A sigmoidal dose-response curve that plots biological response against drug concentration on a logarithmic x-axis, fitted using a four-parameter logistic (4PL) model. This visualization is essential for determining drug potency metrics such as EC50 (half-maximal effective concentration) or IC50 (half-maximal inhibitory concentration), Hill slope steepness, and upper/lower response asymptotes. It enables rapid visual comparison of compound efficacy and is a standard tool in pharmacological analysis.
""" anyplot.ai
curve-dose-response: Pharmacological Dose-Response Curve
Library: plotnine 0.15.7 | Python 3.13.14
Quality: 91/100 | Updated: 2026-06-24
"""
import os
import numpy as np
import pandas as pd
from plotnine import (
aes,
element_blank,
element_line,
element_rect,
element_text,
geom_errorbar,
geom_hline,
geom_line,
geom_point,
geom_ribbon,
geom_segment,
geom_text,
ggplot,
guide_legend,
guides,
labs,
scale_color_manual,
scale_fill_manual,
scale_x_log10,
scale_y_continuous,
theme,
theme_minimal,
)
from scipy.optimize import curve_fit
# Theme tokens (Imprint palette — theme-adaptive chrome)
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
IMPRINT_PALETTE = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477", "#99B314"]
_SUP = str.maketrans("0123456789", "⁰¹²³⁴⁵⁶⁷⁸⁹")
# Data
np.random.seed(42)
concentrations = np.logspace(-9, -4, 8)
compounds = ["Erlotinib", "Gefitinib"]
def logistic_4pl(x, bottom, top, ec50, hill):
return bottom + (top - bottom) / (1 + (ec50 / x) ** hill)
true_params = {
"Erlotinib": {"bottom": 5, "top": 95, "ec50": 1e-7, "hill": 1.2},
"Gefitinib": {"bottom": 10, "top": 85, "ec50": 5e-7, "hill": 0.9},
}
rows = []
for conc in concentrations:
resp_a = logistic_4pl(conc, **true_params["Erlotinib"]) + np.random.normal(0, 3)
resp_b = logistic_4pl(conc, **true_params["Gefitinib"]) + np.random.normal(0, 3.5)
rows.append(
{
"concentration": conc,
"response": resp_a,
"response_sem": np.random.uniform(1.5, 4.0),
"compound": "Erlotinib",
}
)
rows.append(
{
"concentration": conc,
"response": resp_b,
"response_sem": np.random.uniform(2.0, 4.5),
"compound": "Gefitinib",
}
)
df = pd.DataFrame(rows)
# Fit 4PL curves
fit_params = {}
for compound in compounds:
subset = df[df["compound"] == compound]
popt, pcov = curve_fit(
logistic_4pl, subset["concentration"].values, subset["response"].values, p0=[5, 90, 1e-6, 1.0], maxfev=10000
)
fit_params[compound] = {"popt": popt, "pcov": pcov}
# Generate smooth fitted curves with 95% CI via delta method
conc_smooth = np.logspace(-9.5, -3.5, 200)
fit_rows = []
for compound, params in fit_params.items():
popt = params["popt"]
pcov = params["pcov"]
fitted = logistic_4pl(conc_smooth, *popt)
jacobian = np.zeros((len(conc_smooth), 4))
eps = 1e-8
for i in range(4):
popt_up, popt_dn = popt.copy(), popt.copy()
popt_up[i] += eps
popt_dn[i] -= eps
jacobian[:, i] = (logistic_4pl(conc_smooth, *popt_up) - logistic_4pl(conc_smooth, *popt_dn)) / (2 * eps)
se = np.sqrt(np.maximum(np.sum(jacobian @ pcov * jacobian, axis=1), 0))
for j, c in enumerate(conc_smooth):
fit_rows.append(
{
"concentration": c,
"fitted": fitted[j],
"ci_lower": fitted[j] - 1.96 * se[j],
"ci_upper": fitted[j] + 1.96 * se[j],
"compound": compound,
}
)
df_fit = pd.DataFrame(fit_rows)
# EC50 reference data
colors = {"Erlotinib": IMPRINT_PALETTE[0], "Gefitinib": IMPRINT_PALETTE[1]}
ec50_rows = []
for compound, params in fit_params.items():
bottom, top, ec50, hill = params["popt"]
ec50_rows.append(
{
"compound": compound,
"ec50": ec50,
"half_response": bottom + (top - bottom) / 2,
"bottom": bottom,
"top": top,
"x_start": 1e-10,
}
)
df_ec50 = pd.DataFrame(ec50_rows)
# EC50 annotation labels — staggered to prevent crowding
ec50_labels = []
for i, (_, row) in enumerate(df_ec50.iterrows()):
ec50_val = row["ec50"]
exp = int(np.floor(np.log10(ec50_val)))
mantissa = ec50_val / 10**exp
exp_str = str(abs(exp)).translate(_SUP)
label = f"EC₅₀={mantissa:.1f}×10⁻{exp_str} M"
# Erlotinib: left of EC50, above midpoint; Gefitinib: right of EC50, below midpoint
x_pos = ec50_val * 0.12 if i == 0 else ec50_val * 6
y_pos = row["half_response"] + 10 if i == 0 else row["half_response"] - 12
ec50_labels.append({"concentration": x_pos, "response": y_pos, "label": label, "compound": row["compound"]})
df_ec50_labels = pd.DataFrame(ec50_labels)
# Plot
plot = (
ggplot()
+ geom_ribbon(aes(x="concentration", ymin="ci_lower", ymax="ci_upper", fill="compound"), data=df_fit, alpha=0.18)
+ geom_line(aes(x="concentration", y="fitted", color="compound"), data=df_fit, size=1.0)
+ geom_errorbar(
aes(x="concentration", ymin="response - response_sem", ymax="response + response_sem", color="compound"),
data=df,
width=0.08,
size=0.4,
)
+ geom_point(aes(x="concentration", y="response", color="compound"), data=df, size=2.5, fill="white", stroke=0.8)
)
# EC50 reference lines
for _, row in df_ec50.iterrows():
col = colors[row["compound"]]
rd = pd.DataFrame([row])
plot = (
plot
+ geom_segment(
aes(x="ec50", xend="ec50", y=0, yend="half_response"),
data=rd,
linetype="dashed",
color=col,
size=0.5,
alpha=0.5,
)
+ geom_segment(
aes(x="x_start", xend="ec50", y="half_response", yend="half_response"),
data=rd,
linetype="dashed",
color=col,
size=0.5,
alpha=0.5,
)
)
# EC50 value annotations
plot = plot + geom_text(
aes(x="concentration", y="response", label="label", color="compound"),
data=df_ec50_labels,
size=3.0,
ha="left",
fontweight="bold",
)
# Top/bottom asymptote reference lines
for _, row in df_ec50.iterrows():
col = colors[row["compound"]]
plot = (
plot
+ geom_hline(yintercept=row["top"], linetype="dotted", color=col, size=0.4, alpha=0.3)
+ geom_hline(yintercept=row["bottom"], linetype="dotted", color=col, size=0.4, alpha=0.3)
)
# Scales and style
plot = (
plot
+ scale_x_log10(
labels=lambda vals: [f"10⁻{str(abs(int(round(np.log10(v))))).translate(_SUP)}" if v > 0 else "" for v in vals]
)
+ scale_y_continuous(breaks=range(0, 101, 20), limits=(-5, 110))
+ scale_color_manual(values=colors)
+ scale_fill_manual(values=colors)
+ labs(
x="Concentration (M)",
y="Response (%)",
title="curve-dose-response · python · plotnine · anyplot.ai",
color="Compound",
fill="Compound",
)
+ guides(color=guide_legend(override_aes={"size": 3}), fill=guide_legend(title="Compound"))
+ theme_minimal()
+ theme(
figure_size=(8, 4.5),
text=element_text(size=7, color=INK),
axis_title=element_text(size=10, color=INK),
axis_text=element_text(size=8, color=INK_SOFT),
plot_title=element_text(size=12, color=INK),
legend_title=element_text(size=9, color=INK),
legend_text=element_text(size=8, color=INK_SOFT),
legend_position=(0.82, 0.22),
legend_background=element_rect(fill=ELEVATED_BG, color=INK_SOFT),
legend_key_size=12,
panel_grid_major_x=element_blank(),
panel_grid_minor=element_blank(),
panel_grid_major_y=element_line(color=INK, size=0.2, alpha=0.15),
axis_line=element_line(color=INK_SOFT, size=0.4),
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_background=element_rect(fill=PAGE_BG),
)
)
# Save
plot.save(f"plot-{THEME}.png", dpi=400, width=8, height=4.5, units="in", verbose=False)
Part of Pharmacological Dose-Response Curve on anyplot.ai.