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157 lines
4.1 KiB
157 lines
4.1 KiB
TITLE Calcium ion accumulation and diffusion with pump |
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: The internal coordinate system is set up in PROCEDURE coord_cadifus() |
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: and must be executed before computing the concentrations. |
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: The scale factors set up in this procedure do not have to be recomputed |
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: when diam or DFree are changed. |
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: The amount of calcium in an annulus is ca[i]*diam^2*vol[i] with |
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: ca[0] being the second order correct concentration at the exact edge |
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: and ca[NANN-1] being the concentration at the exact center |
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? interface |
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NEURON { |
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THREADSAFE |
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SUFFIX cadifpmp |
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USEION ca READ cao, ica WRITE cai, ica |
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RANGE ica_pmp, last_ica_pmp, k1, k2, k3, k4, DFree |
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GLOBAL vol, pump0 |
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} |
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DEFINE NANN 10 |
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UNITS { |
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(mV) = (millivolt) |
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(molar) = (1/liter) |
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(mM) = (millimolar) |
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(um) = (micron) |
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(mA) = (milliamp) |
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(mol) = (1) |
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FARADAY = (faraday) (coulomb) |
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PI = (pi) (1) |
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R = (k-mole) (joule/degC) |
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} |
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PARAMETER { |
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DFree = 0.6 (um2/ms) <0,1e9> |
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beta = 50 <0, 1e9> |
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k1 = 5e8 (/mM-s) <0, 1e10>:optional mm formulation |
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k2 = .25e6 (/s) <0, 1e10> |
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k3 = .5e3 (/s) <0, 1e10> |
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k4 = 5e0 (/mM-s) <0, 1e10> |
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pump0 = 3e-14 (mol/cm2) <0, 1e9> : set to 0 in hoc if this pump not wanted |
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} |
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ASSIGNED { |
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celsius (degC) |
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diam (um) |
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v (millivolt) |
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cao (mM) |
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cai (mM) |
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ica (mA/cm2) |
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vol[NANN] (1) : gets extra cm2 when multiplied by diam^2 |
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ica_pmp (mA/cm2) |
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area1 (um2) |
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c1 (1+8 um5/ms) |
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c2 (1-10 um2/ms) |
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c3 (1-10 um2/ms) |
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c4 (1+8 um5/ms) |
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ica_pmp_last (mA/cm2) |
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} |
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CONSTANT { |
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volo = 1 (liter) |
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} |
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STATE { |
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ca[NANN] (mM) <1e-6> : ca[0] is equivalent to cai |
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pump (mol/cm2) <1e-15> |
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pumpca (mol/cm2) <1e-15> |
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} |
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INITIAL {LOCAL total |
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parms() |
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FROM i=0 TO NANN-1 { |
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ca[i] = cai |
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} |
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pumpca = cai*pump*c1/c2 |
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total = pumpca + pump |
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if (total > 1e-9) { |
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pump = pump*(pump/total) |
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pumpca = pumpca*(pump/total) |
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} |
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ica_pmp = 0 |
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ica_pmp_last = 0 |
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} |
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BREAKPOINT { |
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SOLVE state METHOD sparse |
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ica_pmp_last = ica_pmp |
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ica = ica_pmp |
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: printf("Breakpoint t=%g v=%g cai=%g ica=%g\n", t, v, cai, ica) |
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} |
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LOCAL frat[NANN] : gets extra cm when multiplied by diam |
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PROCEDURE coord() { |
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LOCAL r, dr2 |
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: cylindrical coordinate system with constant annuli thickness to |
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: center of cell. Note however that the first annulus is half thickness |
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: so that the concentration is second order correct spatially at |
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: the membrane or exact edge of the cell. |
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: note ca[0] is at edge of cell |
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: ca[NANN-1] is at center of cell |
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r = 1/2 :starts at edge (half diam) |
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dr2 = r/(NANN-1)/2 :half thickness of annulus |
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vol[0] = 0 |
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frat[0] = 2*r |
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FROM i=0 TO NANN-2 { |
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vol[i] = vol[i] + PI*(r-dr2/2)*2*dr2 :interior half |
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r = r - dr2 |
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frat[i+1] = 2*PI*r/(2*dr2) :exterior edge of annulus |
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: divided by distance between centers |
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r = r - dr2 |
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vol[i+1] = PI*(r+dr2/2)*2*dr2 :outer half of annulus |
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} |
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} |
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KINETIC state { |
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: printf("Solve begin t=%g v=%g cai=%g ica_pmp=%g\n", t, v, cai, ica_pmp) |
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COMPARTMENT i, (1+beta)*diam*diam*vol[i]*1(um) {ca} |
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COMPARTMENT (1e10)*area1 {pump pumpca} |
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COMPARTMENT volo*(1e15) {cao} |
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? kinetics |
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~ pumpca <-> pump + cao (c3, c4) |
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ica_pmp = (1e-4)*2*FARADAY*(f_flux - b_flux)/area1 |
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: all currents except pump |
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~ ca[0] << (-(ica-ica_pmp_last)*PI*diam*1(um)*(1e4)*frat[0]/(2*FARADAY)) |
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:diffusion |
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FROM i=0 TO NANN-2 { |
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~ ca[i] <-> ca[i+1] (DFree*frat[i+1]*1(um), DFree*frat[i+1]*1(um)) |
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} |
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:pump |
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~ ca[0] + pump <-> pumpca (c1, c2) |
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cai = ca[0] : this assignment statement is used specially by cvode |
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: printf("Solve end cai=%g ica=%g ica_pmp=%g ica_pmp_last=%g\n", |
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: cai, ica, ica_pmp,ica_pmp_last) |
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} |
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PROCEDURE parms() { |
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coord() |
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area1 = 2*PI*(diam/2) * 1(um) |
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c1 = (1e7)*area1 * k1 |
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c2 = (1e7)*area1 * k2 |
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c3 = (1e7)*area1 * k3 |
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c4 = (1e7)*area1 * k4 |
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} |
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FUNCTION ss() (mM) { |
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SOLVE state STEADYSTATE sparse |
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ss = cai |
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} |
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COMMENT |
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At this time, conductances (and channel states and currents are |
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calculated at the midpoint of a dt interval. Membrane potential and |
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concentrations are calculated at the edges of a dt interval. With |
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secondorder=2 everything turns out to be second order correct. |
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ENDCOMMENT
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