growthcurves

A Python package for fitting and analyzing microbial growth curves.

Supports logistic, Gompertz, Richards, and Baranyi parametric models with automatic growth statistics extraction (specific growth rate, doubling time, phase boundaries) and non-parametric methods (spline fitting and sliding window).

Web apps

This package powers two browser-based apps for human-in-the-loop growth curve analysis, hosted at https://biosustain.github.io/growthcurves_app/:

• MicroGrowth - analysis of microtiter plate reader experiments, with support for multi-condition layouts and interactive quality control.
• AutoGrowth - analysis of mini-bioreactor data (e.g. Pioreactor, Chi.Bio), built for continuous culture and real-time monitoring.

Installation

pip install growthcurves

For development:

pip install -e ".[dev]"

Quick start

import growthcurves as gc
import numpy as np

# Example time series (hours) and OD measurements
t = np.linspace(0, 24, 100)
N = 0.01 + 1.5 / (1 + np.exp(-0.5 * (t - 10)))  # synthetic logistic data

# Fit a model and extract growth statistics in one call.
# fit_model returns (fit_result, stats); it dispatches on the model name, so the
# same entry point works for parametric and non-parametric methods alike.
fit_result, stats = gc.fit_model(t, N, "mech_logistic")

print(f"Max OD:               {stats['max_od']:.3f}")
print(f"Specific growth rate: {stats['mu_max']:.4f} h⁻¹")
print(f"Doubling time:        {stats['doubling_time']:.2f} h")

# Or use a non-parametric spline fit
# smooth: "fast" (auto-default), "slow" (GCV), or a float (manual lambda)
spline_fit, spline_stats = gc.fit_model(t, N, "spline", smooth="fast")

print(f"\nSpline fit results:")
print(f"Specific growth rate: {spline_stats['mu_max']:.4f} h⁻¹")
print(f"Doubling time:        {spline_stats['doubling_time']:.2f} h")

giving output like:

Max OD:               1.554
Specific growth rate: 0.4610 h⁻¹
Doubling time:        1.50 h

Spline fit results:
Specific growth rate: 0.4247 h⁻¹
Doubling time:        1.63 h

Available models

We use the formulations as stated in

Ghenu A-H, Marrec L and Bank C (2024) Challenges and pitfalls of inferring microbial growth rates from lab cultures. Front. Ecol. Evol. 11:1313500. https://doi.org/10.3389/fevo.2023.1313500

Parametric models

Mechanistic models (ODE-based)

Model	Function	Parameters
Mech. Logistic	models.mech_logistic_model	mu, K, N0
Mech. Gompertz	models.mech_gompertz_model	mu, K, N0
Mech. Richards	models.mech_richards_model	mu, K, N0, beta
Mech. Baranyi	models.mech_baranyi_model	mu, K, N0, h0

Mechanistic models are defined as ordinary differential equations (ODEs) and fitted using numerical integration.

Phenomenological models (ln-space)

No N0 parameter is present in the phenomenological models. To apply a N0 constant use log_to_linear function to convert the log-space model output to linear space.

Model	Function	Parameters
Phenom. Logistic	models.phenom_logistic_model	A, mu_max, lam
Phenom. Gompertz	models.phenom_gompertz_model_ln	A, mu_max, lam
Phenom. Gompertz*	models.phenom_gompertz_modified_model_ln	A, mu_max, lam, alpha, t_shift
Phenom. Richards	models.phenom_richards_model	A, mu_max, lam, nu

Phenomenological models are fitted directly to ln(OD/OD0) data.

Non-parametric methods

Method	Function	Key parameters
Spline	non_parametric.fit_non_parametric	smooth, use_weights
Sliding window	non_parametric.fit_non_parametric	window_points

The spline method fits a smoothing spline to log-transformed OD data and calculates growth rate from the spline's derivative. Smoothing is controlled by smooth:

• "fast": automatic default lambda rule (fast)
• "slow": weighted GCV selection (slower)
• float: manual lambda value

The sliding window method estimates growth rate by fitting a linear regression to log-transformed data within a moving window, identifying the window with maximum slope.

Spline fitting (non-parametric)

The spline method provides a model-free approach to growth curve analysis by fitting a smoothing spline to log-transformed OD data:

1. Transform OD data: $y_{\text{log}} = \ln(N)$
2. Fit a cubic smoothing spline $s(t)$ to $(t, y_{\text{log}})$ using scipy.interpolate.make_smoothing_spline
3. Calculate specific growth rate: $\mu(t) = \frac{d,s(t)}{dt}$
4. Find maximum growth rate: $\mu_{\max} = \max_{t} \mu(t)$

Parameter	Meaning
smooth	"fast", "slow", or manual float lambda value
use_weights	Apply OD-dependent weighting (default: False)

When smooth is a float, higher values produce smoother curves and lower values follow the data more tightly.

Derived growth statistics

Statistic	Formula
Specific growth rate	$\mu = \dfrac{1}{N}\dfrac{dN}{dt}$
Doubling time	$t_d = \dfrac{\ln 2}{\mu_{\max}}$

Key features

• Parametric fitting - fit logistic, Gompertz, Richards, or Baranyi models with automatic parameter estimation
• Non-parametric methods - model-free growth rate estimation using:
  • Spline fitting - smoothing splines on log-transformed data with derivative-based growth rate calculation
  • Sliding window - moving window linear fits to log-transformed data
• Growth statistics - automatic extraction of max OD, specific growth rate (µ_max), doubling time, and exponential-phase boundaries
• Derivative analysis - first and second derivatives with Savitzky-Golay smoothing
• No-growth detection - automatic identification of non-growing samples
• Model comparison - RMSE fit-quality metric for comparing fits

Documentation and tutorial

An interactive tutorial notebook is available at docs/tutorial/analysis.ipynb. It covers model fitting, derivative analysis, parameter extraction, and cross-model comparison using a realistic microbial growth dataset.

Citation

If you use this package, please cite it as described in CITATION.cff.

License

GPL-3.0-or-later. See LICENSE.