# Fig9.ode # # This XPPAUT file contains the mathematical model used in Figure 7 of # Bertram, Egli, Toporikova, and Freeman, American Journal of Physiology, # in press, 2006. The terminating factor (H) inhibits lactotrophs by # stimulating dopamine neurons. # Variables (dimensionless): p = prolactin concentration # d = dopamine concentration # o = oxytocin concentration # vip = VIP neuron activity # N = interneuron activity # H = terminating factor p(0)=0 d(0)=20 o(0)=0 H(0)=0 N(0)=0 # units of t are hr # prolactin parameters par vo=0.01, Tp=6, q=0.5, kd=1 # dopamine parameters par Td=10, kp=0.03, rv=2, tau=3 # OT-sensing neuron parameters par von=0.0002, rn=0.2 # Externally applied OT pulse (set p_inj=1000 for OT injection) par tinj=48, p_inj=1000, tpdur=2 I = p_inj*(heav(t-tinj)-heav(t-tinj-tpdur)) # CS termination (PL, or other hormone) par rH=15, tH=312, tauH=40 Hswitch = heav(t-tH) # Circadian VIP neuron activity par period=24, tf1=2, vipdur=3 vip = heav(mod(t,period)-tf1)-heav(mod(t,period)-(tf1+vipdur)) # Equations p' = Tp*(1/(kd+d^2))-q*p+vo*o d' = Td*(1-N)+Td*kp*delay(p,tau)^2-q*d-rv*vip*d+rH*H o' = I-q*o H' = Hswitch*((1-H)/tauH) N' = von*o-rn*N*(N-.5)*(N-1) aux tdays=t/24 aux Pulse=H aux Vip=vip # set max delay and other xpp parameters @ delay=6, dt=0.2, total=425, maxstor=20000 @ bounds=10000000, xp=tdays, yp=p, bell=off @ xlo=0, xhi=16, ylo=0, yhi=10 done