Simple Two-Gene Regulatory Network - Linear Time-Invariant Difference Equation

# Computational Medicine
# Simple Two-Gene Regulatory Network (Activation): x --> y
# Linear Time-Invariant Difference Equation
# 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)
y = np.empty(N)          # protein y concentration in uM (vector)
x.fill(10)               # constant x protein concentration (= 10 uM)
y[0] = 0                 # initial y protein concentration (= 0 uM)
Pxy = 0.2                # production parameter
Py = 0.9                 # degradation parameter

for i in range (1, N):              # discrete-time index i
    y[i] = Pxy*x[i-1] + Py*y[i-1]   # difference equation 

plt.plot(n,x,'g',label = 'x')
plt.plot(n,y,'r',label = 'y')
plt.xlabel('time (n)')
plt.ylabel('protein concentration (uM)')
plt.legend(loc='lower right')
plt.title('x --> y')
plt.grid(True)
plt.show()