Assignment - Two Different Dynamics

# Computational Medicine
# Assignment - Two Different Dynamics
# Yong-Jun Shin (2019)

import numpy as np
import matplotlib.pyplot as plt

N = 100                  # Total number of data points
n = np.arange(0, N, 1)   # [0,..., N-1] (vector)
x = np.empty(N)          # Protein x concentration in uM (vector)
y1 = np.empty(N)         # Protein y1 (control) concentration in uM (vector)
y2 = np.empty(N)         # Protein y2 concentration in uM (vector)
y3 = np.empty(N)         # Protein y3 concentration in uM (vector)
x.fill(10)               # Constant x protein concentration (= 10 uM)
y1[0] = 0                # Initial y1 protein concentration (= 0 uM)
y2[0] = 0                # Initial y2 protein concentration (= 0 uM)
y3[0] = 0                # initial y3 protein concentration (= 0 uM)
Pxy1 = 0.4               # Production parameter Pxy1
Py1 = 0.9                # Degradation parameter Py1
Pxy2 = 0.8               # Production parameter Pxy2
Py2 = 0.2                # Degradation parameter Py2

# Increase Pxy (= more protein production)
# Only steady state level changes

for i in range (1, N):                  # discrete-time index i
    y1[i] = Pxy1*x[i-1] + Py1*y1[i-1]   # control
    y2[i] = Pxy2*x[i-1] + Py1*y2[i-1]   # target (change in Pxy)

# Decrease Py ( = more protein degradation)
# Both steady state level and response time change
    
for i in range (1, N):                  # discrete-time index i
    y1[i] = Pxy1*x[i-1] + Py1*y1[i-1]   # control
    y3[i] = Pxy1*x[i-1] + Py2*y3[i-1]   # target (change in Py)

# Pxy plot
plt.subplot(1,2,1)
plt.plot(n,x,'g',label = 'x')
plt.plot(n,y1,'r',label = 'y1')
plt.plot(n,y2,'b',label = 'y2')
plt.xlabel('time (n)')
plt.ylabel('protein concentration (uM)')
plt.legend(loc='upper left')
plt.title('Pxy increase: y1 --> y2 (more production)')
plt.grid(True)

# Py plot
plt.subplot(1,2,2)
plt.plot(n,x,'g',label = 'x')
plt.plot(n,y1,'r',label = 'y1')
plt.plot(n,y3,'c',label = 'y3')
plt.xlabel('time (n)')
plt.ylabel('protein concentration (uM)')
plt.legend(loc='upper left')
plt.title('Py decrease: y1 --> y3 (more degradation)')
plt.grid(True)

show()