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Biological & Biosystems Engineering DISCUSSION
I am running a shake-flask batch culture and measuring optical density at 600 nm every half hour. The OD was 0.12 at 1.0 h and 0.95 at 4.5 h, then the curve flattened above an OD of about 3.
How do I get the specific growth rate and the doubling time from these readings, which part of the curve should I use, and why does growth slow down even though the flask still looks fine?
During exponential growth, dX/dt = µ × X, so X = X0 × exp(µ × t) and µ = ln(X2 / X1) / (t2 - t1). With your two readings: µ = ln(0.95 / 0.12) / 3.5 h = ln(7.92) / 3.5 = 2.07 / 3.5 = 0.59 per hour. Doubling time is ln(2) / µ = 0.693 / 0.59 = 1.17 h, about 70 minutes.
OD stands in for biomass concentration here, which is valid as long as the two are proportional.
Two points are the minimum; a fit is better. Plot ln(OD) against time for all readings. The lag phase shows as a flat start, the exponential phase as a straight line, and the slope of that line is µ. Fit a straight line by least squares to the straight part only, five or more points if you have them. Including lag or late points always drags the estimate down.
If the semi-log plot has no clearly straight section, the culture was never in balanced exponential growth and a single µ does not describe it.
Check the spectrophotometer's linear range before trusting the higher readings. OD is a scattering measurement, and above roughly 0.4 to 0.6 on many instruments multiple scattering makes the reading rise more slowly than the cell concentration. Dilute dense samples with fresh medium to bring them into the linear range and multiply by the dilution factor. Your 0.95 is likely an underestimate if it was read undiluted, which would make the true µ a little higher than calculated.
Blank against sterile medium, and keep to one instrument and cuvette path length, since OD values are not transferable between instruments. For biomass in g/L, calibrate OD against dry cell weight for your organism.
Growth slows because something runs out or builds up. The usual description is the Monod equation, µ = µmax × S / (Ks + S), where S is the concentration of the limiting substrate. While S is much larger than Ks the culture grows at close to µmax; when S falls to the order of Ks, µ drops sharply. Ks is typically small, so the transition from exponential to stationary phase looks abrupt.
In shake flasks the limiting substrate is very often oxygen rather than the carbon source. Oxygen demand rises with cell density while the transfer rate through the liquid surface is fixed, and acid by-products and pH drift add to it.
