# phantom.ode # This XPPAUT file contains the phantom bursting model, with two fast # and two slow variables. Contains the code for phase resetting. # It was used to make Figs. 1-12 in: # M. Watts, J. Tabak, C. Zimliki, A. Sherman, R. Bertram, # "Slow Variable Dominance and Phase Resetting in Phantom Bursting", # Journal of Theoretical Biology, 276:218-228, 2011. # Units: V = mV; t = ms; g = pS; I = fA # Variables: # v -- membrane potential # n -- delayed rectifier K current activation # s1 -- slow K current activation # s2 -- very slow K current activation # Initial conditions v(0)=-39.99798 n(0)=0.0409285 s1(0)=0.01404744 s2(0)=0.5953502 tup(0)=0 tdown(0)=0 dur(0)=0 int(0)=0 # Parameters param lambda=1.1, gca=280, gk=1300 param gl=25, vs1=-40, taus1=1000, vs2=-42, taus2=120000, gs2=32 param gs1=20, vl=-40 param vca=100, vk=-80, cm=4524 param tnbar=9.09, vm=-22, vn=-9, sm=7.5, sn=10 param ss1=0.5, ss2=0.4 #for resetting param ton=0, toff=0, i=0 f(t)=heav(toff-t)*heav(t-ton) awk x=i*f(t) # activation and time-constant functions minf(v) = 1.0/(1.0+exp((vm-v)/sm)) ninf(v) = 1.0/(1.0+exp((vn-v)/sn)) taun(v) = tnbar/(1.0+exp((v-vn)/sn)) s1inf(v) = 1.0/(1.0+exp((vs1-v)/ss1)) s2inf(v) = 1.0/(1.0+exp((vs2-v)/ss2)) # ionic currents ica(v) = gca*minf(v)*(v-vca) ik(v) = gk*n*(v-vk) il(v) = gl*(v-vl) is1(v) = gs1*s1*(v-vk) is2(v) = gs2*s2*(v-vk) # differential equations v' = -( ica(v) + ik(v) + il(v) + is1(v) + is2(v) + i*f(t) )/cm n' = lambda*(ninf(v) - n)/taun(v) s1' = (s1inf(v) - s1)/taus1 s2' = (s2inf(v) - s2)/taus2 tup' = 0 tdown' = 0 dur' = 0 int' = 0 global 1 (v+40) {tup=t;int=t-tdown} global -1 (v+40) {tdown=t;dur=t-tup} # XPP parameters @ dtmax=1, dt=1, total=500000, maxstor=900000 @ bounds=100000000, xp=t, yp=v, toler=1.0e-8, atoler=1.0e-8 @ xlo=0, xhi=30000, ylo=-70, yhi=-10 done