hb05 modelling human nerve excitability

Axonal Excitability Workshop Antalya, December 2012

Modelling human nerve excitability and the

TROND protocolThe MEMFIT program

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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

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EHEKs ELkEKf

GKf

GBB CM

Outside

Inside

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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.

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GH

GLk

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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(%)

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GHGLk

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GLkGKfNCAXCMyGKsIGKsIGBB

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GLkNGKfI

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KOPNap(%)

PNaNCAX

CNCMyGKsI

PNaNPNap(%)

GKfNGKsN

GKfIIPumpNI

KOCAXGBB

GLkNCMy

CNGKsIGLkGH

IPumpNIGBBGKsI

KOGLkGH

GLkNGKfICAX

GKfNGKsI

PNap(%)PNaNCMy

CN

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IPumpNIGKsIGBB

KOGLkN

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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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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

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-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

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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

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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

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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

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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

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Mem

bran

e po

tent

ial

(mV

)

-1 0 1msec

0

1

Stim

ulus

cha

rge

100 101

0.1.2

Cur

rent

(nA

)

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Mem

bran

e po

tent

ial

(mV

)

0 100 200msec

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0

100

Thre

shol

d re

duct

ion

(%)

0 100 200msec

-.20.2

Cur

rent

(nA

)

-150

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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