Axonal Excitability Workshop
Antalya, December 2012
Modelling human nerve excitability and the TROND protocol The MEMFIT program
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). Threshold electrotonus
A
(I/V)
C Current (% threshold)
Threshold charge (mA.ms)
B
100 Threshold reduction (%)
5
Current- threshold relationship
0
-100
0
0
Recovery cycle
100 Threshold change (%)
Charge-duration relationship
D
0
-100 -1
0 1 Stimulus width (ms)
0
100 Delay (ms)
200
-500 0 Threshold reduction (%)
10 100 Interstimulus interval (ms)
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
Electrical model of node and internode with addition of sodium pump currents Outside Myelin GBB
CM
Node ENa
ENap
EKf
EKs
EKf
EKs
EH
ELk
CN GNa
GNap
GKf
GKs
CI GKf
Ipump
GKs
GH
GLk
Ipump
Internode Inside
Equivalent circuit of node and internode used to model electrical excitability properties of human axons.
Modelling the membrane potential changes during excitability testing.
Modelling the membrane potential changes during excitability testing.
Threshold Threshold electrotonus electrotonus
Currentthreshold Currentthreshold (I/V) (I/V) relationship relationship
Recovery Recovery cycle cycle
Charge-duration Charge-duration relationship relationship Strengthduration time constant
Circles = mean normal control data. Lines = standard model.
Modelling the membrane potential changes during excitability testing.
Threshold Threshold electrotonus electrotonus
Currentthreshold Currentthreshold (I/V) (I/V) relationship relationship
Recovery Recovery cycle cycle
Charge-duration Charge-duration relationship relationship Strengthduration time constant
Circles = mean normal control data. Lines = standard model.
Modelling the membrane potential changes during excitability testing.
Threshold Threshold electrotonus electrotonus
Currentthreshold Currentthreshold (I/V) (I/V) relationship relationship
Recovery Recovery cycle cycle
Charge-duration Charge-duration relationship relationship Strengthduration time constant
Circles = mean normal control data. Lines = standard model.
Modelling the membrane potential changes during excitability testing.
Threshold Threshold electrotonus electrotonus
Currentthreshold Currentthreshold (I/V) (I/V) relationship relationship
Recovery Recovery cycle cycle
Charge-duration Charge-duration relationship relationship Strengthduration time constant
Circles = mean normal control data. Lines = standard model.
Modelling the membrane potential changes during excitability testing.
Threshold Threshold electrotonus electrotonus
Currentthreshold Currentthreshold (I/V) (I/V) relationship relationship
Recovery Recovery cycle cycle
Charge-duration Charge-duration relationship relationship Strengthduration time constant
Circles = mean normal control data. Lines = standard model.
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.
EN -82.9 → -80.5
IPumpNI IPumpNI
PNaN 4.1 → 2.2
GKsN 41→ 80
PNaN PNaN
GKsN GKsN
GBB GBB
PNap(%) PNap(%)
PNap(%) PNap(%)
GKsI GKsI
GKfN GKfN
GKfI GKfI
KO KO
GKsN GKsN
IPumpBoth IPumpNI
GLk GLk
GKfI GKfI
GBB GBB
GH GH
IPumpBoth IPumpNI
GKfN GKfN
GLkN GLkN
KO KO
PNaN PNaN
GKfI GKfI
CAX CAX
GH GH
CAX CAX
GBB GBB
GLk GLk
GKfN GKfN
GLkN GLkN
GLkN GLkN
GKsN GKsI
CMy CMy
CN CN
PNap(%) PNap(%)
CN CN
CMy CMy
PNaN PNaN
GKsI GKsI
GKsI GKsI
CMy CMy
GLk GLk
CAX CAX
CN CN
GH GH
KO KO
0
100
0
Discrepancyreduction reduction (%) Discrepancy (%)
100
0
Discrepancy reduction (%) (%) Discrepancy reduction
GLk 1.6 → 8
GKfN 20→ 60 GKfN GKfN
CN CN
PNap(%) PNap(%)
GBB GBB
GKsN GKsN
PNaN PNaN
IPumpNI IPumpNI
GLkN GLkN
GKfI GKfI
GH GH
PNap(%) PNap(%)
IPumpBoth IPumpNI
GLkN GLkN
KO KO
GKsI GKsI
GKfI GKfI
GKfI GKfI
GBB GBB
GKsN GKsN
PNaN PNaN
KO KO
GKfN GKfN
GLk GLk
GLkN GLkN
KO KO
GKfN GKfN
GLk GLk
PNap(%) PNap(%)
CAX CAX
GKsN GKsN
PNaN PNaN
CMy CMy
GH GH
CAX CAX
GKsI GKsI
CAX CAx
CN CN
GH GKsI
CN CN
CMy CMy
GBB GBB
CMy CMy
GKsI GKsI
IPumpNI IPumpNI
100 Discrepancyreduction reduction (%) Discrepancy (%)
0
Discrepancy Discrepancy reduction reduction (%)(%)
100
CN 0.5 → 4
GLk GLk
0
Discrepancy (%) Discrepancyreduction reduction (%)
100
0
Discrepancy (%) Discrepancyreduction reduction (%)
100
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 potential Polarizing currents * Hyperkalemia Hypokalemia Ischaemia
Ion channel dysfunction Na channels (Nav1.6) *
Kf channels (Kv1.1) * Ih channels (HCN) * Ks channels (Kv7.2 = KCNQ2)*
Demyelination Degeneration Regeneration Some simple changes provide a test of the electrical model and the use of MEMFIT to identify membrane changes
Curre (nA)
.2 .1 0
0
0 -100
0
100 msec
200
100 msec
200
-500
-.5 0
0 Threshold reduction (%) 100
200
-70 100
-80 0 -90 .5 10
100 msec
0
200
0
-100
0
100
0
100 msec
200
101
-20 1 -40 -60 -80 0 .2 .1 0
-1
200
0
-100 0
100
0 msec 100
msec msec Blue: 1 mA Red: controls, Green: 1 mA hyperpolarization, depolarization 100 1 Current (% threshold)
100
0
Current (nA)
-150 -100
100 msec
Membrane potential (mV) Stimulus charge
-100
200
1
101
Stimulus charge
0 -100
100 msec
Current (nA)
0
Membrane potential Threshold(mV) change (%)
200
Membrane potential (mV) Current (% threshold)
100
0
Threshold reduction (%)
Curre (nA)
Curre (nA)
100 msec
Threshold change (%)
Current (nA)
Membrane potential Threshold reduction (mV) (%)
0
-150 .2 0 -.2
0
-.5 0 Effects of changing membrane potential by polarizing currents
Current (nA)
Curre (nA)
.2 0 -.2
0 -500
0 Threshold reduction (%)
10
100 msec
-1
0 msec
1
Data 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 hyperpolarized by 1 mA current Data 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)
Fitting standard model to 4 nerves depolarized by 1 mA current Data from Kiernan & Bostock (2000)
-.5
.1 0
Cu (
Cu (
Cu (
Cu (
0 -.2
0
Fitting standard model to nerves in 4 subjects with DC nerve polarization 0
200
100 msec
200 Red:
Current (% threshold)
100
0
-100
-500
-.5
0 Threshold reduction (%)
Current (nA)
0
100 msec
200
-70 100
-80 0 -90 .5 10
100 msec
0
0
100
100 msec
200
101
-20 1 -40 -60 -80 0 .2 .1 0
-1
0 msec 100
1
101
1
0
-100 0
100
0 100 200 hyperpolarization, 0 100 Blue: 200 controls, Green: 1 mA 1 mA msec msec depolarization Threshold change (%)
0
100 msec
Membrane potential (mV) Stimulus charge
0 -100
-150 -100
0
Threshold reduction (%)
200
Current (nA)
-100
100 msec
Stimulus charge
-100 0
-150 .2 0 -.2
0
Membrane potential (mV) Current (% threshold)
100
200
Membrane potential Threshold(mV) change (%)
100 msec
Current (nA)
Current (nA)
Membrane potential Threshold reduction (mV) (%)
0
0 -500
0 Threshold reduction (%)
10
100
-1
msec
0 msec
1
Red: standard model, Green: 5.2 mV hyperpolarization, Blue: 4.5 mV depolarization
Data from Kiernan & Bostock (2000)
Nerve excitability measured by the TROND protocol is sensitive to: Membrane potential Polarizing currents * Hyperkalemia Hypokalemia Ischaemia
Ion channel dysfunction Na channels (Nav1.6) *
Kf channels (Kv1.1) * Ks channels (Kv7.2 = KCNQ2) Ih channels (HCN) * Demyelination Degeneration Regeneration
Puffer Fish Family: Tetraodontidae (Four teeth)
Puffer Fish Family: 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.”
.5
Current (nA)
0
.2 .1 0
Abnormal nerve excitability in 4 patients with puffer-fish poisoning -.5 0 200
Current (% threshold)
100
0
0
-100
100 msec
200
0
0
100 msec
200
100
100 msec
200
101
1
0
-100 0
100
Stimulus charge
100 msec
Threshold change (%)
0
Threshold reduction (%)
Current (nA)
Current (nA)
Current (nA)
.2 0 -.2
0 -500
0 Threshold reduction (%)
10
100 msec
-1
0 msec
1
Red: 29 normal controls, Blue: 4 patients
Control data from Kiernan et al. (2000) Patient data from Kiernan et al. (2005)
Best fit is obtained by 48% reduction in all sodium channel currents
Fitting standard model to nerves in 4 patients with puffer-fish poisoning Data from Kiernan et al. (2005)
Current (nA)
.5
.2 .1 0
200
0
0
100 msec
200
100 msec
200
0
-500
-.5
0 Threshold reduction (%)
-80 0
-90 .5 10 0
Current (% threshold)
0
-100
0
100 msec
100 msec
200
-40 -60 -80 0 .2 .1 0
-1
200
0 msec
100
1
101
msec
100
1
0
-100 0
101
1 -20
msec
100
100
100 -70
0 100 200 0 100 Red: 29 normal controls, Blue: 4 patients
Threshold change (%)
0
Current (nA)
-100 -150
200
Membrane potential Stimulus (mV)charge
0 -100
100 msec
Stimulus charge
-100
100 msec
Current (nA)
0
Membrane potential Current(mV) (% threshold)
Threshold reduction Membrane potential (%) (mV)
0 -100
-150 .2 0 -.2
200
Membrane potential Threshold change (%) (mV)
100 msec
100
Current (nA)
Current (nA)
Current (nA)
0
Threshold reduction (%)
0
Fitting standard model to nerves in 4 patients with puffer-fish poisoning -.5 0
Current (nA)
Current (nA)
.2 0 -.2
0 -500
0 Threshold reduction (%)
10
100 msec
-1
0 msec
1
Red: standard model, Blue: PNaN x 0.52 Control data from Kiernan et al. (2000) Patient data from Kiernan et al. (2005)
Nerve excitability measured by the TROND protocol is sensitive to: Membrane potential Polarizing currents * Hyperkalemia Hypokalemia Ischaemia
Ion channel dysfunction Na channels (Nav1.6) *
Kf channels (Kv1.1) * Ih channels (HCN) * Ks channels (Kv7.2 = KCNQ2)
Demyelination Degeneration Regeneration Some simple changes provide a test of the electrical model and the use of MEMFIT to identify membrane changes
TE +/- 40%
100
TE +/- 20%
100
100
NC
-100
NC
0
Threshold change (%)
EA1
0
Threshold reduction (%)
Threshold reduction (%)
EA1
-100
NC 0
EA1 0
100 Delay (ms)
200
0
100 Delay (ms)
200
10 100 Interstimulus interval (ms)
Brain 2010: 133; 3530-3540
TE +/- 40%
100
TE +/- 20%
100
100
NC
-100
NC
0
Threshold change (%)
Threshold reduction (%)
EA1
0
-100
NC 0
EA1 0
100 Delay (ms)
200
0
100 Delay (ms)
200
10 100 Interstimulus interval (ms)
70
Superexcitability (%)
50
NC
40
EA1
-50
EA1
60 TEd20(peak)
Threshold reduction (%)
EA1
NC
NC 30
0 10
20
30 40 TEd40(Accom)
50
0
10
20 30 Subexcitability (%)
40
GKfRel GBB GKfI GKfN GKsN GLkRel
Best fit is obtained by 51.5% reduction in all fast potassium channel currents
GKsRel PNaN IPumpNI PNap(%) GLk GLkN GH GKsI 0
100 Discrepancy reduction (%)
Fitting standard model to nerves in 3 kindreds with EA1 (Kv1.1 mutations) Data from Tomlinson et al. (2010)
0
.5
Current (nA)
Current (nA)
Current (nA)
Current (nA)
.2 0 -.2
.2 .1 0
Fitting standard model with EA1 (KCNA1 missense) -.5 to nerves in 3 kindreds 0 0
0 -100
100 msec
200
100 msec
200 Red: Current (% threshold)
100
0
-100
0
-500
-.5
0 Threshold reduction (%)
100 msec
200
100 -70
-80 0
-90 .5
0
10 msec
msec
0
100 msec
200
101
1 -20
100
-40 -60 -80 0 .2 .1 0
-1
0 msec 100
1
101
msec
100
1
0
-100 0
100
0 100 200 0 100 29 normal controls, Blue: 11 recordings from 6 200 patients Threshold change (%)
0
Current (nA)
-100 -150
0
Threshold reduction (%)
200
Membrane potential (mV)charge Stimulus
-100
100 msec
Current (nA)
Membrane potential Current(mV) (% threshold)
0 -100
-150 .2 0 -.2
0
Current (nA)
Current (nA)
Membrane potential Threshold reduction (mV) (%)
100
200
Stimulus charge
100 msec
Membrane potential (mV) Threshold change (%)
0
0 -500
0 Threshold reduction (%)
10
100 msec
-1
0 msec
1
Red: standard model, Blue: All GKf x 0.485 Data from Tomlinson et al., 2010
Brain 2012 (in press)
Threshold reduction (%)
100
0
0
100 Delay (ms)
200
Nerve excitability measured by the TROND protocol is sensitive to: Membrane potential Polarizing currents * Hyperkalemia Hypokalemia Ischaemia
Ion channel dysfunction Na channels (Nav1.6) *
Kf channels (Kv1.1) * Ks channels (Kv7.2 = KCNQ2) Ih channels (HCN) * Demyelination Degeneration Regeneration
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)
Modelling human nerve excitability and the TROND protocol 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.