4-parameter logistic curve fit

I am trying to perform a 4-parameter logistic (4PL) curve fit with scipy on data from a scientific assay. The goal is to get a fit that closely matches the results of the software I normally use.

Unfortunately, the lower part of the curve does not fit well, as shown in this figure.

I also tried to create a fit after applying a log10 transform to the x values, but I only get a straight line instead of a curve fit.

Below is my current code:

import numpy as np
import matplotlib.pyplot as plt
import scipy.optimize as opt
from scipy.optimize import curve_fit

conc = np.array([300000, 70376.8, 16509.6, 3873.0, 908.6, 213.1, 50.0, 11.7])

ref = np.array([7.11469e+05, 2.16006e+05, 5.81840e+04, 1.39850e+04,
                3.21300e+03, 8.76000e+02, 2.54000e+02, 1.16000e+02])

# 4pl curve equation
def func(xdata, a, b, c, d): 
    return ((a-d)/(1.0+((xdata/c)**b))) + d

# Calculate example weights as 1/y^2
weights = 1 / (ref **2)

#set bounds
amin = 50 
bounds = ([ amin, -np.inf, -np.inf , -np.inf], [np.inf, np.inf, np.inf, np.inf])


# initial params
a = min(ref) * 0.9
d = max(ref) * 1.1
b = 1
c = (d-a)/2    
initial_guess = [a, b, c, d] 
print('Initial params:', initial_guess)


# # Perform the curve fit
params, params_covariance = curve_fit(func, conc, ref, p0=initial_guess, method='trf',sigma=weights, bounds=bounds, maxfev=100000)
print('params:', params)


# Generate y values from the fitted curve
x_fit = np.arange(min(conc), max(conc), 8) 
y_fit = func(x_fit, *params)

# # Plot the raw data and the fitted curve
#plt.scatter(conc_mlt, ref, label='Raw data')
plt.scatter(conc, ref , label='Weighted Data') #s=weights*100??
plt.plot(x_fit, y_fit, label='Fitted Curve')
plt.xscale('log')
plt.yscale('log')
plt.xlabel('X')
plt.ylabel('Y')
plt.legend()
plt.show()

I'm currently unsure of how to improve the fit of your lower values using scipy. However, if you don't require the use of your specific fitting function, you could potentially look at options like numpy.polyfit. Here is an example in case this could work for you:

import numpy as np
import matplotlib.pyplot as plt

conc = np.array([300000, 70376.8, 16509.6, 3873.0, 908.6, 213.1, 50.0, 11.7])

ref = np.array([7.11469e+05, 2.16006e+05, 5.81840e+04, 1.39850e+04,
                3.21300e+03, 8.76000e+02, 2.54000e+02, 1.16000e+02])

## Trying NumPy Polyfit
np_fit = np.poly1d(np.polyfit(np.log(conc), np.log(ref), deg=4))
x_npfits = np.logspace(1, 6)
y_npfits = []
for i in x_npfits:
    y_npfits.append(np.exp(np_fit(np.log(i))))

plt.figure()
plt.scatter(conc, ref , label='Weighted Data')
plt.plot(x_npfits, y_npfits)
plt.xscale('log')
plt.yscale('log')
plt.grid("both")
plt.show()

Produces: