: Calcium ion accumulation with radial diffusion NEURON { SUFFIX cad USEION ca READ cao, cai, ica WRITE cai, ica RANGE ica_pmp GLOBAL vrat, TotalBuffer, TotalPump } DEFINE Nannuli 4 UNITS { (molar) = (1/liter) (mM) = (millimolar) (um) = (micron) (mA) = (milliamp) FARADAY = (faraday) (10000 coulomb) PI = (pi) (1) (nA) = (nanoamp) } CONSTANT { volo = 1e10 (um2) } PARAMETER { DCa = 0.6 (um2/ms) k1buf = 100 (/mM-ms) : Yamada et al. 1989 k2buf = 0.1 (/ms) TotalBuffer = 0.003 (mM) k1 = 1 (/mM-ms) k2 = 0.005 (/ms) k3 = 1 (/ms) k4 = 0.005 (/mM-ms) : to eliminate pump, set TotalPump to 0 in hoc TotalPump = 1e-13(mol/cm2): 1e-12: 1e-14 } ASSIGNED { diam (um) :L(um) ica (mA/cm2) cai (mM) vrat[Nannuli] : 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 Kd (/mM) B0 (mM) cao (mM) ica_pmp (mA/cm2) parea (um) } STATE { : ca[0] is equivalent to cai : ca[] are very small, so specify absolute tolerance ca[Nannuli] (mM) <1e-10> CaBuffer[Nannuli] (mM) Buffer[Nannuli] (mM) pump (mol/cm2) pumpca (mol/cm2) } BREAKPOINT { SOLVE state METHOD sparse ica = ica_pmp } LOCAL factors_done INITIAL { parea = PI*diam if (factors_done == 0) { factors_done = 1 factors() } Kd = k1buf/k2buf B0 = TotalBuffer/(1 + Kd*cai) FROM i=0 TO Nannuli-1 { ca[i] = cai Buffer[i] = B0 CaBuffer[i] = TotalBuffer - B0 } pump = TotalPump/(1 + (cai*k1/k2)) pumpca = TotalPump - pump ica=0 cai=1e-5 cao=2 ica_pmp=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 CaBuffer Buffer} COMPARTMENT (1e10)*parea {pump pumpca} COMPARTMENT volo {cao} LONGITUDINAL_DIFFUSION i, DCa*vrat[i] {ca} :pump ~ ca[0] + pump <-> pumpca (k1*parea*(1e10), k2*parea*(1e10)) ~ pumpca <-> pump + cao (k3*parea*(1e10), k4*parea*(1e10)) CONSERVE pump + pumpca = TotalPump * parea * (1e10) ica_pmp = 2*FARADAY*(f_flux - b_flux)/parea : all currents except pump ~ ca[0] << (-(ica)*PI*diam/(2*FARADAY)) : ica is Ca efflux FROM i=0 TO Nannuli-2 { ~ ca[i] <-> ca[i+1] (DCa*frat[i+1], DCa*frat[i+1]) } dsq = diam*diam FROM i=0 TO Nannuli-1 { dsqvol = dsq*vrat[i] ~ ca[i] + Buffer[i] <-> CaBuffer[i] (k1buf*dsqvol, k2buf*dsqvol) } cai = ca[0] }