Pepkio Doubling Time Tracker

A Python client and quantitative kinetics toolkit for calculating cell culture doubling times, specific growth rates ($\mu$), and generation times using two-point estimations or multi-point log-linear regression analysis.

What It Does

Tracking population growth kinetics is essential across mammalian cell culture, microbial fermentations, and proliferation bioassays. Routine spreadsheet formulas often introduce calculation errors through mismatched logarithm bases, lack standard error boundaries, or fail to handle multi-timepoint noise.

This package connects to the Pepkio Tools API engine to perform verified cell growth calculations. Input initial and final measurements or multi-timepoint series using cell counts, optical density ($OD_{600}$), percentage confluency, or relative signal units to receive doubling time ($T_d$), specific growth rate ($\mu$), generation time ($g$), and regression goodness-of-fit metrics ($R^2$).

Programmatic execution requires an active network connection and a free Pepkio API key.

Features

• Dual Fitting Modes: Computes rapid two-point growth estimates and multi-point time-series log-linear regressions.
• Flexible Input Metrics: Accepts direct cell counts (cells/mL), optical density ($OD_{600}$), percentage confluency (0–100%), and relative absorbance or fluorescence units.
• Complete Kinetic Derivations: Reports doubling time ($T_d$), specific growth rate ($\mu$), generation time ($g$), and cell divisions per hour or day.
• Goodness-of-Fit Analysis: Evaluates linear fit quality with $R^2$, slope standard error, and residual metrics.
• Automated Unit Conversion: Standardizes time inputs given in minutes, hours, or days to unified hourly rates.
• Automated Quality Control: Flags non-positive inputs, insufficient data points, poor linear fit ($R^2 < 0.90$), and biologically implausible growth rates.
• Programmatic & CLI Interfaces: Accessible via the PepkioClient Python SDK or the pepkio-doubling-time-tracker command-line utility.

Installation

Install the package via pip:

pip install pepkio-doubling-time-tracker

Set your API key as an environment variable before invoking API methods:

export PEPKIO_API_KEY="your-api-key"

Obtain an API key from your Pepkio Account.

Quick Example

from pepkio_doubling_time_tracker import PepkioClient

with PepkioClient() as client:
    # Run multi-point time-series log-linear regression
    sample_input = {
        "mode": "time_series",
        "metric": "cell_count",
        "time_unit": "h",
        "sample_label": "HeLa Proliferation Assay",
        "time_series": [
            {"t": 0, "value": 100000},
            {"t": 12, "value": 141000},
            {"t": 24, "value": 200000},
            {"t": 36, "value": 282000},
            {"t": 48, "value": 400000},
        ],
    }
    result = client.run(sample_input)

    fit = result.result["fit"]
    print(f"Doubling Time: {fit['doubling_time_h']:.2f} hours")
    print(f"Growth Rate (µ): {fit['growth_rate_per_h']:.4f} /h")
    print(f"R² Fit Quality: {fit['r_squared']:.4f}")

Run via CLI:

pepkio-doubling-time-tracker run --example ecoli_od600_two_point

Typical Use Cases

• Mammalian Subculture Scheduling: Computing doubling times for adherent (HEK293, HeLa, CHO) and suspension cell lines to optimize seeding intervals and harvest dates.
• Bacterial Log-Phase Analysis: Determining specific growth rate ($\mu$) and generation time ($g$) from $OD_{600}$ spectrophotometric time series in E. coli or B. subtilis cultures.
• Yeast Growth Kinetic Profiling: Quantifying doubling times for Saccharomyces cerevisiae or Pichia pastoris across varied media compositions and temperatures.
• Drug & Proliferation Screenings: Assessing growth rate inhibition or doubling time extension following compound treatment, siRNA knockdown, or CRISPR editing.
• Automated Reader Processing: Batch-extracting exponential growth parameters from multi-well plate reader optical density or fluorescence measurements.

Scientific Background

Cell population growth during the logarithmic (exponential) phase follows first-order kinetics:

$$N(t) = N_0 \cdot 2^{\frac{t}{T_d}} = N_0 \cdot e^{\mu t}$$

where $N(t)$ is the cell population or signal intensity at time $t$, $N_0$ is the initial baseline value, $T_d$ is the doubling time, and $\mu$ is the specific growth rate ($\text{time}^{-1}$).

Rearranging the exponential growth equation gives the specific growth rate $\mu$:

$$\mu = \frac{\ln(N(t)) - \ln(N_0)}{t - t_0}$$

The doubling time $T_d$ is inversely proportional to the growth rate:

$$T_d = \frac{\ln(2)}{\mu} \approx \frac{0.69314}{\mu}$$

For multi-point time-series data, log-transformed values $\ln(N_t)$ are fitted against time points $t$ using ordinary least squares (OLS) linear regression:

$$\ln(N_t) = \ln(N_0) + \mu \cdot t$$

The regression slope yields $\mu$, while the coefficient of determination ($R^2$) quantifies linearity during the exponential phase.

Web Application

For researchers who prefer a graphical interface, an interactive Doubling Time Tracker is available in the browser.

Web Application: https://www.pepkio.com/tools/doubling-time-tracker

The web application includes interactive growth curve plots, automated exponential phase selection, visual data table editors, batch sample comparisons, and shareable permalinks.

Documentation and Resources

GitHub Repository: https://github.com/pepkio/pepkio-doubling-time-tracker

Web Application: https://www.pepkio.com/tools/doubling-time-tracker

About Pepkio

Pepkio (https://www.pepkio.com/) develops software tools and bioinformatics solutions for life science researchers, including laboratory calculators and analysis services (https://www.pepkio.com/cro).

Keywords

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