growthcurves 0.0.1

A package for fitting and analyzing microbial growth curves.

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 a non-parametric sliding-window method.

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
time = np.linspace(0, 24, 100)
od = 0.01 + 1.5 / (1 + np.exp(-0.5 * (time - 10)))  # synthetic logistic data

# Fit a model and extract growth statistics
fit_result = gc.fitting_functions.fit_model(time, od, model_type="logistic")
stats = gc.fitting_functions.extract_stats_from_fit(fit_result)

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

Available models

Model	Function	Parameters
Logistic	models.logistic_model	K, y0, r, t0
Gompertz	models.gompertz_model	K, y0, mu_max, lam
Richards	models.richards_model	K, y0, r, t0, nu

The Richards model generalizes both logistic (nu = 1) and Gompertz (nu → 0) growth curves via its shape parameter nu.

Logistic

$$ N(t) = y_0 + \frac{K - y_0}{1 + \exp!\bigl[-r,(t - t_0)\bigr]} $$

Parameter	Meaning
$K$	Carrying capacity (maximum OD)
$y_0$	Baseline OD at $t=0$
$r$	Growth rate constant (h⁻¹); equals $\mu_{\max}$
$t_0$	Inflection time

Gompertz (modified)

$$ N(t) = y_0 + (K - y_0),\exp!\left[-\exp!\left(\frac{\mu_{\max},e}{K - y_0},(\lambda - t) + 1\right)\right] $$

Parameter	Meaning
$K$	Carrying capacity (maximum OD)
$y_0$	Baseline OD
$\mu_{\max}$	Maximum specific growth rate (h⁻¹)
$\lambda$	Lag time (h)

Richards (generalized logistic)

$$ N(t) = y_0 + (K - y_0),\bigl[1 + \nu,\exp!\bigl(-r,(t - t_0)\bigr)\bigr]^{-1/\nu} $$

Parameter	Meaning
$K$	Carrying capacity (maximum OD)
$y_0$	Baseline OD
$r$	Growth rate constant (h⁻¹)
$t_0$	Inflection time
$\nu$	Shape parameter ($\nu=1 \Rightarrow$ logistic; $\nu\to 0 \Rightarrow$ Gompertz)

The maximum specific growth rate for the Richards model is $\mu_{\max} = r,/,(1+\nu)^{1/\nu}$.

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
• Sliding-window method — non-parametric growth rate estimation via sliding window fits to log-tranformed 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/tutorial.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.