growthcurves

A Python package for fitting and analyzing microbial growth curves.

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

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 parametric model and extract growth statistics
fit_result = gc.parametric.fit_parametric(t, N, method="mech_logistic")
stats = gc.inference.extract_stats(fit_result, t, N)

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
spline_fit = gc.non_parametric.fit_non_parametric(t, N, umax_method="spline")
spline_stats = gc.inference.extract_stats(spline_fit, t, N)

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")

Available models

Parametric models

Mechanistic models (ODE-based)

Model	Function	Parameters
Mech. Logistic	models.mech_logistic_model	mu, K, N0, y0
Mech. Gompertz	models.mech_gompertz_model	mu, K, N0, y0
Mech. Richards	models.mech_richards_model	mu, K, N0, beta, y0
Mech. Baranyi	models.mech_baranyi_model	mu, K, N0, h0, y0

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

Phenomenological models (ln-space)

Model	Function	Parameters
Phenom. Logistic	models.phenom_logistic_model	A, mu_max, lam, N0
Phenom. Gompertz	models.phenom_gompertz_model	A, mu_max, lam, N0
Phenom. Gompertz*	models.phenom_gompertz_modified_model	A, mu_max, lam, alpha, t_shift, N0
Phenom. Richards	models.phenom_richards_model	A, mu_max, lam, nu, N0

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

Non-parametric methods

Method	Function	Key parameters
Spline	non_parametric.fit_non_parametric	spline_s (smoothing)
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. This provides a flexible, model-free approach that adapts to the data shape. The smoothing parameter spline_s controls the balance between fit quality and smoothness (default: 0.01 for tight fit to data).

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.UnivariateSpline
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
spline_s	Smoothing factor (default: 0.01)
k	Spline degree (default: 3, cubic)

The smoothing parameter spline_s controls the tradeoff between fit quality and smoothness. Lower values produce tighter fits to data; higher values produce smoother curves. The default of 0.01 produces a tight fit that closely follows the data, which can be increased for noisier datasets.

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, or Richards 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.