File: GME & GPE ********************************************************************** * by * Giuseppe Massobrio - Sergio Martinoia - Paolo Massobrio ********************************************************************** * GME: Gold Mushroom-Shaped MicroElectrode * * GPE: Gold planar MicroElectrode * * NEURON: Behavioral model following the Hodgkin-Huxley formalism * * Note: voltage units should be read as multiplied by 10**-3 ********************************************************************** .OPTIONS list node pathnum probe post method=gear numdgt=9 tnom=25.0 ingold=1 .OPTIONS converge=1 gmindc=1.0e-12 acout=0 *--------------------------- .TEMP 25.0 *--------------------------- IstimGME 11 0 PWL (0 0 1us 10 20s 7 20.000001s 0 80s 0) IstimGPE 111 0 PWL (0 0 4s 10 20s 7 20.000001s 0 80s 0) *--------------------------- .TRAN 1E-3 10 0 1E-3 UIC *--------------------------- * Extracellular potential from GME/GPE .PROBE TRAN V(0,840) V(0,940) *--------------------------- .PARAM *--------------------------------------------------------------------- * CONSTANTS *--------------------------------------------------------------------- * k Boltzmann constant [J/k] * TREF temp. at which model params are measured and extracted [°C] * temper current circuit temperature. [°C] * T actual absolute temperature [K] * conv conversion factor from mole/l to mole/m**3 * q electronic charge [Coulomb] * eps0 dielectric permittivity of vacuum [F/m] * epsw relative permittivity of the diffuse layer * epslys relative permittivity of the insulation coating * epsglyco relative permittivity of the glycocalyx EDL * NAv Avogadro constant [1/mole] * Cbulk electrolyte concentration [mole/l] * ros electrolyte resistivity [ohm*m] * roAu resistivity of Au [ohm*m] * roglyco resistivity of the glycocalyx EDL [ohm*m] * dWaals Van der Waals gap [m] *--------------------------------------------------------------------- + conv='1.0e3' + CTOK='273.15' T='(temper+CTOK)' + k='1.380650e-23' PI='(355/113)' PI2='2.0*PI' + q='1.602176e-19' ET='q/(k*T)' + NAv='6.0221415e23' dWaals='0.34n' + eps0='8.854187e-12' epsw='78.5' + epslys='3.0' epsmed='eps0*epsw' epsglyco='81' + ros='0.7' roAu='2.27e-8' roglyco='1.6e6' + Cbulk='150.0m' ********************************************************************** * NEURON PARAMETERS ********************************************************************** * laxont Neuron axon length [m] * daxont Neuron axon diameter [m] * dsomat Neuron soma diameter [m] * Rax axoplasmatic resistance per unit length [ohm*cm] * Ncomp compartments number + Ncomp='5.0' + dsomat='100.0u' daxont='10.0u' laxont='500.0u' + Asomat='(2.0*PI2*(dsomat/2.0)*(dsomat/2.0))' + Aaxont='(PI2*(daxont/2.0)*laxont)' + ANEURt='(Asomat+Aaxont)' + dsoma='(dsomat/Ncomp)' daxon='daxont' laxon='(laxont/Ncomp)' + Asoma='(2.0*PI2*(dsoma/2.0)*(dsoma/2.0))' + Aaxon='(PI2*(daxon/2.0)*laxon)' + ANEUR='(Asoma+Aaxon)' + Rax='0.1' ********************************************************************** * GME PARAMETERS ********************************************************************** * phstalk percentage of engulfed stalk height * hstalk GME stalk height [m] * htstalk GME engulfed stalk height [m] * dmstalk GME stalk diameter [m] * dmhead GME head diameter [m] * Astalk GME stalk area [m**2] * Ahead GME half head area [m**2] * Arim GME rim area [m**2] * AGME GME total area [m**2] * tinsM thickness of the insulation coating [m] + phstalk='1.0' + dmstalk='1.0u' + dmhead='2.0u' + hstalk='1.0u' + htstalk='(hstalk*phstalk)' + cirhead='(PI2*(dmhead/2.0))' + Abstalk='(PI*(dmstalk/2.0)*(dmstalk/2.0))' + Astalk='(PI2*(dmstalk/2.0)*htstalk)' + Aheadt='(2.0*PI2*(dmhead/2.0)*(dmhead/2.0))' + Ahead='(Aheadt/2.0)' + Arim='(PI*((dmhead/2.0)*(dmhead/2.0)-(dmstalk/2.0)*(dmstalk/2.0)))' + AGME='(Astalk+Ahead+Arim)' + tinsM='1.2' *--------------------------------------------------------------------- + Rstalk='(roAu*(htstalk/Abstalk))' + Rhead='(roAu*(1.0/Cirhead))' + RGME='(Rstalk+Rhead)' *--------------------------------------------------------------------- + PHIM='(PI/2.0)' + CshGME='(((PI2*eps0*epslys)/log(tinsM))*(htstalk+(dmhead/2.0)*sin(PHIM)))' ********************************************************************** * NUMBER of GMEs ********************************************************************** * shxn minimum distance between two GMEs head centers [m] * xGME extra distance between two GMEs head centers [m] * shn effective inter-GMEs head distance [m] * lambdaGME Debye length [m] * nGME number of vertically arranged GMEs in the soma compartment *----------------------------- + lambdaGME='(sqrt((epsmed/(q*ET))*(1.0/(2.0*NAv*Cbulk*conv))))' + shxn='(dmhead+dWaals+2.0*lambdaGME)' + xGME='6.0u' + shn='(shxn+xGME)' + AmGME='(PI*shn*shn)' + AmSOMA='(PI*(dsoma/2.0)*(dsoma/2.0))' + nGME='(int(AmSOMA/AmGME))' ********************************************************************** * GPE PARAMETERS ********************************************************************** * dGPE GPE diameter [m] * tGPE GPE thickness [m] * tinsP thickness of the insulation coating [m] *----------------------------- + dGPE='20u' tGPE='200n' AGPE='PI*(dGPE/2.0)*(dGPE/2.0)' + tinsP='1.2' + RGPE='roAu*(tGPE/AGPE)' + CshGPE='(((PI2*eps0*epslys)/log(tinsP))*tGPE)' ********************************************************************** * GME CLEFT PARAMETERS ********************************************************************** * dsealjGME cleft width at the neuron-GME junction [m] * alphahead head starting angle for resistor concentric rings model * etawm covering factor of the cross-sectional area of the solution. * deltawm surface overlapping coefficient: percentage of microel. * sensitive area covered by the neuron *----------------------------- + dsealjGME='5n' + alphahead='0.4294*PI' + Etawm='1.0' * + Rspreadhead='(((ros/PI2)*(dsealjGME/((dmhead/2.0)*((dmhead/2.0)+dsealjGME))))*Etawm)' + H='(htstalk+(dmstalk/2.0)+dsealjGME)' + Rspreadstalk='(((ros/(PI*H))*log((4.0*H)/(PI2*(dmstalk/2.0))))*Etawm)' + RspreadGME='(Rspreadhead+Rspreadstalk)' * + deltawm='1.0' + rodj='(Ros/(PI2*dsealjGME))' * + Rsealhead='(rodj*(log(tan(PI/4.0))-log(tan(alphahead/2.0))))' + Rsealrim='(rodj*(log((dmhead/2.0)/(dmstalk/2.0))))' + Rsealstalk='(rodj*(htstalk/(dmstalk/2.0)))' + RsealGME='((Rsealhead+Rsealrim+Rsealstalk)*deltawm)' ********************************************************************** * GPE CLEFT PARAMETERS ********************************************************************** * dsealjGPE cleft width at the neuron-GPE junction [m] * etawp covering factor of the cross-sectional area of the solution * deltawp surface overlapping coefficient: percentage of microel. * sensitive area covered by the neuron *----------------------------- + dsealjGPE='90n' + etawp='1.0' * + RspreadGPE='((ros/AGPE)*dsealjGPE*etawp)' * + deltawp='1.0' + RsealGPE='((Ros/dsealjGPE)*deltawp)' ********************************************************************** * GME & GPE ELECTROLYTE INTERFACE PARAMETERS ********************************************************************** * Chg capacitance of EDL at the interface microel-solution [F] * Rhg leakage resistance [ohm] *----------------------------- + ChgGME='5.0p' + RhgGME='1500G' * + ChgGPE='1.13n' + RhgGPE='0.141Meg' ********************************************************************** * GME & GPE PROTEIN-GLYCOCALYX EDL PARAMETERS ********************************************************************** * Chd capacitance of EDL at interface of glycocalyx-solution [F] * Rhd resistance of the EDL [ohm] * tglyco glycocalyx thickness [m] * gammaw correction factor * fscale scale factor *----------------------------- + tglyco='100.0n' * + gammawm='1' + ChdGME='((epsglyco*eps0)*(AGME/tglyco)*gammawm)' + RhdGME='(roglyco*(tglyco/AGME)*gammawm)' * + fscale='2.5' + gammawp='fscale*(AGPE/AGME)' + ChdGPE='((epsglyco*eps0)*(AGPE/tglyco)*gammawp)' + RhdGPE='(roglyco*(tglyco/AGPE)*gammawp)' ********************************************************************** * H-H NEURON MODEL PARAMETERS ********************************************************************** * ENa Sodium equilibrium potential [V] * EK Potassium equilibrium potential [V] * El Leakage equilibrium potential [V] * am, ah activation and inactivation degrees of Na channels * an activation degree of K channels * amc,amd,ahc, rates by which channels switch from a closed to an open state * ahd,anc,and rates by which channels switch from a closed to an open state * bmc,bmd,bhc, rates for reverse * bhd,bnc,bnd rates for reverse * fcm,fch,fcn fractions of channels * Cmem neuron membrane capacitance per unit area [F/cm**2] *----------------------------- * Na Channel *----------------------------- + ENa=-115 gNa0=120 + amc=0.1 am=25 amd=10 bmc=4 bmd=18 + ahc=0.07 ahd=20 bhc=1 bh=30 bhd=10 + cm=1 ch=1 + fcm=1 fch=1 *----------------------------- * K Channel *----------------------------- + EK=12 gK0=36 + anc=0.01 an=10 and=10 bnc=0.125 bnd=80 + cn=1 + fcn=1 *----------------------------- * Leakage Channel *----------------------------- + El=-10.613 Rl=3.333 ********************************************************************** * Solving H-H equations system ********************************************************************** .SUBCKT HH_NEURON 1 20 * In Out-Cmem *----------------------------- * Na-circuit block *----------------------------- * GNa=INa=gNa0*(m**3)*h*(Vmem-ENa) GNa 1 2 value='gNa0*(fcm**3)*(V(21,2)**3)*fch*V(22,2)*V(1,2)' * * Gm1=-alpham*(1-m) Gm1 21 2 value='-1*(amc*(V(1,20)+am)*(1-fcm*V(21,2)))/(exp((V(1,20)+am)/amd)-1)' * * Gm2=betam*m Gm2 21 2 value='bmc*exp(V(1,20)/bmd)*fcm*V(21,2)' * * Gh=-[alphah*(1-h)-betah*h] Gh 22 2 value='-1*(ahc*exp(V(1,20)/ahd)*(1-fch*V(22,2))-(bhc*fch*V(22,2))/(1+exp((V(1,20)+bh)/bhd)))' * ENa 2 20 value='ENa' Cm 21 2 C='Cm' IC=52.932m Ch 22 2 C='Ch' IC=596.121m Rm 21 20 1G Rh 22 20 1G *----------------------------- * K-circuit block *----------------------------- * GK=IK=gK0*(n**4)*(Vmem-EK) GK 1 3 value='gK0*(fcn**4)*(V(31,3)**4)*V(1,3)' * * Gn1=-alphan*(1-n) Gn1 31 3 value='-1*anc*(V(1,20)+an)*(1-fcn*V(31,3))/(exp((V(1,20)+an)/and)-1)' * * Gn2=betan*n Gn2 31 3 value='bnc*exp(V(1,20)/bnd)*fcn*V(31,3)' * EK 3 20 value='EK' Cn 31 3 C='Cn' IC=317.677m Rn 31 20 1G *----------------------------- * Leakage-circuit block *----------------------------- * El 4 20 value='El' Rl 1 4 R='Rl' *----------------------------- * Membrane capacitance *----------------------------- Cmem 1 20 1 IC=0 *----------------------------- .ENDS HH_NEURON ********************************************************************** * GME protein-glycocalyx stage model ********************************************************************** .SUBCKT GlycoGME 30 40 * Cmem Rspread Rhd 30 40 R='RhdGME' Chd 30 40 C='ChdGME' .ENDS GlycoGME ********************************************************************** * GPE protein-glycocalyx stage model ********************************************************************** .SUBCKT GlycoGPE 50 60 * Cmem Rspread Rhd 50 60 R='RhdGPE' Chd 50 60 C='ChdGPE' .ENDS GlycoGPE ********************************************************************** * GME Cleft stage model ********************************************************************** .SUBCKT CleftGME 70 80 81 * Glyco Rseal gnd RspreadG 70 80 R='RspreadGME' RsealG 80 81 R='RsealGME' .ENDS CleftGME ********************************************************************** * GPE Cleft stage ********************************************************************** .SUBCKT CleftGPE 90 100 101 * Glyco Rseal gnd RspreadM 90 100 R='RspreadGPE' RsealM 100 101 R='RsealGPE' .ENDS CleftGPE ********************************************************************** * GME-electrolyte stage model ********************************************************************** .SUBCKT GME-el_yte 170 180 * Cleft GME Rhg 170 180 R='RhgGME' Chg 170 180 C='ChgGME' .ENDS GME-el_yte ********************************************************************** * GPE-electrolyte stage model ********************************************************************** .SUBCKT GPE-el_yte 190 200 * Cleft GPE Rhg 190 200 R='RhgGPE' Chg 190 200 C='ChgGPE' .ENDS GPE-el_yte ********************************************************************** * GME stage model ********************************************************************** .SUBCKT GME 220 230 231 * Rhg-Chg Cshunt gnd RmGME 220 230 R='RGME' CshGME 230 231 C='CshGME' .ENDS GME ********************************************************************** * GPE stage model ********************************************************************** .SUBCKT GPE 240 250 251 * Rhg-Chg Cshunt gnd RmGPE 240 250 R='RGPE' CshGPE 250 251 C='CshGPE' .ENDS GPE ********************************************************************** * NEURON coupled to GME ********************************************************************** XHHM1 11 0 HH_NEURON RaxM1 11 22 R='Rax' * XHHM2 22 800 HH_NEURON RaxM2 22 33 R='Rax' * XHHM3 33 801 HH_NEURON RaxM3 33 44 R='Rax' * XHHM4 44 802 HH_NEURON RaxM4 44 55 R='Rax' * XHHM5 55 0 HH_NEURON ********************************************************************** * NEURON-GLYCOCALYX coupling ********************************************************************** XNGLYM2 800 810 GlycoGME * Cmem Rspread XNGLYM3 801 811 GlycoGME XNGLYM4 802 812 GlycoGME ********************************************************************** * GLYCOCALYX-CLEFT coupling ********************************************************************** XNCLEM2 810 820 0 CleftGME * Glyco Rspread Rseal XNCLEM3 811 821 0 CleftGME XNCLEM4 812 822 0 CleftGME ********************************************************************** * CLEFT-GME coupling ********************************************************************** XNELECM2 820 830 GME-el_yte * Cleft GME XNELECM3 821 831 GME-el_yte XNELECM4 822 832 GME-el_yte ********************************************************************** * GME ********************************************************************** XNGMEM2 830 840 0 GME * GME Cshunt gnd XNGMEM3 831 841 0 GME XNGMEM4 832 842 0 GME ********************************************************************** * NEURON coupled to GPE ********************************************************************** XHHP1 111 0 HH_NEURON RaxP1 111 122 R='Rax' * XHHP2 122 900 HH_NEURON RaxP2 122 133 R='Rax' * XHHP3 133 901 HH_NEURON RaxP3 133 144 R='Rax' * XHHP4 144 902 HH_NEURON RaxP4 144 155 R='Rax' * XHHP5 155 0 HH_NEURON ********************************************************************** * NEURON-GLYCOCALYX coupling ********************************************************************** XNGLYP2 900 910 GlycoGPE * Cmem Rspread XNGLYP3 901 911 GlycoGPE XNGLYP4 902 912 GlycoGPE ********************************************************************** * GLYCOCALYX-CLEFT coupling ********************************************************************** XNCLEP2 910 920 0 CleftGPE * Glyco Rspread Rseal XNCLEP3 911 921 0 CleftGPE XNCLEP4 912 922 0 CleftGPE ********************************************************************** * CLEFT-GPE coupling ********************************************************************** XNELECP2 920 930 GPE-el_yte * Cleft GPE XNELECP3 921 931 GPE-el_yte XNELECP4 922 932 GPE-el_yte ********************************************************************** * GPE ********************************************************************** XNGMEP2 930 940 0 GPE * GPE Cshunt gnd XNGMEP3 931 941 0 GPE XNGMEP4 932 942 0 GPE ********************************************************************** .END