Fitting to 1:1:1 competition

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Using experimental competition data, we may obtain system parameters, such as inhibitor KD. Example code is available here: https://github.com/stevenshave/pybindingcurve/blob/master/example_competition_fit.py

Perform the standard imports:

import numpy as np
import pybindingcurve as pbc

We can choose to work in a common unit, typically nM, or µM, as long as all numbers are in the same unit, the result is valid. We assume µM for all concentrations bellow.

Using the following experimental data: |[P] µM | 0|4.2|8.4|16.8|21.1|31.6|35.8|40.0| |—|—|—|—|—|—|—|—|—| Signal|150|330|1050|3080|4300|6330|6490|6960|

Define x and y coordinates from experimental data:

xcoords = np.array([0.0, 4.2, 8.4, 16.8, 21.1, 31.6, 35.8, 40.0])
ycoords = np.array([150, 330, 1050, 3080, 4300, 6330, 6490, 6960])

Construct the PyBindingCurve object, operating on a 1:1:1 (compeittion) system and add experimental data to the plot:

mySystem = pbc.BindingCurve("1:1:1")
mySystem.add_scatter(xcoords, ycoords)

Known system parameters, kdpl will be added to this by fitting:

system_parameters = {"p": xcoords, "l": 10, "i": 10, "kdpl": 10}

Now we call fit, passing the known parameters, followed by a dict of parameters to be fitted along with an initial guess, pass the ycoords, and what the readout (ycoords) is:

fitted_system, fit_accuracy = mySystem.fit(system_parameters, {"kdpi": 0}, ycoords)

Print out the fitted parameters:

for k, v in fit_accuracy.items():
    print(f"Fit: {k}={fitted_system[k]} +/- {v}")

Assign more points to ‘p’ to make a smooth plot:

fitted_system["p"] = np.linspace(0, np.max(xcoords))

Add a new curve, simulated using fitted parameters to our BindingCurve object and show the plot:

mySystem.add_curve(fitted_system)
mySystem.show_plot()

Which results in the following output and plot:

Fit: kdpi=0.44680894202996824 +/- 0.10384753604598472

Fit: ymax=9920.875421523158 +/- 98.92963212643627

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