Defining a Channel. voltage and ligand gated. ion selective. multiple gates. 8transition style (α, β) (, τ) functions tables ligand sensitive

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1 Defining a Channel Classical HH like Kinetic scheme voltage and ligand gated ohmic conductance GHK constant field ion selective multiple gates fractional openness independent identical subunits 8transition style (α, β) (, τ) functions tables ligand sensitive voltage sensitive leave out pumps ionic accumulation

2 Ohmic vs Constant Field 1 i v i = g * (v e) 1 i = p * ghk(v, ci, co, z)

3 Voltage sensitive α and β rates generally have the form of Exponential Einstein 5 Boltzmann functions. 1/ms 4 A*exp(k/2*(v d)) 3 A*k*(v d)/(1 exp( k*(v d))) 2 2*A/(1 + exp( k*(v d))) mv

4 E * E 2 E 1 If the energy difference between states is linear with voltage, then the steady state is a Boltzmann distribution. E P ~ e 2 2 kt 1 = 1 + e E kt 2

5 Iconify NEURON Main Menu File Edit Build Tools Graph Vector Window ChannelBuild[] managed KSChan[] Close Properties leak Density Mechanism NonSpecific ohmic ion current i_leak (ma/cm2) = g_leak * (v - e_leak) g = gmax Default gmax = (S/cm2) e = (mv) Select here to construct gates single compartment Cell Builder NetWork Cell NetWork Builder Linear Circuit Channel Builder Density Point import KSChan SingleComp Close soma pas hh leak

6 ChannelBuild[] managed KSChan[] Close Properties leak Channel Density Name Mechanism NonSpecific Selective for ohmic Ion... ion current i_leak Ohmic (ma/cm2) i=g*(v-e) = g_leak * (v - e_leak) g = Goldman-Hodgkin-Katz gmax Default gmax gmax (or = pmax) (S/cm2) e = (mv) HH sodium channel Select HH potassium here to construct channel gates Clone channel type Copy gates from Text to stdout Provide transition aliases Use fixed step HH rate tables Gate Constructor Close ChannelBuild[1] managed KSChan[1] Properties nahh Density Mechanism na ohmic ion current ina (ma/cm2) = g_nahh * (v - ena) g = gmax * m^3 * h Default gmax = (S/cm2) m = am*(1 - m) - bm*m h = ah*(1 - h) - bh*h

7 Default gmax = (S/cm2) Close m = am*(1 - m) - bm*m h = ah*(1 - h) - bh*h States Transitions Properties ChannelBuildGateGUI[] for ChannelBuild[] Select hh state or ks transition to change properties m h m^3 m = am*(1 - m) - bm*m Power 3 Fractional Conductance m fraction 1 Adjust Run infm taum m <-> m (a, b) (KSTrans[]) Display inf, tau am = A*x/(1 - exp(-x)) where x = k*(v - d) A 1 k.1 d -4 bm = A*exp(k*(v - d)))

8 Adjust Run ah bh h <-> h (a, b) (KSTrans[1]) Display inf, tau ah = A*exp(k*(v - d))) A (/ms).7 k (/mv) -.5 d (mv) -65 bh = A/(1 + exp(-k*(d - v))) A (/ms) 1 k (/mv) -.1 d (mv) EquationType alpha,beta ah bh a,b inf,tau Copy

9 Adjust Run ah bh h <-> h (a, b) (KSTrans[1]) Display inf, tau ah = A*exp(k*(v - d))) A (/ms).7 k (/mv) -.5 d (mv) -65 bh = A/(1 + exp(-k*(d - v))) A (/ms) 1 k (/mv) -.1 d (mv) EquationType alpha,beta ah bh A A*exp(k*(v - d))) A*x/(1 - exp(-x)) where x = k*(v - d) A/(1 + exp(-k*(d - v))) KSChanTable

10 Adjust Run h <-> h (inf, tau) Display inf, tau (KSTrans[1]) 1.8 infh tauh infh = KSChanBGinf K (/ms) 1 vhalf (mv) -2.6 z 4 gam.5.4 tau (ms) tauh = KSChanBGtau EquationType inf,tau infh tauh A A/(1 + exp(-k*(d - v))) KSChanBGinf KSChanTable

11 Close States Transitions Properties O C Drag new state from left. Drag off canvas to delete O ChannelBuildGateGUI[] for ChannelBuild[] no gate selected C C2 Adjust Run no KSTrans selected

12 ChannelBuildGateGUI[] for ChannelBuild[] Close States Transitions Properties New transition pair: select source and drag to target no gate selected C v C2 O Adjust Run no KSTrans selected

13 Close States Transitions Properties Select hh state or ks transition to change properties v v C C2 O ChannelBuildGateGUI[] for ChannelBuild[] O O: 3 state, 2 transitions Power 1 Fractional Conductance C2 fraction O fraction 1 Adjust Run 1.8 ac2o.6 bc2o bc2o = A A (/ms) EquationType alpha,beta ac2o bc2o a,b inf,tau Ligand Copy nai nao ki ko cai cao New Ligand

14 Close States Transitions Properties Select hh state or ks transition to change properties v cai C C2 O ChannelBuildGateGUI[] for ChannelBuild[] O O: 3 state, 2 transitions Power 1 Fractional Conductance C2 fraction O fraction 1 Adjust Run 1 ChannelBuild[] managed KSChan[.8 ac2o.6 bc2o Close.4 Properties.2 kca -9Density Mechanism k ohmic ion current ik (ma/cm2) = g_kca * (v - ek) g = gmax * O Default gmax = (S/cm2) C2 + cai <-> O (a, b) (KSTrans[9]) Display inf, tau ac2o = A O: 3 state, 2 transitions

15 Close States Transitions Properties Select hh state or ks transition to change properties C3 v O2 v cai C C2 O ChannelBuildGateGUI[] for ChannelBuild[] (.25*C2 + O) (.25*C2 + O): 3 state, 2 transitions Power 1 Fractional Conductance C2 fraction.25 O3 O fraction 1 Adjust Run ChannelBuild[] managed KSChan[ 1.8 ac2o Close.6 bc2o Properties.4.2 kca Density Mechanism -9 k ohmic ion current ik (ma/cm2) = g_kca * (v - ek) g = gmax * (.25*C2 + O) * O2 * O3 Default gmax = (S/cm2) C2 + cai <-> O (a, b) (KSTrans[29]) Display inf, tau ac2o = A (.25*C2 + O): 3 state, 2 transiti O2: 2 state, 1 transitions O3 = ao3*(1 - O3) - bo3*o3

16 Close ChannelBuild[3] managed KSChan[3] Properties nahh Point Process (Allow Single Channels) na ohmic ion current ina (ma/cm2) = nahh.g * (v - ena)*(.1/area) g = gmax * m3h1 Default gmax =.12 (us) m3h1: 8 state, 1 transitions Close States Transitions Properties SingleComp Close soma pas hh nahh khh leak Close SelectPointProcess Show nahh[] at: soma(.5) nahh[] PointProcessManager Nsingle gmax (us).12 ChannelBuildGateGUI[] for ChannelBuild[3] g (us) 6.816e-8 Select hh state or ks transition to change properties v v v mh1 m1h1 m2h1 m3h1 v v v v v v v mh m1h m2h m3h m3h1 m3h1: 8 state, 1 transitions Power 1 Fractional Conductance mh fraction m1h fraction Adjust Run mh <-> m1h (a, b) (KSTrans[14]).8 1 Display inf, tau infmhm1.6 taumhm.4.2 amhm1h = A*x/(1 - exp(-x)) where x = k*(v - d)

17 at: soma(.5) at: soma(.5) nahh[] Nsingle gmax (us).12 g (us) 6.816e-8 i (na) e-6 Graph[] x -.5 : 5.5 y -92 : 52 nahh[] Nsingle 1 gmax (us).12 g (us) i (na) - Graph[] Color/Brush x -.5 : 5.5 y -92 : 52 4 v(.5) 4 v(.5) Graph[1] x -.5 : 5.5 y -.3 :.33 Graph[1] Color/Brush x -.5 : 5.5 y -3 : 33.3 nahh[].m3h1 3 nahh[].m3h

18 3 nahh[].m3h points 2 1 Use variable dt Absolute Tolerance.1 Atol Scale Tool Details nahh[].m3h nahh[].m3h

Table of Contents and Schedule of Presentations

The NEURON Simulation Environment Didactic Presentations Table of Contents and Schedule of Presentations NTC MLH WWL AM RMcD TM SS Ted Carnevale Michael Hines Bill Lytton Amit Majumdar Robert McDougal