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)#

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`	`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:

Transform OD data: \(y_{\text{log}} = \ln(N)\)
Fit a cubic smoothing spline \(s(t)\) to \((t, y_{\text{log}})\) using scipy.interpolate.make_smoothing_spline
Calculate specific growth rate: \(\mu(t) = \frac{d\,s(t)}{dt}\)
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: `True`)

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.

growthcurves

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