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Runge_Kutta_solution.py

+import numpy as np
+import matplotlib.pyplot as plt
+
+plt.rcParams['font.size'] = 14
+plt.rcParams['font.family'] = 'Times New Roman'
+
+def dydt(t, Y, Kp, Km, X0, A0):
+    return Kp * (X0 - Y) * (A0 - Y) - Km * Y
+
+def runge_kutta(h, t_max, Kp, Km, X0, A0):
+    t_values = np.arange(0, t_max + h, h)
+    y_values = np.zeros(len(t_values))
+    y = 0 
+
+    for i in range(1, len(t_values)):
+        t = t_values[i-1]
+        k1 = h * dydt(t, y, Kp, Km, X0, A0)
+        k2 = h * dydt(t + 0.5*h, y + 0.5*k1, Kp, Km, X0, A0)
+        k3 = h * dydt(t + 0.5*h, y + 0.5*k2, Kp, Km, X0, A0)
+        k4 = h * dydt(t + h, y + k3, Kp, Km, X0, A0)
+
+        y += (k1 + 2*k2 + 2*k3 + k4) / 6
+        y_values[i] = y
+
+    return t_values, y_values
+
+
+#Set the parameters.
+#Association constant k+.
+Kp = @Kp
+#Dissociation constant k-.
+Km = @Km
+#Initial free binding sites X0 (receptors or antigens).
+X0 = @Xo
+#Initial AB concentration A0.
+A0 = @A0
+#Step width of Runge-Kutta algorythm. Can be set to 0.1 for rough estimation.
+h = @h0
+#Measuring time t_max.
+t_max = @t_max
+
+#Insert time points.
+t_data = @t_data #@t_data=np.array([t1,t2,t3,...])
+#Insert MFI data.
+y_data = @y_data #@y_data=np.array([y1,y2,y3,...])
+#Insert y standard deviation.
+stdev_data = @stdev_data #@stdev_data=np.array([stdev1,stdev2,stdev3,...])
+
+
+t_values, y_values = runge_kutta(h, t_max, Kp, Km, X0, A0)
+
+plt.plot(t_data, y_data, 'o', color='green', label='Label')
+
+
+#Plot the results.
+plt.plot(t_values, y_values, color='#8A2BE2', label='Runge-Kutta Solution')
+lower_bound = y_data - stdev_data
+upper_bound = y_data + stdev_data
+plt.fill_between(t_data, lower_bound, upper_bound, color='lightgreen', alpha=0.3, label='SD')
+plt.xlabel('Time in s')
+plt.ylabel('MFI')
+plt.legend(prop={'weight': 'bold'}, loc='lower right')
+plt.title('Title', fontweight='bold')
+
+#Plot limits.
+plt.xlim(-5, 3600)
+plt.ylim(0,150)
+
+ax = plt.gca() 
+ax.spines['top'].set_visible(False)
+ax.spines['right'].set_visible(False)
+
+
+#plt.savefig('Figure.png', bbox_inches='tight')
+
+plt.show()
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