OD600 Growth Rate, Doubling Time and Gompertz Curve Fitter
Estimate microbial specific growth rate and doubling time and, with the Gompertz fit, lag time, maximum specific rate and the log increase to the plateau from optical density time courses. This reference explains why blank subtraction must precede logarithmic transformation and how log-linear exponential windowing compares with a full-curve modified Gompertz fit.
The growth worked example: a synthetic OD600 time course, blank taken as the mean of three blank readings, with the exponential-window fit already run on a 3 to 9 hour window. The growth analysis can add the full-curve modified Gompertz fit beside the window. The window engine is compared with a nine-case fixture and the Gompertz fit with its own SciPy fixture.
Subtract background turbidity before taking logarithms
Microplate readers measure total light attenuation through a vertical liquid column whose path length depends on well geometry and fill volume. Before fitting any exponential growth rate, subtract the matched uninoculated broth blank from every time-point reading. If early time points near inoculation fluctuate at or below the blank level, those readings are below the turbidimetric detection floor and must not be forced into a logarithmic regression.
Inspect the semilogarithmic trace to verify that a genuinely straight balanced-growth segment exists across several doublings. Microplate cultures often experience oxygen transfer limitation well before carbon exhaustion, bending the semilogarithmic slope downward earlier than a baffled shake flask.
Use full-curve Gompertz models to summarise lag and stationary transitions
When an experiment compares how antimicrobial stress, media formulation or genetic perturbation alters both lag duration and final yield, fitting the Zwietering modified Gompertz equation across the full time course captures three interpretable summaries: lag intercept λ, maximum tangent rate μm and upper asymptote A. Keep window-derived exponential μ and full-curve Gompertz parameters clearly distinguished in your methods report.
Equations and variables
Exponential-window specific growth rate and doubling time
ln(ODcorr(t)) = ln(OD0) + μ × t; td = ln(2) / μ
- ODcorr(t)
- Blank-subtracted optical density within the strictly exponential growth window (OD units)
- μ
- Specific exponential growth rate constant (h⁻¹)
- t
- Elapsed culture time (h)
- td
- Culture doubling time during balanced exponential growth (h)
Zwietering modified Gompertz growth curve
y(t) = A × exp(−exp((μm × e / A) × (λ − t) + 1))
- y(t)
- Logarithmic relative optical density ln(OD(t) / OD0) at time t
- A
- Upper asymptotic logarithmic increase from inoculum to stationary plateau
- μm
- Maximum tangent slope at the inflection point of the growth curve (h⁻¹)
- λ
- Lag-time intercept where the inflection tangent crosses the lower baseline (h)
Scope and limitations
- Subtracting the uninoculated medium blank after taking logarithms is algebraically invalid; blank subtraction must occur on raw optical density first, and non-positive corrected readings cannot be log-transformed.
- Optical density at 600 nm ceases to scale linearly with cell concentration at high turbidity because of multiple light scattering, compressing the apparent stationary plateau unless samples are diluted.
- The inflection tangent slope μm of a sigmoidal Gompertz fit on raw or log-ratio OD is an empirical curve parameter that does not automatically equal the balanced exponential specific growth rate μ.
Sources and provenance
- Published numerical verification inputs and independent referencesOriginal synthetic inputs; see individual fixture notices
The generated inputs are demonstrations, not experimental measurements. Existing versioned fixtures are retained unchanged.
- Independent growth-window rate verification fixtureMIT; SciPy and Python fractions reference
- Independent modified Gompertz fit fixtureMIT; SciPy curve_fit reference on synthetic Gompertz readings
- Zwietering et al.: modeling of the bacterial growth curveCited method; reparameterised biological Gompertz model
Technical questions
Why does forgetting to subtract the media blank bias the specific growth rate downward?
An uninoculated broth well contributes a constant additive background absorbance. Adding a positive constant to an exponential signal flattens its slope on a semilogarithmic plot, especially during early exponential phase when cell turbidity is still small relative to the medium background.
How do I choose the time window for a log-linear growth rate fit?
Plot the natural logarithm of blank-corrected optical density against time and select the straight segment between the end of the lag transition and the onset of nutrient-depletion deceleration. Including lag or stationary points in a linear fit systematically underestimates μ and inflates doubling time.
What is the difference between Gompertz lag time λ and physiological adaptation time?
In the Zwietering reparameterisation, λ is the geometric intersection of the maximum inflection tangent line with the initial baseline. If a culture contains a subpopulation of non-viable cells at inoculation, apparent turbidity lag increases even if the viable fraction begins dividing immediately.
Connected workflows
- Monod fed-batch growth simulation
Compare empirical Gompertz curve fitting with mechanistic Monod substrate-balance simulation.
- Oxygen transfer and uptake modelling
Examine how volumetric oxygen transfer limits high-density microbial growth.
- Viable-cell seeding volumes
Relate optical growth trajectories to initial viable-cell seeding arithmetic.