Growth curves
Fit logistic, Gompertz, and Baranyi growth models to OD time courses from a plate reader, get lag time, μmax, doubling time, and maximum OD for every well with replicate summaries, and plan cell-culture passaging with seeding densities and split ratios.
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How to use it
Plate data. Paste or open a plate-reader export: the first column is time (a number, or h:mm:ss, which is read as hours),
then one column per well. Wells as rows with times across the top also work, and temperature columns are skipped. Choose the
blank — the mean of blank wells (medium only), a fixed OD, or none — and every other well is fitted. Name replicate groups as
Wild type: A1-A3 to get mean ± SD per group. The sample plate is synthetic: three strains in triplicate with two blank wells.
Models. Fits are to y = ln(OD − blank), with four parameters each: the starting level y0, the rise A = ln(ODmax/OD0), the maximum specific growth rate μmax, and the lag λ.
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Logistic and Gompertz, in the reparameterised forms of Zwietering et al. (1990, Appl. Environ. Microbiol. 56:1875): y = y0 + A·exp(−exp(μmax·e/A·(λ − t) + 1)) for Gompertz. Here μmax is the steepest slope of ln OD and λ is where that tangent meets the starting level — the dashed tangent on the detail plot.
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Baranyi and Roberts (1994, Int. J. Food Microbiol. 23:277), with h0 = μmax·λ and curvature m = 1. Its μmax is the rate of unrestricted exponential growth, so it can be a little higher than the steepest slope seen in the data when A is small.
Fitting is Levenberg–Marquardt with a numerical Jacobian, started from a sliding-window estimate of the steepest slope and restarted from three lag guesses. Standard errors come from (JᵀJ)⁻¹·s². The model with the lowest AIC is used by default; a difference above about 2 is meaningful. Doubling time = ln 2 ÷ μmax; generations = A ÷ ln 2.
Limitations. OD is proportional to cell density only at low OD (often below 0.4–0.6 in a plate reader, depending on path length) — dilute or calibrate against plate counts if you need true cell numbers. Condensation, settling, and clumping show up as noise or drift. Diauxic curves (two growth phases) need to be trimmed to one phase.
Passaging. Plans adherent cell culture: the cells to seed for a vessel at a chosen density (nominal growth areas from Corning and Thermo Fisher), the volume of suspension to take, when the culture reaches the target confluence, and the seeding density or split ratio that brings it to target after a set number of days — for example a 3- and 4-day Monday–Thursday routine. Growth is a lag followed by logistic growth toward the confluent density. The population-doubling table adds log₂(harvested ÷ seeded) over passages. Count cells and work out single doubling times in the biolab tool.
| For learning and planning. Measure your own strains' and cell lines' growth parameters; published values vary with medium, temperature, and instrument. |
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