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

# Fit a parametric model and extract growth statistics
fit_result = gc.parametric.fit_parametric(time, od, model="logistic")
stats = gc.utils.extract_stats_from_fit(fit_result, time, od)

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")

# Or use a non-parametric spline fit
spline_fit = gc.non_parametric.fit_non_parametric(time, od, umax_method="spline")
spline_stats = gc.utils.extract_stats_from_fit(spline_fit, time, od)

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

Available models

Parametric 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.

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: 0.1 × number of points).

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.

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 $\mu_{\max} = r,/,(1+\nu)^{1/\nu}$.

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: $0.1 \times n_{\text{points}}$)
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 automatic default typically works well but can be adjusted for noisy or sparse data.

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/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.