#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Tue Dec 13 09:41:01 2022
%File gma_approximations.py
%Figure 3.13: Comparions of GMA and Michaelis-Menten rate laws

@author: bingalls
"""
import numpy as np
import matplotlib.pyplot as plt



K1=1
K2=1
wstar=np.linspace(0,1,100)
vrat1=wstar*(1-wstar+K1)/((1-wstar)*(wstar+K2))

K1=0.1
K2=0.1
wstar=np.linspace(0,1,100)
vrat2=wstar*(1-wstar+K1)/((1-wstar)*(wstar+K2))

K1=0.01
K2=0.01
wstar001=np.linspace(0,1,1000)
vrat3=wstar001*(1-wstar001+K1)/((1-wstar001)*(wstar001+K2))



plt.figure()
plt.plot(vrat1, wstar, linewidth=2)
plt.plot(vrat2, wstar, linewidth=2)
plt.plot(vrat3, wstar001, linewidth=2)
plt.xlabel("Concentration of activating enzyme ([$E_{1T}$], arbitrary units)")
plt.ylabel("Fractional abundance of active protein ($w^*$)")
plt.xlim(0,3)
plt.ylim(0,1)