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
Ohmic vs Constant Field 1 i 5 5 1 15 v i = g * (v e) 1 i = p * ghk(v, ci, co, z) 1 1 1 2
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))) 1 4 2 2 4 6 mv
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
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
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
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.8.6.4.2-9 -4 1 6 1 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)))
Adjust Run 1.8.6.4.2 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) -35-9 -4 1 6 EquationType alpha,beta ah bh a,b inf,tau Copy
Adjust Run 1.8.6.4.2 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) -35-9 -4 1 6 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
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).1.2-9 -4 1 6 tauh = KSChanBGtau EquationType inf,tau infh tauh A A/(1 + exp(-k*(d - v))) KSChanBGinf KSChanTable
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.8 1.6.4.2-9 -4 1 6 no KSTrans selected
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.8 1.6.4.2-9 -4 1 6 no KSTrans selected
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.4.2-9 -4 1 6 bc2o = A A (/ms) EquationType alpha,beta ac2o bc2o a,b inf,tau Ligand Copy nai nao ki ko cai cao New Ligand
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 -4 1 6 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
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 -4 1 6 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
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) -9-4 1 6
at: soma(.5) at: soma(.5) nahh[] Nsingle gmax (us).12 g (us) 6.816e-8 i (na) -8.5813e-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) 1 2 3 4 5 1 2 3 4 5-4 -4-8 -8 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[].m3h1.2 2.1 1 1 2 3 4 5 1 2 3 4 5
3 nahh[].m3h1 2935 points 2 1 Use variable dt Absolute Tolerance.1 Atol Scale Tool Details 1 2 3 4 5 29 nahh[].m3h1 28 268 nahh[].m3h1 27 266 26 264 25 1.2 1.3 1.4 1.5 262 1.32 1.325 1.33 1.335 1.34