# open_cell.ode # This XPPAUT file contains the program for calcium oscillations in a cell # in which total calcium is determined by flux across the plasma membrane # (open cell model). It was used to make Fig. 14B in: S. S. Stoijilkovic, # J. Tabak, R. Bertram, "Ion Channels and Signaling in the Pituitary Gland", # Endocrine Reviews, 31:845-915, 2010. # Variables: # C -- cytosolic calcium concentration # Ct -- total calcium concentration in the cell # h -- inactivation variable for the IP3 receptor # # ER fluxes Jer_out = (L + P*( (IP3*C*h)/((IP3+Ki)*(C+Ka)))^3 )*(Cer - C) Jer_in = (Ve*C^2)/(Ke^2+C^2) # Plasma membrane efflux Jmem_out = (Vp*C^2)/(Kp^2 + C^2) # The equations dC/dt = fi/Vi*( Jer_out - Jer_in + eps*(Jin-Jmem_out) ) dh/dt = A*(Kd-(C + Kd)*h) dCt/dt = fi/Vi*eps*( Jin - Jmem_out ) Cer = (Ct - C)/sigma # # The parameters # IP3 pulse # set pulse=0 for no pulse, pulse=1 for a pulse of IP3 par pulse=1, IP3pulse=0.7 par tpulse=50, tduration=400 # Jin removal par remove=1, tremove=150 # Jin = aMol/s par Jmem_in=1200 # IP3 = uM par IP3bas=0 # Vi = pL par Vi=4 par fi=0.01 # L,P = pL/s par L=0.37 par P=26640 # C, Cer, I, Ki, Ka, Ke, Kd = uM par Ki=1.0 par Ka=0.4 # Ve, Vp = aMol/s [sic] par Ve=400 par Vp=2000 par Kp=0.3 par Ke=0.2 par A=0.5 par Kd=0.4 par sigma=0.185 par eps=0.01 # Apply the pulse protocol ts = t-tpulse ts2 = t-(tpulse+tduration) Ip3 = IP3bas+pulse*(heav(ts)-heav(ts2))*IP3pulse ts3 = t-tremove Jin = Jmem_in*(1-remove*heav(ts3)) # # The initial conditions C(0)=0.02 h(0)=0.95 Ct(0)=4.0 # aux Cer=Cer aux Ip3=Ip3 aux jin=Jin # @ meth=qualrk, total=400, dt=0.1, maxstor=10000 @ xp=t, yp=c, xlo=0,xhi=400,ylo=0,yhi=4 @ bounds=100000000, toler=1.0e-9, atoler=1.0e-9 @ bell=off done