Generating a Growth Curve

Objective

Author(s): Pattarin Blanchard

Monitor bacterial growth over time using spectrophotometric measurements of culture density. This protocol will produce a curve that can be used to determine the target organism’s rate of growth (doubling time).

Materials

PBS (phosphate-buffered saline)
Milli-Q water
Sterile pipette tips or 1 mL serological pipette
x2 disposable cuvettes
Parafilm
Kimwipes
Spectrophotometer
Liquid medium
500 mL culture flask
Waste beaker with 10% bleach

Procedure

Inoculating a new culture

It is desired to have starting optical density (OD) of 0.1 (for the sake of time) in the new flask culture. Therefore, when possible, the volume of inoculum from the mother culture has to be calculated, and the OD of the mother culture has to be measured.

Using a new cuvette, blank the spectrophotometer with 600 µL water. Use a kimwipe to clean the outside of the cuvette prior to measuring. Choose an appropriate wavelength. Dump the contents into a waste beaker.
1. E. coli: 600 nm
2. C. crescentus (CB2A): 600 nm
3. S. elongatus (UTEX): 750 nm
Using the same cuvette, add 600 µL growth medium or diluent and measure the OD. Record this value down, as this will be subtracted from every subsequent measurement. Dump the contents and rinse the cuvette with water using a wash bottle 3 times into the waste beaker.
1. Alternatively skip step 1 and blank with the medium, but step 1 is standard practice.
Under a flame, take 1 mL of the mother culture, add it to a cuvette, and measure its OD. Note that this doesn’t measure the cell color, but rather turbidity, or light scattering.
Generally OD measurements are only accurate between 0.1 and 1. If the initial reading is above 1, dilute it as necessary with medium or PBS so that the absorbance is between 0.1 and 1. Record the value and dump the contents into the waste beaker. Rinse with water 3 times, then set it face down onto a paper towel soaking with ethanol or disinfectant.
1. A cuvette has a max volume just over 3 mL, if up to a 3x dilution is needed, it is okay to dilute in the cuvette itself and mix by pipetting up and down.
Calculate the volume of inocculum needed from the mother culture. First subtract the diluent (PBS or medium) OD, then multiply by the dilution factor to get the “true” OD of the mother culture. $OD_{true}=(OD_{measured}-OD_{diluent})\cdot DF$

Then calculate the volume needed. The final volume shall be 250 mL + volume added, and the starting OD is 0.3. Note the final equation gives volume in mL, so make the appropriate conversion to uL if necessary.

OD\_{inoc}V\_{add}=OD\_{start}(250 + V\_{add})

V_{add}=\frac{250\text{ mL}\cdot OD_{start}}{OD_{inoc}-OD_{start}}

V_{add}=\frac{250 \text{ mL}\cdot 0.3}{OD_{inoc}-0.3}

Under a flame, add 250 mL of medium to a culture flask, then inocculate with $V_{add}$ calculated from the previous step.
Sample 1 mL from the new culture and measure its OD using the same cuvette from earlier. Dump cuvette contents into the waste beaker and rinse 3 times with water, then set face down on a paper towel soaked with ethanol or disinfectant.

Taking measurements

It is recommended a spreadsheet is used instead of a notion table because calculations will have to be performed. Set up a table like so in a spreadsheet, the initial readings should be recorded like so:

Time (h) Dilution factor Measured OD True OD Initials
PBS 1 x 0
0 1 ~0.3+x ~0.3
An appropriate interval should be selected for the organism. For example, UTEX has an expected doubling time of around 2 hours, so samples will be taken in 1 hr intervals.
For each subsequent OD measurement:

Time (h)	Dilution factor	Measured OD	True OD	Initials
PBS	1	x	0
0	1	~0.3+x	~0.3

Always take a sample under a flame with sterile tips or serological pipettes.
Anticipate when a dilution should be increased, knowing that OD is generally accurate between 0.1 and 1.
Ensure the spectrophotomer is set to the correct wavelength. If it is being used frequently by other people, keep a second cuvette with Milli-Q water to blank it as needed.
For dilutions up to 3x, 1 mL of sample can be taken and can be diluted in the cuvette itself since the max working volume is 3 mL. If a higher dilution is anticipated, take a smaller volume of sample (e.g. 5x dilution: sample 0.6 mL, dilute with 2.4 mL).
Wipe the cuvette with a Kimwipe to ensure an accurate reading.
Always rinse the cuvette 3 times with water and set it face down on a paper towel soaking with ethanol or disinfectant. The paper towel needs to be resprayed every once in a while, make sure it does not dry.

Once finished, calculate the true OD using this formula: $OD_{true}=(OD_{measured}-OD_{PBS})\cdot DF$

Analysing the growth curve

Plotting true OD vs. time should give a curve that looks exponential or logistic. Plotting $\ln (\frac{OD_t}{OD_0})$ vs. time should give a linear section. Why this works is during the exponential growth phase, cell growth follows this differential equation:
$\frac{dX}{dt}=\mu X$
Which when solved yields:
$X(t)=X_0e^{\mu t}$
And can be linearized as the following. Here OD is a stand-in for cell concentration $X$
$\ln(\frac{X}{X_0})=\mu t$
Select the log data points in the linear section and run a linear regression versus time. The resulting slope is the growth rate $\mu$ . If using LINEST, the standard error of $\mu$ , $\Delta \mu$ is the value just below it. Choose consecutive data points such that the $R^2$ is maximized, but prioritize as many data points as possible.
Calculate the doubling time $t_d$ :
$t_d=\frac{\ln 2}{\mu}$
The error in doubling time can be propagated from the error in growth rate using a first-order approximation
$\Delta t_d=\bigg |\frac{\partial t_d}{\partial \mu}\bigg |\Delta \mu=\bigg |\frac{\ln 2}{-\mu^2} \bigg |\Delta \mu = \frac{\ln 2}{\mu^2}\Delta \mu$

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