: Calcium ion accumulation with radial and longitudinal diffusion and pump NEURON { SUFFIX cdpAIS USEION ca READ cao, cai, ica WRITE cai RANGE ica_pmp,ca1,ca2,ca3,ca4,ca5,ca9 :RANGE pump_0 GLOBAL vrat, TotalPump : vrat must be GLOBAL--see INITIAL block : however TotalBuffer and TotalPump may be RANGE : THREADSAFE } DEFINE Nannuli 10 UNITS { (mol) = (1) (molar) = (1/liter) (mM) = (millimolar) (um) = (micron) (mA) = (milliamp) FARADAY = (faraday) (10000 coulomb) PI = (pi) (1) } PARAMETER { v celsius =34 (degC) :cainull =2.5e-4 (mM) cainull = 45e-6 (mM) mginull =.59 (mM) DCa = .233 (um2/ms) Dbtc = 0.007 (um2/ms) Ddmnpe = 0.08 (um2/ms) Dcbd1 = .028 (um2/ms) Dcbd2 = 0 (um2/ms) Dpar = .043 (um2/ms) : values for benzothiazole coumarin (BTC) : BTCnull = 0 (mM) : b1 = 5.33 (/ms mM) : b2 = 0.08 (/ms) : values for caged compound DMNPE-4 : DMNPEnull = 0 (mM) : c1 = 5.63 (/ms mM) : c2 = 0.107e-3 (/ms) : values for Calbindin (2 high and 2 low affinity binding sites) : CBnull= .16 (mM) CBnull= .08 (mM) nf1 =43.5 (/ms mM) nf2 =3.58e-2 (/ms) ns1 =5.5 (/ms mM) ns2 =0.26e-2 (/ms) : values for Parvalbumin : PVnull = 0.08 (mM) PVnull = 0.04 (mM) m1 = 1.07e2 (/ms mM) m2 = 9.5e-4 (/ms) p1 = 0.8 (/ms mM) p2 = 2.5e-2 (/ms) kpmp1 = 3e3 (/mM-ms) kpmp2 = 1.75e1 (/ms) kpmp3 = 7.255e1 (/ms) : to eliminate pump, set TotalPump to 0 in hoc TotalPump = 1e-15 : TotalPump = 1e-8 beta = 1(1) :introducing beta to take care of other ER mechanisms(SERCA and leak channel density) vmax =0.1 :Kp = 0.27e-3 (mM) Kp = 2.7e-3 (mM) } ASSIGNED { diam (um) ica (mA/cm2) ica_pmp (mA/cm2) ibg :background calcium current : ica_pmp_last (mA/cm2) parea (um) : pump area per unit length cai (mM) ca1 ca2 ca3 ca4 ca5 ca9 mgi (mM) vrat[Nannuli] (1) : dimensionless : numeric value of vrat[i] equals the volume : of annulus i of a 1um diameter cylinder : multiply by diam^2 to get volume per um length } CONSTANT { cao = 2 (mM) } STATE { : ca[0] is equivalent to cai : ca[] are very small, so specify absolute tolerance : let it be ~1.5 - 2 orders of magnitude smaller than baseline level ca[Nannuli] (mM) mg[Nannuli] (mM) <1e-7> CB[Nannuli] (mM) CB_f_ca[Nannuli] (mM) CB_ca_s[Nannuli] (mM) CB_ca_ca[Nannuli] (mM) iCB[Nannuli] (mM) iCB_f_ca[Nannuli] (mM) iCB_ca_s[Nannuli] (mM) iCB_ca_ca[Nannuli] (mM) PV[Nannuli] (mM) PV_ca[Nannuli] (mM) PV_mg[Nannuli] (mM) pump (mol/cm2) <1e-15> pumpca (mol/cm2) <1e-15> } BREAKPOINT { SOLVE state METHOD sparse : ica_pmp_last = ica_pmp : ica = ica_pmp } LOCAL factors_done INITIAL { if (factors_done == 0) { : flag becomes 1 in the first segment factors_done = 1 : all subsequent segments will have factors() : vrat = 0 unless vrat is GLOBAL } FROM i=0 TO Nannuli-1 { ca[i] = cainull mg[i] = mginull CB[i] = 0.8*ssCB( kdf(), kds()) CB_f_ca[i] = 0.8*ssCBfast( kdf(), kds()) CB_ca_s[i] = 0.8*ssCBslow( kdf(), kds()) CB_ca_ca[i] = 0.8*ssCBca( kdf(), kds()) iCB[i] = 0.2*ssCB( kdf(), kds()) iCB_f_ca[i] = 0.2*ssCBfast( kdf(), kds()) iCB_ca_s[i] = 0.2*ssCBslow( kdf(), kds()) iCB_ca_ca[i] = 0.2*ssCBca(kdf(), kds()) PV[i] = ssPV( kdc(), kdm()) PV_ca[i] = ssPVca(kdc(), kdm()) PV_mg[i] = ssPVmg(kdc(), kdm()) } parea = PI*diam ica = 0 ica_pmp = 0 : ica_pmp_last = 0 pump = TotalPump pumpca = 0 } LOCAL frat[Nannuli] : scales the rate constants for model geometry PROCEDURE factors() { LOCAL r, dr2 r = 1/2 : starts at edge (half diam) dr2 = r/(Nannuli-1)/2 : full thickness of outermost annulus, : half thickness of all other annuli vrat[0] = 0 frat[0] = 2*r FROM i=0 TO Nannuli-2 { vrat[i] = vrat[i] + PI*(r-dr2/2)*2*dr2 : interior half r = r - dr2 frat[i+1] = 2*PI*r/(2*dr2) : outer radius of annulus : div by distance between centers r = r - dr2 vrat[i+1] = PI*(r+dr2/2)*2*dr2 : outer half of annulus } } LOCAL dsq, dsqvol : can't define local variable in KINETIC block : or use in COMPARTMENT statement KINETIC state { COMPARTMENT i, diam*diam*vrat[i] {ca mg CB CB_f_ca CB_ca_s CB_ca_ca iCB iCB_f_ca iCB_ca_s iCB_ca_ca PV PV_ca PV_mg} COMPARTMENT (1e10)*parea {pump pumpca} :pump : ~ ca[0] + pump <-> pumpca (kpmp1*parea*(1e10), kpmp2*parea*(1e10)) : ~ pumpca <-> pump (kpmp3*parea*(1e10), 0) : CONSERVE pump + pumpca = TotalPump * parea * (1e10) : ica_pmp = 2*FARADAY*(f_flux - b_flux)/parea : all currents except pump : ica is Ca efflux ~ ca[0] << (-ica*PI*diam/(2*FARADAY)) :RADIAL DIFFUSION OF ca, mg and mobile buffers FROM i=0 TO Nannuli-1 { ~ ca[i] << (-beta*vmax*vrat[i]*ca[i] / (ca[i] + kpmp2/kpmp1)) } FROM i=0 TO Nannuli-2 { ~ ca[i] <-> ca[i+1] (DCa*frat[i+1], DCa*frat[i+1]) ~ mg[i] <-> mg[i+1] (DCa*frat[i+1], DCa*frat[i+1]) ~ CB[i] <-> CB[i+1] (Dcbd1*frat[i+1], Dcbd1*frat[i+1]) ~ CB_f_ca[i] <-> CB_f_ca[i+1] (Dcbd1*frat[i+1], Dcbd1*frat[i+1]) ~ CB_ca_s[i] <-> CB_ca_s[i+1] (Dcbd1*frat[i+1], Dcbd1*frat[i+1]) ~ CB_ca_ca[i] <-> CB_ca_ca[i+1] (Dcbd1*frat[i+1], Dcbd1*frat[i+1]) ~ PV[i] <-> PV[i+1] (Dpar*frat[i+1], Dpar*frat[i+1]) ~ PV_ca[i] <-> PV_ca[i+1] (Dpar*frat[i+1], Dpar*frat[i+1]) ~ PV_mg[i] <-> PV_mg[i+1] (Dpar*frat[i+1], Dpar*frat[i+1]) } dsq = diam*diam FROM i=0 TO Nannuli-1 { dsqvol = dsq*vrat[i] :Calbindin ~ ca[i] + CB[i] <-> CB_ca_s[i] (nf1*dsqvol, nf2*dsqvol) ~ ca[i] + CB[i] <-> CB_f_ca[i] (ns1*dsqvol, ns2*dsqvol) ~ ca[i] + CB_f_ca[i] <-> CB_ca_ca[i] (nf1*dsqvol, nf2*dsqvol) ~ ca[i] + CB_ca_s[i] <-> CB_ca_ca[i] (ns1*dsqvol, ns2*dsqvol) ~ ca[i] + iCB[i] <-> iCB_ca_s[i] (nf1*dsqvol, nf2*dsqvol) ~ ca[i] + iCB[i] <-> iCB_f_ca[i] (ns1*dsqvol, ns2*dsqvol) ~ ca[i] + iCB_f_ca[i] <-> iCB_ca_ca[i] (nf1*dsqvol, nf2*dsqvol) ~ ca[i] + iCB_ca_s[i] <-> iCB_ca_ca[i] (ns1*dsqvol, ns2*dsqvol) :Paravalbumin ~ ca[i] + PV[i] <-> PV_ca[i] (m1*dsqvol, m2*dsqvol) ~ mg[i] + PV[i] <-> PV_mg[i] (p1*dsqvol, p2*dsqvol) } cai = ca[0] ca1 = ca[1] ca2 = ca[2] ca3 = ca[3] ca4 = ca[4] ca5 = ca[5] ca9 = ca[9] : if (ca[0]