Example lineweaver-burk plot of competitive inhibition

Lineweaver-burk plot.py

import numpy as np

from itertools import chain
from statistics import mean
import pandas as pd

import matplotlib.pyplot as plt
import statsmodels.formula.api as sfa


def chunks(l, n):
    """Yield successive n-sized chunks from l."""
    for i in range(0, len(l), n):
        yield l[i:i + n]


x_axis = [2.5, 5, 10, 15]

a_data = np.array([301, 284, 318, 524, 575, 583, 645, 645])

b_data = np.array([140, 155, 171, 171, 398, 383, 524, 546])

c_data = np.array([24, 27, 50, 54, 90, 91, 296, 255])

a_diff = a_data - c_data

b_diff = b_data - c_data

a_diff = a_diff / 100

b_diff = b_diff / 100

a_raw = list(a_diff / 10.2 * 200)

b_raw = list(b_diff / 10.2 * 200)

a_mean = [mean(i) for i in chunks(a_raw, 2)]

b_mean = [mean(i) for i in chunks(b_raw, 2)]

a_inv = [1 / i for i in a_mean]

b_inv = [1 / i for i in b_mean]
x_inv = [1 / i for i in x_axis]

df = pd.DataFrame({'a': a_inv, 'b': b_inv, 'x': x_inv})

a_reg = sfa.ols('a ~ x', data=df).fit()
b_reg = sfa.ols('b ~ x', data=df).fit()

a_fit = list(a_reg.fittedvalues)
b_fit = list(b_reg.fittedvalues)

a_grad = (a_fit[0] - a_fit[-1]) / (x_inv[0] - x_inv[-1])
b_grad = (b_fit[0] - b_fit[-1]) / (x_inv[0] - x_inv[-1])

a_y_intercept = a_fit[-1] - (a_grad * x_inv[-1])
b_y_intercept = b_fit[-1] - (b_grad * x_inv[-1])


def lin_eq(grad, x, int):
    return (grad * x) + int


x_min, x_max = -0.65, 0.65
x_axis = np.linspace(x_min, x_max, 1000)
a_values = [lin_eq(a_grad, x, a_y_intercept) for x in x_axis]
b_values = [lin_eq(b_grad, x, b_y_intercept) for x in x_axis]

a_x_intercept = -a_y_intercept / a_grad
b_x_intercept = -b_y_intercept / b_grad

plot_df = pd.DataFrame({'a': a_values, 'b': b_values, 'x': x_axis})

y_min, y_max = 0, max(chain(a_values, b_values))

fig = plt.figure()
ax = fig.add_subplot(121)
ax.set_title('Lineweaver-Burk')
mask = plot_df.a >= 0
ax.plot(plot_df.x[mask], plot_df.a[mask], label='uninhibited', color='red')
mask = plot_df.b >= 0
ax.plot(plot_df.x[mask], plot_df.b[mask], label='competitive\ninhibition', color='darkred')
ax.spines['left'].set_position('zero')
ax.spines['right'].set_color('none')
ax.spines['bottom'].set_position('zero')
ax.spines['top'].set_color('none')
ax.spines['left'].set_smart_bounds(True)
ax.spines['bottom'].set_smart_bounds(True)
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')

ax.plot(0, a_y_intercept, color='black', marker='o', markersize=3)
ax.text(0.05, a_y_intercept - 0.001, f'{a_y_intercept:.3f}',)

ax.plot(0, b_y_intercept, color='black', marker='o', markersize=3)
ax.text(-0.25, b_y_intercept - 0.001, f'{b_y_intercept:.3f}',)

ax.plot(a_x_intercept, 0, color='black', marker='o', markersize=3)
ax.text(a_x_intercept - 0.1, -0.0038, f'{a_x_intercept:.2f}',)

ax.plot(b_x_intercept, 0, color='black', marker='o', markersize=3)
ax.text(b_x_intercept - 0.1, -0.0038, f'{b_x_intercept:.2f}',)

ax.text(.06, 0.025, r'$\mathcal{y=0.02x + 0.01}$', color='red', size=12, rotation=34)
ax.text(.11, 0.05, r'$\mathcal{y=0.07x + 0.02}$', color='darkred', size=12, rotation=66)

# Remove first y tick
labels = [str(round(i, 3)) for i in ax.get_yticks()]
labels[1] = labels[2] = ''
ax.set_yticklabels(labels)

labels = [str(round(i, 3)) for i in ax.get_xticks()]
labels[1] = ''
ax.set_xticklabels(labels)


ax.set_xlabel(r'$\frac{1}{[p-nitrophenol\ phosphate]\ (mM)}$', size=14)
ax.text(-1, 0.034, r'$\frac{1}{V_{max}(min\ mmol^{-1})}$', size=14)
ax = fig.add_subplot(122)
ax.set_title('Standard curve')
x_axis = np.linspace(0, 15, 100)

a_km = -1 / a_x_intercept
b_km = -1 / b_x_intercept

a_v_max = 1 / a_y_intercept
b_v_max = 1 / b_y_intercept

a_pred = np.array([(a_v_max * x) / (a_km + x) for x in x_axis])
b_pred = np.array([(b_v_max * x) / (b_km + x) for x in x_axis])

ax.plot(x_axis, a_pred, label='uninhibited', color='red')
ax.plot(x_axis, b_pred, label='competitive\ninhibition', color='darkred')

ax.axhline(a_v_max, linestyle='dashed')
ax.text(8, (a_v_max / 2) + 2,
        r'$\frac{V_{max}}{2} = $' + f'{a_v_max / 2:.2f}', color='red')

ax.text(8, (b_v_max / 2) + 2,
        r'$\frac{V_{max}}{2} = $' + f'{b_v_max / 2:.2f}', color='darkred')

a_s_con = x_axis[np.argmax(a_pred >= (a_v_max / 2))]
b_s_con = x_axis[np.argmax(b_pred >= (b_v_max / 2))]

ax.axhline(a_v_max / 2, linestyle='dashed', color='red')
ax.axhline(b_v_max / 2, linestyle='dashed', color='darkred')

ax.plot([a_km] * 2, [0, a_v_max / 2], linestyle='dashed', color='red', linewidth=1)
ax.plot([b_km] * 2, [0, b_v_max / 2], linestyle='dashed', color='darkred', linewidth=1)

ax.set_ylim(0, 80)
labels = [str(round(i, 3)) for i in ax.get_yticks()]
labels[-1] = ''
ax.set_yticklabels(labels)

ax.spines['left'].set_position('zero')
ax.spines['right'].set_color('none')
ax.spines['bottom'].set_position('zero')
ax.spines['top'].set_color('none')
ax.spines['left'].set_smart_bounds(True)
ax.spines['bottom'].set_smart_bounds(True)
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.legend(loc=(0.45, 0.15))
ax.set_xlabel(r'$p-nitrophenol\ phosphate\ (mM)$')
ax.set_ylabel(r'$V_{max}\ (nmol\ min^{-1})$')

# ax.plot(a_s_con, 0, color='black', marker='o', markersize=4)
ax.text(a_s_con + .2, 4, f'{a_km:.2f}', rotation='45')

# ax.plot(b_s_con, 0, color='black', marker='o', markersize=4)
ax.text(b_s_con + .2, 4, f'{b_km:.2f}', rotation='45')

fig.text(0.15, 0.01, 'https://gist.github.com/jamespeterschinner/059b2be1c69f1ebf9de1d0c09564279a', color='grey',
         size=8)
plt.savefig('lineweaver_burk', )
plt.show()