# plant.ode # # This XPPAUT files contains the Plant model for parabolic bursting. See # http://www.scholarpedia.org/article/Plant_model # for details. It was used to make Fig. 2 in the paper "Two Types of Burst Firing # in Gonadotrophin-Releasing Hormone Neurones", Z. Chu, M. Tomaiuolo, R. Bertram, # S. M. Moenter, Journal of Neuroendocrinology, 24:1065-1077, 2012. # initial conditions # Variables: # v -- membrane potential # h -- inactivation of an inward current # n -- activation of an ooutward potassium current # x -- slow inward current activation # ca -- free cytosolic calcium concentration v(0)=-50 h(0)=0.1 n(0)=0.1 x(0)=0.1 ca(0)=0.1 # parameters par cm=1 par gi=4 par gt=0.01 par gk=0.3 par gkca=0.03 par gleak=0.003 par vi=30 par vk=-75 par vleak=-40 par vca=140 par rho=0.00015 par kc=0.00425 par taux=9400 par noise=0 # functions wiener w vs=(v+65.07)*1.20952 alpham=0.1*(50-vs)/(exp((50-vs)/10)-1) betam=4*exp((25-vs)/18) alphah=0.07*exp((25-vs)/20) betah=1/(exp((55-vs)/10)+1) alphan=0.01*(55-vs)/(exp((55-vs)/10)-1) betan=0.125*exp((45-vs)/80) hinf=alphah/(alphah+betah) minf=alpham/(alpham+betam) ninf=alphan/(alphan+betan) xinf=1/(exp(-0.3*(v+40))+1) tauh=12.5/(alphah+betah) taun=12.5/(alphan+betan) Ihi=gi*minf^3*h*(v-vi) Ixi=gt*x*(v-vi) Ik=gk*n^4*(v-vk) Ikca=gkca*(ca/(0.5+ca))*(v-vk) Ileak=gleak*(v-vleak) Iapp=0 Inoise=noise*w # equations v'=-1/cm*(Ihi + Ixi + Ik + Ikca + Ileak - Iapp - Inoise) h'=(hinf-h)/tauh n'=(ninf-n)/taun x'=(xinf-x)/taux ca'=rho*(kc*x*(vca-v)-ca) @ method=E,dt=0.1,total=2000000,maxstor=10000000,noutput=10 @ xp=t, yp=v, xlo=0, xhi=800000, ylo=-70, yhi=40 set ppb_rep1 {noise=0.06} set ppb_rep2 {noise=0.07} set ppb_rep3 {noise=0.08} set ppb_rep4 {noise=0.09} set ppb_rep5 {noise=0.1} done