) and there
are no channels open
(like an open switch)
33
Capacitive Current
• Close switch (i.e., open a
channel), current will flow.
• Resistor (channel) constricts
the flow of charge
• induces exponential decay:
V = Voe (-t / RC)
• Because current = V / R, current is maximal when the voltage is
maximal, but decays as the voltage decays.
34
Membrane
Capacitance, Voltage
• Apply fixed (clamped) current
to membrane.
• Flow of ions will charge Cm,
increasing Vm with RC time
constant to a maximum.
• Turn off current, voltage decays
with RC time constant as
current flows.
35
Membrane
Capacitance, Current
• Apply fixed (clamped) voltage across
membrane
• Voltage change across Cm results in current
flow
• Current is maximal initially but decays with
RC time constant.
• Turn off voltage clamp, Cm will discharge
due to opposite current flow process.
36
Capacitive Currents vs. Ion Currents
• Hyperpolarization does not cause ion currents, just
capacitive current (ion channels do not open)
• Depolarization causes both capacitive and ion currents (Na
channels open allowing Na+ to flow)
• Subtract Ic from It to get INa
37
Capacitor Currents vs. Ion Currents
• Why a negative peak followed by a positive peak for
hyperpolarization? Positive ions flow in to compensate.
• Why a positive spike followed by a negative spike for
depolarization? Positive ions flow out to compensate.
38
Ion Gradients, Channels and
Transporters in a Typical Cell
39
Ion Gradients, Channels and
Transporters in a Typical Cell
40
Learning Objectives
•
•
•
•
•
•
•
•
•
•
Explain in energetic terms why ion channels are required for ions to pass through membranes.
List and describe the basic structural components and properties of ion channels.
Describe the process of ion channel opening and closing, including the rates for opening and closing
in terms of probabilities, and how this is affected by membrane stimuli. No calculations are required.
A conceptual understanding is sufficient.
Explain the concept of the open or closed dwell time and tell how the average dwell time is obtained
for a channel. How can membrane stimuli affect these dwell times?
Define and explain ion channel gating and selectivity. Describe the effect of voltage- or ligandgating on channel opening or closing.
Explain the saturation behavior of ion channels. Draw a graph of the relationship between channel
conductance (g) and the ion concentration. Label gmax and Km.
Define membrane potential and explain why most cells have a negative potential.
Explain the electric field across a membrane and the direction positive and negative ions move due to
this force.
Explain the electrochemical potential of ions in terms of diffusion and electrical potentials.
Describe the Nernst Equation and how it is used to calculate the resting potential for an ion. Know
the approximate resting potentials for Na+, K+, Ca2+ and Cl- in muscle and other cells (slide 20). That
is, Na+ has a positive resting potential, and Ca2+ has a very highly positive resting potential, and Clhas a negative potential, and K+ a much more negative potential. Calculations are not required
41
Learning Objectives
•
•
•
•
•
•
•
•
•
•
•
Describe an ion current and know the units.
Define a positive or outward cell current and a negative or inward cell current for positive and negative ions.
Define which of these currents are depolarizing and which are hyperpolarizing.
Describe the electrochemical driving force, and explain the factors that determine its magnitude and
direction.
Construct a linear current-voltage (I-V) plot. Define the slope of the plot, the reversal potential and the
direction of current.
Define the term rectification and explain inward versus outward rectified currents
Describe (in qualitative terms) what the Goldman-Hodgkin-Katz Current Equation predicts.
Describe (in qualitative terms) what the Goldman-Hodgkin-Katz Voltage Equation predicts.
Explain (in qualitative terms) how ion permeability changes affect the reversal potential according to the
Goldman-Hodgkin-Katz (GHK) Voltage equation. Use the outward rectification for K+ current as an
example.
Explain modeling a membrane in terms of capacitors, resistors and batteries. Explain why each component
of the membrane matches its electrical component. Tell why conductance is the best model for channels in
the membrane.
Explain the relationship between membrane capacitance and membrane voltage and current. To do this,
describe the time course of membrane current change following a change in Vm and the time course of Vm
change following a change in membrane current.
Explain how one distinguishes membrane capacitive current from membrane ion currents using oocyte Na+
channels as an example