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from __future__ import print_function
import tellurium as te
te.setDefaultPlottingEngine("matplotlib")
%matplotlib inline

r = te.loada ('''
model feedback()
   // Reactions:
   J0: $X0 -> S1; (VM1 * (X0 - S1/Keq1))/(1 + X0 + S1 + S4^h);
   J1: S1 -> S2; (10 * S1 - 2 * S2) / (1 + S1 + S2);
   J2: S2 -> S3; (10 * S2 - 2 * S3) / (1 + S2 + S3);
   J3: S3 -> S4; (10 * S3 - 2 * S4) / (1 + S3 + S4);
   J4: S4 -> $X1; (V4 * S4) / (KS4 + S4);

  // Species initializations:
  S1 = 0; S2 = 0; S3 = 0;
  S4 = 0; X0 = 10; X1 = 0;

  // Variable initialization:
  VM1 = 10; Keq1 = 10; h = 10; V4 = 2.5; KS4 = 0.5;
end''')

res = r.simulate(0, 40, 500)
r.plot()

import matplotlib.pylab as plt
plt.plot(res["[S1]"], res["[S2]"], 'o-', color="black")
plt.xlabel("[S1]")
plt.ylabel("[S2]");