In [1]:

    

%pylab inline

import numpy as np
import scipy
import math


    

    




Populating the interactive namespace from numpy and matplotlib

In [2]:

    

def calc_abc(kd, p_total, l_total, alpha):
    a = 2.0 * kd / alpha + 2.0 * l_total - p_total
    b = (math.pow(kd, 2.0) + 2 * kd * l_total - 2 * kd * p_total) / alpha
    c = -1 * (math.pow(kd, 2) * p_total) / alpha
    return a, b, c


    

In [3]:

    

def calc_qr(a, b, c):
    q = (3 * b - math.pow(a, 2.0)) / 9
    r = (9 * a * b - 27 * c - 2 * math.pow(a, 3.0)) / 54
    return q, r


    

In [4]:

    

def cartesian_cubic(a, q, r):
    first = -1 * a / 3.0
    second = math.pow(r + math.pow(math.pow(q, 3.0) + math.pow(r, 2.0), 0.5), 1.0 / 3.0)
    third = math.pow(r - math.pow(math.pow(q, 3.0) + math.pow(r, 2.0), 0.5), 1.0 / 3.0)
    return first + second + third

def polar_cubic(a, q, r):
    theta =  math.acos(r / math.pow(-1 * math.pow(q, 3), 1.0 / 2.0))
    return math.cos(theta / 3.0) * math.pow(-1 * q, 1.0 / 2.0) * 2 - (a / 3.0)


    

In [5]:

    

def model(kd, p_total, l_total, alpha):
    a, b, c = calc_abc(kd, p_total, l_total, alpha)
    q, r = calc_qr(a, b, c)
    #Use of cartesian or cubic depends on Q^3 + R^2
    if math.pow(q, 3.0) + math.pow(r, 2.0) > 0:
         return cartesian_cubic(a,q,r)
    else:
        print(polar_cubic(a, q, r))
        return polar_cubic(a, q, r)


    

In [6]:

    

#Normalize all values to uM
kd = 1
p_total = .1
alpha = 1

#Create the plot
plot = pylab.figure().add_subplot(111)

lig_range = [0.00001 * math.pow(10, lig_val) for lig_val in np.linspace(1, 10, 91)]
model_vals = [model(kd, p_total, l_total, alpha) / p_total for l_total in lig_range]

plot.plot(lig_range, model_vals)
plot.set_ylabel('[P]')
plot.set_xscale('log')
plot.set_xlabel(r'Ligand (uM)')
plot.grid()


    

    




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