Fitting of data to homodimer formation

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

We define the known experimental data bellow:

xcoords = np.array([0.0,2,4,6,8,10])
ycoords = np.array([0., 0.22, 0.71, 1.24,1.88,2.48])

Construct the PyBindingCurve object, operating on a homodimer formation system and add experimental data to the plot:

mySystem = pbc.BindingCurve("homodimer formation")
mySystem.add_scatter(xcoords, ycoords)

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

system_parameters = {"p": xcoords}

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, {"kdpp": 0}, ycoords)

Print out the fitted parameters:

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

Producing:

Fit: kdpp=9.939776196471206 +/- 0.15729785759220752

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()

Producing:

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