# min_cycle.ode # Published in Bulletin of Mathematical Biology, 70:2211-2228, 2008. # This file is for the minimal estrous cycle model, used to make Figure 6. # Variables: # FSHp = FSH protein level in the gonadotroph # FSHb = FSH level in the blood # FSp = FS protein level # FSb = FS level in the blood # Ab = Activin level in the blood # LHb = LH level in the blood FSHp(0)=0.1 FSHb(0)=0.1 FSp(0)=0.1 FSb(0)=0.1 Ab(0)=0.1 LHb(0)=0.1 G(0)=0.05 # Normalized GnRH pulse frequency. par Gon=0.29,mult=3.2 par ton=66 tdur=96-ton ton2=ton+96 ton3=ton2+96 estrous = (heav(t-ton)-heav(t-ton-tdur)) + (heav(t-ton2)-heav(t-ton2-tdur)) + (heav(t-ton3)-heav(t-ton3-tdur)) mu=Gon*(1-estrous*mult) % aux mu=mu # First order removal parameter (common to all) par d=1 # FSHp parameters par v1=10,k1=5 # FSHb parameters par v2=10,k2=0.1,k3=5 # FSp parameters par v3=4,k5=0.5,k4=1.5 # FSb parameters par v4=100,k6=1,k7=5,p=10 # Ab parameters par v5=10,k8=0.1 # LHb parameters par v6=15,k9=1 term1=Ab/(k1+Ab) # term1=0.42 term2=(G/(k2+G)) # term3=(FSHp/(k3+FSHp)) # term3=0.49 # term3=0.45 term3=0.28 term4=(G/(k4+G)) # term4=0.25 term5=(Ab/(k5+Ab)) # term5=0.87 term6=(G/(k6+G)) # term6=0.33 term7=(FSp/(k7+FSp)) # term7=0.15 term8=(G/(k8+G)) # term8=0.83 term9=(G/(k9+G)) FSHp' = v1*term1 - d*FSHp FSHb' = v2*term2*term3 - d*FSHb FSp' = v3*term4*term5 - d*FSp FSb' = v4*term6*term7 - p*Ab*FSb - d*FSb Ab' = v5*term8 - p*Ab*FSb - d*Ab LHb' = v6*term9 - d*LHb G' = mu*G^2 @ meth=cvode, toler=1.0e-9, atoler=1.0e-9, dt=0.5, total=288, @ maxstor=20000,bounds=10000000, xp=tday, yp=fshb @ xlo=0, xhi=12, ylo=0, yhi=5, bell=off @ BUT=QUIT:fq, BUT=AUTO:fa aux tday=t/24 aux ratio=LHb/FSHb aux term1=term1 aux term2=term2 aux term3=term3 aux term4=term4 aux term5=term5 aux term6=term6 aux term7=term7 aux term8=term8 done