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Axonal Excitability Workshop Antalya, December 2012
Modelling human nerve excitability and the
TROND protocolThe MEMFIT program
0
5
Thre
shol
d ch
arge
(mA
.ms)
-1 0 1Stimulus width (ms)
A
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d re
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0 100 200Delay (ms)
B
-500 0Threshold reduction (%)
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old)
C
0
100
Thre
shol
d ch
ange
(%)
10 100Interstimulus interval (ms)
D
Charge-duration relationship
Threshold electrotonus
Current- threshold (I/V) relationship
Recovery cycle
Multiple measures of nerve excitability (TROND protocol)
Plots of multiple excitability data for motor axons of median nerve (wrist-APB) of 30 normal subjects, each recorded in 9-10 minutes (means +/- SD).
Diagram of myelinate axon structure, illustrating the ion channels, pumps and exchangers responsible for determining axonal excitability. Ion channels are shown in yellow, ion exchangers in orange and energy-dependent pumps in green.
Krishnan, Lin, Park & Kiernan 2009
CN
GNap GKs
ENap EKsEKf
GKfGNa
ENa
CI
GKs GH GLk
EHEKs ELkEKf
GKf
GBB CM
Outside
Inside
Node
Internode
Myelin
IpumpIpump
Electrical model of node and internode with addition of sodium pump currents
Equivalent circuit of node and internode used to model
electrical excitability properties of human axons.
Modelling the membrane potential changes during excitability testing.
Threshold electrotonus
Current- threshold (I/V) relationship
Recovery cycle
Charge-duration relationship
Threshold electrotonus
Current- threshold (I/V) relationship
Recovery cycle
Charge-duration relationship
Circles = mean normal control data. Lines = standard model.
Modelling the membrane potential changes during excitability testing.
Strength-duration
time constant
Threshold electrotonus
Current- threshold (I/V) relationship
Recovery cycle
Charge-duration relationship
Threshold electrotonus
Current- threshold (I/V) relationship
Recovery cycle
Charge-duration relationship
Circles = mean normal control data. Lines = standard model.
Modelling the membrane potential changes during excitability testing.
Strength-duration
time constant
Threshold electrotonus
Current- threshold (I/V) relationship
Recovery cycle
Charge-duration relationship
Threshold electrotonus
Current- threshold (I/V) relationship
Recovery cycle
Charge-duration relationship
Circles = mean normal control data. Lines = standard model.
Modelling the membrane potential changes during excitability testing.
Strength-duration
time constant
Threshold electrotonus
Current- threshold (I/V) relationship
Recovery cycle
Charge-duration relationship
Threshold electrotonus
Current- threshold (I/V) relationship
Recovery cycle
Charge-duration relationship
Circles = mean normal control data. Lines = standard model.
Modelling the membrane potential changes during excitability testing.
Strength-duration
time constant
Threshold electrotonus
Current- threshold (I/V) relationship
Recovery cycle
Charge-duration relationship
Threshold electrotonus
Current- threshold (I/V) relationship
Recovery cycle
Charge-duration relationship
Circles = mean normal control data. Lines = standard model.
Modelling the membrane potential changes during excitability testing.
Strength-duration
time constant
This model has over 30 independent membrane parameters. If a parameter is changed, is it possible to determine correctly which one was changed?
‘Discrepancy’ is scored as the weighted sums of squares of differences between the recorded and modelled values. The ‘Optimize fit’ function in MEMFIT finds
parameter values that minimize discrepancy.
0 100Discrepancy reduction (%)
GH
GLk
GKsI
CN
CMy
GLkN
GBB
CAX
KO
IPumpBoth
GKfI
GKsN
GKfN
PNap(%)
PNaN
0 100Discrepancy reduction (%)
CN
CMy
PNaN
PNap(%)
GKsN
GKfN
CAX
GKfI
GLkN
GH
GLk
KO
GKsI
GBB
IPumpNI
0 100Discrepancy reduction (%)
KO
CAX
GKsI
CMy
CN
GLkN
GLk
GH
PNaN
GKfN
GBB
IPumpBoth
GKfI
PNap(%)
GKsN
0 100Discrepancy reduction (%)
CMy
CN
CAX
GH
GKsN
GLk
GLkN
KO
GBB
GKsI
IPumpBoth
GKfI
PNaN
PNap(%)
GKfN
0 100Discrepancy reduction (%)
GKsI
CMy
CN
CAX
PNaN
PNap(%)
KO
GKfN
GKsN
GKfI
GLkN
GH
IPumpNI
GBB
GLk
0 100Discrepancy reduction (%)
IPumpNI
GBB
GH
GKsI
CMy
CAX
GKfN
GLk
PNaN
GKfI
KO
PNap(%)
GLkN
GKsN
CN
EN -82.9 → -80.5
PNaN 4.1 → 2.2 GKsN 41→ 80
GKfN 20→ 60 GLk 1.6 → 8 CN 0.5 → 4
GKsNPNap(%)
GKfIIPumpNI
GBBGKfNPNaN
GHGLk
GLkNCN
CMyGKsICAX
KO
CNGKsNGLkN
PNap(%)KO
GKfIPNaN
GLkGKfNCAXCMyGKsIGKsIGBB
IPumpNI
GLkGBB
IPumpNIGH
GLkNGKfI
GKsNGKfN
KOPNap(%)
PNaNCAX
CNCMyGKsI
PNaNPNap(%)
GKfNGKsN
GKfIIPumpNI
KOCAXGBB
GLkNCMy
CNGKsIGLkGH
IPumpNIGBBGKsI
KOGLkGH
GLkNGKfICAX
GKfNGKsI
PNap(%)PNaNCMy
CN
GKfNPNap(%)
PNaNGKfI
IPumpNIGKsIGBB
KOGLkN
GLkGKsN
GHCAx
CNCMy
Discrepancy reduction (%)Discrepancy reduction (%)Discrepancy reduction (%)
Discrepancy reduction (%)Discrepancy reduction (%)Discrepancy reduction (%)
Provisional conclusions from model testing:If the model were accurate, there would be
enough information in a Trond recording to identify many single parameter changes correctly.
Model fitting might also identify 2 parameter changes correctly.
However, if more than 2 parameters are abnormal it is most unlikely that they could be identified correctly.
BUT: How accurate is the model??
Nerve excitability measured by the TROND protocol is sensitive to:
Membrane potentialPolarizing currents *HyperkalemiaHypokalemiaIschaemia
Ion channel dysfunctionNa channels (Nav1.6) *Kf channels (Kv1.1) *Ih channels (HCN) *Ks channels (Kv7.2 = KCNQ2)*
DemyelinationDegenerationRegeneration
Some simple changes provide a test of the electrical model and the use of MEMFIT to identify membrane changes
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Effects of changing membrane potential by polarizing currents
Data from Kiernan & Bostock (2000)
Red: controls, Green: 1 mA hyperpolarization, Blue: 1 mA depolarization
Fitting standard model to 4 nerves hyperpolarized by 1 mA currentData from Kiernan & Bostock (2000)
Best fit by single parameter change is obtained by addition
of 29 pA hyperpolarizing
current per internode
Fitting standard model to 4 nerves depolarized by 1 mA currentData from Kiernan & Bostock (2000)
Best fit is obtained by addition of 43 pA depolarizing current per internode (but
fanning in caused in other ways is very
similar)
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Fitting standard model to nerves in 4 subjects with DC nerve polarization
Data from Kiernan & Bostock (2000)
Red: controls, Green: 1 mA hyperpolarization, Blue: 1 mA depolarization
Red: standard model, Green: 5.2 mV hyperpolarization, Blue: 4.5 mV depolarization
Nerve excitability measured by the TROND protocol is sensitive to:
Membrane potentialPolarizing currents *HyperkalemiaHypokalemiaIschaemia
Ion channel dysfunctionNa channels (Nav1.6) *Kf channels (Kv1.1) *Ks channels (Kv7.2 = KCNQ2)Ih channels (HCN) *
DemyelinationDegenerationRegeneration
Puffer FishFamily: Tetraodontidae
(Four teeth)
Puffer FishFamily: Tetraodontidae
(Four teeth)
Tetrodotoxin, synthesized by symbiotic bacteria, is 10,000 times more deadly than cyanide!
Early description of puffer fish poisoning in Captain James Cook's journal from his second voyage in 1774.
“…only the liver and roe was dressed which we did but taste. About 3 o’clock in the morning, we were seized with most extraordinary weakness in all our limbs attended with numbness of sensation caused by exposing one’s hand and feet to a fire after having been pinched much by frost. ….nor could I distinguish between light and heavy objects. We each took a vomit. In the morning one of the pigs which had eaten the entrails was found dead.”
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Abnormal nerve excitability in 4 patients with puffer-fish poisoning
Patient data from Kiernan et al. (2005)Control data from Kiernan et al. (2000)
Red: 29 normal controls, Blue: 4 patients
Fitting standard model to nerves in 4 patients with puffer-fish poisoningData from Kiernan et al. (2005)
Best fit is obtained by 48% reduction
in all sodium channel currents
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(%)
-100
0
Cur
rent
(% th
resh
old)
0 100 200msec
-.5
0
Cur
rent
(nA
)
-150
-100
Mem
bran
e po
tent
ial
(mV
)10 100
msec
0
100
Thre
shol
d ch
ange
(%)
0 100 200msec
0
.5
Cur
rent
(nA
)
-90
-80
-70
Mem
bran
e po
tent
ial
(mV
)
-1 0 1msec
0
1
Stim
ulus
cha
rge
100 101
0.1.2
Cur
rent
(nA
)
-80
-60
-40
-20
Mem
bran
e po
tent
ial
(mV
)
0 100 200msec
-100
0
100
Thre
shol
d re
duct
ion
(%)
0 100 200msec
-.20.2
Cur
rent
(nA
)
-150
-100
Mem
bran
e po
tent
ial
(mV
)
-500 0Threshold reduction
(%)
-100
0
Cur
rent
(% th
resh
old)
0 100 200msec
-.5
0
Cur
rent
(nA
)
-150
-100
Mem
bran
e po
tent
ial
(mV
)10 100
msec
0
100
Thre
shol
d ch
ange
(%)
0 100 200msec
0
.5
Cur
rent
(nA
)
-90
-80
-70
Mem
bran
e po
tent
ial
(mV
)
-1 0 1msec
0
1
Stim
ulus
cha
rge
100 101
0.1.2
Cur
rent
(nA
)
-80
-60
-40
-20
Mem
bran
e po
tent
ial
(mV
)
0 100 200msec
-100
0
100
Thre
shol
d re
duct
ion
(%)
0 100 200msec
-.20.2
Cur
rent
(nA
)
-150
-100
Mem
bran
e po
tent
ial
(mV
)
-500 0Threshold reduction
(%)
-100
0
Cur
rent
(% th
resh
old)
0 100 200msec
-.5
0
Cur
rent
(nA
)-150
-100
Mem
bran
e po
tent
ial
(mV
)
10 100msec
0
100
Thre
shol
d ch
ange
(%)
0 100 200msec
0
.5
Cur
rent
(nA
)
-90
-80
-70
Mem
bran
e po
tent
ial
(mV
)
-1 0 1msec
0
1
Stim
ulus
cha
rge
100 101
0.1.2
Cur
rent
(nA
)
-80
-60
-40
-20
Mem
bran
e po
tent
ial
(mV
)
Fitting standard model to nerves in 4 patients with puffer-fish poisoning
Patient data from Kiernan et al. (2005)Control data from Kiernan et al. (2000)
Red: 29 normal controls, Blue: 4 patients
Red: standard model, Blue: PNaN x 0.52
Nerve excitability measured by the TROND protocol is sensitive to:
Membrane potentialPolarizing currents *HyperkalemiaHypokalemiaIschaemia
Ion channel dysfunctionNa channels (Nav1.6) *Kf channels (Kv1.1) *Ih channels (HCN) *Ks channels (Kv7.2 = KCNQ2)
DemyelinationDegenerationRegeneration
Some simple changes provide a test of the electrical model and the use of MEMFIT to identify membrane changes
0
100
Thre
shol
d ch
ange
(%)
10 100Interstimulus interval (ms)
EA1
NC
-100
0
100
Thre
shol
d re
duct
ion
(%)
0 100 200Delay (ms)
-100
0
100Th
resh
old
redu
ctio
n(%
)
0 100 200Delay (ms)
EA1
EA1
TE +/- 40% TE +/- 20%
NC
NC
Brain 2010: 133; 3530-3540
30
40
50
60
70
TEd2
0(pe
ak)
10 20 30 40 50TEd40(Accom)
NC
EA1
0
100
Thre
shol
d ch
ange
(%)
10 100Interstimulus interval (ms)
EA1
NC
-100
0
100
Thre
shol
d re
duct
ion
(%)
0 100 200Delay (ms)
-100
0
100Th
resh
old
redu
ctio
n(%
)
0 100 200Delay (ms)
EA1
EA1
TE +/- 40% TE +/- 20%
NC
NC
NC0
-50
Sup
erex
cita
bilit
y (%
)
0 10 20 30 40Subexcitability (%)
NC
EA1
Fitting standard model to nerves in 3 kindreds with EA1 (Kv1.1 mutations)Data from Tomlinson et al. (2010)
Best fit is obtained by 51.5% reduction
in all fast potassium channel
currents
0 100Discrepancy reduction (%)
GKsI
GH
GLkN
GLk
PNap(%)
IPumpNI
PNaN
GKsRel
GLkRel
GKsN
GKfN
GKfI
GBB
GKfRel
Fitting standard model to nerves in 3 kindreds with EA1 (KCNA1 missense)
Red: 29 normal controls, Blue: 11 recordings from 6 patients
0 100 200msec
-100
0
100
Thre
shol
d re
duct
ion
(%)
0 100 200msec
-.20.2
Cur
rent
(nA
)
-150
-100
Mem
bran
e po
tent
ial
(mV
)
-500 0Threshold reduction
(%)
-100
0
Cur
rent
(% th
resh
old)
0 100 200msec
-.5
0
Cur
rent
(nA
)
-150
-100
Mem
bran
e po
tent
ial
(mV
)10 100
msec
0
100
Thre
shol
d ch
ange
(%)
0 100 200msec
0
.5
Cur
rent
(nA
)
-90
-80
-70
Mem
bran
e po
tent
ial
(mV
)
-1 0 1msec
0
1
Stim
ulus
cha
rge
100 101
0.1.2
Cur
rent
(nA
)
-80
-60
-40
-20
Mem
bran
e po
tent
ial
(mV
)
0 100 200msec
-100
0
100
Thre
shol
d re
duct
ion
(%)
0 100 200msec
-.20.2
Cur
rent
(nA
)
-150
-100
Mem
bran
e po
tent
ial
(mV
)
-500 0Threshold reduction
(%)
-100
0
Cur
rent
(% th
resh
old)
0 100 200msec
-.5
0
Cur
rent
(nA
)
-150
-100
Mem
bran
e po
tent
ial
(mV
)10 100
msec
0
100
Thre
shol
d ch
ange
(%)
0 100 200msec
0
.5
Cur
rent
(nA
)
-90
-80
-70
Mem
bran
e po
tent
ial
(mV
)
-1 0 1msec
0
1
Stim
ulus
cha
rge
100 101
0.1.2
Cur
rent
(nA
)
-80
-60
-40
-20
Mem
bran
e po
tent
ial
(mV
)
Red: standard model, Blue: All GKf x 0.485
0 100 200msec
-100
0
100
Thre
shol
d re
duct
ion
(%)
0 100 200msec
-.20.2
Cur
rent
(nA
)
-150
-100
Mem
bran
e po
tent
ial
(mV
)
-500 0Threshold reduction
(%)
-100
0
Cur
rent
(% th
resh
old)
0 100 200msec
-.5
0
Cur
rent
(nA
)-150
-100
Mem
bran
e po
tent
ial
(mV
)
10 100msec
0
100
Thre
shol
d ch
ange
(%)
0 100 200msec
0
.5
Cur
rent
(nA
)
-90
-80
-70
Mem
bran
e po
tent
ial
(mV
)
-1 0 1msec
0
1
Stim
ulus
cha
rge
100 101
0.1.2
Cur
rent
(nA
)
-80
-60
-40
-20
Mem
bran
e po
tent
ial
(mV
)
Data from Tomlinson et al., 2010
Brain 2012 (in press)
0
100
Thre
shol
d re
duct
ion
(%)
0 100 200Delay (ms)
Nerve excitability measured by the TROND protocol is sensitive to:
Membrane potentialPolarizing currents *HyperkalemiaHypokalemiaIschaemia
Ion channel dysfunctionNa channels (Nav1.6) *Kf channels (Kv1.1) *Ks channels (Kv7.2 = KCNQ2)Ih channels (HCN) *
DemyelinationDegenerationRegeneration
Koltzenburg (Personal communication)
Koltzenburg (Personal communication)
Best fit to 40 mg Org 34167
responses was obtained by 82% reduction in GH (HCN channel conductance)
Koltzenburg (Personal communication)
Koltzenburg (Personal communication)
Koltzenburg (Personal communication)
Conclusions:
MEMFIT is able to correctly identify selective changes in polarizing current and several individual ion channels.
On the other hand, complex changes in excitability involving several membrane parameters are unlikely to be resolved unambiguously.
However, because of the complexity of interactions between the electrical components of myelinated axons, MEMFIT provides a useful aid to interpreting changes in excitability.
Modelling human nerve excitability
and the TROND protocol
