# Constrain fit parameters to a range of reasonable values¶

So far we have looked at allowing the top and bottom to either be free parameters or fixed values, and let the slope of the curve be fit as a free parameter.

But in some cases, you may want to not let these be entirely free parameters, but also not fix them—but rather constrain them to a reasonable range. For instance, maybe constraining the top to be between 0.75 and 1. Likewise, sometimes you can end up with the slope being fit to an extremely steep or shallow value, so it can also be useful to constrain the slope.

Note that when constraining these parameters, especially the slope, you need to make sure you are choosing a reasonable range. For the slope, what is a reasonable range will depend on the units used for concentration, as well as inherent properties of the serum or antibody in question.

To constrain these parameters, you can use the fixtop, fixbottom, and fixslope parameters to HillCurve or CurveFits. Each of these can be: - False: fit as a free parameter - A single number: value is constrained to this number - A 2-tuple giving the min max range (eg, (0.8, 1)), in which case the value is constrained to this range.

Here is an example.

First, import Python modules:

[1]:

import matplotlib.pyplot as plt

import neutcurve

import pandas as pd


Now we read some example data and fit it with the top and the slope either free (eg, fixtop=False) or constrained to a range (eg, fixtop=(0.8, 1.0)). The curves are then plotted for each type of fitting:

[2]:

# NBVAL_IGNORE_OUTPUT

fit_params = []

for group, group_data in data.groupby("serum"):
for desc, fixtop, fixslope in [
("free top", False, False),
("top constrained to [0.8, 1.0], slope to [1, 2]", (0.8, 1), (1, 2)),
]:
fits = neutcurve.CurveFits(group_data, fixtop=fixtop, fixslope=fixslope)

fig, _ = fits.plotReplicates(
sera=[group],
attempt_shared_legend=False,
legendfontsize=8,
heightscale=1.1,
widthscale=1.1,
subplot_titles="{virus}",
)
_ = fig.suptitle(
f"{group} fit with {desc}",
y=0.95,
fontsize=16,
fontweight="bold",
)
fig.tight_layout()
display(fig)
plt.close(fig)

if desc != "free top":
fit_params.append(
fits.fitParams(average_only=False, no_average=True)
.assign(fit_method=desc)
.drop(columns=["nreplicates", "ic50_str", "midpoint_bound"])
)
print("\n\n")

fit_params = pd.concat(fit_params, ignore_index=True)
fit_params = fit_params[
["fit_method"] + [c for c in fit_params.columns if c != "fit_method"]
]
if fit_params["fit_method"].nunique() == 1:
fit_params = fit_params.drop(columns="fit_method")




/home/jbloom/neutcurve/neutcurve/hillcurve.py:1177: RuntimeWarning: invalid value encountered in power
return b + (t - b) / (1 + (c / m) ** s)
/home/jbloom/neutcurve/neutcurve/hillcurve.py:1177: RuntimeWarning: divide by zero encountered in divide
return b + (t - b) / (1 + (c / m) ** s)





Tabulate the actual fit parameters for each setting:

[3]:

for serum_group, df in fit_params.groupby("serum"):
print(f"\nFit params for {serum_group}")
display(
df.drop(columns="serum").map(
lambda x: f"{x:.2g}" if isinstance(x, float) else x
)
)


Fit params for problematic slopes

virus replicate ic50 ic50_bound midpoint midpoint_bound_type slope top bottom r2 rmsd
0 A/Bangkok/P3755/2023 plate11_r32_75k-CGCAAGGGATACTAAC 0.0009 interpolated 0.001 interpolated 1 0.94 0 0.86 0.12
1 A/Bangkok/P3755/2023 plate11_r32_75k-TAGCTGGGCAAAGGCT 0.0015 interpolated 0.0022 interpolated 1.4 0.8 0 0.67 0.19
2 A/Bangkok/P3755/2023 plate11_r32_75k-TATCATTTCATCTACA 0.00051 interpolated 0.0006 interpolated 1 0.92 0 0.95 0.061
3 A/Chipata/15-NIC-001/2023 plate11_r32_75k-CAGTGCCATCCATCCA 0.00085 interpolated 0.0011 interpolated 1.1 0.9 0 0.87 0.11
4 A/Chipata/15-NIC-001/2023 plate11_r32_75k-CGTATAACTGACGATT 0.0005 interpolated 0.00082 interpolated 1 0.81 0 0.87 0.092
5 A/Chipata/15-NIC-001/2023 plate11_r32_75k-TTTCATATAATTTGAG 0.00034 interpolated 0.00054 interpolated 1 0.82 0 0.95 0.056
6 A/Oman/3011/2023 plate11_r32_75k-AATAGGCCCAAATCCA 0.00094 interpolated 0.0013 interpolated 1 0.87 0 0.52 0.2
7 A/Oman/3011/2023 plate11_r32_75k-TACGAAAATCAAGAGC 0.00035 interpolated 0.00059 interpolated 1 0.8 0 0.35 0.15
8 A/Oman/3011/2023 plate11_r32_75k-TCCTTTAACTAATCGA 0.00021 interpolated 0.00027 interpolated 1.2 0.87 0 0.97 0.043

Fit params for problematic tops

virus replicate ic50 ic50_bound midpoint midpoint_bound_type slope top bottom r2 rmsd
9 A/Catalonia/NSVH102124476/2023 plate11_r32_75k-AATATACCGGCACTAC 0.002 interpolated 0.0025 interpolated 2 0.83 0 0.83 0.14
10 A/Catalonia/NSVH102124476/2023 plate11_r32_75k-ACTGAACAGTATAACT 0.0006 interpolated 0.00097 interpolated 1.1 0.8 0 0.93 0.067
11 A/Catalonia/NSVH102124476/2023 plate11_r32_75k-CTAAGGGCCTGTTCTT 0.0012 interpolated 0.0014 interpolated 1.5 0.9 0 0.92 0.091
12 A/Hong_Kong/2671/2019 plate11_r32_75k-CGAAAACATTACAAAT 0.00022 interpolated 0.00022 interpolated 2 1 0 0.85 0.17
13 A/Hong_Kong/2671/2019 plate11_r32_75k-CGGGAATCTCCCATAC 0.00011 interpolated 0.00011 interpolated 2 1 0 0.77 0.16
14 A/Hong_Kong/2671/2019 plate11_r32_75k-TTCATCAAGTTGGTGC 0.0001 interpolated 0.0001 interpolated 2 1 0 0.85 0.11
15 A/Hong_Kong/4801/2014_(15/192) plate11_r32_75k-CACAGACAATAAAAAA 7.8e-05 upper 4.8e-05 upper 2 1 0 0.99 0.0091
16 A/Hong_Kong/4801/2014_(15/192) plate11_r32_75k-GGTTAACTTTGGAAGC 7.8e-05 upper 4.4e-05 upper 2 1 0 0.93 0.023
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