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Co-culture Model/co_culture_model_version_4_1_bc_production_dependent_on_glucose__2_.py

+# -*- coding: utf-8 -*-
+"""Co-culture model version 4.1 - BC production dependent on glucose
+
+Automatically generated by Colaboratory.
+
+Original file is located at
+    https://colab.research.google.com/drive/1Hf6h8JPN_b7t5grQnsR6pauO-vJLxLQP
+
+### This section calls all the imports and defines the equations
+"""
+
+# Commented out IPython magic to ensure Python compatibility.
+#Import the necessary packages
+from gc import collect
+# %matplotlib inline
+
+import math as math
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.integrate import odeint
+
+# parameter values
+#mumax_xyl = 0.048      # 1/hour
+#literature value
+mumax_c = 0.019  # 1/hour
+Ksxyl = 20        # g/liter
+Si = 20        # g/liter
+
+mumax_col = 0.55     # 1/hour
+Kscol = 0.0024  # g/liter
+Yxscol = 0.38    # g/g
+
+Ypxgluc = 7.62   # g/g 
+Ypxace = 1.15    # g/g
+Yxsbc = 0.24     # g/g
+
+# reaction rates
+def mu(S,Ks,mumax):
+    return mumax*S/(Ks + S)
+
+# differential equations
+def xdot(x,t):
+    BC,Xcol,S, Ace, Gluc= x
+    dBC = BC*mu(S,Ksxyl,mumax_c)
+    dXcol = Xcol*mu(S,Kscol,mumax_col)
+    dS = -((BC*mu(S,Ksxyl,mumax_c))/Yxsbc + (Xcol*mu(S,Kscol,mumax_col))/Yxscol)
+    dAce = Ypxace*BC*mu(S,Ksxyl,mumax_c)
+    dGluc = Ypxgluc*BC*mu(S,Ksxyl,mumax_c)
+    return [dBC,dXcol,dS,dAce,dGluc]
+
+"""### Simulation Results"""
+
+IC = [0.46, 0.054, 20,0,0] #K. xylinus, E. Coli, Substrate
+
+t = np.linspace(0,7,250)
+sol = odeint(xdot,IC,t)
+BC,Xcol,S,Ace,Gluc = sol.transpose()
+
+plt.plot(t,S)
+
+plt.xlabel('Time [hr]')
+plt.ylabel('Concentration [g/liter]')
+plt.title('Concentration of Glucose vs. Time')
+
+plt.plot(t,BC)
+plt.plot(t,Xcol)
+plt.xlabel('Time [hr]')
+plt.ylabel('Concentration [g/liter]')
+plt.legend(['BC Conc.',
+            'E. coli Conc.'])
+
+plt.plot(t,Ace)
+plt.plot(t,Gluc)
+plt.xlabel('Time [hr]')
+plt.ylabel('Concentration [g/liter]')
+plt.legend(['Acetic Acid',
+            'Gluconic Acid'])
+
+"""## Modelling pH change as a result of production of gluconic and acetic acid"""
+
+def get_ace_H_ions():
+    Ace_in_M = []
+    Ka = 1.75*(10**(-5))
+    h_ions_Ace = []
+    for i in range(len(Ace)):  
+          Ace_in_M.append(Ace[i]/60.052)    #convert from g/L to M
+          h_ions = math.sqrt(Ka*Ace_in_M[i])   
+          h_ions_Ace.append(h_ions)
+    return h_ions_Ace
+
+def get_gluc_H_ions():
+    Gluc_in_M = []
+    Ka = 2.5*(10**(-4))
+    h_ions_Gluc = []
+    for i in range(len(Gluc)):
+        Gluc_in_M.append(Gluc[i]/196.16)     #convert from g/L to M
+        h_ions = math.sqrt(Ka*Gluc_in_M[i])
+        h_ions_Gluc.append(h_ions)
+    return h_ions_Gluc
+
+#pHGluc.append(-1*np.log(h_ions))
+
+init_h_ion = 1.0*(10**(-5))
+h_ions_ace = get_ace_H_ions()
+h_ions_gluc = get_gluc_H_ions()
+h_ions = []
+for i in range(len(h_ions_ace)):
+  h_ions.append(h_ions_ace[i]+h_ions_gluc[i]+init_h_ion)
+
+print(h_ions_ace)
+print(h_ions_gluc)
+print(h_ions)
+def pH(h_ions):
+  pH = []  
+  for i in range(len(h_ions)):
+     if(h_ions[i]!=0):
+       pH.append(-1*math.log(h_ions[i],10))
+     else:
+       pH.append(14)
+  return pH
+
+plt.plot(t,pH(h_ions))
+plt.xlabel('Time [hr]')
+plt.ylabel('pH')
+plt.legend(['pH '])
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