Membrane Channels
The Cell Membrane is Selective
• Criteria for passage through the phospholipid
bilayer:
1. Hydrophobic
2. Net zero charge
3. Nonpolar
4. Size is also a consideration
• Chemicals that will NOT pass through the
phospholipid bilayer:
1. Hydrophillic
2. Charged, ionic
3. Polar
4. Size is also a consideration
• But, using the preceding criteria, many
substances vital to cellular function (e.g., ions)
and survival (e.g., glucose) will not gain entry
into the cell!
• So, nature has come up with channels, which
selectively allow certain substances to gain
entry into the cell, even though they do not
meet the criteria on the preceding slide.
The Many Functions of Membrane Proteins
Outside
Plasma
Membrane
Inside
Transported
Cell Surface
Identity Marker
Enzyme Activity
Cell Adhesion
Cell Surface Receptor
Attachment to
the Cytoskleton
Channels are Vital
Without channels it is energetically unfavorable to
move ions across a membrane –
1. the phospholipid bilayer is ~6-8 nm thick.
2. the hydrophilic head of the phospholipid
molecule projects toward the cytoplasm or the
extracellular fluid.
3. the hydrophobic tails of the phospholipid
molecules project toward each other.
Transmembrane Transport
•
•
•
a) communication among neurons
neural systems:
* action potential
* synaptic signaling
b) receptor – brain communication
heart muscle
signaling and regulatory processes
Channel malfunction
Cystic fibrosis
Epilepsy
Diabetes
Migraines
Neurotoxins
For the Cation to Move Through the
Phospholipid Bilayer…,
1) It must lose its waters of hydration so that it is not so huge
and charged; requires energy to break attractive forces
between the ion and the waters.
2) Energy is also required to move a charged highly
hydrophilic particle into the highly hydrophobic area of
the lipid bilayer that contains the “tails” of the
phospholipid molecules.
3) Based on thermodynamic calculations, so much energy
would be required for this process that it would never
occur.
Channels are thermodynamically similar to Enzymes in that the
former lower the Activation Energy required to move ions across
the Membrane
Transition State
The rate of
the reaction
is determined
by the energy
of activation,
the energy
input
required to
produce the
transition
state.
The uncatalyzed
reaction requires a higher
activation energy than the
catalyzed one does. So, the
latter runs more quickly.
A+B
Reactants
(substrates)
AB
transition
state
C+D
products
There is no difference in free
energy (ΔG) between
uncatalyzed and catalyzed
reactions. The ΔG is the
thermodynamic driving force
for the reaction and determines
the direction of the reaction.
Ion Flow Across the Membrane
• A Chemical can move across the membrane
through one of two ways:
1. Movement through the phospholipid bilayer.
2. Movement through a H2O-filled protein
channel.
Channels are thermodynamically similar to Enzymes in that the
former lower the Activation Energy required to move ions across
the Membrane
The rate of
diffusion is
determined
by the
“energy of
activation”,
the energy
input
required to
produce the
“transition
state”.
(Remove
H2Os of
hydration
and/or move
into hydrophobic
environment.)
Movement through a channel
only requires shedding of
waters of hydration (energy
input would be infinite to
move through the bilayer).
So. Diffusion occurs more
quickly.
ΔG determines this!!
Transition State
Change in free energy is
the thermodynamic
driving force for diffusion
and determines the
direction of ion movement
A+B
Reactants
(substrates)
AB
transition
state
C+D
products
What do we know about the structure of
gated ion channels?
A. Biochemical Information –
1.
2.
3.
4.
MWs range from 25-250 kDal.
They are integral membrane glycoproteins.
They usually consist of 2 or more subunits.
The genes that code for the proteins have been isolated,
cloned and sequenced. These sequences have been
grouped into 6-7 protein families.
5. The primary (amino acid) sequences of these channels
is known.
Use of the Hydrophobicity Plots
1) Propose 3-D structures of the channels
2) Propose functions for specific regions of the
channel proteins
Amino Acid Sequence Enables Ion Channel
Structure Determination
Many Techniques Can be Used to Test
the Proposed Functions of Portions of
the Channel Proteins
1) Sequence Homologies – used to determine which
portions of primary sequences of ion channels are
the same/very similar
a) Same channel from several different species – what is
conserved must be critical to channel function
e.g., Ach-gated channel – Ach receptor portion of the
channel is highly conserved
Many Techniques Can be Used to Test
the Proposed Functions of Portions of
the Channel Proteins
1) Sequence Homologies – used to determine which
portions of primary sequences of ion channels are the
same/very similar (continued)
b) Different channels with the same basic function from many tissues
in one species – what is conserved must be critical to channel
function
e.g., Voltage gated channels (K+, Na+, Ca2+) – all have a presumed
membrane-spanning region with charged AAs at each third
position (voltage sensor?), while ligand-gated channels lack this
structure
Many Techniques Can be Used to Test the
Proposed Functions of Portions of the Channel
Proteins
2) Immunocytochemistry –
a) raise antibodies to a portion of the molecule thought to be
on the intracellular or extracellular surface of the membrane
b) Incubate neurons with the labeled antibodies
c) Do antibodies bind to intact neurons? (Note: antibodies are
too large to fit into a channel)
Yes – sequence is on extracellular surface
No – sequence may be in pore or on intracellular surface
d) Next step: lyse cells and repeat exp. to see if there is
binding, i.e. is it an intracellular sequence?
Many Techniques Can be Used to Test the
Proposed Functions of Portions of the Channel
Proteins
3) Site-directed mutagenesis – use molecular biology
techniques to modify specific regions of a channel
with a predicted function – does modification alter
channel function in a predicted fashion?
4) Chimaeric Channel Construction – construct a
mutant channel from sequences from 2 or more
channel genes – which “parent” channel does the
mutant resemble?
•Most channels have
this basic structure:
multimeric
(quarternary
structure), membranespanning, and, by
definition, have a pore
running longitudinally
through the structure.
•Vary in the number of
subunits and
complexity.
Remember your amino acids?
• Primary, secondary, and tertiary structures of
proteins.
• In addition, recall that multimeric proteins are
formed from the attraction of individual
subunits, forming the quarternary structure.
• Recall the structure and ionization of the each
of the amino acid side-chains (R).
-It wouldn’t hurt if you reviewed what a pI is.
The amino acid
side –chains (R)
•The primary amino
acid sequence and
higher –order
structures determine
the channel topology.
Interior of the channel
will be lined with
hydrophilic amino
acids.
Exterior of the channel
will be lined with
hydrophobic amino
acids.
Selectivity Filter
• Many channels are selective for only 1 or 2
different chemicals (ions, sugars, etc.).
• The K+ channel has such a filter, which is a
narrow region towards the extracellular surface
of the membrane.
• Two K+ ions can occupy the selectivity filter
simultaneously, with a third in a H2O-filled
cavity deeper in the pore.
Proposed Mechanisms for Channel Ion
Selectivity
Non-specific cation channel, i.e.
little selectivity other than for
cations
Ach receptor
channel - 6.5 A in
diameter
10-20 X more
Na+ than K+
100 X more K+
than Na+
Voltagegated Na+
channel 4 A in
diameter
Voltagegated K+
channel –
3.3 A in
diameter
Proposed Mechanisms for Channel Ion
Selectivity by Channels: Ionic size
Non-specific cation channel, i.e.
little selectivity other than for
cations
Ach receptor
channel - 6.5
A in diameter
If ionic size explains
channel selectivity, why
is the K+ channel so
selective for K+ since
Na+ is smaller?
10-20 X more
Na+ than K+
Voltagegated Na+
channel - 4 A
in diameter
Nonhydrated K+
ion = 2.7 A
in diameter
100 X more K+
than Na+
Voltage-gated
K+ channel –
3.3 A in
diameter
Nonhydrated
Na+ ion =
1.9 A in
diameter
Proposed Mechanisms for Ion Selectivity by
Channels: Ionic size
Non-specific cation channel, i.e.
little selectivity other than for
cations
Ach receptor
channel - 6.5
A in diameter
Modified Model =
perhaps channels select
based on hydrated ionic
radius?
10-20 X more
Na+ than K+
Voltagegated Na+
channel - 4 A
in diameter
100 X more K+
than Na+
Voltage-gated
K+ channel –
3.3 A in
diameter
Hydrated
Na+ ion =
3.3-4 A in
diameter
Hydrated K+
ion = 3.3 A
in diameter
(K+ is larger, has a lower charge
density and so attracts fewer waters
of hydration.)
Proposed Mechanisms for Ion Selectivity by
Channels: Ionic size
The modified model explains K+ channel
selectivity, i.e. the hydrated K+ just fits into the
channel and the hydrated Na+ is too big to fit.
However, how do we explain the +/- sodium
channel selectivity?
A selectivity filter exists inside the channel
Proposed Mechanisms for Ion Selectivity by
Channels: Ionic size
Sodium recognition site =
selectivity filter
Na+
Na+
How might it work? Similar to
enzymes, but much faster?
Evidence for a Selectivity Filter
If channels are simple resistors, than movement
through an open channel should be a function
of the concentration gradient for the ion across
the membrane
Rate of ion movement = a x [ion]I/[ion]o
(current flow = diffusion)
Linear relationship
with slope = a
Evidence for a Selectivity Filter
Observed data for
Na+ channel
Unitary current
(pa) = recordings
from single
channels
Expected data
External [Na+] mM
Evidence for a Selectivity Filter
Data for voltage-gated Na+ channel do not fit the model
of a channel as a simple resistor in the membrane.
Instead, the current flow through the Na+ channel
plateaus or “saturates” at high [Na+]. This relationship
looks like what happens to an enzyme at high
[substrate]. Perhaps some channels select ions
based on the same biochemical mechanisms used
by enzymes to select their substrates?
In the end, the final determinations of channel gating
mechanisms and ion selectivities will come from Xray crystallography of the purified channels.
Crystal Structure of the K+ Channel
from above and from the side
The K+ channel is structure such that a very narrow
tube through the inverted cone shape allows for only
50 H2O molecules and only 2 K+ in succession.
Because they strongly repel each other, when one enters,
one will be forced out.
Methods for Studying Ion Channels - 1
Biochemistry
– agonist, antagonist or drug binding
– isolation and purification
– reconstitution
Molecular biology
– sequencing, cloning, mutagenesis
Structural biology
– microscopy, crystallography, NMR, ...
Methods for Studying Ion Channels - 2
Electrophysiology
– tissue slice
– extracellular recording
– intracellular recording
– whole-cell recording
– single channel recording
Biochemistry
– radioactive ion flux
Voltage clamp
Current clamp
Concentration jump
Cloning via Protein Purification
Electric eel
Pure Na
channel
proteins
Protein
Purification
Na channel proteins
Microsequence
Oligonucleotide probe with
sequence corresponding
to aa sequence
Design
probe
Hybridize to cDNA
library containing
Na channel cDNA
sss
sss
sss
Synthesize cDNA
library containing
Na channel cDNA (s)
sssss
sssss
ssssss
Amino acid sequence of small
region of Na channel protein
Isolate and sequence
Na channel cDNA
Deduce protein
sequence
Isolate mRNAs including
one encoding Na channel
AA sequence
of entire Na
channel protein
• Positional cloning – Shaker flies
Normal
Shaker
• Cloning by sequence homology
- Use the same strategy as that used in
preceding slide, except that the sequence on
which the cloning is based comes not from the
purified protein, but rather from the alreadyisolated cDNA.
Positional Cloning Enabled Determination of the
Shaker K Channel
Heterologous Expression Systems
Typical Ion Channels with Known Structure:
K+ channel (KCSA)
Acetylcholine receptor M2
transmembrane segment
Types of ion channels:




Simple pores (GA, GAP junctions)
Substrate gated channels (Nicotinic receptor)
Voltage-gated channels (K-channels)
Pumps (ATP-synthase, K+,Na+-ATPase)
•
Ion Channels
•
•
•
ion channels in the PM of neurons and muscles contributes
to their excitability
when open - ions move down their concentration gradients
channels possess gates to open and close them
two types: gated and non-gated
1. Leakage (non-gated) or Resting channels: are always open, contribute to the resting potential
-nerve cells have more K+ than Na+ leakage channels
-as a result, membrane permeability to K+ is higher
-K+ leaks out of cell - inside becomes more negative
-K+ is then pumped back in
2. Gated channels: open and close in response to a stimulus
A. voltage-gated: open in response to change in voltage - participate in the AP
B. ligand-gated: open & close in response to particular chemical stimuli (hormone,
neurotransmitter, ion)
C. mechanically-gated: open with mechanical stimulation
Types of Biochemical Mechanisms that
Open and Close Channels (Cont’d)
• Nt or hormone binding to receptor causes a 2nd
messenger to activate a protein kinase that
phosphorylates a channel and thus opens it.
• Changes in membrane potential.
• Membrane deformation (e.g., mechanical
pressure).
• Selectivity by charge (i.e., positively lined
pore allows anions through; negatively lined
pore allows cations through).
Na+ Channels have
Gates
At rest, one is closed (the
activation gate) and the
other is open (the
inactivation gate).
Suprathreshold
depolarization affects both
of them.
The resting potential, recall, is generated mainly by
open “resting”, non-gated K+ channels
-the number of K+ channels
dramatically outnumbers that
of Na+
-however, there are a few Na
leak channels along the axonal
membrane
AXON
ECF
Channel Gating Mechanisms
AChR: Proposed gating mechanism
(Unwin, 1995)
Closed
Open
Channel Families
•
•
•
•
•
•
Voltage-gated
Extracellular ligand-gated
Intracellular ligand-gated
Inward rectifier
Intercellular
Other
Voltage-gated
• sodium: I, II, III, µ1, H1, PN3
• potassium: KA, Kv (1-5), Kv(r), Kv(s),KSR, BKCa, IKCa, SKCa,
KM, KACh
• calcium: L, N, P, Q, T
• chloride: ClC-0 - ClC-8
Extracellular ligand-gated
• nicotinic ACh (muscle): 2 (embryonic), 2
(adult)
• nicotinic ACh (neuronal): (2-10), (2-4)
• glutamate: NMDA, kainate, AMPA
• P2X (ATP)
• 5-HT3
• GABAA: (1-6), (1-4),  (1-4), , , (1-3)
• Glycine
Intracellular ligand-gated
• leukotriene C4-gated
Ca2+
• ryanodine receptor
Ca2+
• IP3-gated Ca2+
• IP4-gated Ca2+
• Ca2+-gated K+
• Ca2+-gated nonselective cation
Ca2+-gated Cl–
cAMP cation
cGMP cation
cAMP chloride
ATP Cl–
volume-regulated Cl–
arachidonic acidactivated K+
• Na+-gated K+
•
•
•
•
•
•
•
Inward rectifier
• Kir
–
–
–
–
–
–
–
1.1-1.3
2.1-2.4
3.1-3.5
4.1-4.2
5.1
6.1-6.2
7.1
Intercellular
• Gap junction channels
–
–
–
–
–
–
–
–
Cx26
Cx32
Cx37
Cx40
Cx43
Cx45
Cx50
Cx56
Other
•
•
•
•
•
Mechanosensitive
Mitochondrial
Nuclear
Aquaporins
Vesicular (synaptophysin)
G-protein linked receptors coupled to
ion channels
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Acetylcholine (muscarinic)
Adenosine & adenine nucleotides
Adrenaline & noradrenaline
Angiotensin
Bombesin
Bradykinin
Calcitonin
Cannabinoid
Chemokine
Cholecystokinin & gastrin
Dopamine
Endothelin
Galinin
GABA (GABAB)
Glutamate (quisqualate)
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Histamine
5-Hydroxytryptamine (1,2)
Leukotriene
Melatonin
Neuropeptide Y
Neurotensin
Odorant peptides
Opioid peptides
Platelet-activating factor
Prostanoid
Protease-activated
Tachykinins
Taste receptors
VIP
Vasopressin and oxytocin
Structure of the AChR at 4.6Å
Miyazawa et al, (1999)
(left figure was modified)
Outside Cell
Na+
Ca2+
Cl-
K+
Inside Cell
Schematic model of AChR ligand
binding site


NH2
S
-S-

-
Y
W
ACh or
ant agonist
C
C
based on Arias, 1997
NH2
Y
W
T
D
Y
E
.
-S-S
-
empty site in ACh binding protein
Brejc, 2001
filled site in ACh binding protein
Brejc, 2001
K Channel Structure at 3Å Resolution
Doyle et al, 1998
Patch Clamp Recording Technique
A
B
C
D
E
el ect r ode
channel
cel l
cel l- at t ached pat ch
whol e- cel l
out si de- out pat ch
Sizing Up Ion Channels
Gating and Permeation
What are the Biochemical Changes that Lead to
Channel Gating (Opening or Closing)?
Gating involves some type of conformational
change in the protein, but other than that there
are few definitive answers to the question.
However, there are several general proposed
models for gating.
Types of Biochemical Mechanisms that
Open and Close Channels
• Conformational change occurs in a discrete
area of the channel, leading to it opening.
• The entire channel changes conformation (e.g.,
electrical synapses).
• Ball-and-chain – type mechanism.
• Nt or hormone binding causes the channel to
open.
What are the Biochemical Changes that Lead to
Channel Gating (Opening or Closing)?
A. A conformation change occurs in a discrete portion of the
channel Most popular model, but
currently no evidence for
it!
closed
opened
What are the Biochemical Changes that Lead to
Channel Gating (Opening or Closing)?
B. Global change occurs in the channel Evidence that electrical
synapses = gap junctions
function in this manner
closed
opened
What are the Biochemical Changes that Lead to
Channel Gating (Opening or Closing)?
C. A blocking portion of the channel changes position Evidence that voltagegated channels function in
this manner
closed
opened
What Types of Stimuli Can Lead to Gating?
A. Binding of Chemicals = Ligand-gated or
Chemically-gated Channels
1) Extracellular surface – neurotransmitter or hormone
binding causes opening of an ion channel
Neurotransmitter or hormone
Binds to
Opened
channel
receptor
protein
What Types of Stimuli Can Lead to Gating?
A. Binding of Chemicals = Ligand-gated or
Chemically-gated Channels (continued)
2) Intracellular surface – a second messenger is activated
by neurotransmitter or hormone binding to a receptor
Neurotransmitter or hormone
Binds to
1) Binds directly to a
channel and
opens/closes it
receptor
protein
2nd
messenger
2) Activates a protein
kinase that
phosphorylates the
channel and
opens/closes it
What Types of Stimuli Can Lead to Gating?
B. Change in Membrane Potential = Voltage-gated
channels
C. Membrane Deformation = Mechanically-gated
channels (ex. Sensory system where membrane
stretch or pressure on the membrane is
transmitted to the channel via the cytoskeleton?)
Pressure applied
What are the Proposed Mechanisms for Ion
Selectivity by Channels?
A. Channels can select by charge ClAnion selective
channel lined with
positively charged
AAs
+
+
+
+
+
+
ClK+
Cation selective
channel lined with
negatively
charged AAs
-
-
-
-
-
-
K+
What are the Proposed Mechanisms for Ion
Selectivity by Channels?
B. Channels can select based on ionic size –
Experimental approach =
1) sequence data were used to propose 3-D
structures of the channels and to estimate the pore
diameters
2) ionic selectivities were determined using
electrophysiological techniques
A Closer Look at Gating:
Kinetics of Gating
Channel Gating: Two State Model
Closed
k
o



k
c
dClosed
 k o  Closedk c  Open
dt
Open
dOpen
 k o  Closedk c  Open
dt
Channel Gating:
2 State Simulations
Slow kinetics: ko=0.5/ms kc=0.5/ms
0
1
2
Time (ms)
Fast kinetics: ko=5/ms kc=5/ms
3
4
0
0
1
2
Time (ms)
1
2
Time (ms)
Superposition
Open Prob
1.0
0.8
0.6
0.4
0.2
0.0
3
4
3
4
Gating Exercise
Closed
average closed t ime  1
ko
k
o



k
c
Open
st eady st at e p
average open t ime  1
kc
open
onset t ime 

k
o
ko kc
1
ko  kc
Predictions
example
1
ko (1/ms)
0.5
kc (1/ms)
0.5
2
5.0
5.0
3
5.0
0.5
4
0.5
5.0
average
closed time
(ms)
2.0
average
open time
(ms)
2.0
steadystate
p open
0.5
onset
time (ms)
1.0
Channel Gating:
More 2 State Simulations
High popen: ko=5/ms kc=0.5/ms
0
1
2
Time (ms)
3
4
Low popen: ko=0.5/ms kc=5/ms
0
1
2
Time (ms)
Superposition
Open Prob
1.0
0.8
0.6
0.4
0.2
0.0
0
1
2
Time (ms)
3
4
3
4
Channel Gating:
3 State Model
More realistic model
V-gated Na channels
open channel blockers
Closed
k
o



k
c
Open
k
+i




k
-i
Inactive
dClosed
 k o  Closed k c  Open
dt
dOpen
 k o  Closed k c  Open k  Open k  Inactive
+i
-i
dt
dInactive


dt
k
+i
 Open k  Inactive
-i
Channel Gating:
3 State Simulation
k
k
Closed
o





k
c
Open
+i




ko = 0.1/ms kc =0.5/ms
k+i = 1/ms k-i = 5/ms
Inactive
k
-i
Open
Closed
0
10
20
30
time (ms)
40
50
Burst
Current
Open
Inactive
Closed
"Supervision"
4
6
8
10
time (ms)
12
14
Channel Gating:
3 State Superposition
1.0
Popen
Open Prob
0.8
0.6
0.4
0.2
0.0
0
10
20
30
time (ms)
ko = 0.5/ms kc =0.005/ms
k+i = 0.25/ms k-i = 0.025/ms
k+i = 0/ms
k-i = 0/ms
40
50
Channel Gating Mechanisms (1)
The “Ball and Chain” model of channel inactivation gating
At depolarized potentials,
the ball is more stable at the blocking conformation.
Channel Gating Mechanisms (2)
AChR: Open (white) & Closed (blue) conformations
(Unwin, 1995)
Channel Gating Mechanisms (3)
AChR: Proposed gating mechanism
(Unwin, 1995)
Channel Permeation - Nernst
Consider a cell containing a high concentration of KCl
External [KCl] is low
Consider the cell membrane to be permeable to K+ only.
K
KK+++
K
KK+++
++
K
K
-- -
Cl
Cl
Cl
--
Cl
Cl
initial condition
––
-- -
Cl
Cl
Cl
––
++
K
K
––
-Cl
–– Cl
––
after some diffusion
Vr is known as the:
Nernst potential
reversal potential
zero current potential
equilibrium potential
–– –– ––
++ ––
––
K ––
–– K
––
–– Cl
Cl
Cl
Cl-- - –– Cl
––
–– ––
K
KK+++
equilibrium
c 
c 
Vr = RT ln co   58mV log co 
z
zF  i 
 i 
Channel Permeation: Examples


58 mV  co 
Vr =
log 
 c
z
 i 
58 mV  5 mM 
VK =
log
  86 mV
150 mM 
+1
[K]o =5 mM, [K]i=150 mM
Ion
z
co (mM)
ci (mM)
Vr (mV)
K
+1
5
150
-86
Na
150
15
Cl
120
10
Ca
2
0.0001
Channel Permeation: GHK
Goldman-Hodgkin-Katz Voltage Equation
Cell membrane potential depends on ion
gradients and ionic permeabilities (Pi)
Vm = 58 mV log





PK K o PNaNa o  PClCli 
PK Ki  PNaNa i  PClClo


1. Neuron at rest (ci, co from previous slide)
PK=100, PNa=5, PCl=10  Vm= 63 mV
2. Neuron during an action potential
PK=100, PNa=500, PCl=10  Vm=___
Channel Permeation: Ohm's Law
Current (flow) is equal to voltage (driving force)
times conductance (1/resistance)
I = (V-Vr) G
Current (I) is measured in amps (pA, nA, µA)
Voltage (V) is measured in volts (mV)
Conductance (G) is measured in Siemens (pS, nS)
Channel Permeation: Turnover
How much is a picoamp of current?
1 ion
7 ions/s
1pA 10 12 A 10 12 Coul 
10
s
1.6 10 19 Coul
Ion channels are enzymes that catalyze the
flow of ions across cell membranes. The
catalytic rate is on the order of 107 per
second.
Channel Permeation: IV Curves
a) V-independent conductance:
I = (V-Vr) G, G = N popen
1000
1.0
500
Current (pA)
Open Probability
0.8
0.6
0.4
0.2
0.0
-100
-50
0
50
100
0
-500
-1000
-100
-50
Voltage (mV)
0
Voltage (mV)
N=200,
 = 50 pS, V =0
r
50
100
Channel Permeation: IV Curves
b) V-dependent conductance
I = (V-Vr) G(V)
G = N popen(V)
1000
1.0
500
Current (pA)
Open Probability
0.8
0.6
0.4
0.2
0.0
-100
-50
0
50
100
0
-500
-1000
-100
-50
Voltage (mV)
0
Voltage (mV)
N=200,
 = 50 pS, V =+50 mV
r
50
100