Defining a Channelvoltage and ligand gated

leave out pumps ionic accumulation

Classical HH−like Kinetic scheme

ohmic conductance GHK constant field

multiple gates

transition style (α, β) 8( , τ)

fractional openness independent identical subunits

ion selective

voltage sensitiveligand sensitivefunctions tables

−50 0 50 100 150

−20

−10

0

10

i = p * ghk(v, ci, co, z)

v

i

i = g * (v − e)

10 100 1

Ohmic vs Constant Field

−40 −20 0 20 40 600

1

2

3

4

5

A*exp(k/2*(v−d))

A*k*(v−d)/(1 − exp(−k*(v−d)))

2*A/(1 + exp(−k*(v−d)))

1/ms

mV

ExponentialEinsteinBoltzmann

functions.

generally have the form ofVoltage sensitive and rates α β

EE*

0E1

2

e EkT+1

1E−P ~ e kT

=2

2

2

If the energy difference betweenstates is linear with voltage, thenthe steady state is a Boltzmanndistribution.

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Propertiesleak Density MechanismNonSpecific ohmic ion current i_leak (mA/cm2) = g_leak * (v - e_leak)g = gmax Default gmax = 0 (S/cm2) e = 0 (mV)

Select here to construct gates

ChannelBuild[0] managed KSChan[0]

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somapashhleak

SingleCompartment

single compartmentCell BuilderNetWork CellNetWork BuilderLinear CircuitChannel Builder Density

Pointimport KSChan

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Propertiesleak Density MechanismNonSpecific ohmic ion current i_leak (mA/cm2) = g_leak * (v - e_leak)g = gmax Default gmax = 0 (S/cm2) e = 0 (mV)

Select here to construct gates

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Propertiesnahh Density Mechanismna ohmic ion current ina (mA/cm2) = g_nahh * (v - ena)g = gmax * m^3 * h Default gmax = 0 (S/cm2)

m’ = am*(1 - m) - bm*mh’ = ah*(1 - h) - bh*h

ChannelBuild[1] managed KSChan[1]

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Channel NameSelective for Ion...

Ohmic i=g*(v-e)Goldman-Hodgkin-Katz

Default gmax (or pmax) HH sodium channel HH potassium channelClone channel typeCopy gates fromText to stdout

Provide transition aliasesUse fixed step HH rate tables

Gate Constructor

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Propertiesnahh Density Mechanismna ohmic ion current ina = g_nahh * (v - ena)g = gmax * m^3 * h Default gmax = 0 (S/cm2)

m’ = am*(1 - m) - bm*mh’ = ah*(1 - h) - bh*h

ChannelBuild[0] managed KSChan[0]

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Select hh state or ks transition to change propertiesm

h

m^3m’ = am*(1 - m) - bm*m

Power 3Fractional Conductancem fraction 1

Adjust Run

-90 -40 10 600

0.2

0.4

0.6

0.8

1

-90 -40 10 600

0.2

0.4

0.6

0.8

1infmtaum

m <-> m (a, b) (KSTrans[0])Display inf, tau

am = A*x/(1 - exp(-x)) where x = k*(v - d)A 1

k 0.1

d -40

bm = A*exp(k*(v - d)))

ChannelBuildGateGUI[0] for ChannelBuild[0]

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Propertiesnahh Density Mechanismna ohmic ion current ina (mA/cm2) = g_nahh * (v - ena)g = gmax * m^3 * h Default gmax = 0 (S/cm2)

m’ = am*(1 - m) - bm*mh’ = ah*(1 - h) - bh*h

ChannelBuild[0] managed KSChan[0]

Close HideStates Transitions Properties

Select hh state or ks transition to change propertiesm

h

hh’ = ah*(1 - h) - bh*h

Power 1Fractional Conductanceh fraction 1

Adjust Run

-90 -40 10 600

0.2

0.4

0.6

0.8

1

-90 -40 10 600

0.2

0.4

0.6

0.8

1ahbh

h <-> h (a, b) (KSTrans[1])Display inf, tau

ah = A*exp(k*(v - d)))A (/ms) 0.07

k (/mV) -0.05

d (mV) -65

bh = A/(1 + exp(-k*(d - v)))A (/ms) 1

k (/mV) -0.1

d (mV) -35

EquationType

ChannelBuildGateGUI[0] for ChannelBuild[0]

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alpha,betaahbh

a,binf,tauCopy

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Propertiesnahh Density Mechanismna ohmic ion current ina (mA/cm2) = g_nahh * (v - ena)g = gmax * m^3 * h Default gmax = 0 (S/cm2)

m’ = am*(1 - m) - bm*mh’ = ah*(1 - h) - bh*h

ChannelBuild[0] managed KSChan[0]

Close HideStates Transitions Properties

Select hh state or ks transition to change propertiesm

h

hh’ = ah*(1 - h) - bh*h

Power 1Fractional Conductanceh fraction 1

Adjust Run

-90 -40 10 600

0.2

0.4

0.6

0.8

1

-90 -40 10 600

0.2

0.4

0.6

0.8

1ahbh

h <-> h (a, b) (KSTrans[1])Display inf, tau

ah = A*exp(k*(v - d)))A (/ms) 0.07

k (/mV) -0.05

d (mV) -65

bh = A/(1 + exp(-k*(d - v)))A (/ms) 1

k (/mV) -0.1

d (mV) -35

EquationType

ChannelBuildGateGUI[0] for ChannelBuild[0]

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alpha,betaahbh

AA*exp(k*(v - d)))A*x/(1 - exp(-x)) where x = k*(v - d)A/(1 + exp(-k*(d - v)))KSChanTable

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Propertiesnahh Density Mechanismna ohmic ion current ina (mA/cm2) = g_nahh * (v - ena)g = gmax * m^3 * h Default gmax = 0 (S/cm2)

m’ = am*(1 - m) - bm*mh’ = (hinf - h)/htau

ChannelBuild[0] managed KSChan[0]

Close HideStates Transitions Properties

Select hh state or ks transition to change propertiesm

h

hh’ = (hinf - h)/htau

Power 1Fractional Conductanceh fraction 1

Adjust Run

-90 -40 10 600

0.2

0.4

0.6

0.8

1

-90 -40 10 600

0.2

0.4

0.6

0.8

1infhtauh

h <-> h (inf, tau) (KSTrans[1])Display inf, tau

infh = KSChanBGinfK (/ms) 1

vhalf (mV) -20

z 4

gam 0.5

tau0 (ms) 0.1

tauh = KSChanBGtau

EquationType

ChannelBuildGateGUI[0] for ChannelBuild[0]

inf,tauinfhtauh

AA/(1 + exp(-k*(d - v)))KSChanBGinfKSChanTable

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3

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Propertiesleak Density MechanismNonSpecific ohmic ion current i_leak (mA/cm2) = g_leak * (v - e_leak)g = gmax * 0 * 0 * O Default gmax = 0 (S/cm2) e = 0 (mV)

C’ = aC*(1 - C) - bC*CC2’ = aC2*(1 - C2) - bC2*C2O’ = aO*(1 - O) - bO*O

ChannelBuild[0] managed KSChan[0]

Close HideStates Transitions Properties

Drag new state from left. Drag off canvas to deleteOC

C C2

O

no gate selected

Adjust Run

-90 -40 10 600

0.20.40.60.8

1

-90 -40 10 600

0.20.40.60.8

1no KSTrans selected

ChannelBuildGateGUI[0] for ChannelBuild[0]

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Propertieskca Density Mechanismk ohmic ion current ik (mA/cm2) = g_kca * (v - ek)g = gmax * 0 * O Default gmax = 0 (S/cm2)

0: 2 state, 1 transitionsO’ = aO*(1 - O) - bO*O

ChannelBuild[0] managed KSChan[0]

Close HideStates Transitions Properties

New transition pair: select source and drag to target

C C2v

O

no gate selected

Adjust Run

-90 -40 10 600

0.20.40.60.8

1

-90 -40 10 600

0.20.40.60.8

1no KSTrans selected

ChannelBuildGateGUI[0] for ChannelBuild[0]

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Propertiesleak Density MechanismNonSpecific ohmic ion current i_leak (mA/cm2) = g_leak * (v - e_leak)g = gmax * O Default gmax = 0 (S/cm2) e = 0 (mV)

O: 3 state, 2 transitions

ChannelBuild[0] managed KSChan[0]

Close HideStates Transitions Properties

Select hh state or ks transition to change properties

C C2 Ov v

OO: 3 state, 2 transitions

Power 1Fractional ConductanceC2 fraction 0

O fraction 1

Adjust Run

-90 -40 10 600

0.20.40.60.8

1

-90 -40 10 600

0.20.40.60.8

1 aC2ObC2O

bC2O = AA (/ms) 0

EquationType

ChannelBuildGateGUI[0] for ChannelBuild[0]

alpha,betaaC2ObC2O

a,binf,tauLigandCopy

nainaokikocaicaoNew Ligand

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Select hh state or ks transition to change properties

C C2 Ov cai

OO: 3 state, 2 transitions

Power 1Fractional ConductanceC2 fraction 0

O fraction 1

Adjust Run

-90 -40 10 600

0.20.40.60.8

1

-90 -40 10 600

0.20.40.60.8

1 aC2ObC2O

C2 + cai <-> O (a, b) (KSTrans[9])Display inf, tau

aC2O = A

ChannelBuildGateGUI[0] for ChannelBuild[0]

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Propertieskca Density Mechanismk ohmic ion current ik (mA/cm2) = g_kca * (v - ek)g = gmax * O Default gmax = 0 (S/cm2)

O: 3 state, 2 transitions

ChannelBuild[0] managed KSChan[0]

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23

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Close HideStates Transitions Properties

Select hh state or ks transition to change properties

C C2 Ov cai

C3 O2v

O3

(0.25*C2 + O)(0.25*C2 + O): 3 state, 2 transitions

Power 1Fractional ConductanceC2 fraction 0.25

O fraction 1

Adjust Run

-90 -40 10 600

0.20.40.60.8

1

-90 -40 10 600

0.20.40.60.8

1 aC2ObC2O

C2 + cai <-> O (a, b) (KSTrans[29])Display inf, tau

aC2O = A

ChannelBuildGateGUI[0] for ChannelBuild[0]

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Propertieskca Density Mechanismk ohmic ion current ik (mA/cm2) = g_kca * (v - ek)g = gmax * (0.25*C2 + O) * O2 * O3 Default gmax = 0 (S/cm2)

(0.25*C2 + O): 3 state, 2 transitionsO2: 2 state, 1 transitionsO3’ = aO3*(1 - O3) - bO3*O3

ChannelBuild[0] managed KSChan[0]

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Propertiesnahh Density Mechanismna ohmic ion current ina (mA/cm2) = g_nahh * (v - ena)g = gmax * m3h1 Default gmax = 0.12 (S/cm2)

m3h1: 8 state, 10 transitions

ChannelBuild[0] managed KSChan[0]

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Propertieskhh Density Mechanismk ohmic ion current ik (mA/cm2) = g_khh * (v - ek)g = gmax * n4 Default gmax = 0.036 (S/cm2)

n4: 5 state, 4 transitions

ChannelBuild[1] managed KSChan[1]

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Propertiesleak Density MechanismNonSpecific ohmic ion current i_leak (mA/cm2) = g_leak * (v - e_leak)g = gmax Default gmax = 0.0003 (S/cm2) e = -54.3 (mV)

ChannelBuild[2] managed KSChan[2]

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Propertiesnahh0 Point Process (Allow Single Channels)na ohmic ion current ina (mA/cm2) = nahh0.g * (v - ena)*(0.01/area)g = gmax * m3h1 Default gmax = 0.12 (uS)

m3h1: 8 state, 10 transitions

ChannelBuild[3] managed KSChan[3]

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somapashhnahhkhhleak

SingleCompartment

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SelectPointProcessShow

IClamp[0]at: soma(0.5)

IClamp[0]del (ms) 0.5

dur (ms) 0.1

amp (nA) 0.3

i (nA) 0

PointProcessManagerClose Hide

0 1 2 3 4 50

0.1

0.2

0.3

0 1 2 3 4 50

0.1

0.2

0.3 nahh0[0].m3h1

Graph Move Text x -0.5 : 5.5 y -0.03 : 0.33

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SelectPointProcessShow

nahh0[0]at: soma(0.5)

nahh0[0]Nsingle 0

gmax (uS) 0.12

g (uS) 6.816e-08

PointProcessManager

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0 1 2 3 4 5

-80

-40

0

40

0 1 2 3 4 5

-80

-40

0

40v(.5)

Graph[0] x -0.5 : 5.5 y -92 : 52

Close HideStates Transitions Properties

Select hh state or ks transition to change properties

m0h0 m1h0 m2h0 m3h0

m0h1 m1h1 m2h1 m3h1

v v v

v v vv v v v

m3h1m3h1: 8 state, 10 transitions

Power 1Fractional Conductancem0h0 fraction 0

m1h0 fraction 0

Adjust Run

-90 -40 10 600

0.20.40.60.8

1

-90 -40 10 600

0.20.40.60.8

1 infm0h0m1h0taum0h0m1h0

m0h0 <-> m1h0 (a, b) (KSTrans[14])Display inf, tau

am0h0m1h0 = A*x/(1 - exp(-x)) where x = k*(v - d)

ChannelBuildGateGUI[0] for ChannelBuild[3]

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Init (mV) -65

Init & Run

Stop

Continue til (ms) 5

Continue for (ms) 1

Single Step

t (ms) 5

Tstop (ms) 5

dt (ms) 0.025

Points plotted/ms 40Quiet

Real Time (s) 0.01

RunControl

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23

4 567

8 9

10

11

12

Print & File Window Manager

nahh0[0]at: soma(0.5)

nahh0[0]Nsingle 0

gmax (uS) 0.12

g (uS) 6.816e-08

i (nA) -8.5813e-06

PointProcessManager

0 1 2 3 4 5

-80

-40

0

40

0 1 2 3 4 5

-80

-40

0

40v(.5)

Graph[0] x -0.5 : 5.5 y -92 : 52

0 1 2 3 4 50

0.1

0.2

0.3

0 1 2 3 4 50

0.1

0.2

0.3 nahh0[0].m3h1

Graph[1] x -0.5 : 5.5 y -0.03 : 0.33

nahh0[0]at: soma(0.5)

nahh0[0]Nsingle 1000

gmax (uS) 0.00012

g (uS) 0

i (nA) -0

PointProcessManager

0 1 2 3 4 5

-80

-40

0

40

0 1 2 3 4 5

-80

-40

0

40v(.5)

Graph[0] Color/Brush x -0.5 : 5.5 y -92 : 52

0 1 2 3 4 50

100

200

300

0 1 2 3 4 50

100

200

300 nahh0[0].m3h1

Graph[1] Color/Brush x -0.5 : 5.5 y -30 : 330

0 1 2 3 4 50

100

200

300

0 1 2 3 4 50

100

200

300nahh0[0].m3h1

20935 points

1.2 1.3 1.4 1.5250

260

270

280

290

1.2 1.3 1.4 1.5250

260

270

280

290nahh0[0].m3h1

1.32 1.325 1.33 1.335 1.34262

264

266

268

1.32 1.325 1.33 1.335 1.34262

264

266

268nahh0[0].m3h1

Use variable dtAbsolute Tolerance 0.001

Atol Scale Tool Details