Supplementary material for Novak et al. Bacterial growth properties at low optical densities
Methods
Measurements of growth properties
Ancestral and derived populations taken from the -80˚C freezer stocks were conditioned to grow in Davis minimal medium at 25 µg/ml glucose, at 37˚C as follows. Bacterial cultures were first incubated at 37˚C while shaking in the Lab-Term Kuehner Shaker at 400 rpm (shaking radius 3 mm), in 96-well flat-bottom microtiter plates containing Davis minimal medium supplemented with glucose at 1ng/ml. The overnight cultures grown in this manner were washed in 0.85% saline solution, diluted in Davis minimal medium supplemented with glucose at 25 µg/ml and grown overnight to stationary phase under same temperature and shaking conditions. Cultures conditioned in this way were used for subsequent growth in Davis minimal medium at three different glucose concentrations, where optical density measurements took place.
To prevent evaporation of the medium, humidity within the incubator was increased from around 20% to around 75% by placing water holders in the incubator. Water holders were filled with dH2O. Their surface was similar to that of the shaker. They were placed just above the shaking surface with additional 4-8 smaller water holders placed between the racks on the shaking surface.
Mathematical model
The log-transformed measurements for each well were fitted with a stepwise linear model for microbial growth (Buchanan et al. 1997). This model assumes three distinct growth phases: a lag phase with constant OD, a log phase with exponentially increasing OD, and a stationary phase with constant OD. The stepwise linear model is given by
Here, ln is the natural logarithm, t is the time, and v is the exponential growth rate. The time point at which the population enters stationary phase is given by tstationary = tlag + (ln(ODstationary)– ln(ODlag))/v. The model thus assumes that there is an instantaneous switch both from lag phase to log phase and from log phase to stationary phase and uses 4 independent parameters to describe growth, namely tlag, ODlag, ODstationary, and v. As the initial OD in lag phase was below the detection limit of the utilized spectrometer, the assumption of an instantaneous switch from lag to log phase has no consequences for parameter estimation. The assumption of an instantaneous switch from log phase to stationary phase is justified, because the switch from exponential growth to stationary phase occurs typically on a shorter time scale than the time interval between two OD measurements. Although the initial OD was below the detection limit, the duration of the lag phase can be inferred indirectly because the initial OD is given by the factor of dilution, D, from the inoculating culture which was in stationary phase at the time of transfer. Using the relation ODstationary = D* ODlag reduces the 4 parameter model to a model with only three independent parameters. In the analysis in this study, this three-parameter model was always used.