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: plotly 6.8.0 | Python 3.13.14
Quality: 89/100 | Updated: 2026-06-24
"""
import os
import numpy as np
import plotly.graph_objects as go
from scipy.optimize import curve_fit
THEME = os.getenv("ANYPLOT_THEME", "light")
# Theme-adaptive chrome (Imprint palette)
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"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
GRID = "rgba(26,26,23,0.15)" if THEME == "light" else "rgba(240,239,232,0.15)"
# Imprint categorical palette — positions 1 and 2
COLORS = ["#009E73", "#C475FD"]
# --- Data ---
np.random.seed(42)
concentrations = np.logspace(-9, -4, 8)
compound_names = ["Compound A", "Compound B"]
ec50_true = [1e-7, 5e-7]
hill_true = [1.2, 0.9]
top_true = [100, 95]
bottom_true = [5, 10]
raw_data = {}
for i, name in enumerate(compound_names):
responses = []
sems = []
for conc in concentrations:
true_resp = bottom_true[i] + (top_true[i] - bottom_true[i]) / (1 + (ec50_true[i] / conc) ** hill_true[i])
reps = true_resp + np.random.normal(0, 3, 3)
responses.append(np.mean(reps))
sems.append(np.std(reps, ddof=1) / np.sqrt(3))
raw_data[name] = {"concentrations": concentrations, "responses": np.array(responses), "sems": np.array(sems)}
def logistic_4pl(x, bottom, top, ec50, hill):
return bottom + (top - bottom) / (1 + (ec50 / x) ** hill)
fit_results = {}
conc_fine = np.logspace(-9.5, -3.8, 300)
for i, name in enumerate(compound_names):
popt, pcov = curve_fit(
logistic_4pl,
raw_data[name]["concentrations"],
raw_data[name]["responses"],
p0=[bottom_true[i], top_true[i], ec50_true[i], hill_true[i]],
maxfev=10000,
)
perr = np.sqrt(np.diag(pcov))
fit_results[name] = {"popt": popt, "perr": perr}
# --- Plot ---
fig = go.Figure()
for i, name in enumerate(compound_names):
popt = fit_results[name]["popt"]
bottom, top, ec50, hill = popt
color = COLORS[i]
fitted_curve = logistic_4pl(conc_fine, *popt)
# 95% CI band for Compound A
if i == 0:
perr = fit_results[name]["perr"]
upper = logistic_4pl(conc_fine, bottom - perr[0], top + perr[1], ec50, hill)
lower = logistic_4pl(conc_fine, bottom + perr[0], top - perr[1], ec50, hill)
r, g, b = int(color[1:3], 16), int(color[3:5], 16), int(color[5:7], 16)
fill_alpha = 0.18 if THEME == "light" else 0.25
fig.add_trace(
go.Scatter(x=conc_fine, y=upper, mode="lines", line={"width": 0}, showlegend=False, hoverinfo="skip")
)
fig.add_trace(
go.Scatter(
x=conc_fine,
y=lower,
mode="lines",
line={"width": 0},
fill="tonexty",
fillcolor=f"rgba({r},{g},{b},{fill_alpha})",
showlegend=False,
hoverinfo="skip",
)
)
# Fitted sigmoid curve
fig.add_trace(
go.Scatter(
x=conc_fine,
y=fitted_curve,
mode="lines",
name=f"{name} (EC₅₀ = {ec50:.2e} M)",
line={"color": color, "width": 3},
hovertemplate=(f"<b>{name}</b><br>Conc: %{{x:.2e}} M<br>Response: %{{y:.1f}}%<extra></extra>"),
)
)
# Data points with SEM error bars
fig.add_trace(
go.Scatter(
x=raw_data[name]["concentrations"],
y=raw_data[name]["responses"],
mode="markers",
name=f"{name} data",
marker={"size": 10, "color": color, "line": {"color": PAGE_BG, "width": 2}},
error_y={"type": "data", "array": raw_data[name]["sems"], "visible": True, "color": color, "thickness": 2},
showlegend=False,
hovertemplate=(
f"<b>{name}</b><br>Conc: %{{x:.2e}} M<br>Response: %{{y:.1f}} ± %{{error_y.array:.1f}}%<extra></extra>"
),
)
)
# EC50 dashed crosshair reference lines
half_response = bottom + (top - bottom) / 2
fig.add_shape(
type="line", x0=ec50, x1=ec50, y0=-5, y1=half_response, line={"color": color, "width": 1.5, "dash": "dash"}
)
fig.add_shape(
type="line",
x0=1e-10,
x1=ec50,
y0=half_response,
y1=half_response,
line={"color": color, "width": 1.5, "dash": "dash"},
)
# EC50 annotation with arrow
fig.add_annotation(
x=np.log10(ec50),
y=half_response + 5 + i * 8,
text=f"<b>EC₅₀ = {ec50:.2e} M</b>",
showarrow=True,
arrowhead=2,
arrowsize=1,
arrowwidth=1.5,
arrowcolor=color,
ax=40 + i * 30,
ay=-30 - i * 10,
font={"size": 10, "color": color},
bordercolor=color,
borderwidth=1.5,
borderpad=4,
bgcolor=ELEVATED_BG,
)
# Top and bottom asymptote dotted reference lines
fig.add_shape(
type="line", x0=1e-10, x1=1e-3, y0=top_true[0], y1=top_true[0], line={"color": INK_MUTED, "width": 1, "dash": "dot"}
)
fig.add_shape(
type="line",
x0=1e-10,
x1=1e-3,
y0=bottom_true[0],
y1=bottom_true[0],
line={"color": INK_MUTED, "width": 1, "dash": "dot"},
)
# Asymptote labels (placed within axis range)
fig.add_annotation(
x=-4.2, y=top_true[0], text="Top asymptote", showarrow=False, font={"size": 10, "color": INK_MUTED}, yshift=10
)
fig.add_annotation(
x=-4.2,
y=bottom_true[0],
text="Bottom asymptote",
showarrow=False,
font={"size": 10, "color": INK_MUTED},
yshift=-12,
)
# --- Layout ---
fig.update_layout(
autosize=False,
width=800,
height=450,
margin={"l": 80, "r": 40, "t": 80, "b": 60},
title={
"text": "<b>curve-dose-response · python · plotly · anyplot.ai</b>",
"font": {"size": 16, "color": INK, "family": "Arial, Helvetica, sans-serif"},
"x": 0.5,
"xanchor": "center",
},
xaxis={
"title": {"text": "Concentration (M)", "font": {"size": 12, "color": INK}},
"type": "log",
"tickfont": {"size": 10, "color": INK_SOFT},
"showgrid": False,
"showline": False,
"range": [-9.5, -3.8],
},
yaxis={
"title": {"text": "Response (%)", "font": {"size": 12, "color": INK}},
"tickfont": {"size": 10, "color": INK_SOFT},
"showgrid": True,
"gridcolor": GRID,
"gridwidth": 0.5,
"range": [-5, 115],
"zeroline": False,
"showline": False,
},
template="plotly_white",
paper_bgcolor=PAGE_BG,
plot_bgcolor=PAGE_BG,
font={"color": INK},
legend={
"font": {"size": 10, "color": INK_SOFT},
"x": 0.02,
"y": 0.98,
"bgcolor": ELEVATED_BG,
"bordercolor": INK_SOFT,
"borderwidth": 1,
"traceorder": "normal",
},
updatemenus=[
{
"type": "dropdown",
"direction": "down",
"showactive": True,
"x": 0.99,
"xanchor": "right",
"y": 0.01,
"yanchor": "bottom",
"bgcolor": ELEVATED_BG,
"bordercolor": INK_SOFT,
"font": {"color": INK_SOFT, "size": 10},
"buttons": [
{
"label": "Both Compounds",
"method": "update",
"args": [{"visible": [True, True, True, True, True, True]}],
},
{
"label": "Compound A only",
"method": "update",
"args": [{"visible": [True, True, True, True, False, False]}],
},
{
"label": "Compound B only",
"method": "update",
"args": [{"visible": [False, False, False, False, True, True]}],
},
],
}
],
)
# --- Save ---
fig.write_image(f"plot-{THEME}.png", width=800, height=450, scale=4)
fig.write_html(f"plot-{THEME}.html", include_plotlyjs="cdn")
Part of Pharmacological Dose-Response Curve on anyplot.ai.