I have bacteria growth curves for 5 different temperature conditions and these were created using %red-light transmittance. How do I compare these growth curves? Should I calculate the growth rate and if so how do I do that?


Bacterial growth curve

1) A Bacterial growth curve:

When we provide a favorable medium for bacteria to divide regulary and increase in number, we get what's called a "growth curve", measuring the concentration of cells against time as time passes.

2) Phases:

A) The first phase is called the "lag phase", in this phase bacteria are adapting to the new medium, preparing enzymes etc, to start dividing. Therefore little to no growth is observed.

B) The second phase is the "Exponential growth phase", bacterial cells are well adjusted to their medium and ready to reach full potential, "maximum division and growth" happens here.

C) The third phase is the "stationary phase", bacteria are no longer able to grow or feed, they run out of nutrients, and growth is stationary/zero again. It can persist for a long period of time. (Cell growth=cell death, no actual increase in cell number=stationary)

D) The final growth phase is the "death phase", no nourishment is available and toxic metabolites have been accumulating during the stationary phase, death occurs (death here means that an increasing number of bacterial cells are dying, unlike the stationary phase where the number of cells dead equals the number of cells viable), following cell death (which now happens at a faster rate than cell growth), the cell concentration starts to decline. However, it doesn't really reach zero and bacteria might be able to regenerate again when the conditions are healthy again.

3) Recording bacterial growth using transmittance or spectrophotometer:

As bacterial cells increase in number, the turbidity of their medium increases (depends on the concentration of cells), and the incident light (if you shoot a beam of light across the medium) is more deflected away from the receiving detector (to detect the intensity of light), which makes spectrophotometer a reliable and accurate method to measure cell growth (proportional to the intensity of light detected).

4) How to compare growth curves?

Looking at the growth curve will give some idea of the rate of growth in relation to a standard growth curve or some other available growth curves (compare phases and their durations, the exponential phase, etc). However there is a way to calculate growth curve and generation time (doubling time) from a growth curve.

The difference in cell concentration/difference in time = growth rate constant. Or dN/dt = kN or you may use this advanced equation: log10N2 – log10N1 = k(t2 – t1)/2.303

Simply plot any two random points of time on your curve: the first point is t1, the second point is t2, N1 is the number of cells (cell concentration) at t1, N2 is cell concentration at t2.

Or you can simply use dN/dt = (N1 – N2)/(t1 – t2) and compare the resulting k between curves.

I hope this answers your question, please know that I am by no means an expert on the subject and you may search further or get expert advice if you need to.







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Calculating maximal growth rates

Maximal growth rates are indeed important to compare, when evaluating the differences between different growth curves. The higher the value is, the fastest is the exponential phase. In order to calculate the growth rate of each curve, you have at least to possibilities:

The quickest and easiest way is to select two points from the exponential phase and use the following formula:

$\mu_{max} = \frac{ln(X_2) - ln(X_1)}{t_2 - t_1}$

where $X_i$ is your measure of cell density (e.g. dry weight, optical density, etc.) at time $t_i$, and $\mu_{max}$ is the maximal growth rate.

Another way to estimate $\mu_{max}$ is to use modeling techniques. A classical model for bacterial growth is the Gompertz model:

$y(t) = A \cdot exp \left[ - exp \left(1 + \frac{\mu \cdot e}{A} (\lambda - t) \right) \right]$

Where $y$ is the measure of cell density, $A$ the asymptotic value of cell density and $\lambda$ is the duration of the lag phase. Tools exist that can help you fit your curves with this kind of model, like the grofit package for R (it's free!). This package can provide you with estimations of $A$, $\lambda$ and $\mu_{max}$, along with the corresponding intervals of confidence (see figure below).

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Comparing growth curves

When comparing growth curves, key values to compare are: $\mu_{max}$ the maximal growth rate, $A$ the asymptotic value and $\lambda$ the lag phase duration. One should not neglect one of them over the others. Low $\mu_{max}$, low $A$ or high $\lambda$ are each a sign of possible bacterial stress.

Source of the figure: Kahm, M., Hasenbrink, G., Lichtenberg-Fraté, H., Ludwig, J., Kschischo, M. (2010) grofit: Fitting Biological Growth Curves with R, Journal of Statistical Software (33)7

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