TITLE Voltage sensor protein VSFP3.1
COMMENT
Model calculates the displacement current and fluorescence response produced by the voltage-sensing domain in VSFP3.1
Kinetic parameters from least-square fits to experimental data provided by Alica Lundby of VSFP3.1 expressed in PC12 cells
Version 2.0
KINETIC SCHEME:
8-state-Markov-Process
Sensor states: closed = S1n, S2n; open = S1p, S2p
Reporter: off = Rn; on = Rp
Reference: Akemann et al. Biophys. J. (2009) 96: 3959-3976
Laboratory for Neuronal Circuit Dynamics
RIKEN Brain Science Institute, Wako City, Japan
http://www.neurodynamics.brain.riken.jp
Date of Implementation: December 2008
Contact: akemann@brain.riken.jp
ENDCOMMENT
NEURON {
SUFFIX VSFP31M3
NONSPECIFIC_CURRENT i
GLOBAL S1ONzero, S1OFFzero, S2niONzero, S2niOFFzero, S2ipONzero, S2ipONzero, S12pONzero, S12pOFFzero, S12nONzero, S12nOFFzero
GLOBAL R1nONzero, R1nOFFzero, R1pONzero, R1pOFFzero, R2pONzero, R2pOFFzero, R2nONzero, R2nOFFzero
GLOBAL zGateS1, zGateS2, zGateS12p, zGateS12n
GLOBAL deltaGateS1, deltaGateS2ni, deltaGateS2i, deltaGateS2ip, deltaGateS12p, deltaGateS12n
GLOBAL deltaF, Fhalf
GLOBAL baseline
RANGE nc
RANGE fluoSignal
RANGE fluoActivation
}
UNITS {
(mV) = (millivolt)
(mA) = (milliamp)
(nA) = (nanoamp)
(pA) = (picoamp)
(S) = (siemens)
(mS) = (millisiemens)
(nS) = (nanosiemens)
(pS) = (picosiemens)
(um) = (micron)
(molar) = (1/liter)
(mM) = (millimolar)
}
CONSTANT {
e0 = 1.60217646e-19 (coulombs)
kB = 1.3806505e-23 (joule/kelvin)
q10Gate = 1.43 (1) : q10 = 0.9 (70 mV); 0.6 (-30 mV) ON
q10Fluo = 1.67 (1)
tempGate = 25 (degC)
tempFluo = 25 (degC)
}
PARAMETER {
baseline = 1 (1) : 0 = fluorescence baseline set to 0;
nc = 0 (1/cm2)
S1ONzero = 0.48 (1/ms)
S1OFFzero = 0.074 (1/ms)
S2niONzero = 0.4 (1/ms)
S2niOFFzero = 0.38 (1/ms)
S2ipONzero = 2 (1/ms)
S2ipOFFzero = 0.1 (1/ms)
S12pONzero = 0.014 (1/ms)
S12pOFFzero = 0.0066 (1/ms)
S12nONzero = 1e-9 (1/ms)
S12nOFFzero = 0.002 (1/ms)
zGateS1 = 1.2 (1)
zGateS2 = 1.2 (1)
zGateS12p = 0.3 (1)
zGateS12n = 0.3 (1)
deltaGateS1 = 0.35 (1) : location of the S1 transition state (between 0 = internal side to 1 = external side)
deltaGateS2i = 0.2 (1) : location of the transition state of the intermediate state (Si) in S2
deltaGateS2ni = 0.15 (1) : location of the transition state in the reaction of S2n to S2i
deltaGateS2ip = 0.3 (1) : location of the transition state in the reaction of S2i to S2p
deltaGateS12p = 0.4 (1) : location of the transition state in the reaction of S1p to S2p
deltaGateS12n = 0.2 (1) : location of the transition state in the reaction of S1n to S2n
R1nONzero = 1e-12 (1/ms)
R1nOFFzero = 2 (1/ms)
R1pONzero = 1 (1/ms)
R1pOFFzero = 0.7 (1/ms)
R2pONzero = 2 (1/ms)
R2pOFFzero = 1e-12 (1/ms)
R2nONzero = 1e-9 (1/ms)
R2nOFFzero = 0.028 (1/ms)
deltaF = -0.0105 (1) : maximum fluoresence modulation
Fhalf = 1 (1) : fluorescence ratio at vhalf
}
ASSIGNED {
celsius (degC)
v (mV)
i (mA/cm2)
S1ON (1/ms)
S1OFF (1/ms)
S2niON (1/ms)
S2niOFF (1/ms)
S2ipON (1/ms)
S2ipOFF (1/ms)
S12pON (1/ms)
S12pOFF (1/ms)
S12nON (1/ms)
S12nOFF (1/ms)
R1nON (1/ms)
R1nOFF (1/ms)
R1pON (1/ms)
R1pOFF (1/ms)
R2pON (1/ms)
R2pOFF (1/ms)
R2nON (1/ms)
R2nOFF (1/ms)
qtGate (1)
qtFluo (1)
fluoSignal (1) : Fluorescence response
fluoActivation (1)
fluoInit (1)
}
STATE {
S1nRn FROM 0 TO 1
S1pRn FROM 0 TO 1
S2pRn FROM 0 TO 1
S2nRn FROM 0 TO 1
S2iRn FROM 0 TO 1
S1nRp FROM 0 TO 1
S1pRp FROM 0 TO 1
S2pRp FROM 0 TO 1
S2nRp FROM 0 TO 1
S2iRp FROM 0 TO 1
}
INITIAL {
qtGate = q10Gate^((celsius-tempGate)/10 (degC))
qtFluo = q10Fluo^((celsius-tempFluo)/10 (degC))
if ( deltaGateS2ni > deltaGateS2i ) { deltaGateS2ni = deltaGateS2i }
if ( deltaGateS2ip < deltaGateS2i ) { deltaGateS2ip = deltaGateS2i }
rateConst(v)
SOLVE reaction STEADYSTATE sparse
if ( baseline == 0 ) {
fluoInit = Fhalf + deltaF * ( S1nRp + S1pRp + S2pRp + S2nRp + S2iRp - 0.5 )
} else {
fluoInit = 0
}
}
BREAKPOINT {
SOLVE reaction METHOD sparse
i = nc * (1e6) * e0 * ( zGateS1 * gate1Flip() + zGateS2 * gate2Flip() + zGateS12p * gate12pFlip() + zGateS12n * gate12nFlip() )
fluoActivation = S1nRp + S1pRp + S2pRp + S2nRp + S2iRp
fluoSignal = Fhalf + deltaF * ( S1nRp + S1pRp + S2pRp + S2nRp + S2iRp - 0.5 ) - fluoInit
}
KINETIC reaction {
rateConst(v)
~ S1nRn <-> S1pRn (S1ON, S1OFF)
~ S2nRn <-> S2iRn (S2niON, S2niOFF)
~ S2iRn <-> S2pRn (S2ipON, S2ipOFF)
~ S1pRn <-> S2pRn (S12pON, S12pOFF)
~ S1nRn <-> S2nRn (S12nON, S12nOFF)
~ S1nRp <-> S1pRp (S1ON, S1OFF)
~ S2nRp <-> S2iRp (S2niON, S2niOFF)
~ S2iRp <-> S2pRp (S2ipON, S2ipOFF)
~ S1pRp <-> S2pRp (S12pON, S12pOFF)
~ S1nRp <-> S2nRp (S12nON, S12nOFF)
~ S1nRn <-> S1nRp (R1nON, R1nOFF)
~ S1pRn <-> S1pRp (R1pON, R1pOFF)
~ S2pRn <-> S2pRp (R2pON, R2pOFF)
~ S2nRn <-> S2nRp (R2nON, R2nOFF)
CONSERVE S1nRn + S1pRn + S2pRn + S2nRn + S2iRn + S1nRp + S1pRp + S2pRp + S2nRp + S2iRp = 1
}
PROCEDURE rateConst( v(mV) ) {
S1ON = qtGate * S1ONzero * exp( zGateS1 * e0 * deltaGateS1 * v / ( (1000) * kB * celsiusTOkelvin( celsius ) ) )
S1OFF = qtGate * S1OFFzero * exp( -zGateS1 * e0 * (1-deltaGateS1) * v / ( (1000) * kB * celsiusTOkelvin( celsius ) ) )
S2niON = qtGate * S2niONzero * exp( zGateS2 * e0 * deltaGateS2ni * v / ( (1000) * kB * celsiusTOkelvin( celsius ) ) )
S2niOFF = qtGate * S2niOFFzero * exp( -zGateS2 * e0 * (deltaGateS2i-deltaGateS2ni) * v / ( (1000) * kB * celsiusTOkelvin( celsius ) ) )
S2ipON = qtGate * S2ipONzero * exp( zGateS2 * e0 * (deltaGateS2ip-deltaGateS2i) * v / ( (1000) * kB * celsiusTOkelvin( celsius ) ) )
S2ipOFF = qtGate * S2ipOFFzero * exp( -zGateS2 * e0 * (1-deltaGateS2ip) * v / ( (1000) * kB * celsiusTOkelvin( celsius ) ) )
S12pON = qtGate * S12pONzero * exp( zGateS12p * e0 * deltaGateS12p * v / ( (1000) * kB * celsiusTOkelvin( celsius ) ) )
S12pOFF = qtGate * S12pOFFzero * exp( -zGateS12p * e0 * (1-deltaGateS12p) * v / ( (1000) * kB * celsiusTOkelvin( celsius ) ) )
S12nON = qtGate * S12nONzero * exp( zGateS12n * e0 * deltaGateS12n * v / ( (1000) * kB * celsiusTOkelvin( celsius ) ) )
S12nOFF = qtGate * S12nOFFzero * exp( -zGateS12n * e0 * (1-deltaGateS12n) * v / ( (1000) * kB * celsiusTOkelvin( celsius ) ) )
R1nON = qtFluo * R1nONzero
R1nOFF = qtFluo * R1nOFFzero
R1pON = qtFluo * R1pONzero
R1pOFF = qtFluo * R1pOFFzero
R2pON = qtFluo * R2pONzero
R2pOFF = qtFluo * R2pOFFzero
R2nON = qtFluo * R2nONzero
R2nOFF = qtFluo * R2nOFFzero
}
FUNCTION gate1Flip() (1/ms) {
gate1Flip = S1ON * ( S1nRn + S1nRp ) - S1OFF * ( S1pRn + S1pRp )
}
FUNCTION gate2Flip() (1/ms) {
gate2Flip = deltaGateS2i * ( S2niON * ( S2nRn + S2nRp ) - S2niOFF * ( S2iRn + S2iRp ) ) + (1-deltaGateS2i) * ( S2ipON * ( S2iRn + S2iRp ) - S2ipOFF * ( S2pRn +S2pRp ) )
}
FUNCTION gate12pFlip() (1/ms) {
gate12pFlip = S12pON * ( S1pRn + S1pRp ) - S12pOFF * ( S2pRn + S2pRp )
}
FUNCTION gate12nFlip() (1/ms) {
gate12nFlip = S12nON * ( S1nRn + S1nRp ) - S12nOFF * ( S2nRn + S2nRp )
}
FUNCTION celsiusTOkelvin ( c (degC) ) (kelvin) {
UNITSOFF
celsiusTOkelvin = 273.15 + c
UNITSON
}